^v^         /^irfe/^.^ 


THE 


j^]VrERICA-]Nr 


PRACTICAL  NAVIGATOR, 


BEING    AN 


EPITOME 


OF 


NAVIGATION  AND  NAUTICAL  ASTRONOMY. 


BY 


XATHANIEL /BOWDITCH,  LL.  D.,  s 

Fellow  of  the  Royal  Societies  of  London,  Edinburgh,  and  Dublin;  of  the  Astronomical  Society  in  London;  of  the 

American  Philosophical  Society,  held  at  Philadelphia ;   of  the  American  Academy  of  Arts  and  Sciences : 

of  the  Connecticut  Academy  of  Arts  and  Sciences  ;    of  the  Literary  and  Philosophical  Society 

of  New  York;  Corresponding  Member  of  the  Royal  Societies  of  Berlin,  Palermo,  &c. 


REVISED  BY  ORDER  OF  THE 

BUREAU    OF    NAVIGATION, 

NAVY  DEPARTMENT. 


WASHINGTON: 

GOVERNMENT    PRINTING   OFFICE 

18  88. 


NOTICE. 


Bureau  of  Navigation,  Navy  Department, 

ya/iitaiy  i,  i88i. 

In  accordance  with  the  purpose  contemplated  in  the  purchase  of  the  copyright  of  the  New- 
American  Practical  Navigator,  a  thorough  and  complete  revision  has  been  made  by  Com- 
mander P.  H.  Cooper,  U.  S.  N.,  acting  under  the  direction  of  this  Bureau.  The  revision  con- 
sists principally  in  the  substitution  of  the  more  concise  and  convenient  methods  of  the  present 
day  for  the  obsolete  methods  of  the  past,  a  complete  rearrangement  under  proper  chapters 
aiul  paragraphs  for  ready  reference,  keeping  in  view,  however,  the  character  of  the  work  as  a 
Practical  Navigator. 

The  revision  having  been  completed,  it  was  submitted  to  Capt.  Ralph  Chandler,  IT.  S.  N., 
for  a  final  review,  and,  having  received  ?  satisfactory  report  from  that  officer,  it  has  been 
accepted  by  the  Bureau,  and  will  hereafter  be  substituted  for  the  former  editions  of  the  work. 

WILLIAM  D.  WHITING, 

C'  ii  f  oJl  Bureau^ 


a 


11 


PREFACE. 


Thf  copyright  of  the  New  A^[ERICAN  Practical  Navigator,  by  the  late  Dr.  Nathaniel 
Bowditch,  having  become  the  property  of  the  government,  under  the  provision  of  section  2  of 
an  act  to  establish  a  Hydrographic  Office  in  the  Navy  Department,  approved  June  21,  1866, 
it  has  been  deemed  desirable  by  the  Bureau  of  Navigation  to  revise  the  work,  with  a  view  to 
an  improvement  in  the  arrangement  and  the  introduction  of  the  more  precise  and  convenient 
methods  of  the  present  day;  such  as  the  Method  of  Lunar  Distances  by  Professor  Chauvenet; 
his  Method  of  Equal  Altitudes  for  rating  chronometers,  &c. 

The  system  adopted  by  the  Navy  Department  for  keeping  the  ship's  log  and  compiling 
meteorological  data  on  specified  Forms  is  also  described,  since  the  request  is  extended  to  officers 
of  the  Merchant  Marine  to  adopt  this  uniform  system. 

Sumner's  Method  of  finding  the  position  of  a  ship  at  sea  has  been  treated  as  fully  as  the 
necessity  of  the  Navigator  requires.  'J'his  method  is  now  the  main-stay  of  the  Navigator,  the 
simplest  and  most  reliable  of  all  the  appivx'wiatt;  methods  of  defining  a  ship's  position ;  for  no 
method  is  more  than  approximate,  owing  to  the  unavoidable  errors  that  occur  in  sea  observa- 
tions, rendering  it  impossible  to  define  a  point  on  the  surface  of  the  sea.  Sumner's  Method 
enables  the  Navigator  to  reduce  the  probable  area  of  position  to  its  narrowest  limits,  and  to 
exhibit  this  area  graphically  on  the  chart  at  almost  any  instant  required,  if  it  is  possible  to  catch 
a  glimpse  of  any  of  the  known  heavenly  bodies. 

Various  other  observations  have  been  introduced  which  facilitate  the  Navigator's  duty  under 
particular  circumstances,  and  the  object  in  all  has  been  to  prepare  a  work  suitable  in  all  respects 
as  a  text-book  for  Mates  and  junior  officers,  as  well  as  a  Practical  Navigator. 

All  the  original  Tables  requisite  for  the  solution  of  the  problems  have  been  retained,  and 
various  new  ones  incorporated  from  the  publications  of  the  Bureau  of  Navigation;  a  full 
description  of  all  being  given  in  Chapter  XVI,  Part  II,  with  the  formuije  by  which  they  have 
beeu  computed. 

It  will  be  seen  that  the  elementary  chapters  on  Arithmetic,  Geometry,  Trigonometry, 
Logarithms,  Useful  Problems,  iS:c.,  have  been  transferred  to  the  Appendix  of  this  Edition,  with 
the  view  that  the  main  body  of  the  book  should  be  devoted  to  the  subjects  proper  of  Navi- 
gation and  Nautical  Astronomy. 

All  the  subject-matter  of  the  old  editions  not  necessary  to  the  character  of  a  Practical 
Navigator  has  been  omitted  in  the  revision. 

iii 


lVl52iy79 


T^BLE    OF    CONTENTS 


PA-RT    I. 
NAVIGATION. 


Subject. 


Art. 


Page. 


Chap.  I. — Definitions 


Navigation  as  a  Science 

Defining  "Navigation  and  Nautical  Astronomy'" 

Instruments  Employed 

Definitions  relating  to  the  Earth 


2 
3 


Chap.  II. — Instruments  Employed  in  Navigation 


1.  The  Plane  Scale 

2.  Gunter's  Scale 

3.  The  Sector     

Use  of  the  Line  of  Lines 

Use  of  the  Line  of  Chords 

Use  of  the  Line  of  Sines,  Tangents,  and  Secants 

Use  of  the  Line  of  Polygons 

Use  of  Sector  in  Trigonometry 

4.  Dividers,  or  Drawing  Compasses 

5.  Parallel  Rulers 

6.  The  Log 

Log  Chip 

Log  Line 

Principle  of  Marking  Log  Line 

Log  Glass 

Adjustment  of  the  Log 

7.  The  Ground  Log 

8.  jMassey's  Patent  Log 

9.  The  Lead 

10.  The  Mariner's  Compass 

Division  of  Compass  Card 

Principle  of  the  Compass 

Construction  of  the  Compass 

Named  according  to  Use  on  board  Ship     ... 

Navy  Liquid  Compass 

British  Admiralty  Dry  Compass   . 

Azimuth  Circle 

Location  of  Compasses 

The  Compass  Error 

Local  Attraction 

Variation 

Dip - 

To  apply  Variation 

Explanation  of  the  Rule 

Deviation  of  the  Compass 

Effect  of  Magnetism  upon  the  Compass  Needle  caused  by  the  Iron  in  a  Ship  .. 

Soft  Iron 

Hard  Iron 

Semicircular  Deviation 

Quadrantal  Deviation 

Three  kinds  of  Deviation   

Principles  of  Compensating  Compasses 

Neutral  Points 

Heeling  Deviations 

Methods  of  ascertainmg  Deviation 

By  Bearing  of  Distant  Object 

Defining  Deviation 

By  Swinging  Ship  in  a  Tide-way - 

Deviation  Table  

V 


4 

5 
6 

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10 
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12 


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J] 

I] 

J] 

I] 

I] 

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13 
13 


VI 


TABLE    OF    CONTENTS. 

Part  I.— NAVIGATION— Continued. 


Subject. 


Chap.  II. — Instruments  Employed  in  Navigation — Continued. 


lO. 


II. 


The  Mariner's  Compass — Continued. 

By  reciprocal  Bearings 

Deviation  Table 

Using  Theodolite  in  lieu  of  Shore  Compass 

Heeling  Deviations 

To  apply  Deviation  and  Reduce  Courses  . . . 
Archibald  Smith's  Graphic  Deviation  Table 

Napier's  Method 

Correcting  Courses 

The  Chart — Definitions  and  Varieties 


To  construct  a  Chart  on  Plane  Projection  

Mercator's  Projection 

Another  Illustration  of  above 

Construction  according  to  last 

Meridional  Parts 

Mt  rcator's  Chart 

To  construct  a  Mercator's  Chart 

To  measure  Distances  on  Mercator's  Chart.  .. 
Transfer  from  Mercator's  to  other  Projections 
Great  Circle  Charts 


12. 


The  Log  Book 

Instruments  used  to  record  and  furnish  Data. 

Description  of  tlie  Barometer 

Principle  of  the  Barometer 

The  Aneroid  Barometer 

The  Thermometer 

The  Hygrometer 

Log  Book 

Symbols  to  record  state  of  Weather   

Symbols  to  record  Clouds 

Classification  of  Clouds 

Winds 

Instructions  for  keeping  the  Log 

Method  of  compiling  Data,  Form  A    

Example,  as  per  Form  Z 

To  prepare  Log  Book  for  Form  B 

To  prepare  Form  B 

Nature  of  Remarks  on  Form  B 

To  compile  Cyclones  on  Form  B 

Description  of  Form  E 

Description  of  Form  II 

Use  of  the  Forms  when  accumulated 


Chap.  III. — The  Sailings 


First  Considerati  >n  upon  leaving  Port 

Kinds  of  Sailings 

Elements  of  the  Problems  of  Sailings 

Plane  Sailing — Definition 

Terms  used  Exemplified 

Plane  Right  Triangle  of  Plane  Sailing 

A  Traverse  Table 

Solutions  of  Cases  of  Plane  Sailing 

Traverse  Sailing — Problem  involved , 

Solution  of  the  Problem — working  Traverse. .. 
Current  Sailing 

Spherical  Sailing — Definition 

Parallel  Sailing 

Middle  Latitude  Sailing 

Problem  involved    

Solutions  of  various  Cases 

Correction  to  be  applied  to  Middle  Latitude 

When  to  use  Middle  I  .atitude 

Mercator's  Sailing 

Illustration  of  the  Principle     

Rule  to  find  Meridional  Difference  of  Latitude 

When  to  prefer  Middle  Latitude  Sailing 

Cases  of  Mercator's  Sailing 

Great  Circle  Sailing .. 


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IDS 


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53 


TABLE  OF  CONTENTS. 

Part  I.— NAVIGATION— Continued. 


VII 


Subject. 


Art. 


Page. 


Chap.  III. — The  Sailings — Continued. 

2.  Spherical  Sailing — Continued. 

Advantages  of  Mercator's  Sailing 

'Advantages  of  Great  Circle  Sailing. 

Illustration  of  same 

Godfray 's  Chart   

Course  and  '  listance  Diagram 

Rules  for  using  Chart  and  Diagram 

Example  to  illustrate  the  Rule , 

Composite  Sailing 

Example  to  illustrate 

Rapier's  Method 

Solution : 

The  Courses 

The  Distance 

The  Vertex 

The  Maximum  Separation  in  Latitude 

To  find  Point  of  Intersection  at  the  Equator 

Chap.  IV. — Navigating  the  Ship 


Taking  the  Departure 

By  a  Single  Bearing  and  Distance 

By  Two  Bearings  of  the  same  Object 

When  it  may  be  solved  by  the  Traverse  Table 
Solution  by  Table  5 

By  Cross  Bearings 

By  Bearings  and  Distance  of  Three  Objects 

By  Soundings 

6.  Astronomically 

Shaping  the  Course 

The  Day's  Work — Definition 

Rules  for  Working 

Making  the  Land 


m 


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5'r 

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64 


F^^RT    II. 
NAUTICAL  ASTRONOMY. 


Chap.  I.— Definitions 


Definition  of  Nautical  Astronomy 

Definition  of  Celestial  Concave 

Spherical  Astronomy  treats  of 

System  of  Rectangular  Co-ordinates   

System  of  Great-Circle  Co-orciinates    

System  of  Polar  Co-ordinates   

Same  applied  to  the  Sphere 

Co-ordinate  Systems  of  Nautical  Astronomy 

I.  Altitude  and  Azimuth 


Terms  used  in  Horizon  System 

Defining  Altitude  and  Azimuth 

2.  Declination  and  Hour  Angle  System 

Defining  Declination  and  Hour  Angle 

3.  Declination  and  Right  Ascension  System 

Defining  Declination  and  Right  Ascension 
Celestial  Latitude  and  Longitude 


Chap.  II. — Instruments  used  in  Nautical  Astronomy. 
I .  The  Sextant — Description 


Principle  of  the  Sextant 

Application  of  the  Principle  . 
Requirements  of  the  Theory . 
Adjustments  : 

Index  Glass 

Horizon  Glass 


179 
180 


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7J 


VIII 


TABLE    OF    CONTENTS. 
Part  II.— NAUTICAL  ASTRONOMY— Continued. 


Subject. 


Chap.  II. — Instruments  used  in  Nautical  Astronomy — Continued. 

I.  The  Sextant — Description — Continued. 
Adjustments — Continued. 


Telescope 

Index  Error  

How  to  find  Index  Correction 

The  Vernier 

To  measure  Angular  Distance  of  Sun  and  Moon . . . 
To  measure  Angular  Distance  of  Moon  and  Star.. 
To  set  the  Sextant  for  measuring  Lunar  Distances 
To  measure  Altitudes 

2.  The  Artificial  Horizon 

3.  Circle  of  Reflection   

Adjustments 

To  observe  Meridian  Altitudes 

To  observe  Altitudes  by  Cross  Observations 

To  measure  Lunar  Distance,  Sun 

To  measure  Lunar  Distance,  Star 

4.  The  Portable  Transit 

Adjustments 

Method  of  Observation 

The  "Broken  Backed"  Transit  Instrument 

Star  Lists 


5.  The  Chronometer 

Error  and  Rate 

Stovi'age  and  Transportation 

Winding 

Comparisons , 

Form  for  recording  Comparisons , 

Utility  of  Comparisons 

Change  of  Rate  due  to  Change  of  Temperature 

6.  Nautical  Almanac 


Time — From  what  Points  reckoned 

Transit 

Diurnal  Time 

Apparent  Time 

why  Apparent  Time  cannot  be  the  Standard 

The  Mean  Sun 

Mean  Time 

Equation  of  Time 

Sidereal  Time 

Civil  Time 

Astronomical  Time 

Time  at  Difierent  Meridians 

Reduction  of  Time 

Reduction  of  the  Elements  in  the  Nautical  Almanac 

Rule  for  taking  Quantities  from  the  Nautical  Almanac 

Interpolation  by  Second  1  )ifferences   

Description  of  Page  I  of  the  Calendar 

Rule  for  reducing  Quantities  on  Page  I  for  Longitude 

To  find  Right  Ascension  of  Mean  Sun , 

To  find  Local  Time  of  Moon's  Transit 

To  find  Moon's  or  Planet's  Right  Ascension  and  Declination  for  Time  of  Local  Transit . 

To  find  Greenwich  Mean  Time  of  a  given  Lunar  Distance   

Proportional  Logarithms 

To  correct  Time  of  Lunar  Distance  for  Second  Differences 

To  find  Distance  of  Moon  from  a  given  Object  at  a  given  Time 


Chap.  III. — Conversion  of  Time 


Mean  to  Apparent  and  vice  versa , 

Mean  Solar  Interval  to  Sidereal  Interval  and  reverse 

Mean  Solar  Time  ai  a  given  Place  to  Sidereal  Time 

Sidereal  Time  to  Solar  Time . 

To  find  what  Heavenly  Body  next  passes  the  Meridian 

To  find  Mean  Time  of  Meridian  Passage  of  a  Heavenly  Body 

Chap.  IV.— Hour  Angle . 


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Defining  Hour  Angle 

To  find  Hour  Angle  of  the  Sun  at  given  Place  and  Time 


241 

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TABLE    OF    CONTENTS. 
Part  II.— NAUTICAL  ASTRONOMY— Continued. 


IX 


Subject. 


Art. 


Page. 


Chap.  IV. — Hour  Angle — Continued. 


To  find  Hour  Angle  of  any  Celestial  Body  at  gi\  en  Place  and  Time    243 

Given  Hour  Angle  of  a  Celestial  Body  at  given  I'lace  and  Date,  to  find  Local  Mean  Time.  244 

Chap.  V.  —  Corrkctions  of  Observed  Altitude 


The  Corrections  named 

Resi  It  of  applying  Corrections  in  order 

Parallax 

Refraction    , 

Illustration  of  Refraction   

To  apply  Refraction , 

Dip 


Effect  of  Refraction  upon  Dip 

Dip  when  Obstacles  intervene 

To  find  Distance  of  Land  by  using  Table  15 
Semi-diameter 


Chap.  VI. — Findlng  the  Time 


Methods  of  Rating  Chronometers 

By  Transit  of  a  Star 

By  Transit  of  the  Sun 

Stars  to  be  preferred 

By  Single  Altitude 

Most  favorable  Position  of  the  Body 

The  Observation , 

Demonstration  of  the  Problem 

By  Single  Altitude  of  a  Star 

Chauvenet's  Equal  Altitudes 

Sun,  A.  M.  and  P.  M. : 

The  Observation , 

The  Computation 

Sun,  P.  M.  and  A.  M. : 

The  Observation 

The  Computation 

Star : 

The  Observation 

The  Computation , 

To  correct  for  small  Inequalities  in  the  Altitudes 
Degrees  of  Dependence 


Chap.  VII. — Latitude 


1 .  By  Meridian  Altitude , 

Observation 

Computation 

To  correct  Meridian  Altitude  for  change  of  Position  and  Declination 

2.  By  Reduction  to  the  Meridian 

When  the  Local  Time  is  known 

Formulae  for  extending  Limits  of  Table  26   

To  find  the  Reduction  when  Time  exceeds  13  Minutes,  the  Limit  of  Table  27 

3.  By  Two  Altitudes  near  Meridian  when  Time  is  not  known   

Degree  of  Accuracy    . .   

4    By  Single  Altitudes  at  a  given  Time 

5.  By  Change  of  Altitude  near  Prime  Vertical 

Degree  of  Accuracy , 

6.  By  the  Pole  Star 

Rigorous  Method 

7.  By  Two  Altitudes  with  Elapsed  Time 

Of  the  Sun 

Longitude  by  this  Observation -. 

Douwe's  Method 

Of  a  Fixed  Star 

Of  same  or  different  Objects,  the  Declination  being  Different 

Chap.  VIII. — Longitude 


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Definitions  

Telegraphic  Determination  of  Secondary  Meridians 


293 
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lOI 

lOI 
lOI 

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[lO 

[II 

[II 
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>I3 

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[16 

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[18 
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127 


TABLE    OF    CONTENTS. 
Part  II.— NAUTICAL  ASTRONOMY— Continued. 


Subject. 


Chap.  VIII. — Longitude— Continued. 


The  Method  defined , 

Establishment  of  Tertiary  Meridians 

To  correct  Chronometer  Errors  for  change  of  Rate 

Longitude  by  Chronometer 

By  the  Circum-meridian  Observation 

Littrow's  Method 

Degree  of  Accuracy  and  Table 

Lunar  Distances     

Uses  of  Lunar  Distances    

How  to  find  the  Object 

General  Remarks  on  taking  Lunars 

To  correct  the  Lunar  Distance . . . 

The  Observation 

Preparation  of  the  Data 

Computation  of  the  True  Distance 

To  find  the  Greenvt^ich  Time 

Degree  of  Dependence — Computations 

Taking  a  Lunar  (one  observer)  to  compute  the  Apparent  Altitudes. 
Rigorous  Method — Computations 


Chap.  IX.— Sumner's  Method. 


General  Explanation  of  the  Method 

Terms  used 

To  project  a  Parallel  of  Position 

Case  I.  Position  by  Altitude  of  Two  Objects 

Case  II.  Position  by  Altitude  of  same  Object  at  difflreht  Times 

Case  III.   Line  parallel  to  Coast  Line 

General  Remarks 

To  find  Azimuth  of  the  Body  from  ihe  Line  <  f  Position 

Latitude  and  Longitude  by  Sumner's  Method  and  I'restel's  Method  combined 

CiiAP.  X. — Variation  of  the  Co.mpass  

Definitions  and  Methods 

1.  By  an  Ampl  tude 

The  Observation    

The  Computation 

2.  By  Time  Azimuths   

The  Observation 

Finding  the  True  Azimuth 

Swinging  Ships  at  Sea 

To  compute  the  serial  True  Azimuths 

3.  By  Altitude  Azimuths 

The  Observation 

The  Computation 

By  Sumner's  Lines 

4.  By  the  True  Bearing 

The  Observation 

The  Computation 

Cu^p.  XL — Winds 


Definitions 

Cause  of  Wind 

The  Trade- Winds 

The  Anti-Trades    

Land  and  Sea  Breezes 

Monsoons . . 

Variable  Winds    , 

Hot  Winds  of  Deserts    

Peculiarities  of  Mountain  Winds 

Puna  Winds 

Bora 

Mistrals , 


Chap.  XII. — Revolving  Storms 

History  of  the  Theory 

Exception  to  the  Theory  . 
Storm  Problem  


Art. 


295 
296 

297 

298 

299 

300 

301 

302 

303 
304 

305 
306 

307 
308 

309 
310 

3" 
312 

313 


314 

315 

316 

317 
318 

319 
320 
321 
322 


323 

324 

325 
326 

327 
328 
329 
330 
331 
332 

333 
334 
335 
33^ 
337 
338 


339 
340 
341 
342 
343 
344 
345 
346 
347 
348 
349 
350 


351 
352 

353 


TABLE    OK    CONTr.NTR. 
Part  IT.— NAUTICAL  ASTRONOMY— Continued. 


XI 


Subject. 


Page. 


Chap.  XII.— Revolving  Storms — Continued. 


Appearance  of  the  Weather 

Bearing  of  the  Centre,  North  Latitude 

Bearing  of  the  Centre,  South  Latitude 

Rules  for  Storms — Regarding  the  Sliip  

To  ascertain  the  Direction  of  the  Storm  Track  by  Inspection  .. 
To  ascertain  the  Direction  of  the  Storm  Track  by  Observation . 

Rules,  Northern  Hemisphere 

Rules,  Southern  Hemisphere 

Special  Rules 


XIII. -Tides 


Tidal  Phenomena 

Cause  of  the  Tides 

Establishment  of  the  Port 

Spring  and  Neap  Tides 

Types  of  Tides 

To  determine  Type  Form 

Plane  of  Reference 

Bench-mark 

Staff  Gauge     

Box  Gauge 

Self-registering  Gauge    

Off-shore  Tide  and  Sounding  Meter    . . 

General  Observations 

Situation  of  Tide  Gauge 

Remarks    

Rule  for  finding  Time  cf  High  Water  , 
Correction  for  Semi-inensal  Inequality. 
Correction  for  Pacific  Coast 


Chap.  XIV. — Currents 


Definition  of  Currents 

Varieties  of  Currents 

Stream  Currents 

How  to  estimate  Currents 

Caution  about  estimating  Currents 


To  measure  the  set  of  a  Current 
By  bottles 


Submarine  Currents 

Importance  of  Investigations 

Submarine  Currents 

The  Gulf  Stream 

North  Atlantic  Currents 

South  Atlantic  Currents 

Pacific  Currents   

Australian  Currents   

Rossel  Current   

Seas  of  Passage  Currents  . . . 

Antarctic  Drift  Currents 

China  Sea  Currents 

Japan  Currents 

Behring  Currents 

California  Currents 

Panama  Currents 

Chile  and  Peru  Currents 

Cape  Horn  Currents .  .. 

Indian  Ocean  Currents 

Red  Sea  Currents 

Mediterranean  Currents 


354 
355 
356 
357 
358 

359 
360 

361 
362 


363 
364 
365 
366 

367 
368 
369 
370 
371 
372 
0/0 
374 

375  , 

376  i 
377 
378 
379 
380 


381 
382 

383 
384 

385 
386 

387 
388 

389 
390 
391 
392 
393 
394 
395 
396 
397 
398 
399 
400, 401 
402 

403 
404 
405 
406 
407 
408 
409 


Chap.  XV. — Surveying 

1 .  The  Plane  Table 

Adjustments  of  the  Plane  Table . 

2.  The  Telemeter  .  ..*. 

3.  The  Portable  Micrometer-Telescope 

4.  The  Beam  Compasses 

5.  The  Proportional  Dividers 


410 
4H 
412 

413 
414 

41S 


'59 
'59 
'59 
'59 
'59 
'59 
1 60 
[61 
161 

163 

163 
163 
163 
,63 

164 
.64 
[64 

•65 
'65 
«65 

165 
166 
166 
167 
r67 
167 
[67 
[67 

.69 

169 
169 
169 
.69 
169 
169 
169 
[70 
170 
[70 
[71 
[72 
[72 
[72 
[72 
[72 
[72 

'73 

'73 
'73 
'73 
173 
173 
'73 
'74 
t74 
'74 
'74 

'75 

'75 
'75 
[76 

'77 
'79 
179 


XII 


TABLE    OF    CONTENTS. 
Part  II.— NAUTICAL  ASTRONOMY— Continued. 


Subject. 


Chap.  XV. — Surveying — Continued. 


6.  The  Three- Armed  Protractor 


Definitions 

Geodetic  Surveying 

Survey  of  a  Harljor — The  Base  Line 

Astronomical  Determination  of  Observation  Spot 

Triangulation 

Signals 

Observing  the  Angles 

Topography : 

The  use  of  the  Plane  Table 

Preliminary  Work 

Field  Practice 

Three- Point  Problem 

Topography  vi'ith  the  Sextant 

By  Resection 

By  the  Three- Point  Problem   

By  Course  and  Distance 

Hydrography 

Tides  

Plotting 

Running  Survey 

To  determine  the  Positions  by  Observation . . 

To  Measure  a  Base  by  Sound 

Survey  of  a  River 

Plotting 


Explanation  of  the  Tables 


Tables    i,  2,  3,  4,  5,  6 

7,  8,  9,  10,  II,  12,  13,  14,  15 

16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26 
27.  28,  29,  30 

31,  32,  33 

34.  35.  36,  37,  38 

39,  40,  41,  42,  43,  44,  45 

46,  47,  48,  49,  50 


Table. 


416 

4 

417 

m 

418 

i8( 

419 

18: 

420 

i8i 

421 

18] 

422 

i8J 

423 

iSi 

424 

i8s 

425 

18] 

426 

i8l 

427 

i8« 

428 

1 82 

429 

i8« 

430 

iSd 

431 

18^ 

432 

i8j 

433 

18^ 

434 

181 

435 

i8(i 

436 

18^ 

437 

19' 

438 

19' 

439 

i9( 

ARRANGEMENT  OF  THE  TABLES. 


Subject. 


Difference  of  Latitude  and  Departure  for  Points 

Difference  of  Latitude  and  Departure  for  Degrees 

Meridional  Parts,  or  Increased  Latitudes 

Length  of  a  Degree  in  Latitude  and  Longitude 

Distance  of  an  Object  by  Two  Bearings — Points 

Distance  of  an  Object  by  Two  Bearings — Degrees 

Distance  of  an  Object  at  Sea  in  Statute  Miles 

For  turning  Degrees  and  Minnies  into  Time,  and  contrary 

Sidereal  into  Solar  Time 

Mean  Solar  into  Sidereal  Time 

True  Rising  and  Setting 

For  reducing  the  Time  of  the  Moon's  Passage 

For  finding  the  Variation  (  f  the  Sun's   Right  Ascension,  Declination,  and  Equation  Time,  and 

Moork's  Right  Ascension  and  Declination 

For  finding  Sun's  Right  Ascension  for  given  number  of  Hours 

Dip  of  the  Sea  Horizon 

Dip  of  the  Sea  at  Different  Distances 

The  Sun's  Parallax  in  Altitude 

A  Planet's  Parallax  in  Altitude 

Augmentation  of  Moon's  Semi-diameter 

Augmentation  of  Moon's  Horizontal  Parallax 

Mean  Refra  tion 

Correction  for  Height  of  Barometer 

Correction  for  Height  of  Thermometer 

Correction  of  Moon's  Altitude  for  Parallax  and  Refraction 

Correction  of  Moon's  Apparent  Altitude 


I 

2 

3 

4 

5A 

SB 

6 

7 
8 

9 
10 
II 

12 

13 
14 

15 
16 

17 

18 

19 
20 
21 
22 

23 
24 


TABLE    OF    CONTENTS. 
ARRANGEMENT  OF  THE  TABLES— Continued. 


XIII 


Subject. 


Showing  Variation  of  Altitude  of  an  Object  arising  from  a  change  of  lOO  seconds  in  I  )eclination 

Variation  of  Sun's  Altitude  in  One  Minute  from  Noon 

To  reduce  the  Numbers  of  Table  26  to  other  given  Intervals  of  Time  from  Noon 

For  finding  the  Latitude  of  a  Place  by  Altitudes  of  Polaris 

Same 

Same 

Same 

Mean  Reduced  Refraction  for  Lunars 

Logarithms  A,  B,  V,  and  1 ),  for  Computing  First  Correction  of  the  Lunar  Distance 

Second  Correction  of  the  Lunar  I  distance 

Contraction  of  Moon's  Semi-diameter 

Same 


Contraction  of  Sun's  Semi-diameter 

Same ,. 

Logarithms  of  Small  Arcs  in  Space  or  Time 

Correction  in  Finding  the  Greenwich  Time  corresponding  to  a  Corrected  Lunar  Distance  . . . 

For  finding  the  \'alue  of  N 

Logarithms  A  and  P.,  for  Computing  the  Equation  of  Equal  Altitudes 

The  Error  in  Longitude  occasioned  by  an  Error  of  One  Mile  in  Latitude 

Amphtudes  of  Heavenly  Bodies 

Correction  of  the  Observed  Amplitudes 

Natural  Sines  and  Cosines 

Logarithms  of  Numbers 

Logarithmic  Sines,  Tangents,  and  Secants  to  every  Point  and  Quarter  Point  of  the  Compass 

Logarithmic  Functions 

Proportional  Logarithms 

Tide  Table  for  the  Coast  of  the  United  States 

Tide  Table  for  the  World 

Standard  Fixed  Stars — Mean  Places  for  1880 

Maritime  Positions 

Maritime  Positions — Alphabetical  Index 

The  Magnetic  Variation  of  the  Compass 

Appendix 


Decimal  Fractions  . 

Logarithms 

Geometry 

Trigonometry 

Useful  Problems  . . . 
Useful  Memoranda . 


Table,  j  Page. 


25 
26 

27 

28A 

28B 

28C 

28D 

29 

30 

31 
32A 

32  B 
33A 
33B 
34 
35 
36 
37 
38 

39 
40 

41 
42 

43 
44 

45 
46 

47 
48 

49 
49 
50 


317 
219 

323 
324 
325 
325 
330 
.332 
333 
345 
348 
348 
349 
349 

350 
368 

369 
370 
374 

375 
380 

381 
390 
406 

407 

452 
468 

471 
516 
520 

598 
619 

623 

623 
626 
632 

639 
643 
646 


ABBREVIATIONS  USED  IN  THIS  BOOK. 


L Latitude. 

L' Latitude  left. 

L" Latitude  arrived  at. 

Mid.  L Middle  Latitude. 

D.  L Difference  of  Latitude. 

Co-L 90° — Latitude 

Lo Longitude. 

Lo' Longitude  left. 

Lo" I-ongitude  arrived  at. 

D.  Lo Difference  of  Longitude. 

Dist Distance. 

Dep   Departure. 

C -Course. 

D.  or  d Declination. 

P.  D Polar  distance. 

Az     Azimuth. 

Amo Amplitude. 

m.  t Mean  time. 

L.  m.  t Local  mean  time. 

G.  m.  t     Greenwich  mean  time. 

app.  t. Apparent  time. 

Ast.  t Astronomical  time. 


Sid.  t Sidereal  time. 

Eq.  t Equation  of  time. 

H.  A.  or  t Hour  Angle. 

h Altitude. 

Z Zenith  distance. 

r - Refraction. 

par Parallax . 

H.  P  . Horizontal  parallax- 

S.  D Semi-diameter. 

I.  C Lidex  correction. 

H.  D Hourly  difference. 

M.  D Minute  difference. 

D.  R Dead  Reckoning. 

By  Obs By  observation. 

Log Logarithm. 

P.  L Proportional  logaiithm. 

Sin Sine. 

Cos Cosine. 

tan Tangent. 

cot Cotangent. 

sec Secant. 

cosec Cosecant. 


xu 


I 


NAVIGATION". 


CHAPTER  I 


DEFINITIONS. 


N 


7 


Art.  1.  Tliat  science  which  treats  of  the  determination  of  a  ship's  place  at  sea,  and  affords  the  knowledge 

necessary  to  conduct  a  ship  from  place  to  place,  is  called  NAVIGATION. 

There  are  two  methods  of  Navigation  :  one  commonly  called  Navigation,  but  more  correctly  Geo-Naviga- 
TioN;  the  other,  Nautical  AsiRONoMV,  or  Celo-Navigatiun. 

Art.  2.  By  the  first  method  the  ship's  place  is  determined  by  referring  it  to  ihe  land,  to  the  bottom,  or  to 
some  former  position.  The  instruments  employed  are  the  Chart,  to  give  the  landmarks  from  which  bearings 
are  taken ;  the  Lead,  to  ascertain  soundings ;  the  Log  and  Mariner's  Compass,  which,  with  the  Chart,  afford 
the  means  of  establishing  the  position  by  Dead  Reckoning. 

By  the  second  method  the  position  of  the  ship  is  determined  by  finding  the  zenith  of  the  place  from  observa- 
tions of  heavenly  bodies.  In  order  to  solve  the  triangles  projected  upon  the  celestial  concave,  principles  of  spheri- 
cal trigonometry  are  involved,  and  the  necessary  data  are  given  by  the  use  of  the  Sextant,  the  Azimuth  Com- 
pass, the  Chronometer,  an  Astronomical  Register  or  Ephemeris,  as  the  Nautical  Almanac,  and  suitable 
Tables  to  facilitate  the  solution  of  the  various  problems.  The  process  by  this  method  is  called  "  By  Observa- 
tion," to  distinguish  it  from  that  of  the  first  "  By  Dead  Reckoning." 

Art.  3.  Definitions  relating  to  the  Earth. 
• 

Fig.  I  represents  a  stereographic  projection  of  the  Earth  (assumed  to  be  a  sphere)  upon  the  plane  of  the 
meridian  PEP'W. 

The  Axis  of  the  earth,  PP',  is  the  diameter  about  which  the 
earth  rotates  daily.  Jri^.l. 

The  Poles  are  the  extremities  of  the  Axis,  or  the  points  in  ^ 

which  the  axis  meets  the  surface.  The  adjacent  pole  in  our  hemi- 
sphere being  designated  the  North  Pole,  and  the  opposite,  the 
South  Pole.  y<C.       <?■* 

The  great  circle  on  the  earth's  surface,  EQW,  formed  by  a 
plane  perpendicular  to  the  axis,  is  called  the  Equator. 

The  equator  is  equidistant  from  the  North  and  South  poles, 
being  90^  from  each. 

Great  circles,   secondary  to  the  equator,  as  PIMP',  PM'P', 
PGQP',  are  called  Meridians  or  Circles  of  Longitude.   The 
First  or  Prime  Meridian  for  American  and  English  Naviga-   k;>I 
tors  is  that  of  Greenwich. 

Small  circles  formed  by  planes  parallel  to  that  of  the  Equator 
are  called  Parallels  of  Latitude,  as  NT;/,  N'«'T'. 

The  Longitude  of  a  place  on  the  surface  of  the  earth  is  the 
arc  of  the  Equator  intercepted  between  the  Prime  Meridian  and 
the  meridian  of  the  place. 

The  Latitude  of  a  place  on  the  surface  of  the  earth  is  the 
arc  of  the  meridian  intercepted  between  the  Equator  and  the 
place. 

Longitudes  are  reckoned  East  and  West  through  180°  from  JP' 

the  origin,  the  interception  of  the  Prime  Meridian  with  the 
Equator. 

Latitudes  are  reckoned  North  and  South  through  90'-'  from  the  Equator. 

For  instance,  if  T  be  a  place  on  the  earth's  surface  its  position  is  defined  by  the  intersection  of  its  meridian, 
PTMP',  and  its  parallel  of  latitude  NT//;  its  longitude  being  QM  (East)  and  its  latitude  MT  (North). 

The  curved  line  which  joins  any  two  places  on  the  earth's  surface,  cutting  the  intermediate  meridians  at  the 
same  angle,  is  called  a  Rhumb  Line,  Loxodromic  Cukve,  or  Equiangular  Spiral.  Let  T  and  T'  be  two 
places ;  the  hne,  TT',  joining  them  is  a  Rhumb  Line. 

The  Difference  of  Latitude  between  two  places  is  the  arc  of  a  meridian  intercepted  between  their  paral- 
lels of  latitude.     Thus,  Tn'  is  the  difference  of  latitude  belvi'een  T  and  T',  and  is  N^orth. 

The  Difference  of  Longitude  between  two  places  is  the  arc  of  the  Equator  intercepted  between  their 
meridians,  and  is  called  East  or  West,  according  to  the  direction  followed.  Thus,  MM'  is  the  difference  of  longi- 
tude between  T  and  T',  and  is  East. 

Latitudes  are  reckoned  North  and  South  of  the  Equator,  and  longitudes  East  and  West  of  the  Prime  Merid- 
ian. If  these  different  directions  are  considered,  one  positive  and  the  other  negative,  the  difference  of  latitude  and 
the  difference  of  longitude  are  always  found  by  taking  the  algebraic  difference  of  the  latitudes  and  longitudes. 

The  Departure  is  the  East  or  West  distance  between  two  places  measured  on  one  of  their  parallels  of  lati- 
tude; for  instance,  T'«'  is  the  departure  !>etween  T  and  T',  proceeding  in  the  direction  TT'. 


/ 

1        A 

\     \ 

/^^ 

1 

f^lT 

T\ 

T 

Q 

m  m  m 
123 

M' 

/ 

(I) 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


CHAPTER    II. 

INSTRUMENTS  OF   NAVIGATION. 

1.— THE  PLANE  SCALE. 
Art*  4.  Its  construction. 


I 


1st.  With  the  radius  intended  for  the  scale,  describe  a  semicircle,  ADB  (Fig.  2),  and  from  the  centre,  C, 
draw  CD  perpendicular  to  AB,  which  will  divide  the  semicircle  into  two  quadrants,  AI),  BL) ;  continue  CD 
toward  S,  draw  BT  perpendicular  to  CB,  and  join  BD  and  AD. 

2dly.  Divide  the  quadiant  BD  into  9  equal  parts  ;  then  will  each  of  these  be  10  degrees  ;   subdivide  each  of  these 
parts  into   single  degrees,  and,  if  the 
radius  will  admit  of  it,  into  minutes  or 
some  aliquot  parts  of  a  degree  greater 
than  minutes. 

3dly.  Set  one  foot  of  the  compasses 
in  B,  and  transfer  each  of  the  divisions 
of  the  quadrant  BD  to  the  right  line 
BD,  then  will  BD  be  a  line  of  chords. 

4thly.  From  the  points  10,  20,  30, 
&c.,  in  the  quadrant  BD,  draw  right 
lines  parallel  to  CI),  to  cut  the  radius 
CB,  and  they  will  divide  that  line  into  a 
line  of  sines  which  must  be  numbered 
from  C  toward  B. 

5thly.  If  the  same  line  of  sines  be 
numbered  from  B  toward  C,  it  will  be- 
come a  line  of  versed  sines,  which  may 
be  continued  to  180^^,  if  the  same  divis- 
ions be  transferred  on  the  same  line  on 
the  other  side  of  the  centre  C. 

6thly.  From  the  centre  C,  through 
the  several  divisions  of  the  quadrant 
BD,  draw  right  lines  till  they  cut  the 
tangent  BT;  so  will  the  line  BT  be- 
come a  line  of  tangents. 

7thly.  Setting  one  foot  of  the  com- 
passes in  C,  extend  the  other  to  the 
several  divisions,  10,  20,  30,  &c.,  in  the 
tangent  line,  BT,  and  transfer  these  ex- 
tents severally  to  the  right  line,  CS; 
then  will  that  line  be  a  line  of  secants. 

8thly.  Right  lines  drawn  from  A 
to  the  several  divisions,  10,  20,  30,  &c., 
in  the  quadrant  BD,  will  divide  the 
radius  CI)  into  a  line  of  semi-tangents. 

gthly.  Divide  the  quadrant  A I )  into 
eight  equal  parts,  and  from  A,  as  a  cen- 
tre, transfer  these  divisions  severally 
into  the  line  AD ;  then  will  AD  be  a 
line  of  rhumbs,  each  division  answer- 
ing to  il'^  15'  upon  the  line  of  chords. 
The  use  of  this  line  is  for  protracting 
and  measuring  angles,  according  to  the 
common  division  of  the  mariner's  com- 
pass. If  the  radius  AC  be  divided  into 
100  or  1000,  &c  ,  equal  parts,  and  the 
lengths  of  the  several  sines,  tangents, 
and  secants,  corresponding  to  the  sev- 
eral arcs  of  the  quadrant,  be  measured 
thereby,  and  these  numbers  be  set  down 
in  a  table,*  each  in  its  proper  column, 
you  will  by  these  means  have  a  collec- 
tion of  numbers  by  which  the  several 
cases  in  trigonometry  may  be  solved. 
Right  lines,  graduated  as  above,  being 
placed  severally  upon  a  ruler,  form  the 
instrument  called  the  Plane  Scale  (Fig. 
3),  by  which  the  lines  and  angles  of  all 
triangles  may  be  measured.  All  right 
lines,  as  the  sides  of  plane  triangles,  &c.,  when  lliey  are  considered  simply  as  such,  without  having  any  relation 
to  a  circle,  are  measured  by  scales  of  equal  parts,  one  of  which  is  subdivided  equally  into  10,  and  this  serves  as 
a  common  division  to  all  the  rest.     In  most  scales,  an  inch  is  taken  for  a  common  measure,  and  what  an  inch  is 


AWOISOISO  140 


Plane  Scale     Fig.  3. 


Rhuiu. 


Clioi 


Sine 


S.T. 


10 

z±= 


20 

Z±ZL 


30 


40 


80 

=1= 


10 


20 


30 


60    70   9  0 

I    nil 


30 

-f— 


60   Secants 


10 


4.0 

=dcz 


50 


60 

-t- 


30 


30 


50 

—I— 


70 

—I— 


90 

— t— 


100 

—I 


110 

-1— 


120 

I 


Djagonal    Scale  Fi£.  4. 


*  In  Table  41  are  given  the  sine  an()  cosine  to  every  minute  of  tlie  ciuadrant,  to  five  places  of  decimals. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION.  3 

divided  into  is  generally  set  at  the  end  of  the  scale.  By  any  common  scale  of  equal  parts,  divided  in  this  nianner, 
any  number  less  than  loo  may  be  readily  taken  ;  but  if  the  number  should  consist  of  three  places  of  figures,  the 
value  of  the  third  figure  cannot  be  exactly  ascertained,  and  in  this  case  it  is  lietter  to  use  a  diagonal  scale,  by  which 
aiiv  number  consisiing  of  three  places  of  figures  may  be  exactly  found.  The  figure  of  this  scale  is  given  in  Fig. 
4 ;  its  construction  is  as  follows  : 

Having  prepared  a  ruler  of  convenient  breadth  for  the  scale,  draw  near  the  edges  thereof  two  right  lines,  af, 
eg,  parallel  to  each  other;  divide  one  of  these  hues,  as  af,  into  equal  parts,  according  to  the  size  of  the  scale;* 
and  through  each  of  these  divisions  draw  right  lines  perpendicular  to  af,  to  meet  (■<,•■;  then  divide  the  breadth  into 
10  equal  parts,  and  through  each  of  these  divisions  draw  right  lines  parallel  to  ({/and  eg;  divide  the  lines  al>,  cd,  into 
lO  equal  parts,  and  from  the  point  a  to  the  first  division  in  the  line  cd,  draw  a  diagonal  line;  then,  parallel  to  that 
line,  draw  diagonal  lines  through  all  the  other  divisions,  and  the  scale  is  complete.  Then,  if  any  number  consist- 
ing of  three  places  of  figures,  as  256,  be  required  from  the  larger  scale,  gd,  place  one  foot  of  the  compasses  on  the 
figure  2  on  the  line  ,<,■•(/,  then  the  extent  from  2  to  the  point  d  will  represent  200.  The  second  figure  being  5,  count 
five  of  the  smaller  divisions  from  d  toward  c,  and  the  extent  from  2  to  that  point  will  be  250.  Move  both  points 
of  the  compasses  downward  till  they  are  on  the  sixth  j^arallel  line  below  gd,  and  open  them  a  little  till  the  one 
point  rests  on  the  vertical  line  drawn  through  2,  and  the  other  on  the  diagonal  line  drawn  through  5 ;  the  extent 
then  in  the  compasses  will  represent  256.     In  the  same  way  ihe  quantities  25.6,  2.56,  0.256,  &c. ,  are  measured. 

Besides  the  lines  already  mentioned,  there  is  another  on  the  Plane  Scale,  marked  ML,  which  is  joined  to  a 
line  of  chords,  and  shows  how  many  miles  of  easting  or  westing  correspond  to  a  degree  of  longitude  in  every 
latitude. t  These  several  lines  are  generally  put  on  one  tide  of  a  ruler  two  feet  long;  and  on  the  other  side  is  laid 
down  a  scale  of  the  logarithms  of  the  sines,  tangents,  and  numbers,  which  is  commonly  called  Gunter's  Scale ; 
and  as  it  is  of  general  use,  it  requires  a  particular  description. 

2.— GUNTER'S  SCALE. 
Art.  5.    Description  of  Gunter's  Scale. 

On  Gunter's  Scale  are  eight  lines,  viz : 

1st.  Sine  rhumbs,  marked  (SR),  corresponding  to  the  logarithmst  of  the  natural  sines  of  every  point  of  the 
mariner's  compass,  numbered  from  the  left  hand  toward  the  right,  with  i,  2,  3,  4,  5,  6,  7,  to  8,  where  is  a  brass 
pin.     This  line  is  also  divided,  where  it  can  be  doi  e,  into  halves  and  quarters. 

2dly.  Tangent  rhumbs,  marked  (TR),  correspond  to  the  logarithms  of  the  tangents  of  every  point  of  the  com- 
pass, and  are  numbered  i,  2,  3,  to  4,  at  the  right  hand,  where  there  is  a  pin,  and  thence  toward  the  left  hand 
with  5.6,  7 ;  it  is  also  divided,  where  it  can  be  done,  into  halves  and  quarters. 

3dly.  The  hne  of  numbers,  marked  (Num.),  corresponds  to  the  logarithms  of  numbers,  and  is  marked  thus: 
Near  the  left  hand  it  begins  at   i,  and  toward  the  right  hand   are  2,  3,   4,  5,  6,  7,  8,  9 ;  and  I   in  the  middle, 
at  which  is  a  brass  pin;   then  2,   3,  4,   5,   6,  7,   8,   9,  and   10,    at   the   end,  where   there  is   another  pin.      The 
values  of  these  numbers  and  their  intermediate  divisions    depend  on  the  estimated  values  of  the  extreme  num- 
bers I  and  10;  and  as  this  line  is  of  great  importance,  a  particular  description  of  it  will  be  given.     The  first  i 
may  be  counted  for  i,  10,  100,  or  1000,  &c.,  and  then  the  next  2  will  be  2,  20,  200,  or  2000,  &c.,  respectively. 
Again,  the  first  i  may  be  reckoned  I  tenth,  l  hundredth,  or  i  thousandth  part,  &c. ;   then  the  next  will  be  2  tenth, 
or  2  hundredth,  or  2  thousandth  parts,  &c. ;   so  that,  if  the  first  i  be  esteemed  i,  the  middle  I  will  be  10;  2  to  its 
right,  20;   3,  30;  4,  40  ;  and  10  at  the  end,  100.     Again,  if  the  first   I   is   10,  the  next  2  is  20,  3  is  30,  and  so  on, 
i   making  the  middle  I,  100  ;   the  next  2  is  200,  3  is  300,  4  is  400,  and  10  at  the  end  is  1000.     In  like  manner,  if  the 
i   first  I  be  esteemed  i  tenth  part,  the  next  2  will  be  2  tenth  parts,  and  the  middle  i  will  be  I  ;   the  next  2,  2  ;   and 
i    10  at  the  end  will  be  10.     Again,  if  the  first   i   be  counted   i   hundredth  part;   the   next,  2  hundredth  parts ;   the 
(   middle  i  will  be  10  hundredth  parts,  or  i  tenth  part ;  and  the  next  2,  2  tenth  parts;   and  10  at  the  end  will  be  but 
j   one  whole  number  or  integer. 

i  As  the  figures  are  increased  or  diminished  in  their  value,  so  in  like  manner  must  all  the  intermediate  strokes 

\  or  subdivisions  be  increased  or  diminished  ;   that  is,  if  the  first  i  at  the  left  hand  be  counted  i,  then  2  (next  foUow- 

i   ing  it)  will  be  2,  and  each  subdivision  between   them  will  be   i   tenth  part  ;    and  so  all  the  way  to  the  middle  1, 

I  which  will  be  10;   the  next  2,  20;  and  the  longer  strokes  between  i  and  2  are  to  be  counted  from  i  thus  :    11,  12 

(where  is  a  brass  pin);   then  13,  14,  15,  sometimes  a  longer  stroke  than  the  rest;  then  16,  17,  18,  19,  20,  at  the 

figure  2 ;  and  in  the  same  manner  the  short  strokes  between  the  figures  2  and  3,  3  and  4,  4  and  5,  &c.,  are  to  be 

reckoned  as  units.     Again,  if  i  at  the  left  hand  be   10,  the  figures  between  it  and  the  middle  I  will  be  common 

tens,  and  the  subdivisions  between  each  figure  will  be  units  ;   from  the  middle  i  to  10  at  the  end,  each  figure  will 

be  so  many  hundreds  ;   and  between  these  figures  each  longer  division  will  be  10.     From  this  description  it  will  be 

easy  to  find  the  divisions  representing  any  given   number,  thus  :   Suppose  the  point  representing  the  number  12 

were  required;   take  the  division  at  the  figure  i  in  the  middle,  for  the  first  figure  of  12  ;   then  for  the  second  figure 

count  two-tenths,  or  longer  strokes  to  the  right  hand,  and  this  will  be  the  point  representing  12,  where  the  brass 

pin  is. 

Again,  suppose  the  number  22  were  required ;  the  first  figure  2  is  to  be  found  on  the  scale,  and  for  the  second 
figure  2,  count  two-tenths  onward,  and  that  is  the  point  representing  22. 

Again,  suppose  1728  were  required;  for  the  first  figure  i,  take  the  middle  i,  for  the  second  figure  7,  count 
onward  as  before,  and  that  will  be  1700.  And,  as  the  remaining  figures  are  28,  or  nearly  30,  note  the  point 
which  is  nearly  -,'u  of  the  distance  between  the  marks  7  and  8,  and  this  will  be  the  point  representing  1 728. 

If  the  point  representing  435  was  retjuired,  from  the  4  in  the  second  interval  count  toward  5  on  the  right, 
three  of  the  larger  divisions  and  one  of  the  smaller  (this  smaller  division  being  midway  between  the  marks  3  and  4), 
and  that  will  be  the  division  expressing  435.     In  a  similar  manner  other  numbers  may  be  found. 

All  fractions  found  in  this  line  must  be  decimals;  and  if  they  are  not,  they  must  be  reduced  into  decimals, 
which  is  easily  done  by  extending  the  compasses  from  '.he  denominator  to  the  numerator ;  that  extent,  laid  the 
same  way  from  i  in  the  middle  or  right  hand,  will  reach  to  the  decimal  recjuired. 

♦The  length  of  one  of  these  equal  parts  at  the  end  of  the  scale  to  which  this  description  refers  is  ab  or  ed\  the  length  of  one 
of  the  equal  parts  of  the  scale  of  the  other  end  being  the  half  of  ab. 

t  As  it  would  confuse  tlie  adjoined  figure  to  describe  on  it  the  line  ot  longitudes,  il  is  neglected,  but  the  construction  is  as 
follows :  Divide  the  line  ( "  \\  into  do  equal  parts  (if  it  can  be  done),  and  tlirough  each  point  draw  lines  parallel  to  CD,  to  intersect 
the  arc  HD  ;  about  li,  as  a  centre,  transfer  the  several  points  ol  iiUersection  to  the  line  of  cliords,  HD,  and  tlien  number  it  from 
D  toward  M,  from  o  to  60,  and  it  will  be  the  line  of  longitudes,  correspv)nding  to  the  degiees  on  the  line  of  chords. 

X  The  description  and  use  of  logarithms  arc  given  in  the  Appendix.  The  log.  sines,  tangents,  &c.,  are  marked  on  these  scales 
by  means  of  a  line  of  equal  parts,  corresponding  to  the  size  of  the  scale. 


4  INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 

Example.  Required  the  decimal  fraction  equal  to  f .  Extend  from  4  to  3 ;  that  extent  will  reach  from  i  on 
the  middle  to  .75  toward  the  left  hand.     The  like  may  be  observed  of  any  other  vulgar  fraction. 

Multiplication  is  performed  on  this  line  by  extending  from  i  to  the  multiplier;  that  extent  will  reach  from  the 
multiplicand  to  the  product. 

Suppose,  for  example,  it  were  required  to  find  the  product  of  16  multiplied  by  4;  extend  from  I  to  4;  that 
extent  will'reach  from  16  to  64,  the  product  required. 

Division  being  the  reverse  of  multiplication,  there'ore  extend  from  the  divisor  to  unity  ;  that  extent  will  reach 
from  the  dividend  to  the  quotient. 

Suppose  64  to  be  divided  by  4;  extend  from  4  to  1 ;   that  extent  will  reach  from  64  to  16,  the  quotient. 

Questions  in  the  Rule  of  Three  are  solved  liy  this  line  as  follows:  Extend  from  the  first  term  to  the  second; 
that  extent  will  reach  from  the  third  term*  to  the  fourth.  And  it  ought  to  be  particularly  noted,  that  if  you  extend 
to  the  left,  from  the  first  number  to  the  second,  you  must  also  extend  to  the  left,  from  the  third  number  to  the 
fourth;  and  the  contrary. 

Example.  If  the  diameter  of  a  circle  be  7  inches,  and  the  circumference  22,  what  is  the  circumference  of 
another  circle,  the  diameter  of  which  is  14  inches?  Extend  from  7  to  22  ;  that  extent  will  reach  from  14  to  44, 
the  same  way. 

The  superficial  content  of  any  parallelogram  is  found  by  extending  from  i  to  the  Ijreadth ;  that  extent  will 
reach  from  the  length  to  the  superficial  content. 

Example.  Suppose  a  plank  or  board  to  be  15  inches  broad  and  27  feet  long,  the  content  of  which  is  required. 
Extend  from  I  to  i  foot  3  inches  (or  1.25);  that  extent  will  reach  from  27  feet  to  33.75  feet,  the  superficial  content. 
Or  extend  from  12  inches  to  15,  &c. 

The  solid  content  of  any  bale,  box,  chest,  &c.,  is  found  by  extending  from  i  to  the  breadth;  that  extent  will 
reach  from  the  depth  to  a  fourth  number,  and  the  extent  from  i  to  that  fourth  number  will  reach  from  the  length  to 
the  solid  content. 

Example  I.  What  is  the  content  of  a  square  pillar  whose  length  is  21  feet  9  inches  and  breadth  i  foot  3 
inches?  The  extent  from  i  to  1.25  will  reach  from  1.25  to  1. 56,  the  content  of  one  foot  in  length;  again,  the 
extent  from  i  to  1.56  will  reach  from  the  length  21.75  ^'^  33-9'  o""  34'  ^^e  solid  content  in  feet. 

Example  II.  Suppose  a  square  piece  of  timber,  1.25  feet  broad,  .56  deep,  and  36  long,  be  given  to  find  the 
content.  Extend  from  i  to  1.25  ;  that  extent  will  reach  from  .56  to  .7;  then  extend  from  I  to  .7;  that  extent  will 
reach  from  36  to  25.2,  the  solid  content.  In  like  manner  may  the  contents  of  bales,  &c.,  be  found,  which,  being 
divided  by  40,  will  give  the  number  of  tons. 

4thly.  The  line  of  sines,  marked  (Sin.),  corresponding  to  the  log.  sines  of  the  degrees  of  the  quadrant,  begins 
at  the  left  hand,  and  is  numbered  to  the  right,  i,  2,  3,  4,  5,  &c.,  to  10;  then  20,  30,  40,  &c.,  ending  at  90  degrees, 
where  is  a  brass  center-pin,  as  there  is  at  the  right  end  of  all  the  lines. 

5thly.  The  line  of  versed  sines,  marked  (V.  S. ),  corresponding  to  the  log.  versed  sines  of  the  degrees  of  the 
quadrant,  begins  at  the  right  hand  against  90'  on  the  sines,  and  from  thence  is  numbered  toward  the  left  hand, 
10,  20,  30,  40,  &c.,  ending  at  the  left  hand  at  about  169"-' ;  each  of  the  subdivisions,  from  10  to  30,  is  in  general 
two  degrees;   from  thence  to  90  is  single  degrees;  from  thence  to  the  end  each  degree  is  divided  into  15  minutes. 

6thly.  The  line  of  tangents,  marked  (Tang.),  corresponding  to  the  log.  tangents  of  the  degrees  of  the  quad- 
rant, begins  it  the  left  hand,  and  is  numbered  toward  the  right,  i,  2,  3,  &c.,  to  10,  and  so  on,  20,  30,  40,  and  45, 
where  is  a  brass  pin  under  90°  on  the  sines;  from  thence  it  is  numbered  backwards,  50,  60,  70,  80,  &c.,  to  89, 
ending  at  the  left  hand  where  it  began  at  i  degree.  The  subdivisions  are  nearly  similar  to  those  of  the  sines. 
With  any  extent  in  the  compasses,  to  be  set  off  from  any  number  less  than  45"  on  the  line  of  tangents,  toward 
the  right,  and  it  is  found  to  reach  beyond  the  mark  of  45^,  see  how  far  it  extends  beyond  that  mark,  and  set  it  off 
from  45"^'  toward  the  left,  and  see  what  degree  it  falls  upon,  which  will  be  the  number  sought,  which  must  exceed 
45"^ ;  if,  on  the  contrary,  to  set  off  such  a  distance  to  the  right  from  a  number  greater  than  45°,  proceed  as  before, 
only  remembering  that  the  answer  must  be  less  than  45'^,  and  always  consider  the  degrees  above  45"  as  if  they 
were  marked  on  the  continuation  of  the  line  to  the  right  hand  of  45^. 

7thly.  The  line  of  the  meridional  parts,  marked  (Mer.),  begins  at  the  right  hand,  and  is  numbered,  10,  20, 
30,  &c.,  to  the  left  hand,  where  it  ends  at  87  degrees.  This  line,  and  the  line  of  equal  parts,  marked  (E.  P.), 
under  it,  are  used  together,  and  only  in  Mercator's  Sailing.  The  upper  line  contains  the  degrees  of  the  meridian, 
o;  latitude  in  a  Mercator's  chart,  corresponding  to  the  degrees  of  longitude  on  the  lower  line. 

3.— THE  SECTOR. 

Al't.  6.  This  inslrument  consists  of  two  rules  or  legs,  movable  round  an  axis  or  joint  as  a  centre,  having  sev- 
eral scales  drawn  on  the  faces,  some  single,  others  double ;  the  single  scales  are  like  those  upon  a  common  Gunter's 
Scale;  the  double  scales  are  those  which  proceed  from  the  centre,  each  being  laid  twice  on  the  same  face  of  the 
instrument,  viz,  once  on  each  leg.  From  these  scales,  dimensions  or  distances  are  to  be  taken,  when  the  legs  of 
the  instrument  are  set  in  an  angular  position. 

The  single  scales  being  used  exactly  like  those  on  the  common  Gunter's  .Scale,  it  is  unnecessary  to  notice  them 
particularly.  We  shall  therefore  only  mention  a  few  of  the  uses  of  the  double  scales,  the  number  of  which  is 
seven,  viz,  the  scale  of  I>ines,  marked  Lin.  or  L. ;  the  scale  of  Chords,  marked  Cho.  or  C.  ;  the  scale  of  Sines, 
marked  Sin.  or  S. ;  the  scale  of  Tangents  to  45^,  and  another  scale  of  Tangents  from  45^  to  about  76^,  both  of 
which  are  marked  Tan.  or  T. ;   the  scale  of  Secants,  marked  Sec.  or  S. ;   and  the  scale  of  Polygons,  marked  Pol. 

The  scales  of  lines,  chords,  sines,  and  tangents  under  45°  are  all  of  the  same  radius,  beginnings  at  the  center 
of  the  instrument  and  terminating  near  the  other  extremity  of  each  leg,  viz,  the  lines  at  the  division  10,  the  chords 
at  60°,  the  sines  at  90°,  and  the  tangents  at  45^  ;  the  remainder  of  the  tangents,  or  those  above  45^,  are  on  other 
scales,  beginning  at  a  quarter  of  the  length  of  the  former,  counted  from  the  centre,  where  they  are  marked  with 
45°,  and  extend  to  about  76°.  The  secants  also  begin  at  the  same  distance  from  the  centre,  where  they  are  marked 
with  o,  and  are  from  thence  continued  to  75^.  The  scales  of  polygons  are  set  near  the  inner  edge  of  the  legs,  and 
where  these  scales  begin  they  are  marked  with  4,  and  from  thence  are  numbered  backward,  or  toward  the  centre, 
to  12. 

In  describing  the  use  of  the  Sector,  the  terms  lateral  distance  and  transverse  distance  often  occur.     By  the 

*  Or,  extend  from  the  first  to  the  third  ;  for  tliat  extent  will  reach  from  the  second  to  the  fourth.  This  method  must  be 
adopted  when  using  the  lines  of  sines,  tangents,  &c.,  if  the  first  and  third  terms  are  of  the  same  name,  and  different  from  the 
second  and  fourth. 


INSTEUMENTS    EMPLOYED    IN    NAVIGATION.  5 

former  is  meant  the  distance  taken  with  the  compasses  on  one  of  the  scales  only,  beginning  at  the  centre  of  the 
Sector;  and  by  the  latter,  the  distance  taken  between  any  two  corresponding  divisions  of  the  scales  of  the  same 
name,  the  tegs  of  the  Sector  being  in  an  angular  position. 

The  use  of  the  Sector  depends  upon  the  proportionality  of  the  corresponding  sides  of  sim- 
ilar triangles.  For  if,  in  the  triangle  ABC,  we  take  AB  =  AC,  and  AD^^AE,  and  draw  UE, 
BC,  it  is  "evident  that  DE  and  BC  will  be  parallel;  therefore,  by  the  above-mentioned  proposi- 
tion, AB:  BC:  :  AD:  DE;  so  that,  whatever  part  AD  is  of  AB,  the  sane  part  DE  will  be  of 
BC ;  hence,  if  DE  be  the  chord,  sine,  or  tangent  of  any  arc  to  the  radius  AD,  BC  will  be  the 
same  to  the  radius  AB. 

Use  of  the  line  of  Lines, 

Art.  "y.  The  line  of  lines  is  useful  to  divide  a  given  line  into  any  number  of  equal  parts,  or  in  any  propor- 
tion, or  to  find  third  and  fourth  proportionals,  or  mean  proportionals,  or  to  increase  a  given  line  in  any  proportion. 

Example  I.  To  divide  a  given  line  into  any  number  of  equal  parts,  as  suppose  9  ;  make  the  length  of  the 
given  line  a  transverse  distance  to  9  and  9,  the  number  of  parts  proposed;  then  will  the  transverse  distance  of  i 
and  I  be  one  of  the  parts,  or  the  ninth  part  of  the  whole  ;  and  the  transverse  distance  of  2  and  2  will  be  two  ot 
the  equal  parts,  or  %  of  the  whole  line,  &c. 

Example  II.     If  a  ship  sails  52  miles  in  8  hours,  how  much  would  she  sail  in  3  hours  at  the  same  rate  ? 

Take  52  in  the  compasses  as  a  transverse  distance,  and  set  it  off  from  8  to  8 ;  then  the  transverse  distance,  3 
and  3,  being  measured  laterally,  will  be  found  equal  to  19^,  which  is  the  number  of  miles  required. 

Example  III.  Having  a  chart  constructed  upon  a  scale  of  6  miles  to  an  inch,  it  is  required  to  open  the 
Sector  so  that  a  corresponding  scale  may  be  taken  from  the  line  of  lines. 

Make  the  transverse  distance,  6  and  6,  equal  to  i  inch,  and  this  position  of  the  Sector  will  produce  the  given 
scale. 

Example  IV.     It  is  required  to  reduce  a  scale  of  6  inches  to  a  degree  to  another  of  3  inches  to  a  degree. 

Make  the  transverse  distance,  6  and  6,  equal  to  the  lateral  distance,  3  and  3  ;  then  set  off  any  distance  from 
the  chart  laterally,  and  the  corresponding  transverse  distance  will  be  the  reduced  distance  required. 

Example  V.  One  side  of-any  triani^le  being  given,  of  any  length,  to  measure  the  other 
two  sides  on  the  same  scale. 

Suppose  the  side  AB  of  the  triangle  ABC  measures  50,  what  are  the  measures  of  the  other 
two  sides  ? 

Take  AB  in  the  compasses,  and  apply  it  transversely  to  50  and  50;  to  this  opening  of  the 
Sector  apply  the  distance  AC,  in  the  compasses,  to  the  same  number  on  both  sides  of  the  rule 
transversely;  and  where  the  two  points  fall  will  be  the  measure  on  the  line  of  lines  of  the  distance  required;  the 
distance  AC  will  fall  against  63,  63,  and  BC  against  45,  45,  on  the  line  of  lines. 

Use  of  tlic  line  of  Chords  on  the  Sector. 

Art.  8.  The  line  of  chords  upon  the  Sector  is  very  useful  for  protracting  any  angle,  when  the  paper  is  so 
small  that  an  arc  cannot  be  drawn  upon  it  with  the  radius  of  a  common  line  of  chords. 

Suppose  it  was  required  to  set  off  an  arc  of  30'^  from  the  point  C  of  the  small  circle  ABC, 
whose  centre  is  D. 

Take  the  radius,  DC,  in  the  compasses,  and  set  it  off  transversely  from  60'^'  to  60°  on  the 
chords ;  then  take  the  transverse  extent  from  30°  to  30^^  on  the  chords,  and  place  one  foot  of  the  i^ 
compasses  in  C;  the  other  will  reach  to  E,  and  CE  will  be  the  arc  required.  And  by  the  converse 
operation  any  angle  or  arc  may  be  measured,  viz,  with  any  radius  describe  an  arc  about  the  angular 
point ;  set  that  radius  transversely  from  60°  to  60° ;  then  take  the  distance  of  the  arc,  intercepted 
between  the  two  legs,  and  apply  it  transversely  to  the  chords,  which  will  show  the  degrees  of  the  given  angle. 

Note. — When  the  angle  to  be  protracted  exceeds  60°,  lay  off  60°,  and  then  the  remaining  part ;  or,  if  it  be 
above  120^,  lay  off  60^  twice,  and  then  the  remaining  part;  and  in  a  similar  manner  any  arc  above  60°  may  be 
measured. 

Uses  of  the  lines  of  Sines,  Tnngenfs,  and  Secants. 

Art.  9.   By  the  several  lines  disposed  on  the  Sector,  we  have  scales  of  several  radii ;   so  that — 

1st.  Having  a  lengtli  or  radius  given,  not  exceeding  the  length  of  the  Sector  when  opened,  we  can  find  the 
chord,  sine,  &c.,  of  an  arc  to  that  radius  ;  thus,  suppose  the  chord,  sine,  or  tangent  of  20°  to  a  radius  of  2  inches 
be  required.  Make  2  inches  the  transverse  opening  to  60°  and  60*^  on  the  chords ;  then  will  the  same  extent 
reach  from  45^  to  45-^  on  the  tangents,  and  from  90'^  to  90°  on  the  sines ;  so  that,  to  w  hatever  radius  the  lines  of 
chords  are  set,  to  the  same  are  all  the  others  set  also.  In  this  disposition,  therefore,  if  the  tranverse  distance 
between  20"  and  20^  on  the  chords  he  taken  with  the  compass,  it  will  give  the  chord  of  20° ;  and  if  the  transverse 
of  20'-'  and  20"  be  in  like  manner  taken  on  the  sines,  it  will  be  the  sine  of  20^;  and,  lastly,  if  the  transverse  dis- 
tance of  20°  and  20"^'  be  taken  on  the  tangents,  it  will  be  the  tangent  of  20"^  to  the  same  radius  of  2  inches. 

2dly.  If  the  chord  or  tangent  of  70^  were  recpiired  :  For  the  chord  first  set  off  the  chord  of  60^  (or  the  radius; 
upon  the  arc,  and  then  set  off  the  chord  of  10  ".  To  find  the  tangent  of  70'^,  to  the  same  radius,  the  scale  of  upper 
tangents  must  be  used,  the  under  one  only  reaching  to  45"  ;  making,  therefore,  2  inches  the  transverse  distance 
to  450  and  45°  at  the  beginning  of  that  scale,  the  extent  between  70'^  and  70°  on  the  same  will  be  the  tangent 
of  70°  to  2  inches  radius. 

3dly.  To  find  the  secant  of  any  arc ;  make  the  given  radius  the  transverse  distance  between  o  and  o  on  the 
secants  ;   then  will  the  transverse  distance  of  20'^  and  20  \  or  70^  and  70^,  give  the  secant  of  20'=  or  70°  respectively. 

4thly.  If  the  radius  and  any  line  representing  a  sine,  tangent,  or  secant  be  given,  the  degrees  corresponding 
to  that  line  may  be  found  by  setting  the  Sector  to  the  given  radius,  according  as  a  sine,  tangent,  or  secant  is  con- 
cerned; then,  taking  the  given  line  between  the  compasses,  and  applying  the  two  feet  transversely  to  the  proper 
scale,  and  sliding  the  feet  along  till  they  both  rest  on  like  divisions  on  both  legs,  then  the  divisions  will  show  the 
degrees  and  parts  corresponding  to  the  given  line. 


6  INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 

Use  of  the  line  of  Polygons.  . 

Art.  10.  The  use  of  this  line  is  to  inscribe  a  regular  polygon  in  a  circle.  For  example,  let  it  be  required 
to  inscribe  an  octagon  or  polygon  of  eight  equal  sides,  in  a  circle.  Open  the  Sector  till  the  transverse  distance  6 
and  6  is  equal  to  the  radius  of  the  circle ;  then  will  the  transyer;  e  distance  of  8  and  8  be  the  side  of  the  inscribed 
polygon. 

Use  of  the  Sector  ill  Trigononielry. 

Art.  11.  All  proportions  in  Trigonometry  are  easily  worked  by  the  double  lines  on  the  Sector;  ooserving 
that  the  sides  of  triangles  are  taken  upon  the  line  of  lines,  and  the  angles  are  taken  upon  the  sines,  tangents,  or 
secants,  according  to  the  nature  of  the  proportion.  Thus,  if,  in  the  triangle  ABC,  we  have  given  AU  =  56, 
AC  ^  64,  and  the  angle  ABC  =  46'^  30',  to  find  the  rest ;  in  this  case  we  have  the  following  propoi'tions :  As 
AC  (64)  :  sine  angle  B  (46°  30')  :  :  AB  (56) :  sine  angle  C ;  and  as  sine  B :  AC  :  :  sine  A  :  BC. 
Therefore,  to  work  these  proportions  by  the  Sector,  take  the  lateral  distance,  64  =  AC,  from 
the  line  of  lines,  and  open  the  Sector  to  make  this  a  transverse  distance  of  46*^  30'  =  angle  B 
on  the  sines  ;   then  take  the  lateral  distance  56  =  AB  on  the  lines,  and  apply  it  transversely  on 

2jZ ^O  the  sines,  which  will  give  39^  24'  =  angle  C.     Hence  the  sum  of  the  angles  B  and  C  is  '85"^  54', 

which  taken  from  180^  leaves  the  angle  A  =  94"^  6'.  Then,  to  work  this  second  proportion, 
the  Sector  being  set  at  the  same  opening  as  before,  take  the  transverse  distance  of  94*^  6'  =  the  angle  A  on  the 
sines,  or,  which  is  the  same  thing,  the  transverse  distance  of  its  supplement,  85°  54';  then  this,  applied  laterally 
to  the  lines,  gives  the  sought  side,  BC  ^  88.  In  the  same  manner  we  might  solve  any  problem  in  Trigonometry 
vidiere  the  tangents  and  secants  occur,  by  Only  measwring  the  transverse  distances  on  the  tangents  or  secants, 
instead  of  measuring  them  on  the  sines,  as  in  the  preceding  example.  All  the  problems  that  occur  in  Nautical 
Astronomy  may  be  solved  by  the  Sector;  but  as  the  calculation  by  logarithms  is  mu;h  more  accurate,  it  will  be 
useless  to  enter  into  a  further  detail  on  this  subject. 

4.— DIVIDERS,  OR  DRAWING  COMPASSES. 

Art.  12.  This  instrument  consists  of  two  legs  movable  about  a  joint,  so  that  the  points  at  the  extremities 
of  the  legs  may  be  set  at  any  required  distance  from  each  other.  It  is  used  to  take  and  transfer  distances  and  to 
describe  arcs  and  circles.     When  used  for  the  former  purpose  it  is  termed  dividci's. 

5.— PARALLEL  RULERS. 

Art.  13.  Parallel  Rulers  are  used  for  drawing  lines  parallel  to  each  other  in  any  direction,  and  are 
particularly  useful  in  transferring  the  rhumb-line  on  the  chart  to  the  nearest  compass-rose  to  ascertain  the  course, 
or  to  lay  off  bearings  and  courses. 

6.— THE  LOG. 

Art.  14.  An  instrument  for  measuring  the  rate  of  sailing,  consisting  of  three  parts,  viz :  the  Log-Chip, 
the  Log-Line,  and  the  Log-Glass. 

The  principle  of  it  is  simply  this :  A  light  substance  thrown  from  the  ship  ceases  to  partake  of  the  motion  of 
the  vessel  as  soon  as  it  strikes  the  water,  and  will  be  left  behind  on  the  surface ;  after  a  certain  interval  if  the  dis- 
tance of  the  ship  from  this  stationary  object  be  measured  the  approximate  rate  of  sailing  will  be  given.  The  log- 
chip  is  the  float,  the  log-line  is  the  measure  of  the  distance,  and  the  log  glass  defines  the  interval  of  time. 

Art.  15.  The  Log-Chip  is  a  thin  wooden  quadrant  of  about  5  inches  radius,  loaded  with  lead  on  the  circu- 
lar edge  sufficiently  to  make  it  swim  upright  in  the  water.  There  is  a  hole  in  each  corner  of  the  log-chip,  and  the 
log  line  is  knotted  in  the  one  at  the  apex  At  about  8  inches  from  the  end  there  is  seized  a  wooden  socket.  A 
piece  of  line  of  proper  length  being  knotted  in  the  other  holes  has  seized  into  its  bight  a  wooden  peg  to  fit  snugly 
into  the  socket  before  the  log-chip  is  thrown,  which  becomes  freed  as  soon  as  the  line  is  checked,  thus  allowing  the 
log-chip  to  be  hauled  in  with  the  least  resistance. 

Art.  16.  The  Log-Line  is  about  150  fathoms  in  length,  one  end  made  fast  to  the  log-chip,  the  other  to  a 
reel  upon  which  it  is  wound.  At  a  distance  of  from  15  to  20  fathoms  from  the  log-chip  a  permanent  mark  of  red 
bunting  about  6  inches  long  is  placed  to  allow  sufficient  stray  line  to  permit  the  log-chip  being  thrown  clear  of  the 
vessel's  eddy  or  wake.  The  rest  of  the  line  is  divided  into  lengths  of  47  feet  3  inches  called  knots,  by  thrusting  pieces 
offish-line  through  the  strands,  with  one,  two,  three,  &c.,  knots,  according  to  the  number  from  stray  line  mark. 

Art.  17.  The  principle  of  marking  the  log-line  is  this  :  the  length  of  a  knot  depends  upon  the  number  of 
seconds  which  the  log-glass  used  measures.  The  length  of  each  knot  must  bear  the  same  ratio  to  the  nautical 
mile*  (i/u  of  a  degree  of  a  great  circle  of  the  earth,  or  6,080  feet)  that  the  time  of  the  glass  does  to  an  hour. 

If  the  30-seconds  glass  be  used,  then  the  knot  would  be  7.^,7  of  a  nautical  mile  =:  51  feet  nearly. 

In  the  U.  S.  Navy  the  log-glasses  feeing  usually  28  seconds  and  14  seconds,  the  proportion  must  be — 

3600  :  6080  =  28^e':  :  X 
X,  being  the  length  of  the  knot. 

Hence,  x  ^=  47^'. 29,  or  47''*  3'". 

The  speed  of  the  ship  is  estimated  in  knots  and  tenths  of  a  knot. 

Art.  1§.    The  Log-CIlass  is  a  sand  glass  of  the  same  shape  and  construction  as  the  old  hour-glass.     Two 
glasses  are  used,  one  of  28  seconds  and  one  of  14  seconds;   the  latter  being  used  when  the  ship  is  going  at  a  hig! 
rate  of  speed,  the  number  of  knots  indicated  being  doubled,  to  attain  the  true  rate  of  speed. 

Art.  19.  The  log  in  all  its  parts  should  be  frequently  examined  anil  adjusted ;  the  peg  must  be  found  to  fit. 
sufficiently  tight  to  keep  the  log-chip  upright;  the  log-line  shrinks  and  stretches  and  sh'/uld  be  ofien  verified;  the' 
log-glass  should  be  compared  with  a  watch  beating  seconds.  One  end  of  the  glass  is  stopped  with  a  cork  to  be 
removed  when  the  sand  needs  drying  or  its  quantity  corrected. 

The  log  may  be  found  to  be  in  error  after  repeated  use,  and  the  necessary  allowances  should  be  ascertained 
from  direct  measurements. 

7.— THE  GROUND  LOG. 

Art.  20.  An  adaptation  of  the  common  log-line  to  be  used  in  shoal  water  when  the  ship  is  drifting  in  a  tide- 
way or  current,  no  land  being  visible  or  distant  objects  to  fix  the  ship's  position.  It  consists  of  a  lead  made  fast 
to  the  log-line  and  cast  overboard,  the  rate  of  drift  being  marked  as  usual.  The  course  (by  compass)  anil  distance 
are  obtained  at  once. 


*The  Nautical  Mile  as  given  by  Fruf.  J.  E.  Hilganl,  Supt.  V .  S.  Coast  and  Geodetic  Survey. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


8.— MASSEY'S  PATENT  LOG. 

Art.  ^1.  Called  after  the  patentee,  luhvanl  Massey.  An  instrument  for  showing  the  distance  a  ship  actually 
goes  through  the  water.  It  consists  of  a  rotator  or  fly,  F,  and  a  register,  R,  the  whole  being  towed  astern  by  a  line 
varying  from  20  to  50  fathoms  according  to  the  size  of  the  ves- 
sel, an  essential  point  being  to  keep  the  machine  out  of  the  ^  ^- 
eddy  of  the  ship's  wake.  As  it  is  thus  drawn  along  through 
the  water  in  a  horizontal  position,  the  oblique  direction  of 
the  vai)es  causes  the  Hy  to  rotate,  and  this  motion  is  commu- 
nicated by  means  of  the  connecting  cord,  C,  to  the  wheel-work  within  the  register,  and  sets  in  motion  the  indices 
of  the  dials,  i,  2,  3.  The  vanes  of  the  rotator  are  so  adjusted,  by  very  accurate  experimental  trials,  to  the  internal 
machinery  of  the  register  that  when  the  ship  has  towed  the  instrument  through  one  mile  (whether  quickly  or  with 
mere  steerage-way)  the  index  of  the  first  dial  will  have  made  one  complete  revolution,  the  index  of  the  second  will 
have  moved  through  one-tenth,  and  the  index  of  the  third  through  one-hundredth  of  a  revolution,  and  this  is 
repeated  for  every  subsequent  mile.  By  this  means  100  miles  can  be  registered  without  taking  in  the  log.  Every 
time,  however,  the  course  is  changed  the  log  must  be  taken  in,  and  a  fresh  commencement  of  the  register  made. 


9.— THE  LEAD. 

Art.  22.  This  instrument  for  ascertaining  the  depth  of  water  merits  notice  here  as  an  instrument  of  Navi- 
gation, for  by  means  of  its  use  the  Navigator  connects  the  ship's  positions  or  locates  the  vessel  by  comparing  the 
soundings  with  those  indicated  upon  the  chart.  It  becomes  invaluable  when  navigating  upon  certain  coasts  in  thick 
or  foggy  weather,  and  often  when  out  of  sight  of  land. 

Two  leads  are  used  for  soundings,  the  ha)id-kad,  weighing  from  7  to  14  pounds,  with  a  line  marked  to  20 
fathoms,  and  the  deep-sea  lead,  weighing  from  40  to  loo  pounds,  the  line  being  about  100  fathoms  in  length. 

Both  lines  are  marked  as  follows  : 


1 7  fathoms  from  the  lead,  same  as  at  7  fathoms. 

20  fathoms  from  the  lead,  with  2  knots. 

25  fathoms  from  the  lead,  with  i  knot. 

30  fathoms  from  the  lead,  with  3  knots. 

35  fathoms  from  the  lead,  w'lXh  I  knot. 

40  fathoms  from  the  lead,  with  4  knots. 

And  so  on. 


2  fathoms  from  the  lead,  with  2  strips  of  leather. 

3  fathoms  from  the  lead,  with  3  strips  of  leather. 
5  fathoms  from  the  lead,  with  a  white  rag. 
7  fathoms  from  the  lead,  with  a  red  rag. 
io  fathoms  from  the  lead,  with  leather  having  a  hole 

in  it. 

13  fathoms  from  the  lead,  same  as  at  3  fathoms. 

15  fathoms  from  the  lead,  same  as  at  5  fathoms.  | 

The  intermediate  soundings  are  called  "  deeps^\  and  the  only  fractions  of  a  fathom  used  are  a  half  and  a  quarter. 

There  are  also  various  instruments  for  soundings  which  register  the  depth  as  the  lead  descends,  and  the  most 
refined  and  elaborate  machinery  for  ascertaining  the  greatest  depths  of  the  ocean,  a  description  of  which  scarcely 
falls  within  the  province  of  this  work. 

10.— THE  MARINER'S  COMPASS. 

Art.  23.  The  Mariner's  Compass,  being  the  most  important  instrument  of  Navigation,  merits  careful  and 
thorough  study.  By  its  guidance  the  ship,  with  its  valuable  souls  and  property,  may  be  conducted  unerringly  over 
the  vast  sea ;  but  he  who  consults  it  must  have  no  superficial  knowledge,  but  a  thorough  and  complete  research 
into  the  various  causes  for  variation 
from  the  facts  which  the  compass- 
card  would  apparently  indicate,  and  the 
ability  to  apply  the  causes  to  attain  the 
truth. 

Could  the  horizon  be  accurately 
marked  out  as  the  Navigator  sails  over 
the  ocean  with  the  meridian  line  always 
visible,  that  line  to  which  the  course 
is  actually  referred,  then  the  art  of 
Navigation  would  be  simplified. 

In  the  Mariner's  Compass  there 
are  to  be  found  the  marks  and  divis- 
ions which  do  not  appear  upon  the 
horizon,  and  also  a  line  approximating 
more  or  less  closely,  according  to 
locality  and  other  circumstances,  to  be 
hereafter  described,  to  the  direction 
of  the  standard  line  of  reference,  the 
Merididii. 

Art.  24.  The  circular  card  of 
the  Compass  is  divided  at  its  circum- 
ference into  360^,  and  also  into  32 
divisions  of  ii-i'^  each  caWed.  points,  the 
latter  subdivided  into  half-points  and 
quarter-points. 

The  four  principal  points,  called 
the  cardinal  points,  are  named  after 
the  principal  horizon  points.  North, 
South,  East,  and  West.  The  inter- 
mediate points  are  called  by  names 
composed  of  those  according  to  the 
quadrant  within  which  they  fall. 

Fig.  5  will  fully  illustrate  the  sys- 


FlG.  5. 


8 


INSTRUMENTS   EMPLOYED   IN   NAVIGATION. 


tern.  The  four  points  45°  from,  or  midway  between,  the  cardinals  are  named  N.  E.,  S.  E.,  S.  W.,  N.  W. ;  those 
midway  between  the  cardinals  and  these  secondaries,  by  a  composition  of  their  titles,  N.  N.  E.,  E.  N.  E.,  E.  S.  E., 
S.  S.  E.,  S.  S.  W.,  W.  S.  W.,  W.  N.  W.,  N.  N.  W. 

The  points  next  the  cardinals  and  secondaries  take  the  word  by  between  the  name  of  the  adjacent  point  and 
the  next  cardinal.  Thus  the  point  next  E.  of  N.  is  called  N.  by  E.;  the  point  next  E.  of  N.  E.  is  called  N.  E.  by 
E.,  &c. 

The  names  of  the  half-points  and  the  quarter-points  will  be  observed  in  the  following  table,  which  shows  the 
degrees,  minutes,  and  seconds  in  each  quarter-point  of  the  Compass : 


N.  to  E. 


North : 

N.  XE 

N.  Y^Y. 

N.  XE 

N.byE 

N,  by  E.  X  E... 

N.  by  E.  jl  E... 

N.  by  E.  %  E... 
N.  N.  E 

N.  N.  E.  X  E... 

N.  N.  E.  >^E... 

N.  N.  E.  XE-.. 
N.E.  byN 

N.  E.  XN 

N.  E.  >^  N 

N.  E.  X  N 

N.E 

N.  E.  X  E 

N.E.X  E 

N.  E.  X  E 

N.  E.  by  E 

N.  E.  by  E.  XE. 

N.  E.  by  E.  X  E- 

N.  E.  byE.  XE. 
E.  N.  E 

E.N.  E.  X  E  ... 

E.  N.  E.  X  E  ... 

E.  N.  E.  X  E  . . . 
E.byN 

E-XN 

E.XN 

E-XN 

East 


N.  to  W. 


North : 

N.XW 

N.  X  W 

N.  X  W 

N.byW 

N.  by  W.  X  W  . . 

N.  byW.  X  W.. 

N.byW.  X  W.. 
N.  N.W 

xN.  N.W.  X  W.. 

N.  N.W.  X  W.. 

N.N.  W.  X  W.. 
N.  W.  by  N 

N.W.  X  N 

N.W.  X  N 

N.W.  X  N 

N.W 

N.W.  X  W 

N.  W\  X  W 

N.W.  X  W 

N.  W.  by  W 

N.W.byW.X'W. 

N.W.byW.XW. 

N.W.byW.XW. 
W.  N.W 

W.  N.W.  X  W.. 

W.  N.W.  X  W.. 

W.  N.  W.  X  W.. 
W.by  N 

W.  X  N 

W.X  N 

W.  X  N 

West 


S.  to  E. 


South : 

S.  XE. 
S.  X  E, 

S.  X  E  , 


S.  byE 

S.  by  E.  X  E...- 
S.  by  E.  X  E.... 
S.  byE.  34:  E.... 

s.  s.  E : 

S.  S.  E.  X  E  . . . . 

S.  S.  E.  X  E  . . . . 

S.  S.  E.  X  E  . . . . 
S.  E.byS 

S.  E.  X  S 

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E.  S.  E.  XE-... 
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East 


S.  to  W. 


W. 


South : 

s.  X  w. 
s.  X  w . 

S.  by  W 

S.  by  W. 

S.  by  W. 

S.  by  W. 
S.  S.  W 

S.  S.  W. 

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S.  W.  X 

S.  W.  X 

s.  w.  X 

s.  w 

s.w.  X 

s.  w.  X 
s.  w.  X 

S.  W.  by  W  . 
S.  W.  by 
S.  W.  by 
S.  W.  by 

W. S   W .  . . . 

w.  s.  w^ 
w\  s.  w 
w.  s.  w 

W.  by  S  . 
W.  \ 
W 

w.  X  s 

West 


Xw 

X  w 
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xw 
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w 
w 
w 


w.  X  w. 
w.  X  w. 

W.X  w. 


XW.., 
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/4S 

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Pts. 


I 

iX 
IX 

iX 

2 

2X 
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3 


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1% 


2  48  45 

5  37  30 

8  26  15 

II  15    o 

14  3  45 
16  52  30 

19  41  15 
22  30  o 
25  18  45 
28  7  30 
30  56  15 
33  45  o 
36  33  45 
39  22  30 
42  II  15 
45  o  o 

47  48  45 
50  37  30 
53  26  15 
56  15  o 

59  3  45 
61  52  30 

64  41  15 
67  30  o 
70  18  45 
73  7  30 
75  56  15 
78  45  o 
81  33  45 
84  22  30 

87  II  15 
90  o  o 


Art.  25.  The  general  principle  of  the  Compass  is  this :  a  bar  of  magnetized  steel  apart  from  disturbing 
forces,  having  a  free  horizontal  motion  on  a  pivot,  points  in  a  definite  direction,  or  to  that  point  known  as  the 
Magnetic  Pole. 

To  that  direction  all  others  may  be  referred,  and  hence  a  ship  kept  in  any  desired  course. 

Art.  26.  The  needle  carries  with  it  a  card  divided  as  above  described,  ajid  all  enclosed  in  a  brass  bowl  and 
covered  with  glass.  The  bowl  is  hung  within  a  brass  hoop  and  the  hoop  itself  hung  at  points  90°  distant  from  the 
compass-bowl  bearings;  in  other  words  the  compass  is  placed  \\\  g'lDibals  to  allow  the  card  to  retain  a  horizontal 
position  in  spile  of  the  pitching  and  rolling  of  the  ship. 

A  vertical  l)lack  line,  called  the  lubber'' s point, '\v,  marked  on  the  interior  surface  of  the  bowl,  and  the  compass  is 
so  mounted  that  a  line  through  the  pivot  and  lubber's  point  will  be  parallel  to  the  direction  of  the  keel. 

Art.  27.  According  to  the  use  to  which  the  Mariner's  Compass  is  applied  on  board  ship  it  is  called  a 
Binnacle,  or  Steering  Compass,  Standard  Compass,  or  Azimuth  Compass,  with  a  smaller  one  for  use  in  boats. 

Art.  2S.  The  compass  now  adopted  for  general  use  in  the  U.  S.  Navy,  manufactured  by  Mr.  E.  S.  Ritchie, 
of  Boston,  Mass.,  having  reached  the  highest  jioint  of  excellence  will  be  described  here.  Prof  B.  F.  Greene,  Super- 
intendent of  Compasses,  U.  S.  Navy,  says  : 

"The  Navy  Compass  has  the  distinctive  peculiarities  of  a  buoyant  card  in  a  liquid  resisting  medium;  the 
mean  density  of  the  card  being  so  adjusted  to  the  density  of  the  liquid  as  to  oroduce  a  small  (/(^zcv/tcw;-;/ pressure 
upon  the  pivot  in  the  ordinary  forms  of  ship  and  boat  compasses,  or  a  small  ufavard  pressure  in  the  special  form 
of  ^  tell -talc''  or  cabin  compasses.  The  com{)ass-bowl  is  provided  with  a  self-adjusting  expansion  chamber,  by 
means  of  which  the  bowl  is  kept  constantly  full,  without  the  show  of  air  bubbles  on  the  one  hand,  or  the  develop- 
ment of  undue  pressure  on  the  other  from  changes  of  temperature. 

"The  ship-compass  of  general  use  has  a  7:2-inch  skeleton-card,  with  provision  for  one  symmetrical  pair  of 
magnets,  a  division  on  the  outer  ring  to  quarter-points,  and  a  card-circle  adjusted  to  the  ring,  which  is  divided  to 
half-degrees.  The  bowl-circle,  or  outer  edge  of  the  rim  upon  the  bowl  is  made  rigid  and  turned  strictly  to  gauge, 
so  as  to  admit  of  the  interchange  from  one  bowl  to  another  of  every  azimuth-circle  of  its  class.  The  compass  is 
alike  used  in  the  steering-binnacle  or  for  azimuth  purposes." 

Art.  29.  The  standard  for  excellence  for  (Ai' compasses  is  the  British  Admiralty  pattern,  in  which  each  card 
has  two  pairs  of  needles  arranged  symmetrically,  their  extremities  respectively  15'-^  and  45-  from  the  North  and 
South  points  of  the  card.  It  will  readily  be  seen  that  the  advantage  gained  by  using  a  pair,  or  pairs,  of  needles 
rather  than  a  single  needle,  is  in  steadiness  of  the  card. 


INSTRUMENTS   EMPLOYED    IN   NAVIGATION.  9 

Four  small  sliding  weights  of  brass  are  attached  to  the  frame  which  carries  the  needle,  to  be  adjusted  when 
necessary  to  overcome  the  dip  of  the  needle  and  to  preserve  the  card  level  when  at  rest. 

In  additton  to  the  ordinary  division  of  ([uarter-ptjints  the  rim  of  the  card  is  graduated  to  20'.  This  card  is 
enclosed  in  a  copper  bowl,  sufticiently  heavy  to  diminish  vibrations  of  the  card  which  has  its  pivot  suspension  at  the 
intersection  of  the  axes  of  the  gimbals. 

Art.  30.  The  Azimuth  Circle. — To  facilitate  taking  bearings  the  azimuth  circle  is  applied  to  the  compass. 
The  general  principle  of  its  construction  is  this  :  An  accurately  fitting  circle  carrying  with  it  sight-vanes,  mirror, 
prism,  and  verniers  for  reading  graduation  of  circle.  Mr.  Ritchie's  latest  adaptation  consists  of  a  circle  to  be  used 
with  the  Navy  Liquid  Compass,  the  card  of  which  is  graduated  to  half-degrees  with  erect  figures. 

On  the  ring  near  the  observer  is  mounted  a  right-angular  reflecting  eye-prist)2,  opposite  which  is  a  reflecting 
lenticular  prism,  and  on  the  same  support  two  black  glass  mirrors  (to  be  used  according  to  altitude  of  object 
observed),  a  hair  line,  two  shade  glasses,  and  a  concave  lens  for  the  use  of  observers  who  require  spectacles.  On 
the  inner  face  of  the  support  there  is  adjusted  a  small  spirit-level. 

In  use,  the  rays  of  light  from  the  graduated  circle  of  the  card  pass  upward  and  are  reflected  by  the  lenticular 
prism  across  the  bowl  to  the  eye-prism  and  by  it  reflected  to  the  eye  ;  the  rays  from  the  Sun,  or  object  observed, 
pass  either  directly  or  from  the  lower  mirror  across  to  the  eye-prism,  and  are  seen  with  those  from  the  card. 
The  observer  can  at  the  same  time  see  the  bubble  of  the  spirit-level  and  hence  choose  the  time  when  the  compass- 
bowl  is  level  to  note  the  observation. 

There  are  various  other  forms  of  azimuth  circles,  but  the  applications  of  all  are  similar, 

LOCATION   OF  COMPASSES. 

Art.  31.  The  Standard  Compass  should  be  located  on  the  amidship  fore-and-aft  line  of  the  ship,  at  a  neutral 
point,  so  far  as  circumstances  will  permit.  It  should  be  free  from  the  magnetic  influence  of  any  mass  of  iron, 
particularly  any  that  is  vertical,  such  as  davits,  capstan-spindle,  &c.,  and  erected  at  a  proper  height  for  observing 
azimuths  and  bearings  over  the  ship's  rail.  All  courses  and  bearings  are  referred  to  this  compass  and  recorded  in 
the  log-book. 

The  Binnacle  Compasses  used  for  the  steering  of  the  ship  should  be  at  such  height  that  the  helmsman  can  see 
the  card  and  the  lubber's  point  without  stooping,  and  if  two  in  number,  should  be  sufficiently  far  apart  to  prevent 
the  needles  having  mutual  influence  upon  each  other.  If  but  one,  it  should  be  on  the  amidship  line,  or  if  made  to 
traverse,  so  as  to  be  in  front  of  the  helmsman  on  each  tack,  it  should  be  compared  frequently  with  the  Standard, 
and  at  every  change,  because  the  influences  which  cause  deviation  alter  with  each  change  of  position. 

With  any  position  of  the  binnacles  the  compavisons  should  be  frequent  with  the  Standard  by  which  the  course 
is  set,  and  for  the  determination  of  whose  deviation  the  ship  is  swung,  and  repeated  observations  taken. 

THE  COMPASS   ERROR. 

Art.  32.  There  is  probably  no  fact  so  evident  to  the  Seaman  or  Navigator  as  this:  that  the  Compass  docj 
not  on  its  face  tell  the  truths  which  its  readings  would  apparently  indicate.  And,  further,  there  is  no  subject 
which  merits  more  diligent  and  careful  study  than  this  one  of  the  Compass  Error. 

It  is  beyond  the  scope  of  this  work  to  give  more  than  definitions  of  general  principles  and  their  application  to 
Navigation,  but  there  are  many  valuable  guides  to  a  full  and  complete  understanding  of  the  theory  of  magnetism 
as  applied  to  the  Mariner's  Compass;  of  the  methods  of  correcting  and  of  compensating  therefor;  the  rules  foi: 
guidance  from  danger  and  rules  by  which  the  zealous  Navigator  may  afford  additional  subject-matter  for  the 
advancement  of  science,  passing  as  he  does  from  one  magnetic  hemisphere  to  the  other,  approaching  the  magnetic 
pole,  and  often  thrown  into  intimate  contact  with  various  accidental  magnetic  disturbances. 

There  are  three  causes  which  produce  error  in  the  compass  named  Local  Attraction,  Variation,  and 
Deviation. 

Art.  33.  Local  Attraction  is  the  term  applied  to  any  incidental,  extraneous  influences,  such  as  thosv- 
resulting^  from  volcanic  or  other  natural  magnetic  bodies,  or  from  iron  cranes,  pipes,  or  derricks  on  docks,  or  th'c 
vicinity  of  an  iron  ship. 

Art.  34.  Variation. — The  magnetic  pole  is  not  identical  with  the  true  pole  of  the  earth,  and,  since  the 
needle  is  drawn  to  the  magnetic  pole,  the  line  of  its  direction  varies  from  the  direction  of  the  true  meridian;  the 
angle  which  measures  this  difference  of  direction  is  called  the  Valuation  of  the  Compass,  and  is  named  Easterly 
when  the  north  end  of  the  needle  is  drawn  to  the  eastward,  and  Westerly  when  drawn  to  the  westward  of  true  North. 

The  variation  is  different  in  different  places,  and  at  any  fixed  place  it  is  undergoing  a  gradual  periodic  change, 
besides  having  a  small  diurnal  fluctuation.  Charts  are  now  constructed  upon  which  are  drawn  the  lines  of  equal 
variation,  or  isotonic  lines,  to  assist  the  Navigator  in  separating  the  deviation  from  the  variation. 

Art.  35.  The  term  Variation  expresses  the  action  of  the  earth's  magnetic  force  in  a  horizontal  plane,  but 
that  force  has  another  action  upon  a  freely  suspended  needle.  Along  the  line  of  the  magnetic  equator,  which  varies 
but  little  from  the  earth's  true  equator,  the  needle  alone  lies  in  a  horizontal  plane ;  proceeding  northward,  the  north 
pole  of  the  needle  is  drawn  downward  at  an  increasing  angle  called  the  DlP,  or  Inclination,  until  it  reaches  a 
value  of  90-  at  the  magnetic  pole;  but  proceeding  southward,  the  north  end  of  the  needle  inclines  upward;  hence 
the  sUding  weights  on  the  frame  which  carries  the  needles  for  overcoming  this  inclination. 

Joules /or  applying  the  Variation — To  obtain  True  Bearing. 

Art.  36.  When  the  variation  is  easterly,  apply  it  to  the  right  of  the  magnetic  bearing;  if  the  variation  is 
westerly,  apjily  it  to  the  lej't  of  the  magnetic  bearing  to  obtain  the  true  bearing. 

Art.  37.  In  Figs.  6  and  7  NS  represents  the  line  of  the  true  meridian,  N.  and  S.  the  north  and  south  points 
|of  the  horizon.      Let  N'  S'  repre^^ent  the  direction  of  the  compass-needle  as  affected  by  the  earth's  attraction  alone. 

In  Fig.  6  the  north  end  of  the  needle  is  drawn  to  the  eastward  of  the  true  north  jioint  of  the  horizon;  hence 
the  variation  is  easterly.  Iq  Fig.  7  the  north  end  of  the  needle  is  drawn  to  the  westward  of  the  true  north ;  hence 
the  variation  is  westerly. 

Suppose  the  value  of  the  variation  in  each  case  is  equal  to  2  points.  Given  the  magnetic  bearing  of  an  object 
North  ;  find  the  true  bearing. 

By  inspection  of  Fig.  6  it  will  plainly  be  seen  to  be  N.  2  points  E.,  or  N.  N.  E. ;  in  Fig.  7,  N.  2  points  W., 

Hence  the  rule  to  apply  easterly  variation  to  the  right  of  compass  reading  and  westerly  to  the  left. 
This  rule  is  to  be  reversed  when  the  true  bearing  is  given  tq  find  the  magnetic  bearing. 


10 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


In  Figs.  8  and  9,  let  NESW  represent  the  plane  of  the  horizon;  the  inner  circle,  N'E'S'W,  the  compass-card 
as  affected  by  terrestrial  magnetism.  In  Fig.  8  the  magnetic  bearing  of  an  object,  A,  is  given  N.  N.  E.,  variation  2 
points  easterly  to  find  the  true  bearing. 

Applying  the  rule,  the  true  bearing  will  be  found  to  be  N.  E.,  which  will  be  verified  by  an  inspection  of  the 
figure. 

In  Fig.  9,  the  variation  being  2  points  westerly,  the  magnetic  bearing  of  an  object,  A,  is  given  to  be  W.  S.  W.; 
the  true  bearing  will  be  S.  W. 


Fig.  9. 


DEVIATION    OF   THE   COMPASS. 

Art.  38.  The  Deviation  is  tne  error  of  the  compass  caused  by  attraction  of  the  iron  of  the  snip,  and 
depends  upon  the  quantity,  the  kind  of  iron,  and  its  position  with  respect  to  the  needle.  It  is  named  easterly  or 
-ivesterly  according  as  the  north  point  of  the  needle  is  drawn  to  the  eastward  or  westward  of  magnetic  north. 

In  order  to  illustrate  tlie  effect 
of  iron  in  causing  deviation,  let  it  be 
supposed,  as  in  Figs.  10  to  17,  that 
there  is  a  mass  of  iron  abaft  and 
below  the  compasses,  and  its  effect 
in  producing  easterly  or  westerly 
deviation  will  be  observed. 

It  must,  however,  be  understood 
that  this  represents  but  a  particular 
case  ;  for  llie  iron  of  a  ship  may  be, 
and  in  all  iron  ships  is,  difterently 
disposed;  but  this  will  illustrate  the 
example  of  a  wooden  ship,  whose 
compass  is  mounted  but  a  short  dis- 
tance forward  of  iron  work  con- 
nected with  the  steering  apparatus, 
or  in  the  stern. 

In  the  several  figures  the  line 
N'S'  represents  the  line  of  the  mag- 
netic   meridian,    ns    the    compass 
needle,  with  the  mass  of  iron  at  I.     In  Figs.  10  and  14  it  will  be  seen  that  the  action  of  the  iron  is  in  the  direc- 
tion of  the  magnetic  meridian ;  hence  no  deviating  influence  upon  the  needle.     As  the  ship's  head  is  drawn  to 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


11 


the  E.  the  iron  moves  to  the  westward  and  draws  the  north  point  of  the  needle  toward  it,  or  to  the  westward  of 
the  magnetic  North,  reaching  a  maximum  when  the  ship's  head  is  due  East,  diminishing  in  quantity  between  East 
and    South.      As    the    ship's    head 

moves  from  N.  to  W.   the  iron  ap-  jj'  ]V' 

proaclies  I'last  and  deflects  the  North 
end  of  the  needle  to  the  eastward  of 
magnetic  North,  reaching  a  maxi- 
mum as  the  ship's  head  reaches 
West. 

Therefore,  with  the  ship's  head 
to  the  t-iJst'Mini  of  the  magnetic  me- 
ridian, the  deviation  is  -uvsft'rh',  and, 
to  the  wi'shuard,  the  deviation  is 
iijsii-rly. 

In  wooden  ships  the  amount  of 
the  deviation  is  ordinarily  small  and 
constant,  but  when  iron  enters  into 
the  construction  the  problem  be- 
comes a  very  complicated  one,  re- 
quiring deeper  research  into  the 
causes,  the  variety  of  actions,  and 
the  law  of  change  with  change  of 
time,  change  of  magnetic  latitude, 
heeling  of  the  ship,  &c. ;  also,  the 
effect  produced  by  the  direction  of 
the  ship's  head  when  building. 

The  total  force  exerted  upon 
ships'  compasses  is  sometimes  so 
great  that  without  compensation 
they  become  unreliable  and  uncer 
tain.  In  order  to  accomplish  this 
purpose,  the  magnetic  force  must 
be  resolved  into  its  component  parts 
so  that  each  may  be  dealt  with  intel- 
hgently.  A  thorough  study  of  this 
important  subject  may  be  had  by 
reference  to  the  Reprints  of  the  Bu- 
reau of  Navigation,  Navy  Depart- 
ment, of  the  "  Liverpool  Compass 
Committee's  Reports,"  and  the  "  Se- 
ries of  Papers  from  the  Transactions 
of  f^oreign  Societies." 

EFFECT  OF  MAGNETISM  UPON  THE 
COMPASS-NEEDLE  AS  CAUSED  BY 
THE    IRON    IN    A    SHIP. 

Art.  39.  The  iron  used  in 
the  construction  of  a  ship  consists  of 
two  kinds,  soft  and  /lard  iron. 

Art.  40.  Soft  iron  is  that 
which  becomes  instantly  magnetized 
to  its  full  capacity  when  exposed  to 
the  influence  of  any  magnetized 
body,  but  loses  its  magnetism  upon 
the  removal  of  the  magnet.  This  is 
called  magnetism  by  induction. 

Art.  41.  Hard  iron  is  that 
which  does  not  liecome  magnetized 
by    ordinary    induction,    but    when 

magnetized  retains   its   magnetism.  q'  S' 

This  practically  is  not  strictly  true;  -p.-    ^/r  p.^    ,- 

for  as  iron   usually  exists,   it  is  in 

such  an  intermediate  state  that  time  and  a  disturbance  of  its  molecules  by  blows,  hammering,  &c.,  are  required  for 
it  to  receive  or  part  with  magnetism.      Hence  this  magnetism  is  termed  sitb-pcnnanent. 

Art.  42.  Semi-Circular  Deviation. — The  effect  of  hard  iron  on  the  compass  becomes  a  single  force  of 
rwwA/;// amount  acting  in  a  constant  direction,  which  may  be  resolved  into  three  forces  of  constant  amount;  one 
acting /('r<'-(7 ;/</-(?/?,  the  second  acting  athwartship^  and  the  third  acting  vertically. 

The  fore-and-aft  force  will  produce  a  deviation  proportional  to  the  sine  of  the  azimuth  of  the  ship's  head. 

The  athwartship  force  will  produce  a  deviation  proportional  to  the  cosine  of  the  azimuth  of  the  ship's  head. 

The  vertical  force  will  produce  no  deviation  when  the  ship  is  on  an  even  keel. 

The  combined  effect  is  termed  semi-circular  Ativ\2X\on.  The  deviation  illustrated  in  the  Figures  lo  to  17,  Art. 
38,  being  greatest  when  the  ship's  head  is  East  or  West,  and  at  its  minimum  when  the  ship's  head  is  North  or  South. 

The  magnetism  induced  by  the  earth's  vertical  force  in  the  soft  iron  produces  a  semi-circular  deviation,  in 
amount  directly  proportional  to  the  tangent  of  the  dip. 

Art.  43.  QuADRAXTAi,  Deviation. — The  deviation  caused  by  the  magnetism  of  the  soft  iron,  induced  by 
the  horizontal  force  of  the  earth,  is  more  complex.  It  may  be  resolved  into  two  parts ;  one  acting  toward  the 
ship's  head,  equal  to  the  horizontal  force  multiplied  by  the  cosine  of  the  azimuth  of  the  ship's  head ;  the  second  acting 
toward  the  starboard  side,  equal  to  the  horizontal  force  multipHed  by  the  sine  of  the  azimuth  of  the  ship's  head. 


12  INSTRUMENTS   EMPLOYED   IN   NAVIGATION. 

The  combination  of  the  two  parts  gives  a  disturbing  force  acting  fore-and-aft,  varying  partly  as  the  cosine  and 
partly  as  the  sine  of  the  azimuth ;  and  a  similar  force  acting  athwartship. 

That  part  of  the  fore-and-aft  force  proportional  to  the  cosine,  and  that  part  of  the  athwartship  force  propor- 
tional to  the  sine  of  the  azimuth,  produce  no  deviation  when  the  ship's  head  is  either  N.,  E.,  S.,  or  W.  ;  for  it  will 
be  plainly  seen  that  in  either  case  the  force  resulting  will  be  either  zero  or  acting  in  the  direction  of  the  needle. 
Again,  it  will  be  apparent  that  the  deviating  force  will  be  at  its  maximum  when  the  ship's  head  is  either  N.  E., 
S.  E.,  S.  W.,  or  N.  W. 

Hence  the  deviation  caused  by  this  disturbing  force  is  called  the  q  iia  dm  n  fa  I  Ae\ia.t\on,  and  is  nearly  propor- 
tional to  the  sine  of  twice  the  azimuth. 

That  part  of  the  fore-and-aft  force  which  is  proportional  to  the  sine  of  the  azimuth  produces  a  minimum  when 
the  ship's  head  is  N.  or  S.,  and  a  maximum  when  E.  or  W. ;  but  this  is  not,  although  it  would  at  first  appear  so, 
a  Jt-wZ-ivVr/^^r  deviation,  because  the  two  maxima  act  in  the  same  direction;  the  mean  therefore  gives  a  constant 
force  in  one  direction,  but  the  variable  part  is  a  qiiadrantal  force,  the  maxima  produced  when  the  ship's  head  is  on 
the  four  cardinal  points,  proportional  nearly  to  the  cosine  of  twice  the  azimuth. 

That  part  of  the  athwartship  force  proportional  to  the  cosine  of  the  azimuth  causes  a  deviation  precisely  sim- 
ilar to  the  last. 

Art.  41 .    Hence  there  exist — 

1st.  A  qiiadrantal  z.x\A  a  (W7,r/(z«/ deviation  independent  of  latitude,  caused  by  the  transient  magnetism  of  the 
soft  iron  induced  by  the  Earth's  horizontal  force. 

2d.  A  senii-circiilar  A&sx'xixow  proportional  to  the  tangent  of  the  dip,  caused  by  the  transient  magnetism  of  the 
soft  iron  induced  by  the  Earth's  vertical  force. 

3d.  A  semi-circular  deviation  inversely  proportional  to  the  horizontal  force,  caused  by  the  permanent  magnetism 
of  the  hard  iron. 

Art.  45.  Compensation. — The  general  principle  followed  in  practice  for  compensating  compasses  is  as 
follows  : 

1st.  The  quadrantal  deviation  compensated  by  soft-iron  chain  in  boxes,  or  cast-iron  cylinders  with  globular 
ends,  in  the  plane  of  the  compass-card. 

2d.  The  semi-circular  deviation  caused  by  the  induced  magnetism  of  soft  iron  compensated  by  vertical  soft- 
iron  bars. 

3d.  The  semi-circular  deviation  caused  by  the  sub-permanent  magnetism  of  the  hard  iron  compensated  by  a 
system  of  magnets  in  the  deck. 

Art.  46.  Neutral  Points. — The  points  of  no  semi-circular  deviation  are  called  neutral  points,  and  in 
wooden  ships  coincide  nearly  with  the  North  and  South  points;  in  other  words  the  deviation  is  zero  when  the 
ship's  head  is  North  or  South  liy  compass,  and  the  deviation  is  (in  northern  latitudes)  generally  easterly  when  the 
ship's  head  is  east ;  westerly  when  the  ship's  head  is  west. 

But  in  iron  ships  the  neutral  points  are  those  to  which  the  ship's  head  and  stern  were  pointed  while  building; 
the  deviation  being  easterly  lohen  that  part  of  the  ship  is  east  which  was  south  in  building,  ivesterly  when  it  is  west. 
Hence,  if  the  ship  was  built  head  north  the  deviation  will  be  westerly  when  the  ship's  head  is  east,  and  easterly  when 
the  ship's  head  is  west.     This,  it  will  be  seen,  is  the  reverse  of  the  rule  with  wooden  ships  in  northern  latitudes. 

Art.  47.  Heeling  Deviations. — Before  proceeding  to  describe  the  methods  of  ascertaining  the  deviation 
of  the  compass  attention  must  be  directed  to  the  fact  that  deviation  thus  found  is  with  the  ship  upon  an  even  keel 
Although  in  wooden  ships  the  alteration  of  deviation  in  heeling  is  slight,  it  assumes  serious  proportions  in  iron 
built  ships ;  therefore  to  be  considered  when  the  ship  heels  under  sail,  or  is  rolling  heavily.  This  variation  should 
frequently  be  observed  for  given  degrees  of  heel,  bearing  of  ship's  head,  and  the  tack  upon  wliich  the  ship  is  sail- 
ing at  the  time.  The  general  rule  is  that  this  alteration  is  at  its  minimum  when  the  ship's  head  is  East  or  West 
by  compass,  at  i,s  maximum  when  the  ship's  head  is  North  or  South  by  compass ;  and  in  northern  latitudes  the 
north  end  of  the  needle  is  generally  drawn  to  the  weather  side. 

determination  of  the  deviation. 

Art.  48.   The  several  meihods  for  ascertaining  the  deviation  of  the  compass  are — 

1st.   By  the  ])earing  of  a  distant  object  whose  magnetic  bearing  is  known. 

2d.  By  reciprocal  bearings. 

3d.  Swinging  ship  at  sea. 

4th.  Observations  for  azimuths  and  amplitudes. 

The  first  and  second  methods  being  those  resorted  to  with  the  ship  in  port  will  be  considered  here.  An 
explanation  of  the  third  and  fourth  methods  will  follow  under  the  heads  of  Azimuths  and  Amplitudes  in  the 
Astronomical  division  of  the  work. 

Art.  49.  />!'  the  Bearing  of  a  Distant  Object. — The  prime  consideration  in  this  prolilem  is  that  the  ship  should 
in  all  respects  be  ready  for  sea;  stores  and  weights  on  board  and  properly  disposed;  boats  hoisted;  anchors 
weighed  (if  possible)  and  ship  moored  to  a  buoy.  If  a  steamer  with  telescopic  funnels,  the  ship  should  be  swung 
first  for  a  table  of  deviations  with  the  funnels  raised,  then  again  with  the  funnels  lowered.  The  ship  should  be  so 
far  distant  from  wharves,  piers,  derricks,  and  from  other  vessels  that  no  local  attraction  will  be  felt  to  disturb  the 
compass-needle. 

A  well-defined  object  should  be  selected  so  far  distant  that  the  diameter  of  the  space  through  which  the  ship 
is  swung  will  make  no  sensible  difference  in  the  real  bearing  from  a  central  point. 

The  Navy  Department  has  established  compass  stations  for  convenience  and  rapidity,  with  several  points 
whose  magnetic  bearings  are  accurately  determined  and  tabulated ;  but  this  is  not  absolutely  essential  to  the 
solution  of  the  problem,  for  the  bearing  of  an  object  may  be  taken  from  a  chart  of  large  scale;  or  the  Standard 
Compass  may  be  taken  to  some  point  on  shore  from  which  the  ship  anil  the  distant  object  are  in  the  same  line  as 
the  observer.  Then  with  care  taken  that  the  needle  is  not  affected  by  magnetic  influences,  the  magnetic  bearing  is 
at  once  established.  Then  the  ship's  head  is  successively  brought  to  the  various  points  of  the  compass  and  being 
steadied  at  each,  the  bearing  of  the  distant  object  is  taken  by  the  Standard  Compass  and  recorded. 

The  difference  between  the  magnetic  bearing  and  the  bearing  by  compass  will  be  the  deviation  due  to  the  iron  op 
board  ship  for  each  point  of  the  compass  to  which  the  ship's  head  was  directed  at  the  time  of  taking  the  bearing. 

Art.  50.    The  invariable  rule  to  be  remembered  is  that — 

Deviation  is  east  when  the  north  point  of  the  needle  is  drawn  to  the  east  of  magnetic  north,  and  west  whe» 
drawn  to  the  west  of  magnetic  north. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


13 


Or,  the  If  ue  definition  is — 

If  the  correct  magnetic  bearing  be  to  the  right  of  the  compass  l^earing,  the  deviation  is  easterly  ;  if  to  the  left^ 
the  deviation  is  ivcstciiy. 

In  Fig.  i8  the  outer  circle  represents  the  compass-card  affected  by  variation  alone;  hence  the  bearings  by 
it  will  be  magnetic.  The  inner 
circle  represents  the  card  affected 
by  the  magnetic  influence  of  the 
iron  of  the  ship ;  hence  the  dif- 
ference of  the  bearings  by  the 
two  cards  will  be  the  deviation. 
;  In  this  case  the  correct  magnetic 
bearing  of  the  object  A  is  N.  4 
points  E.,  the  compass  bearing 
is  N.  5  points  E. ;  hence  the 
"correct  magnetic  bearing  is  I 
point  to  the  left  of  the  compass 
bearing";  or,  "  the  north  point 
of  the  needle  is  drawn  to  the  west 
of  magnetic  north  "  ;  therefore  the 
deviation  is  -iVcstcrly,  i  point. 

Art.  51.  In  a  tide-way,  or 
where  the  ship  swings  constantly, 
some  well-defined  object  should 
be  selected,  such  as  a  church 
spire,  peak,  isolated  tree,  or 
light-house,  sufficiently  distant 
to  overcome  any  effect  of  paral- 
lax, and  as  the  ship's  head 
reaches  various  points  of  the 
compass  the  bearing  should  be 
recorded. 

The  magnetic  bearing  of  the 
object  should  be  accurately  de- 
termined. Care  must  be  taken 
to  note  the  direction  of  the  ship's 
head  at  each  bearing,  for  without 
it  no  application  of  the  deviation 
could  be  made. 

Art.  52.  The  following 
form  should  be  used  to  tabulate  the  results 

Form  for  registeritig  the  observations  for  determining  tJ^e  effect  of  local  attraction  on  standard  compass. — Real  {or 
correct)  magnetic  bearing  of  steeple  from  ship,  N.  83°  o'  E.,  distant  eight  ?niles. 


Ship's  head  by  Standard 
Compass. 


North 

N.  by  E 

N.  N.  E.... 
N.  E.  by  N  , 
N.  E 

N.  E.  by  E  , 
E.  N.  E  . . . . 
E.  by  N  . . . . 

East 

E.byS  .... 
E.  S.E 


Bearing  of 
steeple  by  Stand- 
ard Compass. 


N.  83  II  E. 

N.  82  7  E. 
N.  81  20  E. 
N.  80  23  E. 
N.  79  23  E. 
N.  78  y:,  E. 
N.  77  38  E. 
N.  77  ID  E. 
N.  77  38  E. 
N.  78  3  E. 
N.  78  26  E. 


Deviation 

of  Standard 

Compass. 


S.  E.  by  E !  N.  79  10  E. 

S.E I  N.  79  51   E. 

S.  E.byS N.  80  30  E. 

S.  S.  E N.  8i   18  E. 

S.  by  E N.  82     9  E. 

South N.  82  52  E. 


o     / 

o  II  W. 

0  53  K. 

1  40  E. 

2  37  E. 

3  37  E. 

4  27  E. 

5  22  E. 
5  50  E. 
5  22  E. 
4  57  E. 
4  34  E- 
3  50  E. 
3  9  E. 
2  30  E. 
I  42  E. 
o  51  E. 
o    8  E. 


£,,.,,      J  ,      r.^     J     J  Bearing  of       '  Deviation 

Ship  s  head  by  Standard    ^teeplebyStand- of  Standard 

Compass.  r_    -'  „ 


ard  Compass. 


S.byW 1     N.83  55  E. 

'^    N.  84  38  E. 


N 
N 
N 


s.  s.  w . 

S.  W.by  S : 

s.  w 

S.  W.  by  W 

W.  S.W 

W.  by  S j 

West !     N.  88  55  E. 

W.  byN \     N.  88  35  E. 


85  24  E. 

86  8  £. 
86  50  E. 

N.  87  39  E. 
N.  88  17  E. 


W.  N.  W  ... 

N.  W.  by  \V 

N.  W 

N.  W.  byN. 

N.N.  W 

N.'y  W.... 
North 


N.  88  8  E. 

N.  87  39  E. 

N.  86  56  E. 

N.  86  9  E. 

N.  85  31  E. 

N.  84  35  E. 

N.  83  II  E. 


Compass. 


o    / 

0  55  W. 

1  38  W. 

2  24  W. 

3  8W. 

3  50  W. 

4  39  W. 

5  17  W. 
5  55  W. 
5  35  W. 
5  8  W. 
4  39  W. 
3  56  W. 
3  9W. 
2  31  W. 

I  35  w. 

o  II  W. 


*  N.  B. — The  nearest  degree  is  quite  sufficient,  in  ordinary  practice. 

f  Art.  53.  By  Reciprocal  Bearings. — When  it  so  happens  that  there  is  no  suitable  object  visible  from  the  ship 
sufficiently  distant,  the  deviations  must  be  determined  by  reciprocal  bearings.  A  careful  observer  should  go  on 
shore  with  a  second  compass,  set  it  up  at  a  point  free  from  magnetic  influences,  and  from  which  a  clear  view  can 
be  had  of  the  j)osition  of  the  Standard  Compass,  immediately  over  which  some  signal  should  be  exhibited.  The 
two  observers  should  ha\e  compared  watches  to  note  the  time  of  taking  each  bearing  as  a  check  against  any  possi- 
ble accidents,  such  as  a  misunderstanding  of  any  signal. 

As  the  ship's  head  is  brought  to  each  point  of  the  Compass  and  there  steadied,  at  a  preconcerted  signal  the 
mutual  bearings  are  taken  simultaneously  and  the  times  noted,  as  well  as  the  direction  of  the  ship's  head. 

Either  before  or  after,  or  still  better,  both  before  and  after  the  observations,  the  Standard  Compass  should  be 
landed  and  compared  with  the  Shore  Compass,  being  careful  to  mount  it  at  such  distance  from  the  other  as  to  free 
them  from  mutual  influence.  The  comparison  is  made  by  taking  the  bearing  of  some  distant  object,  noting  the 
difference,  which  should  be  applied  properly. 


h 


14 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


I 


The  observations  should  be  tabulated  in  a  form  similar  to  the  following : 

To  obtain  the  deviaMon,  or  difference  of  mutual  bearings,  the  bearings  by  the  Shore  Compass  should  be 
reversed;  remembering  if  "  the  correct  magnetic  bearing  is  to  the  right  of  the  Compass  bearing,  the  deviation  is 
easterly;  if  to  the  left,  it  is  westerly." 

Table, 
[The  difference  between  the  Compasses  was  found  to  be  30' ;  to  be  deducted  from  the  bearings  by  the  Shore  Compass.] 


Time. 


h.    m. 
9     10 

14 
17 
21 


Ship's  head  by  the 
Standard  Com- 
pass. 


North. 

N.  by  E. 

N.  N.  E. 

N.  E.  by  N. 


Bearing  f  Shore 
Compass  from 
Standard  Com- 
pass. 


Bearing  of  Standard  Compass    from 
Shore  Compass. 


Observed. 


S.  36  II  W. 
S.  34  7  W. 
S.  32  20  w. 
S.  30  23  w. 


N. 
N. 
N. 
N. 


36  30  E 
35  30  E 
34  30  E 
33  30  E 


Corrected. 


N.  36  o  E. 
N.  35  o  E. 
N.  34  o  E. 
N.  33  o  E. 


Deviation    of   theS 
Standard   Com- 
pass. 


o  II  W. 

0  53  E. 

1  40  E. 

2  37  E. 


And  so  on  for  all  points  of  the  Compass. 

N.  B. — The  nearest  degree  is  usually  sufficient. 

Art.  54.    From  the  above  form  should  be  prepared  a  Deviation  Table  similar  to  the  following: 

Deviatiofk  Table. 


I. — Ship's  head,  or  course  by  the  Standard  Com- 
pass. 


North 

N.  by  E  ... 
N.  N.  E... 
N.  E.  by  N . 

N.  E 

N.  E.  by  E 
E.  N.  E  ... 
E.byN.... 

East 

E.  byS 

E.  S.  E 

S.  E.  by  E  . 

s!  E.  by  S".' 

S.  S.  E 

S.  by  E 

South 

S.  by  W  . . . . 
S.  S.  W  . . . . 
S.  W.  by  S.. 

s.w. ...... 

S.  W.  by  W 

w.  s.  w.... 

W.  by  S  . . . 

West 

W.  by  N..., 
W.  N.  W... 
N.  W.  by  W 

N.W 

N. W.  by  N 
N.  N.  W.... 
N.  byW.... 
North 


2. — Deviation  of 
the  Standard 
Compass. 


o    ' 

O    II 


53 
40 

37 

37 
27 

22 

50 
22 

57 
34 
50 
9 
30 
42 
t;i 
"8 


0  55 

1  3« 

2  24 

3 
3 
4 
5 
5 
5 


50 
39 
17 
55 

_  35 

5/« 

4 

3 

3 

2 

I 

o 


39 

56 

9 

31 

35 
II 


W. 

E. 

E. 

E. 

E. 

E. 

E, 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

E. 

\\\ 

W. 

W. 

w. 
w. 
w. 
w. 
w. 
w. 
w. 
w. 
w. 
w. 
w. 
w. 
w. 


3. — Real  or  correct 
magnetic  course 
steered. 


4. — In  points. 


N.  o 
N.   12 

N.  24 
N.  36 
N.  48 
N.  60 
N.  72 
N.  84 


S. 
S. 


84 
73 


S.  62 

S.  52 

S.  41 

s.  31 

S.  20 

S.  10 

S.  o 

S.  10 

S.  20 

S.  31 

S.  41 

s.  52 

S.  62 

S.  73 

S.  84 

N.  84 

N.  72 

N.  60 

N.  48 

N.  36 

N.  25 

N.  12 

N.  o 


II  W. 
8  E. 

10  E. 
22  E. 

37  E. 
42  E. 
52  E. 
35  E. 

38  E. 
48  E. 
56  E. 
25  E. 

51  E. 
15  E. 
48  E. 

24  E. 
8  W. 

20  W. 

52  W. 

21  W. 
52  w. 

25  w. 
51  w. 
28  w. 

5  W. 
20  W. 
38  W. 
54  W. 
56  W. 
54  W. 

I  W. 
50  w. 

11  w. 


North. 

N.  by  E. 

N.  N.  E.  X  E. 

N.  E.  34:  N. 

N.  E.  14:  E. 

N,  E.  by  E.  %  E. 

E.  by  N.  yi  N. 

E.  XN. 

E.  %^. 

E.  by  S.  %,  S. 

S.  E.  by  E.  %,  E. 

S.  E.  %  E. 

S.  E.  ^  S. 

S.  S.  E.  ^  E. 

S.  by  E.  %  E. 

S.  by  E. 

South. 

S.  by  W.  ; 

S.  by  W.  %  W.        • 

S.  S.  W.  %  W. 

s.  w.  %  s. 
s.  w.  y^  w. 

S.  W.  by  W.  Yi  W. 

W.  by  S.  %,  S. 
W.  X  s. 

W.  y^  N. 
W.  by  N.  ^  N. 
N.  W.  by  W.  >^  W. 
N.  W.  X  W. 
N.  w.  y  N. 
N.  N.  W.  X  W. 
N.  by  W. 
North. 


To  obtain  the  real  or  correct  magnetic  course  of  the  vessel  from  the  course  shown  by  the  Standard  Compass, 
look  in  the  ist  column  of  the  above  table  for  the  apparent  course;  the  2d  column  gives  the  deviation  when  her 
head  is  on  that  point ;   and  in  the  3d  column  (the  deviation  having  been  applied)  is  the  real  magnetic  course. 

To  correct  any  bearings  taken  by  the  Standard  Compass,  the  table  is  to  be  entered  with  the  direction  of  the 
ship's  head  at  the  time,  in  the  Ist  column,  and  corresponding,  in  the  2d  column,  will  be  found  the  amount  of  devi- 
ation to  be  applied. 

To  obtain  tlie  Standard  Compass  course  from  the  correct  magnetic  course,  look  in  the  third  column  for  the 
correct  or  real  magnetic,  and  opposite,  in  the  first  column,  will  be  the  Standard  Compass  course  to  be  steered. 

Art.  55.  Should  there  be  a  theodolite  on  board  ship  it  would  be  a  convenient  and  advisable  plan  to  use  it  in 
lieu  of  the  Shore  Compass.  Then  the  same  Compass  would  be  used  for  taking  both  bearings.  For  instance,  the 
Standard  Compass  would  be  taken  on  shore  and  by  it  bearings  taken  of  some  fixed  point ;  then  the  theodolite 
being  mounted  on  the  same  spot  would  have  its  zero  directed  to  the  fixed  point,  and  the  angle  read  between  it  and 
llie  Standard  Compass  mounted  on  board  ship  at  each  signal  from  the  ship.  Then  by  applying  the  Compass  bear- 
ing first  taken  to  the  theodolite  angles  tlie  deviations  will  be  found. 

Art.  50.  Ilceliiig  Dci'iatioiis. — Opportunities  should  be  availed  of  for  observing  the  deviations  for  various 
degrees  of  heeling,  and  so  tabulated  that  at  a  glance  to  know  what  Compass  course  is  necessary  to  be  set  tt)  make 
good  a  certain  magnetic  course. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


15 


Art.  S"?.  To  Apply  Deviation. — The  deviation  is  applied  in  the  same  manner  as  the  variation,  and  may  be 
combined  with  it  according  to  proper  names  or  signs,  in  reducing  the  Compass  course  to  the  true  course ;  but  not 
in  the  reverse  retluclion,  for  the  deviations  are  determined  for  different  directions  of  the  ship's  head  as  indicated  ly 
L'.'inpiiss.  Hence  the  variation  sliould  first  be  applied  to  the  true  course  to  get  tlie  correct  magneiic  course,  and 
then  llie  deviation  for  that  point  talien  from  the  deviation  table  and  applied  to  the  correct  magnetic  course  to  get 
the  Compass  course.     This  rule  should  be  particularly  observed  when  the  deviations  are  large. 

Al't.  58.  In  order  to  facilitate  the  process  of  reducing  courses  from  iiiaii-iit'tic  to  true  and  the  reverse,  there 
are  several  Graphic  Methods ;  such  as  Napier's  and  Archibald  Smith's.  The  following  Table  and  Diagram  will 
ilkistrate  the  latter : 


Standard  Com 
jKiss  courses. 


Correct  mag- 
netic courses. 


N.  by  W 

North 


16 


INSTKUMENTS   EMPLOYED    IN   NAVIGATION. 


The  outer  graduated  circle  is  intended  to  represent  the  correct  Magnetic  Points  of  the  horizon.  The  innetl 
graduated  circle  is  intended  to  show  Ship's  Head  "  by  Compass,"  and  the  lines  leading  from  it  to  the  outer  circlej 
indicate  the  corresponding  direction  of  Ship's  Head  "  Correct  Magnetic"  for  each  point  of  the  Compass.  j 


Art.  59.  A'^apu'i's  Method  \%  a  combination  of  a  curved  line  and  a  straight  line,  the  deviation  between  which 
shows  at  once  the  amount  of  compass  deviation  for  each  point.  Its  chief  merit  is  that  the  deviation  may  be 
determined  for  a  few  points,  and  a  symmetrical  curve  traced  through  them  will  give  a  graphical  illustration  of  the 
deviation  for  each  point  and  fractional  part  of  a  point  of  the  compass. 

The  diagram  (see  figure)  consists  of  a  vertical  line  of  any  convenient  length  and  divided  into  32  equal  parts 
representing  the  points  of  the  compass  from  N.  at  the  top  downward;  or  it  may  be,  as  in  the  figure,  divided  into 
two  equal  parts,  one  from  N.  to  S.  by  the  way  of  E.,  and  the  other  from  S.  to  N.  by  way  of  W.  The  line  is  also 
divided  into  360°,  and  also  from  o-  at  N.  and  S.  to  90"  at  E.  and  W.,  similarly  to  the  compass-card.  The  vertical 
line  is  intersected  at  each  of  the  32  points  by  two  straight  lines  inclined  to  it  at  an  angle  of  60^  ;  one  dotted  line 
and  one  plain  line.  These  lines  therefore  form  equilateral  triangles  ;  the  scale  on  each  being  the  same,  the  amount 
of  deviation  may  therefore  be  taken  from  the  vertical  scale  of  degrees.  Easterly  deviations  are  laid  down  to  the 
right  hand  and  westerly  deviations  to  the  left.  If  the  deviation  has  been  determined  on  an  exact  point  of  the 
compass,  lay  down  the  deviation  on  the  dottcdYm^  passing  through  that  point;  if  not  on  an  exact  point,  then  lay  it 
down  on  a  line  drawn  parallel  to  the  dotted  line,  the  direction  of  the  ship's  head  being  taken  from  the  vertical  line. 
Mark  the  points  of  deviation  and  draw  through  them  as  nearly  as  possible  a  curve.  Should  the  deviations  be 
determined  on  correct  magnetic  courses,  the  plain  line  is  used  instead  of  the  dotted,  but  this  is  very  rarely  the  case 
in  practice. 

To  find  the  Magnetic  Course  front  the  course  steered. 

On  the  vertical  line  take  the  given  compass  course.  Move  in  a  direction  parallel  to  the  dotted  lines  till  the 
curve  is  reached,  and  then  parallel  to  the  plain  lines  until  the  vertical  line  is  reached  again.  The  point  arrived  at 
on  the  vertical  line  is  the  magnetic  course  required. 

Example.    What  is  the  magnetic  course  corresponding  to  course  by  compass  N.  E.  by  E.  ? 

N.  74O  E. 

To  find  the  Compass  Course,  having  given  a  Magnetic  Course. 
On  the  vertical  line  take  the  given   magnetic  course.     Move  in  a  direction  parallel  to  the  f!ai7i  lines  till  the 


curve  is  reached,  then  back  parallel  to  the  dotted  lines  to  the  vertical  line, 
compass  course  required. 


Ihe  point  there  arrived  at  will  be  the 


i'ltS".    ^-i- 


M2b 

1 

\ 

! 

,    .    '    ^_ 

i 

I 

,      ! 

1 

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, 1 , 

1 

1 

1 

1 

tx — ' 

a 

-^ — 1  -  '  -  1  ■  '  - 

-J \ \ ! \ ■ 

a: 

3025 

SO' 

- 

30 

; 

• 

; 

■ 

- 

29 

- 

?fl 

- 

2?!' 

28 

- 

27' 

- 

2,7 

^ 

28' 

2e 

2a' 

25 

- 

- 

24 

H 

n 

n 

24 

■- 

2;l° 

r; 

f 

G 

23' 

r.5; 

■i\\ 

22° 

F 

f 

F 

■— 

E 

K 

2« 

> 

c 

B 

b 

1 1-,   .°:'^ 

^—^ — J ■ i ^ \ ^ 1 ^ i  •  '   '  •   '  i      •  '  • — !•'•■'   •  i   — ' — ^ ' 1 ii^.^g-...." 

16 


INSTRUMENTS   EMPLOYED    IN   NAVIGATION. 


The  outer  graduated  circle  is  intended  to  represent  the  correct  Magnetic  Points  of  the  horizon.     The  inner] 
graduated  circle  is  intended  to  show  Ship's  Head  "  by  Compass,"  and  the  lines  leading  from  it  to  the  outer  circle 
indicate  the  corresponding  direction  of  Ship's  Head  "Correct  Magnetic"  for  each  point  of  the  Compass. 


\0L^_J^ 


$-§ 


Fig.  19. 

Art.  59.  A^i7/>/c->'s  J\It'f/iod\s  a  combination  of  a  curved  line  and  a  straight  line,  the  deviation  between  which 
shows  at  once  the  amount  of  compass  deviation  for  each  point.  Its  chief  merit  is  that  the  deviation  may  be 
determined  for  a  few  points,  and  a  symmetrical  curve  traced  through  them  will  give  a  graphical  illustration  of  the 
deviation  for  each  point  and  fractional  part  of  a  point  of  the  compass. 

The  diagram  (see  figure)  consists  of  a  vertical  line  of  any  convenient  length  and  divided  into  32  equal  parts 
representing  the  points  of  the  compass  from  N.  at  the  top  downward ;  or  it  may  be,  as  in  the  figure,  divided  into 
two  equal  parts,  one  from  N.  to  S.  by  the  way  of  E.,  and  the  other  from  S.  to  N.  by  way  of  W.  The  line  is  also 
divided  into  360°,  and  also  from  o^  at  N.  and  S.  to  90"^  at  E.  and  W.,  similarly  to  the  compass-card.  The  vertical 
line  is  intersected  at  each  of  the  32  points  by  two  straight  lines  inclined  to  it  at  an  angle  of  60°  ;  one  dotted  line 
and  one  plain  line.  These  lines  therefore  form  equilateral  triangles  ;  the  scale  on  each  being  the  same,  the  amount 
of  deviation  may  therefore  be  taken  from  the  vertical  scale  of  degrees.  Easterly  deviations  are  laid  down  to  the 
right  hand  and  westerly  deviations  to  the  left.  If  the  deviation  has  been  determined  on  an  exact  point  of  the 
compass,  lay  down  the  deviation  on  the  dotted  line  passing  through  that  point;  if  not  on  an  exact  point,  then  lay  it 
down  on  a  line  drawn  parallel  to  the  dotted  line,  the  direction  of  the  ship's  head  being  taken  from  the  vertical  line. 
Mark  the  points  of  deviation  and  draw  through  them  as  nearly  as  possible  a  curve.  Should  the  deviations  be 
determined  on  correct  magnetic  courses,  the  plain  line  is  used  instead  of  the  dotted,  but  this  is  very  rarely  tlie  case 
in  practice. 

To  find  the  Magnetic  Course  from  the  course  steered. 

On  the  vertical  line  take  the  given  compass  course.  Move  in  a  direction  parallel  to  the  dotted  lines  till  the 
curve  is  reached,  and  then  parallel  to  the  plain  lines  until  the  vertical  line  is  reached  again.  The  point  arrived  at 
on  the  vertical  line  is  the  magnetic  course  required. 

Example.    What  is  the  magnetic  course  corresponding  to  course  by  compass  N.  E.  by  E.  ? 

N.  74°  E. 

To  find  the  Compass  Course,  having  given  a  Magnetic  Course. 

On  the  vertical  line  take  the  given  magnetic  course.  Move  in  a  direction  parallel  to  the  plain  lines  till  the 
curve  is  reached,  then  back  parallel  to  the  dotted  lines  to  the  vertical  line.  The  point  there  arrived  at  will  be  the 
compass  course  required, 


CURVE  OF  DEVIATIONS  CONSTRUCTED  UPON  THl 


DEVIATION    WEST, 


Fkom  o°  North  to  i8o°  South. 

deviation  ea< 
NORTH. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


17 


ExAMri.K.    What  is  the  compass  course  corresponding  to  a  magnetic  course  S.  71°  W.  ? 

West. 

By  comparing  the  (hagram  with  the  deviation  table  in  Art.  58  its  construction  will  be  readily  seen. 

CORRECTING   COURSES. 

Art>  CO.  In  Fig.  20,  NCS  represents  the  meridian ;  N.  and  S.  the  North  and  South  points  of  the  liorizon; 
(.'V  the  direction  of  the  magnetic  meridian,  or  the  direction  of  the  compass  needle  affected  liy  terrestrial  magnetism 
alone  ;  CD  the  direction  of  the  needle  under  the  influence  of  the  iron  in  its  vicinity;  then  the  angle  NCV  is  the  vari- 
ation, east  in  this  case;  the  angle  VCD  is  the  deviation  west. 

If  a  ship  is  sailing  on  the  rhumb  CT,  her  true  course 
i>  NCT ;  her  compass  course  is  DCT;  hence,  it  will  be 
sfcn  that  the  true  course  and  the  compass  course  can  be 
derived  from  each  other  by  proper  application  of  the  varia- 
tion and  deviation. 

In  reducing  compass  course,  DCT,  to  the  true  course, 
NCT,  the  algebraic  sum  of  the  two  corrections  may  be  ap- 
plied at  once.  But  to  find  the  compass  course,  DCT,  from 
the  true  course,  NCT,  the  two  corrections  must  be  sepa- 
rately applied,  since  tables  of  deviations  are  made  for  dif- 
ferent directions  of  the  ship's  head,  as  indicated  by  com- 
pass; hence,  the  true  course  must  first  be  corrected  for 
variation  to  get  VCT,  the  compass  course  nearly,  and  then 
take  from  the  table  the  proper  deviation  for  that  direction 
of  the  ship's  head.* 

One  more  correction  must  be  considered  in  finding  Ihe 
course  nunic good  \\\\&xi  the  ship  is  under  sail,  and  not  running 
before  the  wind.  A  ship  sailing^  on  the  rhumb  CT,  under 
the  influence  of  the  wind  indicated  by'  the  arrow,  is  de- 
flected from  the  course  steered  at  a  certain  angle  TCCr,  the 
value  of  which  depends  upon  various  circumstances  ;  there- 
fore, the  angle  TCvi  must  be  determined  and  applied  to  the 
right  or  left  of  the  indicated  compass  course,  according  as 
the  ship  is  on  the  port  or  starboard  tack,  to  obiain  NCG, 
the  true  course  made  good. 

In  fact  it  may  occur  that  in  the  case  of  a  screw  steamer 
under  sail  there  are  seven  distinct  causes  to  produce  the 
course  made  good,  all  of  which  must  be  considered  under 
certain  circumstances.     These  are — 

I.   Set  of  Tide,  or  Current. 


Variation  of  the  Compass. 
Deviation  of  the  Compass. 
Heeling  Deviation. 


2.  Set  of  Screw. 

■3.  Leeway. 

4.  Good  or  Bad  Steerage. 

Examples.   Let  it  be  required  to  correct  for  deviation  the  following  courses  steered,  using  the  Table  of  Devi- 
ations of  Art.  58 : 

(I)     Course,  N.  E.  by  E.  (2)  S.  W.  (3)  W. 


Deviation, 


N.  56^  15'  E. 
17    45   E. 


Deviation, 


Magnetic  course.  N.  74      o  E. 
(4)     Course,  S.  by  W.  \  W. 


(5) 


Deviation, 


S.  16C  52-L'  W. 

I    15    w. 


Deviation, 


s. 

45" 
9 

W. 
W. 

s. 

S.  E 

36    W. 
•  IE. 

s.  50^ 
13 

37V  E. 
15     E. 

(6) 


Deviation, 

S.  90°  W. 
19    W. 

S.  71    W. 

) 

N.  iW. 

N. 
Deviation, 

50  37-V  W. 
5    15     W. 

S.  15    37i  W, 


S.  37    2.z\  E. 

E.XAMI'LE.  Given  Compass  course  E.  N.  E.  and  variation  12"^  E.,  to  find  the  true  course 

Course,  E.  N.  E.  =  N.  67°  30'  E. 
Deviation,  19    30  E.  ?  o  30' £. 

Variation,  12      O   L.  ^       -^      -^ 


N.  ID    52^  W, 


Course, 


N.  99      o  E.  or  S.  81°  E. 


Example.  Given  compass  course  N.  by  E.  and  the  variation  12-  W.,  to  find  the  true  course: 

Course,  N.  11-  15'  E. 

Deviation,  3    45   E.  ?       j.^ 

o  W. 


Variation, 
True  course. 


12 


:8C    15'    W. 


N. 


o  ]-:. 


Example.  Given  Compass  course  S.  W.  by  W.  and  the  variation  20°  E.,  to  find  the  L-ue  courses 

Course,  S.  56°  15'  W. 

Deviation,  il    45   W.  ^_go  jc'  £. 


Variation, 
True  course, 


20 


+5  W.  ?      , 
o  E.    \~' 


S.  64    30  W. 


2   B 


*  Only  true  when  the  deviations  arc  small.    See  next  page. 


18 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


In  the  above  examples  it  will  be  readily  seen  that  the  variation  and  deviation  may  be  coml)ined,  but  the  fol 
lowing  examples  to  find  the  Compass  courses  will  show,  not  only  that  these  quantities  must  be  separately  applied, 
but  also  that  when  the  deviations  are  large  this  will  give  only  an  approximation  to  the  Compass  course ;  then  ihe 
corresponding  deviation  must  be  applied  to  the  correct  magnetic  course,  which  will  give  a  second  approximation. 
The  proper  deviation  to  apply  to  the  correct  magnetic  course  will  fall  between  the  deviations  corresponding  to  these 
two  approximations. 

Example.  Suppose  a  true  N.  N.  E.  course  is  required  where  the  variation  is  2  points  W. 


True  course, 
Variation, 


N.  22|o  E_ 

22i     W. 


Correct  magnetic  course,     N.  45      E 
Deviation,  16      E 

Compass  course, 


N.  29      E.     1st  App. 


Correct  magnetic  course,     N.  45      E. 
Deviation,  11      E. 


Compass  course. 


N.  34      E.     2d  App, 


Correct  magnetic  course,     N.  45       E. 
Deviation,  12      E. 


Compass  course. 


N.  33      E. 


Compass  course. 
Deviation, 

N. 

290  E. 
II    E. 

Correct  magnetic  course, 

N. 

40    E. 

Variation, 

22i  W. 

True  course. 

N. 

17^  E. 

Compass  course. 
Deviation, 

N. 

34    E. 

I2iE. 

Correct  magnetic  course, 

N. 

46!  E. 

Compass  course, 
Deviation, 

N. 

33  E. 
12    E. 

Correct  magnetic  course, 


N.  45    E. 


Example.  Suppose  a  true  W.  by  N.  course  is  required  when  the  variation  is  2  points  W. 


True  course. 
Variation, 


N,  78fo  W. 

22i     W. 


Correct  magnetic  course,     N,  56^    W. 
Deviation,  22^    W. 

Compass  course. 


N.  34      W.     1st  Ajip. 


Correct  magnetic  ccjurse,     N.  56^    W. 
Deviation,  16^    W. 


Compass  course, 


N.  39f    W.     2d  App. 


Correct  magnetic  course,     N.  56^    W. 
Deviation,  18      W. 


Compass  course, 


N.  38^    W. 


Compass  course 
Deviation, 


N.  34°    W. 
i6i    W. 


Correct  magnetic  course, 

N 

5"^ 

W. 

Variation, 

22  0 

W. 

True  course. 

N 

73 

w. 

Compass  course. 
Deviation, 

course. 

N. 

N. 

39.1 

w. 
w. 

Correct  magnetic 

5«i 

w. 

Corapass  course. 
Deviation, 

N. 

38i 
18 

w. 

Correct  magnetic  course,        N.  56^    W. 


11.— THE  CHART.  ^ 

Art.  61.  A  Chart  is  a  representation  ujv'/n  jiaper  of  any  portion  of  the  earth's  surface  for  the  service  of 
the  Navigator  ;  or,  in  other  words,  it  is  the  llydrographer's  Map.  According  to  the  extent  of  surface  to  be  rep- 
resented or  the  manner  used,  dei)ends  the  style  of  cliart. 

Raper  says :  "  As  the  surface  of  the  globe  is  round,  while  that  of  the  paper  is  flat,  every  chart  exhibiting  any 
extent  of  surface  is  necessarily  an  artificial  construction,  or,  as  it  is  called,  projection  of  the  real  state  of  things." 

When  the  extent  was  limited,  such  as  plans  of  harbors,  islands,  small  sections  of  the  coast,  &c.,  the  chart 
was  formerly  constructed  on  Plane  Projection,  but  now  on  the  Polyconic  Projection.  For  the  general 
purposes  of  Navigation  the  Mercator's  Projection  is  adopted,  for  on  this  alone  is  the  ship's  track  represented 
as  a  straight  line  when  steering  the  same  course.  For  the  purpose  of  representing  areas  of  large  or  small  extent 
along  the  coast  line  the  Polyconic  projection  is  used,  in  which  each  parallel  of  latitude  is  supposed  to  be  developed 
upon  its  own  cone,  the  vertex  of  which  is  on  the  axis  at  its  intersection  with  the  tangent  to  the  meridian  at  the 
parallel.     Each  sheet  is  an  independent  one,  and  adjoining  ones  are  connected  by  the  triangulation  points. 

For  the  convenience  of  representing  the  track  to  be  followed  in  Great  Circle  Sailing  as  a  straight  line,  sjiecial 
charts  are  constructed  on  the  Central,  or  Gnomonic  Projection.  Upon  this  projection  all  great  circles  are 
represented  as  straight  lines,  thereby  answering  the  same  purpose  for  Great  Circle  Sailing  that  Mercator's  Chart 
does  for  Rhumb  Sailing. 

There  are  many  other  systems  of  projection  but  these  are  all  that  are  required  by  the  Navigator  for  purposes 
of  Navigating  and  Marine  Surveying. 

To  construct  a  Chart  on  Plane  Projection* 

Art.  62.    Divide  the  limits  East  and  West  by  the  number  of  miles  of  longitude  required  to  be  embraced 
Take  out  the  Meridional  Parts,  Table  3,  for  any  number  of  miles  of  latitude  between  the  extremes  of  llie  she?" 
.lay  100  miles. 

*  Mayne's  Nautical  Surveying. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


19 


M 


M 


Fig.  21. 


Then,  as  lOO  miles  :  number  of  inches  measured  by  the  paper  =  the  meridional  parts  for  loo  miles  :  the 
number  of  inches  for  100  miles  of  latitude.  u     r-u     ►  i  i     f„  i 

If  the  latitude  and  longitude  of  any  two  places  at  some  distance  apart  are  known,  the  Chart  can  Ijc  graduated 
thus  •  Find  a  course  and  distance  between  the  two  places,  working  to  hundredths.  Take  out  the  meridional  parts 
of  sVio,  or  20  miles  between  the  latitudes  of  the  given  places.  Take  from  the  Chart  the  number  of  inches  between 
the  two  places. 

Then,  for  Laiitiidc  Scale :  •^        .y.  -u        i 

As  the  distance  in  miles  :  the  number  of  inches  between  the  two  pFaces  =  5,  10,  or  20  miles  :  the  number  oi 

inches  in  5,  10,  or  20  miles  of  latitude. 

For  Lou n tilde  Scale:  ,       j.,v.  r 

As  the  number  of  miles  of  longitude  (found  by  taking  the  difference  ot 

the  meridional  parts  of  5,  10,  or  20  miles)  :  number  of  inches  in  5,  10,  or  20 

miles  of  latitude  =  5,  10,  or  20  miles  of  longitude  :  number  of  inches  in  5, 

10,  or  20  miles  of  longitude. 

Lay  off  die  true  North  from  l)oth  places  with  compasses,  and  measure  otl 
the  miles  of  latitude  and  longitude,  having  first  taken  care  that  the  two  places 
arc  in  their  proper  positions.  .      ,        ,         ,  1 

These  charts  arc  now  rarely  used.  In  high  latitudes  they  show  truly 
no  directions  but  North  and  South,  East  and  West,  and  no  distances  but 
those  on  a  meridian.  Hence,  the  figure  of  every  portion  of  surface,  however 
small,  is  distorted.  •      •        1     .. 

Art.  63.  Mercator's  /r^y'trZ/Vw.— This  is  not  strictly  a  projection,  but 
may  be  said  to  result  from  the  development  upon  a  plane  of  a  circumscribing 
cylinder  tangent  to  the  earth  along  the  equator;  the  various  points  of  the 
earth's  surface  having  been  projected  upon  the  cylinder  m  such  manner  as 
to  satisfy  the  following  condidon :  That  the  Rhumb,  or  ship's  track  on  the 
surface  of  the  sea  under  a  constant  bearing,  shall  appear  on  the  develop- 
ment as  a  right  line,  preserving  the  same  angle  of  bearing  with  respect  to 

the  meridians  it  intersects  as  that  of  the  ship's  track.  ,    .         ,        .  ,  r        •   ,  ,        .•„,    „<■  u,^ 

In  order  to  realize  the  foregoing  condition,   the  equator,  being  the  circumference  of  a  right  section  of  the 
cylinder,  will  appear  as  a  straight  line  on  the  development,  while  different  right-hned  elements  of  the  cylinder 
cm-responding  to  the  meridians,  will  appear  as  a  system  of  equidistant  straight  lines,  parallel  to  each  other  and 
perpendicula?to  the  development  of  the  equator,  maintaining  the  same  distances  apart  and  same  relative  positions 
on  that  equator  as  the  primitive  meridians  have  on   the 
terrestrial  spheroid.     Moreover,  the  series  of  parallels 
of  latitude  will  also  appear  as  a  system  of  right  lines 
parallel  to  each  other  and  to  the  equator,  and  will  so 
intersect  the  meridians  as  to  form  a  system  of  rectangles, 
u>Iiose  successive  widths  must  be  variable,  increasing  from 
the  equator  toward  the  poles  in  such  manner  that  the 
required  equality  of  angles  shall  be  maintained,  for  cor- 
responding elements  of  the  ship's  track,  on  the  spheroid 
and  on  the  chart  representation. 

Fig.  21  will  illustrate  this.  Let  pp',  pip'i,  p-2P  2, 
pap's,  &c.,  be  arcs  of  equidistant  parallels  of  latitude  inter- 
cepted between  the  two  meridians  PM,  PM',  and  there 
fore  decreasing  in  length  as  they  recede  from  the  equator  ; 
the  figures  pp'p'ipi,  pip'ip'^Pi,  P:p'-2p':!P3,  &c.,  are  sup- 
posed to  be  indefinitely  small  on  the  projection ;  the  cor- 
responding arcs  of  the  par-allels/Zj/j/i./j/'-i,/:?/:!,  &c., 
are  all  equal  to  MAP,  and  therefore  have  been  unduly 
lengthened,  and  more  and  more  so  as  they  recede  from 
the  equator  ;  hence  the  increments  of  the  meridian  (/.  e., 
the  small  portions  successively  added  to  the  length  under 
consideration),  which  are  equal  on  the  globe  (ppi,  pipa, 
p.p;3,  P3P4,  &c'.),  must  be  magnified  in  the  projection  (//i, 
/i/',  /^/s.  /sA'  "^c.),  and  more  and  more  so  as  they 
recede  from  the  equator.  If  they  are  made  to  lengthen 
in  the  same  proportion  as  the  arcs  of  the  parallels  of  lati- 
tude (pip'i,  p,p'.2,  psp's,  &c.)  were  lengthened  in  the  pro- 
jection (/i/i,  p-ip'i,  p3p'^,  &c.),  then  the  small  areas  of 
the  projection  pp'p'ipi,  pip'ip'ip-2,  pip'i  p'ip?,,  &c.,  w-ill 
be  depicted  similar  to  the  corresponding  areas  of  the 
sphere  pp'p'iPu  pip'ip'iP-2,  P2P'jP'3P3,  &c.,  and  the  rep- 
resentation is  a  Alercator's  projection.* 

Art.  64.    A  second  system  may  well  be  inserted 
here  as  a  more  simple  and  graphic  representation  of  Mer- 

catoi^s^projec^on^  is  the  centre  of  the  globe;  PjPo,  two  points  near  one  another  on  the  same  meridian 
a  lin°  touching  the  meridian  at  the  equator, 
the  i  ncrement  of  latitude  of  P2,  be  dl. 
It  is  evident  that — 


Fig.  22. 
Hence,  PiCA  is  the  latitude  Pi,  which  represent  by  /,  and  let  F1CF2, 


Similarly- 


QiA  =  CA  tan  PjCA  =  CA  tan  / 
Q.2A  =  CA  tan  {I  +  dl) 


*  Reed's  Naval  Science. 


20 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


Hence,  Q2Q1,  i-  e.,  the  projection  of  the  arc  P1P2  on  the  circumscribing  cylinder 

=  CA  (tan  (/  +  dl)  —  tan  /) 


tan  /  +  tan  dl 
tan  /  tan  dl 


tan  /) 


sec^  /  tan  dl 


—  tan  /  tan 


\i) 


Now,  if  (//be  taken  sufficiently  small,  tan  /  tan  dl  may  be  neglected  in  comparison  with  unity,  and  for  tan  a 
may  be  written  (//. 

Hence,  Q2Q1  ^  CA  sec-,  l.dl  ^  P1P2  sec-/,  but  in  Mercator's  ])rojection  the  corresponding  projection  is  P1P5 
sec  /. 

Hence,  Q:Qi  is  greater  than  the  arc  of  Mercator's  projection  in  the  ratio  of  sec /to  I,  and  as  /increases  this 
ratio  increases,  until  toward  the  poles  it  is  indefinitely  great. 

Now,  from  P^  let  fall  the  perpendicular  P.^M  on  the  line  CA,  cutting  CQi,  in  Sj. 

Then,  by  similar  triangles — 

P2SJ  :  Q2Q1  =  CS, :  CQi 


P2S, 


Q2Q, 


CM 
CA 


Q2Q1  cos  / 


Then- 


Q2Q,  =  P.P.,  sec-/ 
P2S,  =  PiPasec/ 

or,  P2S1  represents  the  arc  of  Mercator's  projection  corresponding  to  the  arc  of  !he  meridian  PnPi. 

This  construction  may  be  stated  in  words  as  follows  : 

To  represent  the  proper  length  of  an  arc  of  a  meridian  on  Mercator's  projection,  draw  a  tangent  to  the  merid- 
ian  at  the  equator ;  draw  two  radii  through  the  extremities  of  the  arc  (supposed  very  small),  and  from  the  higher 
of  the  two  extrernities  draw  a  line  parallel  to  the  tangent  already  drawn.  The  length  of  the  line  intercepted  between 
the  upper  extremity  of  the  arc  and  the  radius  drawn  to  the  lower  extremity,  is  the  corresponding  distance  betweer 
these  points  on  Mercator's  projection. 

Art.  65.   The  following  construction  shows  how  the  chart  itself  may  be  drawn : 

In  Fig.  23  let  the  arc  of  the  me- 
ridian be  divided  into  a  sufficient 
number  of  equal  small  portions,  A  Pi, 
P1P2,  PsPn,  P3P^,  &c.  Draw  the  cor- 
responding radii  and  the  ]5erpendicu- 
lars  Pi  Ml,  P2M2,  PjM:,  on  CA,  and 
let  MiPi  be  prolonged  indefinitely; 
then  PiM,,  P.Si,  P;,S2  are  the  dis- 
tances on  Mercator's  projection  cor- 
responding to  the  arcs  AP|,  PiP.,, 
P2P3. 

Let  CA  be  produced  as  the  base 
of  the  projection,  and  let  equal  dis- 
tances N1N2,  N-:N:j,  N:jN4,  &c.,  be 
taken  on  this  line  to  represent  equal 
arcs,  say  of  i'-  of  longitude. 

Draw  PiP,'Pi"P,"'Pi""  pamllel 
to  CA  ;  then  tliis  line  is  the  parallel 
of  latitude  of  the  point  Pi. 

Draw  PjR.;  parallel  to  CP„ 
meeting  MiPi  produced  in  R.,;  draw 
RiPiTi"!'./"  parallel  to  CA ;  this 
represents  the  parallel  of  the  point  P.,. 

Join  Sd<2.  Draw  P3R:,  parallel 
to  S2R2»  meeting  Ml  Pi  produced  in 
R3,  and  draw  Ral'sTs'T::'",  &c., 
parallel  to  CA;  then  this  is  the  paral- 
lel of  P3 ;  and  so,  by  a  similar  con- 
struction for  any  number  of  points. 

Art.  66.  Meridional  Parts. — At  the  equator  a  degree  of  longitude  is  equal  to  a  degree  of  latitude,  but 
approaching  the  poles,  while  (supposing  the  earth  to  be  a  perfect  sphere)  the  degrees  of  latitude  remain  the  same, 
the  degrees  of  longitude  become  less  and  less. 

In  Mercator's  projection  the  degrees  of  longitude  are  made  everywhere  of  the  same  length,  and,  therefore,  to 
preserve  the  proportion  that  exists  at  different  parts  of  the  earth's  surface  between  the  degrees  of  latitude  and 
longitude,  the  former  must  be  increased  from  their  natural  lengths  more  and  more  as  we  recede  froni  the  equator. 
The  lengths  of  small  portions  of  the  meridian  thus  increased,  expressed  in  minutes  of  the  equator,  are  called 
Meridional  /'ur/s,  and  the  meridional  parts  for  any  latitude  is  the  line,  expressed  in  minutes  of  the  equator,  into 
which  the  latitude  is  thus  cxj^anded.  The  meridional  parts  computed  for  every  minute  of  latitude  from  o-  to  90° 
form  the  I'a/di-  of  Mrridioiial  I'liris,  which  is  chiefly  used  for  finding  the  meridional  difference  of  latitude,  in  solving 
problems  in  Mercator's  Sailing,  and  for  constructing  charts  on  the  Mercator  projection. 

Art.  6Y.  Meiralor''s  CItart. — The  feature  which  makes  this,  the  A'avii:;ator''s  Cliart,  chiefly  valuable  is,  that 
on  it  the  track  of  a  ship  always  steering  the  same  course  appears  as  a  straight  line.  It  represents  with  perfect 
accuracy  the  relative  positions  of  places,  but  not  their  relative  distances. 


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20 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


Hence,  QjQi,  /.  e.,  the  projection  of  the  arc  P1P2  on  the  circumscribing  cyhnder 

=  CA  (tan  (/  +  dl)  —  tan  /) 

,_, .    /  tan  I  -\-  tan  dl         ,        ,, 

=  CA  I .    '  ,^ -T,  —  Ian  /) 

\  I  —  tan  /  tan  dl 


/     sec-  /  tan  dl 
^  CA  \-~ 


tan  /  tan 


(//) 


ill  ct)niparison  with   unity,  and  for  tan  a 
j,  projection  is  PiPj 


Now,  if  (?'/l)e  taken  sufficiently  small,  tan  /  tan  dl  may  be  neglected 
may  be  written  dl. 

Hence,  Q^Qi  =  CA  sec^.  l.dl  ^^  P1P2  sec'-/,  but  in  Mercator's  projection  the  correspondin 
sec  /. 

Hence,  QjQi  is  greater  than  the  arc  of  Mercator's  projection  in  the  ratio  of  sec /to  I,  and  as  /increases  this 
ratio  increases,  until  toward  the  poles  it  is  indefinitely  great. 

Now,  from  Po  let  fall  the  perpendicular  P^M  on  the  line  CA,  cutting  CQi,  in  Si. 

Then,  by  similar  triangles — 

P2S,  :  Q.2Q1  =  CSi :  CQ> 


PaS,  =  QoQ, 


CSi 


CQ, 


Q2Q, 


CM 


CM 
CA 

cos  / 


Then — 


q,q^  =  p.p.,  sec-/ 
P2S,  =  Pi  P.,  sec/ 

or,  P2S1  represents  the  arc  of  Mercator's  projection  corresponding  to  the  arc  of  Oie  meridian  PoPi. 

This  construction  may  be  stated  in  words  as  follows  : 

To  represent  the  proper  length  of  an  arc  of  a  meridian  on  Mercator's  projection,  draw  a  tangent  to  the  merid 
ian  at  the  equator ;  draw  two  radii  through  the  extremities  of  the  arc  (supposed  very  small),  and  from  the  highei 
of  the  two  extremities  draw  a  line  parallel  to  the  tangent  already  drawn.  The  length  of  the  line  intercepted  betweer 
the  upper  extremity  of  the  arc  and  the  radius  drawn  to  the  lower  extremity,  is  the  corresponding  distance  between 
these  points  on  Mercator's  projection. 

Art.  65.    The  following  construction  shows  how  the  chart  itself  may  be  drawn  :  M 

In  Fig.  23  let  the  arc  of  the  me-  f 

ridian  be  divided  into  a  sufficient 
number  of  equal  small  portions,  A  Pi, 
P1P2,  P.P.-i,  PsPj,  &c.  Draw  the  cor- 
responding radii  and  the  perpendicu- 
lars Pi  Ml,  P.2M2,  PsMri  on  CA,  and 
let  MiPi  be  prolonged  indefinitely; 
then  PiMi,  P.Si,  P:iS2  are  the  dis- 
tances on  Mercator's  projection  cor- 
responding to  the   arcs  AP|,   PiP., 

P2P3. 

Let  CA  be  produced  as  the  base 
of  the  projection,  and  let  equal  dis- 
tances NiNo,  N.2N3,  N:5N4,  &c.,  be 
taken  on  this  line  to  represent  equal 
arcs,  say  of  i'^  of  longitude. 

DrawPiPi'P,"P,"'Pi""pamllel 
to  CA  ;  then  this  line  is  the  parallel 
of  latitude  of  the  point  Pi. 

Draw  P2R.2  parallel  to  CP„ 
meeting  MiPi  produced  in  Ro;  draw 
R.,Po'P2"P2"'  parallel  to  CA ;  this 
represents  the  parallel  of  the  point  P^. 

Join  S.R,,.  Draw  P3R:!  parallel 
to  S2R2,  meeting  M|Pi  produced  in 
R„  and  draw  R:iP.,'P:/'Pi"',  &c., 
parallel  to  CA ;  then  this  is  the  paral- 
lel of  P3 ;  and  so,  by  a  similar  con- 
struction for  any  number  of  points. 

Art.  66.  Meridional  Parts. — At  the  equator  a  degree  of  longitude  is  equal  to  a  degree  of  latitude,  but 
approaching  the  poles,  while  (supposing  the  earth  to  be  a  perfect  sphere)  the  degrees  of  latitude  remain  the  same, 
the  degrees  of  longitude  become  less  and  less. 

In  Mercator's  projection  the  degrees  of  longitude  are  made  everywhere  of  the  same  length,  and,  therefore,  to 
preserve  the  proportion  that  exists  at  different  parts  of  the  earth's  surface  between  the  degrees  of  latitude  and 
longitude,  the  former  must  be  increased  from  their  natural  lengths  more  and  more  as  we  recede  from  the  equator. 
The  lengths  of  small  portions  of  the  meridian  thus  increased,  expressed  in  minutes  of  the  equator,  are  called 
Meridional  Parts,  and  the  meridional  parts  for  any  latitude  is  the  line,  expressed  in  minutes  of  the  equator,  into 
which  the  latitude  is  thus  e.vjDanded.  The  meridional  parts  computed  for  every  minute  of  latitude  from  o-  to  90° 
form  the  Ta/de  of  Meridional  Paiis,  which  is  chiefly  used  for  finding  the  meridional  difference  of  latitude,  in  solving 
problems  in  Mercator's  Sailing,  and  for  constructing  charts  on  the  Mercator  projection. 

Art.  67.  .Mc'rea/or\\-  Chart. — The  feature  which  makes  this,  the  A'aTit^a tor's  Chart,  chiefly  valuable  is,  that 
on  it  the  track  of  a  ship  always  steering  the  same  course  appears  as  a  straight  line.  It  represents  with  perfect 
accuracy  the  relative  positions  of  places,  but  not  their  relative  distances. 


Fig.  7.'. 


A 


3025 


30 


29 


28' 


27'  _ 


I  OR' 


29 


28 


27 


26 


nautical  miles  may  be  taken  betwee'n  the  dividers  and  stepped  oi,  on  i.iu.  umc. 


.^.-i  t  V    «-not».lH»-V-3, 


M 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION.  21 

Since  the  unit  of  measure,  the  mile  a  minute  of  latitude,  has  a  different  value  in  every  latitude,  there  is  an 
ppearance  of  distortion  in  Mercator's  chrirt  when  covering;  any  large  extent  of  surface ;  for  instance,  an  island 
lear  the  pole  of  the  same  size  as  one  near  tae  ccpiator  will  be  represented  as  l)eing  much  larger,  due  to  the  differ- 
iH  scale  usedHo  preserve  the  character  of  the  projection. 

Art.  6§.  '/''  Constniit  a  Mercator's  Chart. — If  the  chart  for  which  a  projection  is  to  be  made  includes  the 
•quator,  the  values  to  be  measured  ofT  are  given  directly  by  Table  3.  If  the  equator  does  not  come  upon  the 
hart,  then  the  parallel  of  latitude  to  be  laid  down  should  be  referred  to  :^  principal  parallel ;  preferably  the  lowest 
)aialicl  to  be  drawn  on  the  chart.  The  distance  of  any  other  parallel  of  latitude  from  the  principal  parallel  is  then 
he  iliffcrcucc  of  the  values  found  for  the  two  taken  from  Table  3. 

The  values  so  found  may  either  be  measured  off,  without  previous  numerical  conversion,  by  means  of  a  diag- 
)nal  scale  constructed  on  the  chart,  or  they  may  be  laid  down  on  the  chart  by  means  of  any  jiroperly  divided  scale 
)f  yards,  metres,  &c.,  after  having  been  reduced  to  the  scale  of  proportions  adopted  for  the  chart. 

If,  for  example,  it  be  required  to  construct  a  chart  on  a  scale  of  one-quarter  of  an  inch  to  five  minutes  of  arc 
m  the'equator,  a  diagonal  scale  may  first  be  constructed,  on  which  ten  meridional  parts,  or  ten  minutes  of  arc  on 
he  equator,  have  a  length  of  half  an  inch;  then,  in  the. usual  manner,  multiples  of  one  meridional  part  may  be 
neasured  on  the  base  line;  multiples  of  o.i  on  the  hnes  parallel  to  the  base  line;  and  multiples  of  o.oi  may  be 
.•stimated  between  the  parallel  lines.  If  an  inch  scale  be  used,  the  meridional  parts,  before  being  laid  down  on 
.'he  projection,  must,  of  course,  be  multiplied  by  0.05  or  divided  by  20,  since  20  minutes  of  arc  on  the  equator,  or 
JO  meridional  parts,  have  to  be  made  equal  to  one  inch. 

Often  it  may  be  desirable  to  transfer  a  chart  constructed  according  to  any  other  projection  to  a  Mercator  pro- 
lection,  and  to  adapt  the  scale  to  a  certain  allotment  of  paper.  In  this  case,  the  lowest  and  the  highest  parallels 
Df  latitude  may  first  be  drawn  on  the  sheet  on  which  the  transfer  is  to  be  made.  The  distance  between  these 
parallels  may  then  be  measured,  and  the  number  of  meridional  parts  between  them  ascertained.  Dividing  the 
distance  bv  this  number  will  then  give  the  length  of  one  meridional  part,  or  the  quantity  by  which  all  the  merid- 
ional parts  taken  from  the  Table  3  must  be  multiplied.     This  quantity  will  represent  the  scale  of  the  chart. 

When  a  numerical  conversion  of  all  the  values  is  thus  required,  it  will,  in  general,  be  found  convenient  to 
prepare  first  a  rough  eye-sketch  of  the  projection,  and  to  note  on  it  all  the  distances  which  will  have  actually  to  be 
measured  off. 

Example.  The  process  of  constructing  a  Mercator  projection  is  best  shown  l)y  an  example. 

Let  a  projection  be  recpiired  for  a  chart  of  14'-'  extent  in  longitude  between  the  parallels  of  latitude  20'-  30'  and 
30*^  25'  (Fig.  24),  and  let  the  space  allowable  between  the  paper  lietween  thesf  parallels  measure,  say,  10  inches. 
Entering  the  column  in  Table  3  headed  20^,  and  running  down  to  the  line  marked  30'  in  the  side  column,  will  be 
found  1249.1  ;  then,  entering  the  column  30-',  and  running  down  to  the  line  of  25',  will  be  found  1905.7.  The 
difference,  or  1905.7—  1249. i  =656.6,  is  the  value  of  the  meridional  arc  between  these  latitudes,  for  which  l'  of 
arc  of  the'equator  is  taken  as  the  unit.     On  the  intended  projection,  therefore,  i'  of  arc  of  longitude  will  measure 

I0"^^_^  0152  inch,  which  will  be  the  scale  of  the  chart.  For  the  sake  of  brevity  call  it  0.015.  By  this  quantity 
656.6  J  '  .      .        .r   , 

all  the  values  derived  from  Table  3  will  have  to  be  multiplied  before  laying  them  down  on  the  projection,  li.  they 
are  to  be  measured  on  a  diagonal  scale  of  one  inch. 

Draw  now,  in  the  centre  of  the  sheet,  a  straight  line,  ah,  in  Fig.  24,  and  assume  it  to  be  the  Middle  Meridian 
of  the  chart.  Construct  very  carefully  in  this  line  a  perpendicular,  cd,  near  the  lower  border  of  the  sheet,  and 
assume  this  perpendicular  to  be  the  parallel  of  latitude  20*-'  30',  and  at  the  same  time  draw  the  southern  inner  « 
neat  line  of  the  chart.  From  the  point  /',  which  is  the  intersection  of  the  lines  ah  and  cd,  lay  off  on  the  hne  cd,  on 
each  side  of  the  Middle  Meridian,  ah,  seven  degrees  of  longitude,  or  the  distances  /'B  and  /'B',  each  equal  to 
0.015  X  60  X  7  =  6.3  inches  ;  and  through  the  points  B  and  B'  thus  obtained  draw  parallel  lines  to  ab,  which 
lines,  AB  and  A'B',  will  be  the  eastern  and  western  neat  lines  of  the  chart. 

In  order  to  construct  the  parallel  of  latitude  for  21^  o',  find,  in  Table  3,  the  meridional  parts  for  2i>-'  o',  which 
are  1281.0.  Subtracting  from  this  number  the  number  for  20^  30',  and  multiplying  the  difference  by  0.015,  we 
obtain  0.478  inches,  \\hich  is  the  distance  on  the  chart  between  20°  30'  and  21'-  o'.  On  the  lines  BA,  ha,  and 
B'A',  lay  off  the  distances,  BE,  be,  and  B'E',  each  equal  to  0.47S  inch,  and  through  E,  e,  E'  draw  the  straight  line, 
Et-E',  which  will  be  the  parallel  of  21^  o'.  r      •     j        1.     •     1 

Proceed  in  the  same  manner  to  lay  down  all  the  parallels  answering  to  full  degrees  of  latitude ;  that  is,  lay  off 
11. \,  ha,  and  B'A'  from  B,  /',  B',  respectively. 

o'".oi5  X  (1345. 1  —  1249. 1)  =  1.440  inches, 
o'".oi5  X  (1409.7  —  1249. 1)  =  2.409  inches, 
oin.015  X  (1474-7  —  1249.1)  =  3.384  inches,  &c., 

and  draw  the  lines  F/F',  Q^G',  H/^H',  c^c,  which  will  be  the  parallels  of  latitude  22°  o',  23°  o',  24O  o',  &c. 
Finally,  lay  down  in  the  same  way  the  parallel  of  latitude  30*^  25',  which  will  be  the  northern  inner  neat  line  of 
the  chart. 

A  degree  of  longitude  will  measure,  on  this  chart,  oi".oi5  X  60  =  o'".9.  Lay  off,  therefore,  on  the  lowest 
parallel  of  latitude  drawn  on  the  chart,  on  a  middle  one,  and  on  the  highest  parallel,  measuring  from  the  meridian, 
on  each  side,  the  distances,  respectively,  of  oi".9,  I'n.S,  2i".7,  y^\(i,  &c.,  in  order  to  determine  the  points  where 
meridians  answering  to  full  degrees  cross  the  parallels  drawn  on  the  chart.  Through  the  points  thus  found  draw 
the  meridians.  Draw  then  the  outer  neat  lines  of  the  chart  at  a  distance,  say,  of  the  twentieth  part  of  an  inch 
outside  of  the  inner  neat  lines,  and  extend  to  them  the  meridians  and  parallels.  Between  the  inner  and  outer  neat 
lines  of  the  chart  subdivide  the  degrees  of  latitude  and  longitude  as  minutely  as  the  scale  of  the  chart  will  permit, 
the  subdivisions  of  the  degrees  of  longitude  being  found  by  dividing  the  degrees  into  equal  parts,  and  the  sub 
divisions  of  the  degrees  of  latitude  being  found  in  the  same  manner  as  the  full  degrees  of  latitude  previous'v 
described. 

Art.  69.  The  subdivisions  between  the  two  eastern  as  well  as  those  between  the  two  western  neat  lines  will 
serve  for  measuring  or  estimating  terrestrial  distances.  1  )istances  between  points  bearing  North  and  South  of 
each  other  may  be  ascertained  by  referring  them  to  the  subdivisions  between  the  same  parallels.  Distances  repre- 
sented by  lines  at  an  angle  to  the  meridians  {loxodromic  lines')  may  be  measured  by  taking  a  small  number  of  the 
■modivisions  near  the  middle  latitude  of  the  line  to  be  measured  between  the  dividers  and  stepping  them  off  on  that 
line.  If,  for  instance,  the  terrestrial  length  of  a  line  running  at  an  angle  to  the  meridians  between  the  parallels  of 
latitude  of  24^  o'  and  29'^  o'  be  required,  the  distance  shown  on  the  neat  space  between  26^  15'  and  26^  45' =  30 
nautical  miles  may  be  taken  between  the  dividers  and  stepped  off  on  that  line. 


I 


22 


INSTRUMENTS   EMPLOYED    IN    NAVIGATION. 


Al't>  TO.  A  chart  may  be  transferred  from  any  other  projection  to  that  of  Mercator  by  drawing  a  system  o 
corresponding  parallels  of  latitude  and  meridians  over  both  charts,  so  close  to  each  other  as  to  form  minute  squares 
and  then  the  lines  and  characters  contained  in  each  square  of  the  map  to  be  transferred  may  be  copied  by  the  eyi 
in  the  corresponding  squares  of  the  Mercator  projection. 

Art.  71.  Great  Circle  Charts. — This  chart,  useful  to  the  Navigator  in  laying  out  his  track  in  Grea 
Circle  Sailing,  is  supplementary  to  the  Mercator  chart;  for,  having  drawn  the  track  on  it,  a  transfer  can  be  niadi 
to  the  Mercator  chart  by  means  of  the  ordinates,  latitude  and  longitude,  of  various  points. 

It  is  drawn  on  the  Central,  or  Gnomonic,  projection,  and  on  it  all  great  circles  appear  as  straight  lines.  Th( 
pole  is  made  the  centre  of  projection,  and  the  plane  of  projection  is  that  of  any  parallel  of  latitude. 

A  series  of  concentric  circles  represents  the  parallels  of  latitude,  the  radius  of  any  particular  one  being  rcot  L 
where  r  is  any  convenient  linear  magnitude  and  equals  the  radius  of  the  parallel  of  45°.  The  meridians  are  straigh 
lines  drawn  from  the  centre,  dividing  each  circumference  into  360  equal  parts. 

These  charts  are  only  valuable  to  represent  the  higher  latitudes,  because  within  the  tropics  the  difference 
between  tracks  by  the  Great  Circle  and  by  the  Rhumb  is  so  small  that  the  Mercator  chart  will  answer  every  pur 
pose.     And,  again,  the  existence  of  the  trade  winds  governs  the  track  to  be  followed  within  their  limits. 

The  application  and  use  of  the  Great  Circle  Chart  will  be  exemplified  in  Great  Circle  Sailing,  Chap.  Ill,  Par 
I,  Art.  129,  &c. 

12.— THE  LOG  BOOK. 

Art.  YS.  The  Log  Book  is  a  record  or  journal  of  the  ship's  cruise.  It  should  afford  not  only  the  data  fron 
which  the  Navigator  establishes  the  ship's  position  by  that  method  commonly  called  Dead  Reckoning,  but  be  sc 
complete  in  all  its  details  as  to  be  a  valuable  Meteorological  Journal ;  to  accomplish  which,  there  should  be  £ 
thorough  knowledge  of  the  various  instruments  used,  a  careful  personal  recording  on  the  part  of  the  Officer  of  the 
Watch,  and  as  careful  a  revision  on  the  part  of  the  Navigator  or  Master. 

Since  the  Masters  of  vessels  in  the  Merchant  Marine  are  requested  to  co-operate  with  the  Navy  in  a  uniform 
system  of  collecting  and  reporting  meteorological  data,  this  subject  can  best  be  illustrated  by  describing  the  Log 
Book  and  Meteorological  Journal  used  in  the  United  States  Navy. 

Art.  TS.    Of  the  instruments  employed  in  collecting  data  for  the  Log  Book,  (^^\ 

the  Log,  the  Lead,  and  the  Compass  have  heretofore  been  described.     To  ascer-  vJ'^ 

tain  the  meteorological  data  there  are  necessary  the  Barometer,  the  Thermom- 
eter, and  the  Hygrometer. 

The  Barometer  shows  the  press7(re  of  the  air. 

The  Thermometer  (in  the  shade)  shows  the  temperature  of  the  air. 

The  Hyg7vmeter  shows  the  degree  of  moisture  of  the  air. 

The  three  combined  form  an  efficient  weather  guide, 

THE   barometer. 

Art.  VA.  The  barometer  consists  of  a  brass  tube  (Fig.  25)  terminating  at 
top  in  a  ring.  A,  for  suspension,  and  at  bottom  in  a  flange,  B,  to  which  the  several 
parts  forming  the  cistern  are  attached.  |{||||  [IffliC 

The  upper  part  of  this  tube  is  cut  through  so  as  to  expose  the  glass  tube  and 
mercurial  column  within,  seen  in  Fig.  28.  Attached  at  one  side  of  this  opening  is 
a  scale,  graduated  in  inches  and  parts ;  and  inside  this  slides  a  short  tube,  r,  con- 
nected to  a  rack-work,  arrangement,  moved  by  a  milled  head,  D :  this  sliding  tube 
carries  a  vernier  in  contact  with  the  scale,  which  reads  off  to  g^^  (.002)  of  an  inch. 

In  the  middle  of  the  brass  tube  is  fixed  the  thermometer,  E,  the  bulb  of  which 
being  externally  covered,  but  inwardly  open,  and  nearly  in  contact  with  the  glass 
tube,  indicates  the  temperature  of  the  mercury  in  the  barometer-tube,  not  that  of 
the  external  air.  This  central  position  of  the  thermometer  is  selected  that  the 
mean  temperature  of  the  whole  column  may  be  obtained;  a  matter  of  importance, 
as  the  temperature  of  the  barometric  column  must  be  taken  into  account  in  every 
scientific  application  of  its  observed  height.  |j||||  II  illTlblll) 

The  cistern  (Fig.  26)  is  made  up  of  a  glass  cylinder,  F,  which  allows  the  sur- 
face of  the  mercury  q  to  be  seen,  and  a  top  plate,  G,  through  the  neck  of  which 
the  barometer  tube  t  passes,  and  to  which  it  is  fastened  by  a  piece  of  kid  leather, 
making  a  strong  but  flexible  joint.  To  this  plate,  also,  is  attached  a  small  ivory 
point,  h,  the  extremity  of  which  marks  the  commencement  or  zero  of  the  scale  above. 
The  lower  part,  containing  the  mercury,  in  which  the  end  of  the  barometer-tube  t 
is  plunged,  is  formed  of  two  parts,  /,/,  held  together  by  four  screws  and  two  divided  ^p"'"'"""!!!!! 
rings,  L,  M,  in  the  manner  shown  in  Figs.  26  and  27.  To  the  lower  piecey  is  fast- 
ened the  flexible  bag  N,  made  of  kid  leather,  furnished  in  the  middle  w  ith  a  socket, 
k,  which  rests  on  the  end  of  the  adjusting-screw  O.  These  parts,  with  the  glass 
cylinder  F,  are  clamped  to  the  flange  B  by  means  of  four  long  screws  P  and  the 
ring  R ;  on  the  ring  R  screws  the  cap  S,  which  covers  the  lower  parts  of  the  cis- 
tern, and  supports  at  the  end  the  adjusting-screw  O.  G,  /,  j,  and  /•,  are  of  box- 
wood;  the  other  parts  of  brass  or  German  silver.  The  screw  O  serves  to  adjust  ^.  ^J^  I  |||E 
the  mercury  to  the  ivory  point,  and,  also,  by  raising  the  bag,  so  as  to  completely 
fill  the  cistern  and  tube  with  mercury,  to  put  the  instrument  in  condition  for  trans- 
portation. 

Art.  75.  The  principle  of  the  barometer  is  now  so  generally  known,  being, 
too,  in  almost  universal  use  at  sea,  that  it  need  hardly  be  mentioned  here.  While 
the  mercury  in  the  cistern  falls,  or  is  pressed  down  by  the  air,  the  column  rises  in 
the  exhausted  tube;  and  when  the  mercury  in  the  cistern  rises,  owing  to  diminished 
pressure  of  the  air,  the  column  of  mercury  in  the  tube  falls.  But  the  actual  length  of  the  column  of  mercury  is 
required  (in  order  to  know  the  weight  or  pressure  of  the  atmosphere),  as  measured  from  the  actual  surface  f  f  the 
mercury,  which  is  variable;  therefore,  a  correction  is  required  for  most  instruments  on  account  of  the  difference 
from  the  neutral  line  or  point,  namely,  that  defining  the  base  of  the  column  when  the  scale  attached  to  it  was 
graduated. 


TiW 


0 


Fig.  25. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


28 


In  some  barometers  the  graduated  scale  can  l)e  adjusted  so  that  the  lower  point  just  touches  the  mercury,  in 
which  case  no  correction  for  the  relative  cajiacitics  of  the  tube  and  cistern  is  necessary.  In  small  tubes  an  error  is 
caused  by  what  is  called  capillarity  and  by  friction.  Unlike  other  Ibiids,  mercury  is  depressed  by  capillary  action. 
Other  error*  to  be  noticed  and  allowed  for  are  caused  by  the  expansion  or  contraction  of  the  mercury  by  higher  or 

lower  temperature  than  that  of  the  mer- 
cury when  the  scale  was  graduated,  and 
by  the  dilatation  or  contraction  of  the  tube 
and  scale. 


^MllMta!® 


wm 


Also,  the  corrected  height  of  the  mer- 
cury in  the  tube  must  be  reduced  to  the 
standard  of  observation,  or  what  it  would 
have  been  had  the  temperature  of  the  ah" 
and  mercury  been  at  32-  P\ah.,  with  the  ba- 
rometer at  the  level  of  the  sea.  More- 
over, there  are  errors  in  most  barometers, 
occasioned  by  the  variation  of  the  scale,  or 
incorrect  graduation,  or  both,  besides  that 
occasioned  by  air,  moisture,  or  gas  in  or 
above  the  column,  which  affects  its  height. 
Some  of  these  may  be  comprehended  as 
index  errors,  and  are  so  in  instruments  on 
the  Kew  Observatory  principle. 

The  barometer  requires  very  careful 
handling,  the  glass  tube  being  exceedingly 
liable  to  fracture.  When  moved  from  one 
place  to  another  the  cistern  end  should  be 
kept  uppermost,  the  instrument  having 
been  gently  reversed. 

When  suspended  for  use  it  should 
hang  freely  in  a  vertical  position,  where 
neither  the  sun's  rays,  nor  a  fire,  nor  any 
local  cause  of  heat  or  cold  may  be  likely  to 
affect  it.  Every  observation  of  the  height 
of  column  should  be  accompanied  by  a 
notation  of  the  degree  of  temperature  shown 
by  the  attached  thermometer  (which  indi- 
cates the  temperature  of  the  mercury)  as 
well  as  by  those  of  the  air.  In  reading 
off,  the  edge  of  the  vernier  scale  should 
appear  to  touch  (or  be  tangent  to)  the  up- 
permost point  of  the  mercury  when  the 
eye  is  at  an  equal  height  and  looking  hori- 
zontally at  the  tube.  A  card  or  a  piece  of 
white  paper  behind  or  at  the  side  of  the 
tube  aids  the  eye  by  reflecting  light,  or 
showing  the  edge  of  the  quicksilver  more  plainly. 

The  vernier  scale  enables  one  to  read  off  hundredths  of  an  inch,  or,  in 

the  instruments  used  for  the  most  scientific  purposes,  thousandths  of  an 

inch.     Its  principle  is  the  same  as  that  of  the  sextant,*  substituting  sra/f 

for  arc,  and  divisions  of  inches  for  parts  of  arc.     An  extreme  degree  of 

minuteness  in  reading  is  scarcely  necessary  in  marine  barometers  at  sea, 

which  are  unavoidably  liable  to  errors  exceeding  even  hundredths,  partly 

from  defective  construction  or  adjustment,  partly  from  the  motion  of  the 

vessel,  which  causes  oscillation  (often  called  pumping)  of  the  mercury  in  the  tube.     To  prevent  the  barometer  from 

acquiring  too  much  motion  (from  the  movement  of  the  vessel),  from  acquiring  a  momentum  which  augments  its 

swinging  and  gives  impetus  to  the  mercury,  soft  cushions.  India-rubber  straps,  or  weak  springs  may  be  employed. 

Ai't.  76.   The  Aneroid  Barometer,  from  its  small  size  and  portability  with  comparative  safety,  is  an 

admirable  adjunct  to,  and  can  be  usefully  employed  where  a  mercurial  one  cannot  be  taken.     It  can,  however, 

~  *Art.  184,  Chap.  II,  Part  II. 


-i 


^C 


Fig. 


24  INSTRUMENTS    EMPLOYED    IN   NAVIGATION. 

only  be  relied  upon  when  it  can  be  frequently  compared  with  a  standard  inercurial  barometer.  The  advantage  of 
size  and  easy  portability  has  brought  it  into  a  general  use  far  beyond  its  real  merits  as  a  proper  measurer  of  the 
vveight  of  the  atmosphere.  As  a  "weather  glass"  (if  corrected  for  temperature)  it  will  generally  do  good  service. 
It,  however,  requires  some  care,  as  its  safe  transportation  is  rather  apparent  than  real.  Slight  shocks  will  not 
ordinarily,  but  a  jar  or  knock  that  would  break  a  mercurial  barometer  will  quite  likely,  change  the  reading  an 
unknown  qumtity  that  may  vary  from  i',t  to  i  inch,  and  if  this  amount  can  be  found  by  a  direct  comparison  (after 
travel  or  rough  handling)  with  a  standard  barometer  it  can  be  allowed  for,  or  the  aneroid  may  l)e  adjusted;  but  if 
there  is  no  standard  at  hand  it  will  require  a  series  of  observations  to  olitain  from  a  mean  of  them  an  approximate 
correction.  It  will,  however,  be  useful,  even  without  this,  for  its  relative  reading,  but  may,  without  great  care, 
lead  to  mistakes.  If  the  instrument  is  on  shipboard,  and  will  remain  undisturbed  in  its  place,  then  the  most  im- 
portant point  is  to  get  its  correction  for  temperature.  The  correction  for  temperature  in  the  mercurial  barometer 
is  a  known  quantity,  and  a  table  short  enough  to  be  convenient  can  be  used,  but  in  the  aneroid  it  must  be  found 
for  each  instrument.  The  temperature  of  the  aneroid  may  be  obtained  approximately  by  placing  it  in  the  coldest 
place  nearly,  and  then  in  the  warmest,  and  noting  the  change,  leaving  it  in  each  place  long  enough  to  acquire  the 
temperature,  say  about  half  an  hour.  If  possible,  this  operation  should  be  repeated.  During  a  staljle  condition  of 
the  air,  if  a  mercurial  or  another  aneroid  can  be  set  and  kept  at  a  uniform  temperature  during  the  time,  it  will  cor- 
rect for  any  change  of  pressure,  and  fewer  trials  will  be  required. 

The  aneroid  may  be  hung  up  or  placed  flat  on  its  back,  but  changing  from  one  position  to  another  ordinarily 
changes  the  readings  sensibly,  and  it  should  therefore  be  kept,  while  in  use,  constantly  in  its  selected  position  and 
place.     It  is  usual  to  adjust  them  to  the  standard  mercurial  Ijarometer  while  they  are  lying  flat  in  their  cases. 

An  additional  merit  which  the  aneroid  possesses  is,  that  being  more  sensitive  than  the  mercurial  one,  its  varia- 
tions take  place  simultaneously  with  their  causes.  Its  mechanism,  liowever,  like  other  pieces  of  mechanism,  is 
liable  to  derangement,  which  can  only  be  detected  by  frequent  comparison  with  a  correct  standard. 

Well- constructed  and  thoroughly  tested  aneroids,  if  issued  for  use  with  a  record  of  their  variable  index  errors, 
and  properly  cared  for  thereafter,  will  not  only  be  found,  even  with  mercurial  barometers,  very  useful  on  board 
ship,  but  in  the  event  of  accident  to  the  mercurial  one,  which  frequently  happens,  an  indispensable  instrument  to 
the  careful  and  intelligent  seaman. 

Aneroid  barometers,  if  often  compared  with  good  barometric  columns,  are  similar  in  their  indications  and 
valuable ;  but  it  must  not  be  forgotten  that  they  are  not  independent  instruments,  that  they  are  set  originally  by  a 
mercurial  barometer,  by  the  application  of  a  small  turnscrew  gently  to  the  screw-head  at  the  back.  They  require 
adjustment  occasionally  in  the  same  way  that  they  are  in  the  first  place  set.  They  may  also  deteriorate  in  time, 
though  slowly. 

The  aneroid  barometer  is  quick  in  indicating  the  variation  of  atmospheric  pressure,  and  to  the  navigator,  who 
knows  the  difficulty  in  using  mercurial  barometers  at  times,  this  instrument  is  a  great  boon,  for  it  is  steady  under 
all  circumstances  of  weather,  at  the  same  time  giving  indication  of  increased  or  diminished  pressure. 

In  ascending  or  descending  elevated  land,  the  hand  of  the  aneroid  may  be  seen  to  move  like  the  hand  of  a 
watch,  showing  the  height  above  the  level  of  the  sea  or  place  of  comparison  by  allowing  o.ooii  of  an  inch  for  each 
foot. 

The  principle  on  which  the  aneroid  is  constructed  may  be  explained  in  a  few  words,  without  going  into  a  scien- 
tific or  minute  detail  of  its  various  parts.  The  weight  of  a  column  of  air,  which  in  the  mercurial  barometer  acts  on 
the  mercury,  in  the  aneroid  (a  name  intended  to  express  "without  fluid")  presses  on  a  small  round  metal  box, 
from  which  nearly  all  air  is  extracted ;  to  this  box  is  attached  by  nice  mechanical  arrangement  the  hand  seen  to 
work  over  the  face  of  the  instrument.  When  the  atmospheric  pressure  is  lessened  in  the  vacuum-box,  a  spring, 
acting  on  a  lever,  turns  the  hand  to  the  left,  and  when  the  pressure  increases  the  spring  is  pressed  down  by  the  lever, 
and  the  hand  is  turned  to  the  right.     It  acts  in  any  position,  but  may  vary  several  hundredths  with  such  a  change. 

The  known  expansion  and  contraction  of  metals  under  varying  temperatures  might  cause  a  doubt  as  to  the 
accuracy  of  the  aneroid  under  such  changes ;  but  the  inventor  has  met  this  difficulty  by  introducing  into  the  vac- 
uum-box a  small  quantity  of  gas  as  a  compensation  for  the  effects  of  heat  and  cold;  the  gas  in  the  box  changing 
its  bulk  on  a  change  of  temperature,  is  intended  to  compensate  for  the  effect  on  the  metal  of  which  the  aneroid  is 
made.     Additional  compensations  have  also  been  devised. 

Art.  77.  The  Thermometer  is  an  instrument  founded  on  the  principle  tliat  most  bodies,  fluids  especially, 
expand  Ijy  heat  and  contract  by  cold.  It  is  used  for  the  purpose  of  measuring  the  amount  of  heat  in  the  atmos- 
phere or  other  substances  brought  into  contact  with  or  in  the  vicinity  of  it.  In  construction  it  differs  from  the 
barometer  in  having  the  tube  closed  at  each  end.  The  mercury  contained  in  the  tube  moves  in  a  vacuum  caused 
by  the  expulsion  of  the  air  by  boiling  the  mercury  and  then  closing  the  top  of  the  tube  by  means  of  the  blow-pipe. 
There  are  three  descriptions  of  thermometers  in  common  use,  all  constructed  on  the  same  principle,  but  differing 
in  the  divisions  or  graduations  of  their  respective  scales.  Fahrenheit's  thermometer  is  generally  used  in  England 
and  America. 

Upon  Fahrenheit's  thermometer  melting  ice  is  marked  32°  and  boiling  water  212'-,  the  interval  Ijeing  divided 
into  180  equal  parts.  The  same  graduation  is  extended  downward  from  32"  to  zero  (o'),  and  may  be  continued 
below  zero  as  far  as  desired.     Degrees  below  zero  are  distinguished  by  tlie  minus  ( — )  sign. 

For  the  purpose  of  measuring  the  temperature  of  air  on  board  ship,  the  thermometer  should  be  exposed  in 
the  open  air,  where  the  circulation  is  unobstructed ;  it  should  be  always  in  the  shade,  removed  at  least  a  foot  from 
the  bulkhead  or  other  material  from  or  near  which  it  is  hung,  protected  against  the  heat  reflected  from  the  neigh- 
boring objects,  and  kept  sheltered  from  the  rain  and  spray. 

If  the  thermometer  should  happen  to  become  moistened  by  rain  or  spray,  the  bulb  should  be  carefully  dried 
about  5  minutes  iDefore  reading  and  recording  the  observations.  A  wooden  frame  of  open  lattice-work  will  lie 
found  to  be  a  good  covering  for  a  thermometer,  provided  it  is  so  constructed  as  to  admit  a  perfectly  free  circulation 
of  air  about  the  instrument. 

The  thermometer  is  an  invaluable  instrument  to  the  careful  navigator  in  making  observations  of  temperature, 
simultaneously,  of  the  air  and  the  surface  of  the  ocean.  The  difference  in  the  temperature  of  the  air  and  the 
surface  of  the  sea  gives  warning  to  the  seaman  of  his  approach  to  icebergs,  banks,  shoals,  or  land,  and,  Ijeing  on 
soundings,  by  being  lower  than  where  there  are  none  of  these  obstructions  to  navigation  ;  and  by  showing  a  higher 
temperature  of  the  surface-water  upon  entering  the  Gulf  Stream,  the  Brazil  Current,  the  equatorial  currents  of  the 
Atlantic  and  Pacific  Oceans,  the  Japan  Current,  &c.,  and  a  lower  temperature  on  leaving  them,  which  are  now 
more  or  less  accurately  laid  down  on  our  charts. 

In  approaching  land  at  night,  or  in  navigating  in  the  vicinity  of  shoals,  ol)servations  for  temperature  of  llic  air 
and  water  should  be  frequently  made,  and  at  regular  intervals  of  time,  with  the  greatest  care  and  precision,  ant'- 
the  differences  and  changes  ol)served  and  noted. 


INSTRUMENTS    EMPLOYED    IN    NAVIGA.TION. 


25 


It  has  been  found   that  tlie  Guinea  Current,  with  a  temjieraturc  of  80*'  or  90°  Fah.,  sets  to  the  eastward, 
I  while  in  close  proximity  to  it  on  its  southern  edge  the  ecjuatorial  current  is   met,  setting  to  the  westward,  with  a 
temperature  of  70^^  or  lower. 

A  tem]iwature  of  only  66^'  in  the  Guinea  Current  itself  has  lieen  recorded  liy  a  very  competent  observer,  show- 
ing that  variations  in  surface  temperature  similar  to  those  known  to  exist  in  tlie  Gulf  Stream  are  traceable  in  this 
current,  so  close  to  tlie  equator. 

The  resulting  deductions,  obtained  from  observations  t)f  the  surface  temperatures  of  the  ocean,  are  of  the  greatest 
importance  to  the  navigator,  and  should^,  therefore,  never  be  neglected  to  be  taken  by  those  having  the  necessary 
means  and  opportunities  for  iloing  so.  Every  additional  fact  discovered  and  reported  in  surface  temperature  of  the 
ocean  is  an  advance  toward  the  solution  of 
the  great  problem  of  tho^e  currents,  which 
is  of  so  much  interest  to  .all  seafaring  per- 
sons. 

Art.   "IS.     The    Hygrometer   is   a 

most  valualile  and  useful  instrument  to  the 

1  seaman,    especially    as    an    adjunct    to    the 

barometer    and   thermometer  in   foretelling 

weather. 

Any  instrument  (and  there  are  several 
instruments  of  the  kind)  adapted  to  measure 
the  amount  of  moisture  in  the  air  is  called  a 
hygrometer  (or  psychrometer,  "cold-meas- 
uring moisture  measurer"),  but  the  one 
best  suited  to  use  on  board  ship  is  the  wet- 
bulb  thermometer. 

The  psychrometric  hygrometer  consists 
of  two  good  equal  thermometers,  mounted 
on  the  same  frame  of  wood,  6  inches  wide 
by  12  inches  long,  or  thereabouts,  the  bulb 
of  one  thermometer  being  naked,  while  the 
bulb  of  the  other  is  wrapped  in  some  thin, 
absorbent  covering,  such  as  a  little  muslin 
bag,  with  a  kind  of  wick  reaching  from  it 
into  a  small  cistern  of  water,  such  as  a  small 
preserve  pot,  or  a  short-necked  bottle  (see 
Fig.  29). 

For  the  instrument  to  act  truly,  great 
care  must  be  taken  to  choose  two  thermom- 
eters, which  correspond  exactly,  degree  for 
degree,  from  about  15*^  up  to  90*-".  This  is 
not  at  all  an  easy  matter,  for  thermometers 
vary  in  the  most  tiresome  manner,  even 
when  both  are  superior  instruments.  Both 
the  bulbs  (naked  and  covered,  or  "dry"  and  "wet")  should  project  an  inch  or  two,  clear  all  round,  below  their 
frame,  for  the  action  of  the  air  to  be  exerted  on  them  more  perfectly. 

The  little  cistern  of  water  should  be  suspended,  so  that  the  surface  of  the  water  mav  be  from  i  to  3  inches 
away  from  the  bulb  to  which  it  is  connected  by  the  wick,  and  it  should  be  placed  on  the  side  farthest  from  the  dry 
bulb,  so  that  its  evaporation  may  not  affect  the  dry  bulb,  as  well  as  the  wet  Indb. 

The  evaporation  of  the  water  produces  cold,  and  this  (the  wet  bulb)  thermometer  habitually  (with  very  rare 
exceptions)  stands  lower  than  a  dry-bulb  thermometer  similarly  exposed.  This  depression,  strictly,  measures 
only  the  t-vapcvaiing  ■p'^wQv  of  the  air;  yet,  as  the  latter  depends  upon  the  amount  of  moisture  present  in  the  air, 
the  depression  of  the  wet-bulb  thermometer  measures  the  humidity  of  the  air. 

When  the  temperature  is  in  the  neighborhood  of  the  freezing-point,  the  observation  of  the  psychrometer 
requires  very  peculiar  care. 

During  foi^  the  7i.vt-l>ulf>  tJicnitoimtcr  ))i.cy  soiiutiiiws  he  Jiighcr  tliaii  tlic  dry  bulb  :  then  the  air  is  cn'crsatiiratt'd, 
and  contains,  besides  the  vapor  at  its  maximum  of  tension,  water  suspended  in  a  disseminated  liquid  state.  This  is, 
however,  not  a  frequent  occurrence. 

If  the  temperatAire  of  the  air  (/.  e,,  the  dry  bulb)  should  have  descended  below  32^^,  it  will  often  happen  that 
the  wet-bulb  thermometer  will  for  a  time  read  higher  than  the  dry  bulb.  SueJi  ohseii<atio)is  must  not  be  recorded  ; 
but  when  the  water  surrounding  the  wet  bulb  has  begun  to  freeze,  the  proper  readings  will  take  place. 

If  the  water  in  the  muslin  covering  the  wet  bulb  be  frozen,  the  readings  will  be  perfectly  correct. 

If  the  muslin  be  found  dry,  it  should  be  wetted  with  a  brush  or  small  sponge,  and  then  be  left  a  little  while  for 
the  water  in  the  muslin  to  be  frozen ;  and  when  satisfied  that  such  is  the  case  the  observer  may  proceed  to  take 
the  readings  in  the  usual  way.  Unless  this  caution  is  attended  to,  the  \\et  bulb  will  read  as  high  or  higher  than 
the  dry  bulb.  When  the  weather  is  frosty,  the  muslin  should  be  thoroughly  wetted  some  time  (say  an  hour)  before 
the  usual  and  chief  hour  of  observation. 

If  the  temperature  should  have  ascended  abcn>e  "pP  (in  frosty  weather),  immerse  the  wet-bulb  thermometer  in 
warm  water  for  a  minute  or  so,  that  any  ice  remaining  on  the  muslin  may  be  melted.  Unless  this  be  attended  to, 
the  wet-bulb  thermometer  will  continue  to  read  32*^,  so  long  as  any  ice  remains  in  contact  with  it. 

The  muslin  and  wick  should  so  act  as,  by  capillarity,  to  keep  the  wet  liull)  always  wet,  but  lu^t  actually  drip- 
ping, so  that  rapid  evaporation  may  lie  constantly  going  on.* 

If  the  air  is  very  still,  it  is  well  to  increase  the  evaporation  by  setting  the  air  in  motion  by  a  fan.  If  the  wind 
is  too  strong,  the  instrument  should  be  protected  by  the  movable  blind.  The  reading  must  be  made  rapidly,  and, 
as  much  as  possible,  at  a  distance,  and  without  opening  the  window;  for  the  proximity  of  the  observer,  either  by 
the  heat  radiating  from  his  body  or  by  his  breath,  as  well  as  the  temperature  and  hygrometrical  state  of  the  air 
issuing  from  the  chamlier,  which  is  always  ditferent  from  that  of  the  external  air,  especially  in  winter,  would  infal- 
libly act  upon  the  instruments,  and  would  falsify  the  observation. 

*The  little  muslin  ba<r  und  its  cottuu  wick  should  be  changed  about  once  a  month. 


Fig.  29. 


26 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


Art.  79.  The  Log  Book  is  the  record  and  journal  of  a  ship's  cruise.  In  it  are  contained  all  the  data 
relating  to  the  run  at  sea,  a  complete  meteorological  record  while  under  way  or  in  port,  and  a  register  of  the  mis- 
cellaneous events  of  the  cruise. 

In  the  United  States  Navy  it  is  an  ofiicial  record,  being  sent  to  the  Navy  Department  when  completed,  to  be 
preserved  there,  and  from  it,  in  connection  with  many  others,  are  compilecl  valuable  wind  and  weather  charts, 
sailing  directions,  and  much  more  that  is  of  great  benefit  to  science,  provided  the  records  have  been  carefully  and 
conscientiously  kept.  From  tlie  log  book  on  board  naval  vessels  at  stated  periods  certain  compilations  of  meteoro- 
logical data  are  made  and  entered  in  blank  forms  provided  for  the  purpose,  and  forwarded  to  the  llytlrographic 
Office.  Since  the  officers  of  the  Merchant  Marine  have  been  requested  to  co-operate  with  the  naval  profession  in 
the  collection  of  these  data,  various  forms  will  serve  to  exemplify  the  method  of  '■'■Keeping  the  Shifs  Log  Book" 
and  for  "  Compiling  the  Meteorological  Returns.'''' 

In  order  to  more  completely  illustrate  the  method,  an  abstract  of  two  days'  run,  marked  Z,  is  given,  with  the 
attendant  remarks.  The  record  is  that  of  a  civil  day,  commencing  at  midnight,  the  two  parts  of  the  day  being 
separated  by  the  data  which  marks  the  beginning  of  the  astronomical  day. 


Art.  80.    Symbols  to  be  used  in  recording  the  State  op'  the  Weather  in  the  proper  cohtnins. 


h.  Clear  blue  sky. 

c.  Cloudy  weather. 

d.  Drizzling,  or  light  rain. 

f.  Fog,  or  foggy  weather. 

g.  Gloomy,  or  dark  stormy  looking  weather. 
//.  Hail. 

/.  Lightning. 

ni.  Misty  weather. 

o.  Overcast. 


Passing  showers  of  rain. 

Squally  weather. 

Rainy  weather,  or  continuous  rain. 

Snow,  snowy  weather,  or  snow  falling. 

Thunder. 

Ugly  appearances,  or  threatening  weather. 

Variable  weather. 
■IV.   Wet,  or  heavy  dew. 
z.     Hazy. 


Art.  81.    SymhoI.s  to  he  used  in  recording  the  Forms  and  Appearance  of  Clouds  in  the  proper  coluiiiu. 


Cir Cirrus Primary  form. 

Cir.-Cum Cirro-cumulus Secondary  form. 

Cir.-Str Cirro-stratus Secondary  form. 

Cum Cumulus Primary  form. 

Cum.-Str Cumulo-stratus Secondary  form. 

Nimb   Nimbus   Primary  form. 

Str Stratus Primary  form. 

Art.  82.    Classijicat'wn  of  Clouds. 

PRIMARY   CLOUDS. 

Cirrus. — Consists  of  light  and  feathery  streaked  filaments,  seen  in  clear  weather. 

Cum7tlus. — Is  composed  of  huge  hemispherical  masses,  apparently  resting  on  a  horizontal  base;  occurring  chiefly 

in  summer,  and  presenting  the  appearance  of  heaps  of  snow. 
Stratus. — Is  an  extended  horizontal  layer  of  cloud,  increasing  from  below,  and  appearing  at  times,  about  sunset, 

of  extraordinary  brilliancy. 
Nimbus. — Rain  cloud. 

SECONDARY,    OR    COMPOUND    CLOUDS. 

Cirro-cumulus. — Forms  the  transition  state  from  cirrus  to  cumulus,  and  constitutes  the  aggregation  of  small  round 

white  clouds,  resembling  sheep  in  a  meadow. 
Cirro-Stratus. — Consists  of  cirrus  combined  in  horizontal  or  slightly  inclined  layers  of  considerable  extent. 
Cumulo-Stratus. — Often  gives  to  the  horizon  a  bluish-black  color,  frequently  seen  in  great  perfection  toward  night 

of  dry  and  windy  weather. 

Art.  83.    Winds.  X 


^ 

XI 

<u 

c 

rt 

^ 

l<-. 

o 

m 

H) 

o 

o 

-4-* 

9-< 

S 

O 

r( 

P^ 

C 

o 


Nautical  designation. 


Calm. 


Light  airs. 


Light  breezes. 


Gentle  breezes. 


Sail  that  a  full-rigged  ship 
may  carry,  close-hauled  by 
the  wind;  also  her  prob- 
able speed. 


All  sail. 


All  plain  sail  and  stay-sails ; 
smooth  sea;  0.5  to  i  knot  per 
hour. 


All  plain  sail  and  stay-sails  ; 
smooth  sea;  about  2  knots. 


All  plain  sail  and  stay-sails; 
smooth  sea ;  3  to  4  knots. 


Sail  that  a  full-rigged  ship 
may  carry,  wind  on  quarter ; 
also  her  probable  speed. 


All  sail. 


h  11  plain  sail  and  studding- 
sails ;  smooth  sea;  I  to  1.5 
knots  per  hour. 


All  plain  sail  and  studding- 
sails;  smooth  sea;  2  to  3.5 
knots. 


All  plain  sail  and  studding- 
sails  ;  smooth  sea ;  4  to  5 
knots. 


So 

O    rt 


o 

o 

w 


m 


0.004 

to 
0.019 


0.08 


0.36 


O    1) 


I  to  2 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


27 


IVmd — Continued. 


Force  of  wind, 
nautical  scale. 

Nautical  designation. 

Sail   that   a   full-rigged    ship 
may  carry,  close-hauletl  liy 
the  wind ;    also  her  prob- 
able speed. 

Sail    that   a    full-rigged    ship 
may  carry,  wind  on  (piarier; 
also  her  probable  speed. 

Force  of  wind 
^            in  pounds  per 
square  foot. 

Velocity  of 
_^           wind  in  miles 
per  hour. 

4 

Moderate  breezes. 

All  plain  sail  and  stay-sails ; 
smooth  sea ;  5  to  6  knots. 

All  plain  sail  and  studding- 
sails  ;     smooth    sea ;     6    to    7 
knots. 

5 
6 

Stiff  breezes. 

Courses,  top-sails,  to'gallant- 
sails  and  stay-sails;   moderate 
sea ;  6  to  7  knots. 

All  plain  sail  and  studding- 
sails;    moderate  sea;    8  to  9 
knots. 

1-5 

17 

Fresh  breezes. 

Courses,    single-reefed   top- 
sails,  to'gallant  sails;   moder- 
ate sea ;   7  to  9  knots. 

Courses,  top-sails,  to'gallant- 
sails,  lower  and  topmast  stud- 
ding-sails ;    moderate  sea;    10 
to  12  knots. 

2 

20 

7 

Very  fresh  breezes. 

Courses,  double-reefed  top- 
sails,  fore  topmast    stay-sail ; 
moderate  sea ;  about  7  knots. 

Coui  ses,   single-reefed   top- 
sails,  to'gallant-sails ;    moder- 
ate sea;    12  to  14  knots. 

3 

24 
30 

S 

Moderate  gale. 

Single-reefed    courses,    tre- 
ble-reefed fore  and  main  top- 
sails, close- reefed  mizzen,  fore 
topmast  stay-sail;   rough  sea; 
4  to  5  knots. 

Single-reefed  courses,  dou- 
ble-reefed fore  and  main  top- 
sails,     close-reefed      mizzen ; 
rough  sea;  about  10  knots. 

5 

9 

Strong  gale. 

Close-reefed  courses,  close- 
reefed  fore  and  main  top-sails, 
storm  stay-sail ;   rough  sea. 

Close-reefed  courses,  close- 
reefed  fore  and  main  top-sails, 
storm  stay-sails;  rough  sea. 

8 

40 

10 

Very  strong  gale. 

Close-reefed  fore-sail,  close- 
reefed  main  top-sail,  fore  storm 
stay-sail;   very  rough  sea. 

Close-reefed  fore-sail,  close- 
reefed  main  top-sail,  fore  storm 
stay-sail ;  very  rough  sea. 

23 

67 

11 

Violent  gale. 

Storm-sails,   or   close-reefed 
main   top-sail  and  fore   storm 
stay-sail ;   very  rough  sea. 

Close-reefed  fore-sail,  close- 
reefed  main  top-sail,  fore  storm 
stay-sail. 

32 

80 

Hurricane,           i      ^^^^        ^.        ^^      ^^.^^^ 

Typhoon,                bodily  to  leeward.                    ^ 
Cyclone.                       ■' 

Scudding  under  bare  poles. 

50  and 
upward. 

100  and 
upward. 

The  above  tabulated  sail  and  speed  corresponding  to  various  forces  of  the  wind  are  but  approximations  to 
what  really  takes  ])lace  according  to  particular  circumstances,  such  as  model  of  ship,  course  steered  with  reference 
to  the  wind,  condition  of  sea,  &c. 

INSTRUCTIONS    FOR    KEEPING   THE   LOG. 

Art.  S4.  In  all  the  columns  intended  for  figures  never  use  "ditto"  marks;  in  those  intended  for  letters 
o.lways  use  "ditto"  marks  for  observations  that  are  consecutively  the  same. 

Al't.  85.  Only  very  light  airs  flying  all  round  the  compass  are  to  be  designated  as  "varidlih''^ ;  when  the 
wind  has  any  appreciable  force,  and  can  possibly  be  averaged  for  the  hour,  then  its  magnetic  direction  is  to  be 
recorded  to  the  nearest  whole  point.  The  indefinite  expression  Sd.  and  Wd.,  for  example,  or  any  fraction  of  a 
point,  must  never  be  entered  in  the  log. 

Art.  86.    The  readings  of  the  mercurial  luiroineter  only  shall  l)e  entered  in  the  log. 

Art.  87.  When  the  psychrometer  of  the  Signal  Service  is  not  furnished  to  ships  the  method  of  mounting 
a  wet  and  a  dry  Indb  thermometer  in  a  lattice  case,  as  described  in  Art.  78,  will  be  adopted. 

Art.  88.  The  permanent  temperature  oi  i\\e  sea- water  is  the  object  sought;  and  to  attain  this,  freed  from  all 
accidental  changes,  such  as  heating  by  the  sun,  friction  of  the  wind  on  the  waves,  settling  of  rain-water  on  the  sur- 
face, &c.,  the  bucket  in  which  the  water  is  drawn  should  be  weighted  and  sunk  to  at  least  a  fathom  below  the  sur- 
face ;    i/ie  thermometer  should  remain  at>out  one  minute  in  the  ivater  before  reading. 

Art.  89.  The  columns  headed  "  State  of  the  weather  by  symbols  ",  "  Forms  of  clouds  ",  "  Prop,  of  clear 
sky",  are  very  important ;  the  Symbols  in  Arts.  80  and  81  are  ample  for  fully  and  accurately  describing  every 
phase  of  weather,  and  if  a  careful  selection  of  them  be  made,  these  columns,  in  connection  with  the  others,  leave 
nothing  to  Ije  desired  as  a  meteorological  record. 

Art.  90.  In  the  columns  headed  "  Recortl  of  Sail",  state  at  the  top  whether  under  sail  or  steam,  or  both  ; 
if  under  sail,  its  amount.  When  a  change  is  made,  such  as  setting,  reefing,  or  taking  it  in,  enter  it  opposite  the 
hour  of  its  occurrence. 

Art.  91.  The  position  by  account  should  always  be  entered,  and  that  I)y  observation,  whenever  taken  ;  thf 
word  North  or  South  is  to  precede  the  latitude,  and  flast  or  West  the  longitude,  as  the  case  recjuires. 


28  INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 

Art.  92.  Currents. — This  is  probably  the  most  difficult  item  of  all  to  give  correctly.  It  is  information 
regarding  the  />i'r//itr//c'/if  a/nr/ifs  of  the  ocean  that  is  sought,  and  in  order  to  discriminate  between  the  permanent 
and  the  temporary  the  following  probable  causes  of  currents  in  general  may  be  briefly  glanced  at : 

1.  Tcmpci-iXtitrc. — Of  two  contiguous  bodies  of  water,  one  hot  the  other  cold,  the  latter  being  specifically  the 
heavier  will  displace  the  former,  and  hence  a  permanent  current  is  established. 

2.  Evaporation. — Since  no  salts  are  taken  up  in  the  vapor,  a  body  of  water  from  which  great  evaporation  takes 
place  will  be  specifically  heavier  than  an  adjoining  one  that  gives  off  less  vapor,  and  so  a  continuous  flow  from  the 
dense  to  the  light  fluid  will  be  maintained. 

3.  U^inds. — In  a  gale,  the  waves  roll  one  after  anotlier  in  huge  volumes  toward  the  point  to  wliich  the  wind 
blows  ;  the  friction  of  tlic  wind  upon  the  water  produces  a  temporary  set  to  leeward.  In  the  zone  of  trade-winds 
tliis  set  is  no  doubt  constantly  to  the  westward.  In  the  region  of  monsoons  the  set  should  be  ivilh  the  monsoon, 
changing  wlien  that  changes. 

4.  Difference  of  barometric  pressure. — In  gales  of  wind  it  is  common  for  the  liarometer  to  fall  from,  say  30.20 
to  29.70 — half  an  inch  in  less  than  a  day,  and  while  the  ship  is  passing  over  a  comparatively  small  extent  of  ocean. 

Take  a  very  extreme  case,  merely  for  illustration:  Suppose  two  contiguous  square  miles  of  ocean,  tlie  barom- 
eter standing  30.20  over  one  of  them,  and  29.70  over  the  other.  This  difference  of  half  an  inch  in  the  barometer 
is  equal  to  a  difference  of  about  one-quarter  of  a  pound  pressure  per  square  inch  of  surface,  or  36  pounds  per  square 
foot. 

Taking  6,086  feet  as  the  side  of  a  square  mile,  it  will  contain  37,039,396  square  feet:  each  square  foot  sus- 
tains a  difference  of  pressure  of  36  pounds,  so  that  there  are,  in  all,  1,333,418,256  pounds  more  pressure  on  the 
square  mile  over  which  the  barometer  stands  30.20  tlian  on  the  one  over  which  it  stands  29.70.  It  is  evident  that 
in  order  to  attain  an  equality  of  level  a  very  decided  set  must  take  place  from  the  former  square  mile  toward  the 
latter. 

Now,  instead  of  confining  the  case  to  tlie  impossible  small  area  of  two  square  miles,  lei  us  suppose  a  gradual 
fall  of  Ijarometer  from  one  part  of  the  ocean  to  the  other,  such  a  fall,  in  fact,  over  such  an  area  as  comes  often 
within  the  experience  of  every  naval  officer,  and  it  seems  reasonable  that  waves  of  the  ocean,  like  those  of  the  air, 
only  smaller  and  more  sluggish,  are  consequent  upon  every  change  of  the  barometer.  These,  however,  are  all 
temporary  currents. 

5  Rotatioti  of  the  tv?;///,  — First,  suppose  the  earth  at  rest ;  then  conceive  it  to  revolve  from  west  to  east,  as  at 
present.  On  starting,  the  water  of  the  ocean  would,  owing  to  its  inertia,  recede  from  the  western  shores  of  all  the 
continents,  and,  as  the  earth  continued  to  revolve,  it  would  flow  to  the  westward;  for  two  reasons,  however,  it 
would  be  confined  to  equatorial  regions  :  i,  the  centrifugal  force  there  being  greatest ;  and,  2,  because  the  meridians 
converge  as  we  near  the  poles. 

This  second  reason  will  appear  the  more  forcible,  if  we  suppose  a  body  of  water  of  5°  area  and  any  depth  to 
set  out  from  the  Equator  toward  either  pole.  At  every  remove  it  would  find  fewer  miles,  feet,  and  inches,  less 
linear  breadth  and  width,  in  a  surface  of  5'  square.  The  depth  remaining  constant,  its  volume  would  be  too  great 
for  an  area  of  5-  square  in  latitude  30'- ;  still  more  so  for  one  in  latitude  60'-,  and  so  on.  This  constant  crowding 
in  extra- tropical  zones  would  therefore  constitute  an  opposing  force  sufficient  to  confine  tlie  flow  of  the  water  to  a 
zone  where  its  volume  would  undergo  no  change  of  shape,  that  is,  the  equatorial  zone.  Arri\'ing,  tlien,  at  the 
eastern  shores  of  the  continents  to  the  westward  of  those  from  which  it  started,  at  the  North  and  Soutii  American 
shores  ;  for  instance,  having  started  from  Europe  and  Africa,  and  being  banked  up  by  constantly  arriving  volumes, 
it  would  be  forced  to  the  northward  and  to  the  southward  along  the  coast  line  of  each  continent;  it  would  then 
flow  to  the  eastward  in  high  latitudes  until  reaching  the  western  shores  of  the  continent  from  which  it  started, 
where,  owing  to  the  divergence  of  tlie  meridiaas  toward  the  Equator  and  the  greater  centrifugal  force  tliere,  it 
would  flow  from  the  north  and  the  south  along  the  shore  lines  of  the  continents  until  reaching  the  ecpiatoriai  zone, 
where  it  would  again  start  westward  on  its  circuit.  Imagine  tliis  system  of  circulation  once  set  up,  and  nothing  is 
more  natural  than  that  it  should  continue  while  the  earth  revolves.  Indeed,  glance  at  any  current  chart  of  the 
world,  and  in  a  most  striking  way  is  this  general  system  of  circulation  presented  to  the  view. 

It  will  now  be  seen  how  important  a  part  the  thermometer  and  hydrometer  play  in  the  discovery  of  currents. 
By  the  first  a  difference  of  temperature,  and  by  the  second  a  difference  of  density,  is  quickly  detected;  and,  if  a 
decided  difference  of  either  nature  is  found,  a  permanent  current  may  be  fairly  inferred.  A  consiileration  of  the 
winds,  whether  an  accidental  gale,  the  constant  trades,  or  the  seasonal  monsoon,  may  lead  us  to  deduce  intelligently 
whether  a  set  that  may  have  been  experienced  for  days  is  a  temporary  surface  flovv'  or  n  permanent  current.  So, 
also,  keeping  in  view  the  range  of  the  barometer  for  a  few  days — the  locality  and  amount  of  its  rise  and  fall — may 
help  us  in  deciding  whether  a  certain  set  be  due  to  its  extreme  range  or  not. 

A  consideration  of  the  rotation  of  the  earth  is  of  assistance  only  in  d'etermining  the  general  direction  of  the 
great  ocean  currents 

The  usual  practice  among  navigators  is  to  ascribe  to  current  the  whole  difference  between  the  position  by 
observation  and  that  by  account.  But  nothing  can  l)e  more  erroneous.  Consider  the  errors  in  observing  and 
calculating  to  wliich  the  position  by  observation  is  liable;  consider  also  the  gross  errors  which  affect  the  position 
by  account;  the  frequent  incorrectness  of  the  log-lines  and  sand-glasses;  the  inaccuracy  of  steering;  the  number 
of  watch  officers  that  judge  of  the  speed,  the  course,  and  the  leeway ;  and  would  it  not  be  most  strange  if  the  posi- 
tions by  the  two  methods  did  coincide?  In  addition  to  these  reasons,  if  a  ship  be  close-hauled  by  the  wind,  it  is 
evident  tliat  the  liability  to  inaccuracy  in  the  reckoning  is  very  much  greater  than  when  steering  a  course  with  the 
wind  free. 

The  Navigator  should  always  insure  the  absolute  accuracy  of  the  log-lines  and  sand-glasses  liefore  leaving 
port — the  length  of  a  t-cnot  should  be  rigo'viisly  the  proportional  part  of  a  mile  that  the  sand-glass  is  of  an  hour  ;  the 
watch  officers  should  agree  ujion  a  uniform  method  of  heaving  the  log  and  estimating  the  speed,  and  great  care  be 
taken  i  1  the  steering. 

Even  with  these  ]irecaulions,  it  should  be  remembered  that  there  is  still  some  inaccuracy  in  both  tlie  position 
by  account  and  that  by  observation,  and,  besides,  that  one  of  the  causes  heretofore  enumerated  as  producing  tem- 
porary currents  may  be  at  ]5lay ;  so  when  a  difference  of  even  5'  in  the  latitudes,  in  the  longitudes,  or  in  both, 
occurs,  it  may  be  safe  to  attribute  it  to  accidental  causes. 

^Vhen  the  difference  exceeds  5'  and  is  quite  regular  in  both  direction  and  amount,  especially  if  this  evidence 
of  a  current  be  corroborated  by  a  change  in  the  tem])erature  or  density  of  the  water,  then,  and  only  after-care  fully 
7aeighing  all  the  circumstances,  should  the  Navigator  enter  in  the  log  that  there  is  a  current.  It  should  be  given 
in  knots  and  tenths  of  a  knot  per  hour,  and  its  set  to  a  definite  whole  point. 

Art.  03.     The  deviation  of  tlie  compass  to  be  determined  by  sivinging  ship  before  leaving  port. 

When  the  compass-error  is  determined  at  sea  by  azimullis  or  amplitudes — and  this  must  be  done  whenever 


Fold 
Out 


28  INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 

Art.  02.  Currents. — This  is  probably  the  most  difficult  item  of  all  to  give  correctly.  It  is  information; 
regarding  \\\c  pcrniaitoit  currents  of  the  ocean  that  is  sought,  and  in  order  to  discriminate  between  the  permanent 
and  the  temporary  the  following  probable  causes  of  currents  in  general  may  be  briefly  glanced  at : 

1.  Temperature. — Of  two  contiguous  bodies  of  water,  one  hot  the  other  cold,  the  latter  being  specifically  the 
heavier  will  displace  the  former,  and  hence  a  permanent  current  is  established. 

2.  Evaporation. — Since  no  salts  are  taken  up  in  the  vapor,  a  body  of  water  from  which  great  evaporation  takes  , 
place  will  be  specifically  heavier  than  an  adjoining  one  that  gives  off  less  vapor,  and  so  a  continuous  flow  from  the  \ 
dense  to  the  light  fluid  will  be  maintained. 

3.  Winds. — In  a  gale,  the  waves  roll  one  after  another  in  huge  volumes  toward  the  point  to  which  the  wind 
blows  ;  the  friction  of  the  wind  upon  the  water  produces  a  temporary  set  to  leeward.     In  the  zone  of  trade-winds  i 
this  set  is  no  doubt  constantly  to  the  westward.     In  the  region  of  monsoons  the  set  should  be  iDith  the  monsoon, 
changing  when  that  changes. 

4.  Difference  of  barometric  pressure. — In  gales  of  wind  it  is  common  for  the  barometer  to  fall  from,  say  30.20 
to  29.70 — half  an  inch  in  less  than  a  day,  and  while  the  ship  is  passing  over  a  comparatively  small  extent  of  ocean. 

Take  a  very  extreme  case,  merely  for  illustration:   Suppose  two  contiguous  square  miles  of  ocean,  the  barom- 
eter standing  30.20  over  one  of  them,  and  29.70  over  the  otlrer.     This  difference  of  half  an  inch  in  the  barometer 
is  equal  to  a  difference  of  about  one-quarter  of  a  pound  pressure  per  square  inch  of  surface,  or  36  pounds  per  square  i' 
foot.  I  ■ 

Taking  6,086  feet  as  the  side  of  a  square  mile,  it  will  contain  37,039,396  square  feet:   each  square  foot  sus-> 
tains  a  difference  of  pressure  of  36  pounds,  so  that  there  are,  in  all,  1,333,418,256  pounds  more  pressure  on  the 
square  mile  over  which  the  barometer  stands  30.20  than  on  the  one  over  which  it  stands  29.70.     It  is  evident  that  ' 
in  order  to  attain  an  equality  of  level  a  very  decided  set  must  take  place  from  the  former  s<juare  mile  toward  the 
latter. 

Now,  instead  of  confining  the  case  to  tlie  impossible  small  area  of  two  square  miles,  lei  us  suppose  a  gradual 
fall  of  barometer  from  one  part  of  the  ocean  to  the  other,  such  a  fall,  in  fact,  over  such  an  area  as  comes  often 
within  the  experience  of  every  naval  officer,  and  it  seems  reasonable  that  waves  of  the  ocean,  like  those  of  the  air, 
only  smaller  and  more  sluggish,  are  consequent  upon  every  change  of  the  barometer.  These,  however,  are  all 
temporary  currents. 

5  Rotation  of  the  eart/i.  — First,  suppose  the  earth  at  rest ;  then  conceive  it  to  revolve  from  west  to  east,  as  at 
present.  On  starting,  the  water  of  the  ocean  would,  owing  to  its  inertia,  recede  from  the  western  shores  of  all  the 
continents,  and,  as  the  earth  continued  to  revolve,  it  would  flow  to  the  westward ;  for  two  reasons,  however,  it 
would  be  confined  to  equatorial  regions  :  i,  the  centrifugal  force  there  being  greatest ;  and,  2,  because  the  meridians 
converge  as  we  near  the  poles. 

This  second  reason  will  appear  the  more  forcible,  if  we  suppose  a  body  of  water  of  5°  area  and  any  depth  to 
set  out  from  the  Equator  toward  either  pole.  At  every  remove  it  would  find  fewer  miles,  feet,  and  inches,  less 
linear  breadth  and  width,  in  a  surface  of  5^'  square.  The  depth  remaining  constant,  its  volume  would  be  too  great  ■ 
for  an  area  of  5'^  square  in  latitude  30'^';  still  more  so  for  one  in  latitude  60*^,  and  so  on.  This  constant  crowding 
in  extra- tropical  zones  would  therefore  constitute  an  opposing  force  sufficient  to  confine  the  flow  of  the  water  to  a 
zone  where  its  volume  would  undergo  no  change  of  shape,  that  is,  the  equatorial  zone.  Arriving,  then,  at  the 
eastern  shores  of  the  continents  to  the  westward  of  those  from  which  it  started,  at  the  North  and  South  American 
shores  ;  for  instance,  having  started  from  Europe  and  Africa,  and  being  banked  up  by  constantly  arriving  volumes, 
it  would  be  forced  to  the  northward  and  to  the  southward  along  the  coast  line  of  each  continent;  it  would  then 
flow  to  the  eastward  in  high  latitudes  until  reaching  the  western  shores  of  the  continent  from  which  it  started, 
where,  owing  to  the  divergence  of  the  meridiaas  toward  the  Equator  and  the  greater  centrifugal  force  there,  it 
would  flow  from  the  north  and  the  south  along  the  shore  lines  of  the  continents  until  reaching  the  equatorial  zone, 
where  it  would  again  start  westward  on  its  circuit.  Imagine  this  system  of  circulation  once  set  up,  and  nothing  is 
more  natural  than  that  it  should  continue  while  the  earth  revolves.  Indeed,  glance  at  any  current  chart  of  the 
world,  and  in  a  most  striking  way  is  this  general  system  of  circulation  presented  to  the  view. 

It  will  now  be  seen  how  important  a  part  the  thermometer  and  hydrometer  play  in  the  discovery  of  currents. 
By  the  first  a  difference  of  temperature,  and  by  the  second  a  difference  of  density,  is  quickly  detected;  and,  if  a 
decided  difference  of  either  nature  is  found,  a  permanent  current  may  be  fairly  inferred.  A  consideration  of  the 
winds,  whether  an  accidental  gale,  the  constant  trades,  or  the  seasonal  monsoon,  may  lead  us  to  deduce  intelligently  »: 
whether  a  set  that  may  have  l)een  experienced  for  days  is  a  temporary  surface  flow  or  a  permanent  current.  So, 
also,  keeping  in  view  the  range  of  the  barometer  for  a  few  days — the  locality  and  amount  of  its  rise  and  fall — may 
help  us  in  deciding  whether  a  certain  set  be  due  to  its  extreme  range  or  not. 

A  consideration  of  the  rotation  of  the  earth  is  of  assistance  only  in  determining  the  general  direction  of  the 
great  ocean  currents 

The  usual  practice  among  navigators  is  to  ascribe  to  current  the  whole  difference  between  the  position  by 
observation  and  that  by  account.     But  nothing  can  be  more  erroneous.     Consider  the  errors  in  observing  and 
calculating  to  which  the  position  by  observation  is  liable;  consider  also  the  gross  errors  which  affect  the  position 
l)y  account;   the  frequent  incorrectness  of  the  log-lines  and  sand-glasses;   the  inaccuracy  of  steering;   the  number  fi 
of  watch  officers  that  judge  of  the  speed,  the  course,  and  the  leeway ;   and  would  it  not  be  most  strange  if  the  posi-  ;> 
>ions  by  the  two  methods  did  coincide?     In  addition  to  these  reasons,  if  a  sliip  be  close-hauled  by  the  wind,  it  is  ji 
evident  that  the  liability  to  inaccuracy  in  the  reckoning  is  very  much  greater  than  when  steering  a  course  with  the  |1 
wind  free. 

The  Navigator  should  always  insure  the  absolute  accuracy  of  the  log-lines  and  sand-glasses  before  leaving; 
port — the  length  of  a  tcnol  should  he  rigvonsly  the  proportional  part  of  a  mile  that  the  sand-glass  is  of  an  hour  ;   the 
watch  officers  should  agree  upon  a  uniform  method  of  heaving  the  log  and  estimating  the  speed,  and  great  care  be  u 
taken  i  1  the  steering. 

Even  with  these  jirecautions,  it  should  be  remembered  that  there  is  still  some  inaccuracy  in  both  the  position 
by  account  and  that  by  observation,  and,  besides,  that  one  of  the  causes  heretofore  enumerated  as  producing  tem- 
porary currents  may  be  at  play;  so  when  a  difference  of  even  5'  in  the  latitudes,  in  the  longitudes,  or  in  both, 
occurs,  it  may  be  safe  to  attribute  it  to  accidental  causes. 

When  the  difference  exceeds  5'  and  is  quite  regular  in  both  direction  and  amount,  especially  if  this  evidence 
of  a  current  be  corroborated  by  a  change  in  the  temperature  or  density  of  the  water,  then,  and  only  after^carefitlly 
weighing  all  the  circuDistanees,  should  the  Navigator  enter  in  tlie  log  that  there  is  a  current.  It  should  be  given 
in  knots  and  tenths  of  a  knot  pei  hour,  and  its  set  to  a  definite  whole  point. 

Art.  93.     The  deviation  of  the  compass  to  be  determined  by  swinging  ship  before  leaving  port. 

When  the  compass-error  is  determined  at  sea  by  azimuths  or  amplitudes — and  this  must  be  done  whenever 


I 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION.  29 

possible — lhe»(leviation  for  the  particular  course  the  ship  was  heading  at  the  time  shall,  in  all  instances,  be  separ- 
ated from  the  wliole  compass-orror,  and  only  the  7'ariatio)i  proper  shall  be  entered  in  the  h{i;:  Write  before  tlie  vari- 
ation tlie  latitude  and  longitude  in  which  it  was  determined. 

Al"f.  941.  The  heading  of  the  log  should  show  the  names  of  the  ports  between  which  the  passage  is  beingr 
made,  and  the  day  of  the  week,  as  well  as  the  day  of  the  month. 

Art.  05.  Tides. — Instead  of  writing  "At  anchor  "  in  the  column  "  Courses  steered,"  write  opposite  each  hour 
the  nearest  whole  point  of  the  compass  which  the  ship  was  headed  by  the  tide,  and,  at  the  beginning  of  each  tide,  the 
word  "Flood"  or  "Ebb,"  as  the  case  may  1)6.  When  moored  head  and  stern,  state  it  so,  at  head  of  column 
"Courses  steered."  v\  hen  the  ship  heads  practically  the  same  point  tluring  a  v\  hole  tide,  enter  this  point  at  the 
beginning  of  the  tide,  and  ditto  marks  for  the  other  hours.  Enter  in  the  "  Remarks"  the  exact  time  of  change  of 
tide,  and  how  long  it  took  the  ship  to  swing  from  one  tide  to  the  other.  Once  a  watch,  when  the  tide  is  strongest, 
determine  its  velocity  by  heaving  the  log,  and  enter  it  in  the  "Remarks."  Each  day,  the  Navigator  shall  enter 
after  all  the  remarks,  from  the  Nautical  Almanac,  the  phase  of  the  moon,  and  her  declination  (N.  or  S. )  to  the 
■  nearest  degree,  at  midnight,  local  time. 

Art.  96.  All  the  meteorological  information,  such  as  particulars  of  wind  and  weather,  &'c.,  shall  he  the  frst 
item  oitered  in  the  '■'Remarks"  of  each  watch.  The  wind  and  weather  should  be  more  minutely  described  than  has 
been  the  custom.  The  character  and  frequency  of  squalls  are  to  be  entered  in  the  "  Remarks:"  all  that  necessi- 
tate clewing  down  the  topsails  to  be  denominated  "  Heavy;"  those  to  which  lo'gallant  sails  are  taken  in,  "  Mod- 
erate;" and  those  to  which  royals,  "  Light."  Also  enier  the  latitude  and  longitude  of  meeting  or  losing  the  trades, 
monsoons,  or  other  constant  and  well-defined  winds.     State  whether  steering  a  course  or  "  full  and  by." 

METHOD    OF   COMPILING   THE    DATA. 

Art.  97.    Forms  A,  B,  E,  and  H  are  supplied  with  ihe  Log-Book,  of  which  Form  Z  is  a  sample. 

Form  A,  the  Diagram  of  Squares,  is  a  Mercator's  projection  of  those  parts  of  the  ocean  most  frequently 
traversed,  comprising  all  the  surface  of  the  globe  between  the  70th  parallels  of  latitude  N.  and  S.,  and  divided  into 
squares  of  5-'  of  latitude  by  5'-''  of  longitude.  They  are  numbered  consecutively  from  I  to  1667,  so  that  either  by 
its  number,  or  by  its  limits  in  latitude  and  longitude,  the  area  of  ocean  covered  by  any  particular  square  can  be 
designated. 

Art.  98.  Suppose  a  ship  to  sail  from  Acapuico  for  San  Francisco,  intending  to  take  advantage  of  the  winds 
alone  to  make  the  passage.  She  would  cross  certain  squares,  say,  numbers  106,  105,  104,  103,  102,  84,  ?>t^,  82,  64, 
:  63,  and  45,  with  the  wind  generally  from  the  Northward  and  Eastward :  toward  the  northern  limit  of  square  45 
she  would  probably  get  Northwesterly  winds  and  stand  in  for  San  Francisco  across  squares  No.  46,  28,  29,  and  30. 
The  length  of  time  in  each  square  would  vary  according  to  her  course  across  it ;  but,  however  many  hours  she  may 
be  in  any  square — whether  three  or  three  hundred — the  observations  for  those  hours  ai-e  to  be  compiled  from  ihe  log- 
book on  ONE  blank  of  Form  B. 

Art.  99.  In  order  to  prepare  the  log-book  for  this,  the  limits  of  all  the  squares  crossed  by  the  ship  must 
be  worked  up  and  entered  in  the  margin  of  the  page.  Take  the  accompanying  pages  "Z"  of  a  log-book  as  a 
sample.  The  position  by  observation  at  noon  of  January  22d  places  the  ship  (by  reference  to  Form  A)  in  square 
No.  28;  it  is  now  necessary  to  ascertain  at  what" hour  she  entered  the  square;  so,  working  back  from  the  noon 
position  by  observation  (in  every  instance  correcting  the  courses  so  as  to  use  only  true  courses),  it  is  found  that  she 
crossed  the  southern  limit  of  the  square,  viz,  the  35th  parallel,  in  longitude  134*^  21'  W.,  between  7  and  8  a.  m.  of 
the  22d.  The  position  by  observation  at  noon  of  the  23d  still  places  her  in  square  No.  28,  and  a  glance  at  the 
courses  steered  between  the  two  noon  positions  shows  the  ship  to  have  been  in  square  No.  28  during  the  whole 
time.  At  noon  of  the  24lh,  she  was  in  latitude  36-  21'  N.,  longitude  128-  21'  W.— therefore  (w/ of  square  28  and 
in  square  29.  The  intervening  courses  show  that  she  must  have  crossed  the  eastern  limit  of  square  28.  Working 
forward  from  the  noon  position  by  observation  of  the  23d,  it  is  found  that  she  crossed  the  •130th  meridian— the 
eastern  limit — in  latitude  36^-  15'  N  ,  between  11  and  12  p.  m.  of  the  23d.  Now,  drawing  heavy  lines  at  the  hours 
of  entrance  and  exit,  writing  the  latitude  and  longitude  opposite  them,  and,  finally,  entering  the  number  of  the 
square  in  the  margin,  the  preparation  of  the  log-book  is  complete  so  far  as  this  square  is  concerned.  The  whole 
of  every  passage  is  to  be  similarly  treated;  the  limits  of  all  the  squares  traversed  to  be  worked  up,  heavy  lines 
drawn  between  the  hours  \\here  these  limits  fall,  the  latitude  and  longitude  written  opposite  these  lines,  and  the 
number  of  each  square  in  the  margin. 

Art.  100.  The  statement  that  only  one  blank  of  Form  B  is  to  be  used  for  each  square  is  subject  to  a  single 
exception.  Suppose  a  ship  to  enter  a  square  on  the  30///  September,  for  example,  and  leave  it  on  the  \st  October. 
In  this  case  tiw  blanks  would  be  necessary,  one  for  the  hours  of  each  month  in  the  square.  Thus,  the  observations 
on  each  blank  are  limited  in  space  to  one  of  the  squares  shown  on  Form  A,  and  in  time  to  the  same  month  of  the 
year.  A  mere  inspection  of  Form  B  is  almost  sufficient  to  understand  the  method  of  making  the  compilation,  but 
the  procedure  may  be  briefly  described,  as  follows :  By  Form  A  it  is  seen  that  the  parallels  •35^  N.  and  40'-'  N. 
and  the  meritlians  130^  W.  and  135-  W.  limit  scpiare  No  28;  by  "Z,"  the  date  in  the  square,  name  of  the  ship, 
and  the  time  of  beginning  and  finishing  her  log-book  are  seen ;  also,  that  the  time  in  the  square  was  40  hours, 
viz,  from  7  a.  m.,  January  22d,  to  1 1  p.  m.  of  the  23d.  The  small  chart  on  Form  B  is  one  of  the  5  sciuares  of 
Form  A  on  a  larger  scale.  It  is  divided  by  lines  at  every  whole  degree,  thus  forming  25  subsquares  of  i^  each. 
These  are  lettered  for  convenience  of  reference.  The  dots  on  the  lines  are  30'  marks,  to  facilitate  plotting  the 
ship's  track. 

The  latitudes  and  longitudes  of  entrance  and  exit,  together  with  the  intervening  noon  positions,  afford  the 
requisite  points  for  laying  down  the  track,  and  an  arrow-head  at  its  terminus  indicates  the  direction. 

As  the  Navigator  works  up  the  position  at  8  a.  m.  and  8  p.  m.  he  should  enter  them  in  the  margin  of  the  log- 
book for  additional  points  in  determining  the  track. 

The  current  arrows  are  explained  by  a  little  note  on  the  blank  itself.  To  compile  the  wind  observations,  it  is 
seen  that  on  the  22d  the  wind  was  seven  hours  from  N.  W.,  viz,  from  8  a.m.  to  2  p.  m. ;  on  the  23d  it  was  six 
hours  from  the  same  point,  viz,  at  6  a.  m.  and  from  11  a.  m.  to  3  p.  m.,  making  a  total  of  thirteen  hours,  which  is 
entered  on  Form  B,  opposite  N.  W.  The  force  was  very  variable,  however,  but  a  mean  of  the  thirteen  hourly 
forces  is  struck  and  entered  as  6,  opposite  N.  W.  Next,  on  the  22d,  the  wind  was  nine  hours  from  N.  W.  by  W., 
viz,  from" 3  to  11  p.  m  It  was  not  again  from  this  point  while  the  ship  was  in  this  square,  so  9  is  entered  on  the 
blank  opposite  N.  W.  by  W.,  and  a  mean  of  the  nine  hourly  forces  as  5. 

At  midnight  of  the  22d  it  was  one  hour  from  W.  S.  W.,  force  6  ;  at  i  and  2  a.  m.  of  the  23d  it  was  two  hours 
from  W.,  force  7;  at  3  and  4  a.  m.  it  was  two  hours  from  W.  by  S.,  force  7;  and  at  5  a.  m.  it  was  one  hour  from 
N.  by  W.,  force  7;  all  of  which  are  duly  transcribed  on  the  blank.     Finally,  from  7  to  10  a.  m.  of  the  23d,  fou'- 


30 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


liours,  the  wind  was  N.  W. by  N.,  and,  again,  from  4  to  ii  p.m.,  eight  hours,  from  same  point  making  a  total  of^ 
twelve  hours,  with  a  mean  of  the  forces  as  7.     The  summation  of  all  these  hours  is  forty,  which  proves  the  cor- 
r  ectness  of  the  work. 

Had  there  been  hours  of  "variable  winds"  and  "calms"  interspersed  throughout  these  forty  hours,  they 
should  have  been  entered  in  their  proper  places  on  the  blank,  and  then  the  summation  of  the  winds,  variables, 
and  calms,  should  be  40. 

To  compile  the  barometric  and  thermometric  observations  see  Form  B. 

For  the  daily  ranges,  take  the  difference  between  the  maximum  and  minimum  of  each  day,  then  the  sum  of 
these  differences,  and  divide  by  tlie  number  of  days  in  the  square.  In  reckoning  the  days  for  this  purpose,  when 
the  ship  has  been  in  a  square  during  the  12  a.m.  hours  or  the  12  p.m.  hours  of  any  day,  take  the  difTerence 
between  the  maximum  and  minimum  recorded  during  the  whole  twenty-four  hours  of  that  date.  For  instance,  on 
January  23  (see  Z),  if  the  maximum  or  minimum  of  any  quantity  had  occurred  previous  to  7  a.m.,  altliough  out- 
side of  square  28,  still  it  would  be  used  to  get  the  difference  that  constitutes  the  daily  range.  But  if  tlie  limit  35° 
N.  fell  between  4  and  5  p.  m.  of  the  22(1,  then  the  daily  ranges  would  be  used,  not  for  square  28,  but  for  the  one 
in  which  tlie  greater  portion  of  the  day  was  passed. 

The  daily  ranges  are  to  be  carried  to  hundredths  of  an  inch  and  tenths  of  a  degree.  For  the  record  of  squalls, 
every  hour  in  which  the  letter  ^  occurs  is  called  an  hour  of  squalls,  and  whether  it  is  to  be  called  "Heavy,' 
"Moderate,"  or  "Light"  must  be  judged  from  the  "Remarks."  Likewise,  every  hour  in  which  the  letter/ 
occurs  is  called  an  hour  of  fog,  and  so  entered.  So,  also,  every  hour  in  which  the  letter  w,  d,  />,  or  ;-  occurs  is  to 
be  placed  under  the  heading  "  Rain"  or  "  Mist."  Every  phase  of  weather  experienced  in  the  square  is  to  be 
denoted  by  Its  proper  symbol ;  also  the  various  forms  of  clouds  by  their  symbols.  The  mean  of  all  the  hourly 
observations  of  clear  sky  is  to  be  entered. 

Only  two  places  are  given  for  magnetic  observations,  since,  in  a  5°  square,  this  quantity  is  seldom  likely  to 
vary  so  much  as  to  require  more.  The  latitude  and  longitude  in  which  the  variation  was  determined,  is  to  be 
entered  as  in  the  sample  copy  of  Form  B.  Where  several  magnetic  observations  are  taken  within  a  small  area, 
and  they  do  not  differ  materially,  the  mean  of  all  is  to  lie  given.  In  all  instances,  as  heretofore  stated,  it  is  the  varia- 
tion  alone,  separated  from  the  whole  compass  error  by  applying  the  deviation  for  tlie  particular  course  the  ship  tvas  head- 
ing 7vhe)i  the  obsei-'ation  toas  taken,  that  must  be  given  on  Fonn  B,  as  mell  as  in  the  log-book. 

Art.  101«  Form  B  may  be  regarded  as  giving  the  abstract  features  of  a  5°  square  of  ocean  surface,  and, 
in  order  that  it  may  do  this  accurately.  Remarks  are  essential  to  complete  the  outline  given  in  the  columns.  The 
nature  of  the  Remarks  required  will  be  easily  understood  by  comparing  those  on  the  sample  of  Form  B  with  the 
sheets  "Z  "  of  the  log-book  from  which  they  are  deduced. 

It  is  required  to  give  such  a  minute  account  of  the  wind  and  weather  in  each  subsquare  (referring  to  it  by  its 
letter)  as  will  fully  illustrate  what  the  ship  experienced.  So,  also,  the  veering  of  the  wind  and  its  character,  and 
the  corresponding  changes  of  weather  and  temperature,  with  the  locality  of  their  occurrence,  are  fully  given  in  the 
Remarks.  Besides  the  foregoing,  the  following  details  are  to  be  given  in  the  remarks,  viz :  The  latitude  and 
longitude  in  which  a  gale  began  ;  the  veerings  of  the  wind,  with  its  duration  and  force  from  each  point,  and  the 
accompanying  changes  of  barometer  and  thermometer ;  and  the  latitude  and  longitude  in  which  it  ceased ;  also 
the  condition  of  wind,  weather,  barometer,  and  thermometer  for  at  least  twenty-four  hours  previous  to  such  a  gale; 
tide-rips;  discolored  water ;  sea-weed;  icebergs;  specific  gravity  of  sea-water,  and  any  sudden  change  in  its  tem- 
perature and  density;  particulars  of  currents,  when  such  are  judged  to  exist;  longitude  of  crossing  the  line; 
latitude  and  longitude  of  meeting  or  losing  the  trades,  monsoons,  or  any  other  constant  and  well-defined  winds; 
distance  from  shore  the  land  and  sea  breezes  are  felt,  their  strength  and  time  of  setting  in ;  and,  in  fact,  any  other 
matter  of  information  the  Navigator  deems  of  value  in  contributing  to  a  knowledge  of  the  ocean. 

Art.  103.  When  a  cyclone  or  hurricane  occurs,  a  very  careful  and  frequent  observation  of  the  instruments, 
wind,  weather,  sea,  &c.,  shall  be  kept  by  some  officer — by  the  A^avigator  or  Alaster  himself ,  if  practicable — so  that 
accurate  information  regarding  these  meteors  may  be  collected.  After  the  record  of  the  storm  is  transferred  to  the 
log-book,  it  will  be  compiled  on  Form  1>  in  the  manner  of  the  one  there  given.  It  will  be  seen  that  this  is  a  tran- 
script of  such  parts  of  the  log  as  are  essential  to  a  full  history  of  the  storm. 

The  basis  of  arrangement  in  the  log  is  by  hours  ;  here  it  is  by  the  veering  of  the  wind.  For  instance,  the 
wind  was  first  from  the  S.  E.  for  two  hours ;  it  then  veered  to  S.  E  by  E.  and  was  steady  one  hour ;  next  to  S. 
by  E.  and  was  steady  one  hour ;  again  to  E.  S.  E.  and  was  steady  five  hours,  and  so  on.  The  data  in  the  other 
columns  are  given  for  the  periods  the  wind  was  from  each  point.  A  short  account  of  wind,  weather,  swell,  run 
of  ship,  &c.,  previous  to,  during,  and  after  the  cyclone,  should  be  given,  as  in  the  sample,  and  a  little  chart  with 
the  cyclone  plotted  should  accompany  Form  B. 

Art.  103.  The  compilation  on  Form  B  breaks  up  the  observations  of  a  passage  and  groups  them  by 
squares  ,  this  is  necessary  in  order  to  use  them  for  the  meteorological  charts  for  which  they  are  intended.  But  it 
is  also  desirable  to  l^five  a  continuous  record  of  the  passage,  as  by  it  many  phenomena  that  would  otherwise  be 
maslted  are  made  apparent. 

Therefore,  Form  E  is  supplied.     It  is  ruled  for  a  fifteen-day  passage — one  line  for  each  day. 

When  the  passage  exceeds  this  number,  two  or  more  blanks  are  to  be  used,  and  parts  of  two  different  months, 
when  the  passage  so  occurs,  are  to  be  put  on  the  same  blank. 

A  mere  inspection  of  the  blank  is  sufficient  to  understand  it;  but,  to  be  entirely  explicit,  the  observations  of 
the  two  days  in  the  sheets  "Z"  are  filled  out  for  a  sample,  as  follows  : 


Jan. 22 
Jan. 23 

Sail. 
Sail. 

350  10'  N., 
134°  01'  W. 

36°  03'  N., 
131^  14'  W. 

N.W 

N.W.byN. 

4-6-8 
7-6 

Steady  in  direc, 

strong  q. 
Veering     from 

W.  to  N.  by 

W.,  q. 

30. 16  to  29.89 
29.65  to  29.92 

59°  58° 
58°  50° 

S6o  52° 
58°  50° 

Boisterous,  wet, 

cloudy. 
Cloudy  and  wet, 

then  clearing. 

By  the  "  Range"  of  the  barometer  in  this  and  Form  H  is  to  be  understood  the  daily  maximum  and  minimum 
attained;  but  these  are  to  be  given  in  the  order  in  which  they  occur;  for  instance,  in  the  above  example  from  Z, 
on  January  22(1,  the  barometer  was  falling,  so  the  record  stands  30.16  to  29.89.  On  the  23d  it  was  rising;  hence 
it  is  recorded  29.65  to  29.92 ;  and,  furthermore,  it  appears  by  this  method  that  during  the  night,  January  22d-23d, 
the  barometer  was  falling  from  29.89  to  29.65. 

Art.  104.  Form  H  is  for  harbor  observations — 07ie  line  for  each  day,  but  different  months  are  not  to  be  put 
on  the  same  blank ;  and  it  is  so  much  like  Form  E  that  no  example  for  filling  it  is  necessary. 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


31 


j  Remarks-»-%vliatever  their  nature,  ]')rovicled  they  add  to  a  knowledge  of  the  passage  or  of  the  harl)or  in  wliich 
ihe  ship  is  anchored — are  to  be  made  on  Forms  E  and  H.  This  gives  full  scope  for  imparting  a  variety  (jf  infor- 
mation regarding  the  ports  visited. 

Al't«  105.  From  the  Log-Book  and  these  Forms,  when  accumulat'^d  in  sufficient  numbers,  are  compiled 
hose  meteorological  charts  which  give  to  the  Navigator  that  graphical  representntion  of  liuud  and  uieather  \m\\\c\\ 
onveys  the  needed  information  so  much  more  forcibly  to  the  mind  than  volumes  of  printed  matter,  and  serves  as 
n  infallible  aid  in  the  selection  of  the  safest  and  shortest  track  to  be  followed. 

FORM  B. 

(for  meteorological  data.) 


Hydrographic  Office,  Meteorological  Department. 
Limits  of  Sqitari. 
Latitude,  35"  N.  to  40*^  N.  ;  "Longitude,  130'    W.  to  135'^  W. 
Date  ship  was  in  this  square,  January  22  and  23,  1876. 

Compiled  from  the  log-book  of  the  U.  S.  S. . 

Commencing  January  i,  1876,  and  ending  June  30,  1876. 


Magnetic     ^    o 
direction  of  •°    '~ 


wind. 


lU 


:^ 


N. 


N.  by  E. 


N.  X.  E. 


N.  E.byN. 


!  N.  E. 


N.  E.  byE. 


E.  N.  E. 


E.  by  N. 


MERCl'RLVL   I'.A- 
RilMElER,     m 

inches. 


-Mea 


29.91 


Magnetic 
direction  of  \'2. 


wind. 


E. 


E.  by  S. 


E.  S.  E. 


S.  E.  by  E. 


S.  E. 


S.  E.  by  S. 


S.  S. E. 


S.  by  E. 


Magnetic     t 

direction  of  >2 

wind.         g 


S.  by  W. 


S.  S.  W. 


S.  W.  by  S. 


S.  W. 


S.W.  byW. 


W.  S.W. 


W.  by  S. 


W. 


W.  by  N. 


W.  N.W. 


9   N.W.  by W. 


13        N.  W, 


12 


N.W.  by  N, 


N.  N.  W. 


N.  by  W. 


Magnetic   |  't 

direction  of  :>2 

wind.        I  5 


Fahrenheit's  Thermometer. 


No.  of  hours  of 

Squalls. 


DRY  BULB.  '  WET  BULB. 


C 
4; 


O 
56.4 


Q  2 


c 


Q  2 


4-5  152.41 


o 
8 


SEA  W.  AT 
SURF. 


C 


o 

60.6 


Q  t 


o 
I 


oJ 

^-t 

, 

<A 

>> 

> 

T) 

1) 

0 

w 

S 

'3 

19 

Square  No. 


28 


No.  OF  HOURS 
IX  SQUARE. 


40 


Ship's  track  thr()Ugii  square. 


£ 


m. 


i 


n 


TV 


No.  OF  HOURS  OF- 


Var 
wind. 


Calm. 


Fog. 


Rain  or 

mist. 


22 


Weather  by  symbols. 


b. 


p.    q. 


r.  d.  h. 


Forms  of  Clouds.  '   Clear  sky. 
Cit.  ft/////i.  2 


Mag.  var.  in — 

Lat. 

Long. 

Lat. 

Long. 

35^2' 

1340  30' 

35°  59' 

131'-^  36' 

15°  E. 


140  30'  E. 


CuRRENr,  its  set  and  velocity  in  knots  and  tenths  per 
hour  is  given  opposite  shi]i's  position  each  noon. 


Remarks. — In  suljsquares  7'  and  -c  wind  northwestward,  steady  in  direction,  always  strong,  but  often  vary- 
ing in  force  between  4-6.  Bar.  steadily  fell  from  30.13  to  29.90  in  17''.  D.  B.  and  W.  B.  quite  steady  about  59^^ 
and  55^  respectively.  Mostly  overcast,  a  few  periods  of  b.  c.  In  x,  wind  westerly,  strong  and  steady.  Cloudy 
and  wet.  D.  B.  and  W.  B.  unchanged.  Bar.  continued  to  fall  during  6''  to  29.65.  In  y,  wind  again  north- 
westerly— very  strong  and  squally,  varying  in  force  between  5-9,  and  so  continued  to  end  of  track.  Bar.  steadily 
rose  during  17''  to  29.90.  D.  B.  and  W.  B.  steadily  fell  to  53'  and  47  '  respectively,  while  weather  was  mostly 
b.  c,  clearing  and  dry.  Frequent  heavy  and  moderate  sipialls,  with  p.  d.  r.  all  along  track.  Very  rough  sea. 
Whole  fall  of  bar.  30.13  to  29.65 — 0,48  inch,  in  23'' ;  whole  rise  29.65  to  29.90 — 0.35  inch,  in  17''. 


32 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


METHOD    OF   COMPILING   THE   DATA   OF   A   CYCLONE,  HJ 

At  noon  of  September  27,  1S70,  sailed  from  Mazatlan,  and  for  la'i  stood  W.  S.  W.,  p.  c,  under  steam,  makiiw^' 
5  knots  per  hour.     Weather  the  whole  time  warm,  c.  d.  r.  t.  1.  u.     Very  light  variable  airs  and  calms.     Bar.  steady 
about  29.78.    Continued  heavy  swell  from  S.  S.  W,     Beginning  atmidnight  of  September  28,  the  record  is  as  follows: 


Hours. 

1 

Knots. 

5 

Courses. 

Winds. 

Force. 

Lee- 
way. 

Mecur.  bar., 
inches. 

D.  B. 

W.B. 

Weather.   Clouds. 

\ 

Clear 
sky. 

\ 

Sea. 

2 

S. 

S.  E. 

4-6 

2  pts. 

29.79  to  29.72 

830 

81° 

0.  c.  r.     Nimbus. 

0 

L. 

I 

2 

S. 

S.  E.  by  E. 

7 

3 

29.70 

83 

81 

(C 

(« 

I 

3 

S.  by  W. 

S.  by  E. 

10 

5 

29.72 

83 

82 

<< 

(C 

5 

12 

S. 

E.  S.  E. 

11 

6 

29-73 

78 

n 

0.  r. 

c 

3 

7 

S.  by  E. 

S.E.byE. 

10-11 

7 

29. 70  to  29.52 

77 

76 

0.  m. 

< 

4 

12 

S.  W. 

S.  S.  E. 

II 

7 

29.34  to  29.08 

76 

75 

0.  q.  u.  g. 

t 

ii 

2 

6 

W.  S.  w. 

S.byW. 

1 1-9 

7 

28.98  to  29.05 

76 

75 

0. 1.  q.  r. 

( 

2 

6 

S.  w. 

S.  S.  W. 

O-II 

7 

29.15  to  29.27 

75 

74 

0.  q.  r. 

( 

4 

12 

w.  s.  w. 

S.W. 

1 1-7 

5 

29.36  to  29.62 

77 

74 

0.  q.  b.  c.         ' 

( 

5 

10 

W.  by  S. 

S.  S.  w. 

6-3 

3 

29.56  to  29.84 

78 

75 

b.  c.  q.           ' 

< 

I 

3 

W.  by  S. 

S.W.  by  S. 

3-4 

I 

29.86 

79 

75 

JC                           c 

t 

The  above  are  all  the  hourly  observations  of  September  28,  and  up  to  6  a.  m.,  inclusive,  of  September  29. 
Subsequent  to  this,  the  wind,  weather,  sea,  &c.,  usually  attendant  upon  the  blowing  out  of  a  gale,  were  experi- 
enced. From  6  a.  m.  until  noon  of  29th,  stood  W.  S.  W.  p.  c.,  4  knots  per  hour ;  at  noon,  by  observations  (Sum- 
ner's method),  was  in  latitude  23'-  55'  N.,  longitude  105°  13' W.  At  7  p.  m.  of  the  29th  a  decided  lull  and  then  a 
calm  occurred  for  a  few  moments ;  then,  again,  wind  began  in  violent  shrieking  squalls.  A  most  confused,  but  not 
very  rough,  sea  was  running  during  the  storm;  it  seemed  to  be  beaten  down  by  the  violence  of  the  wind,  and  was 
streaked  with  foam,  like  soap-suds.  Could  carry  no  sail — hove-to  with  tarpaulins  in  the  rigging — and  drifting  to 
leeward.     Frequent  vivid  lightning  and  sharp,  loud  peals  of  thunder  during  the  cyclone. 

Under  steam,  sail,  or  both  ?  )  Sail  alone,  topsails  and  courses  in  V  and  W;  double-reefed  topsails, 

In  which  subsquares  was  each  used  ?    \     and  courses  in  X,  Y,  T;  treble-reefed  topsails,  courses  in  U. 

Compiled  January  24,  1876,  by ,  Lieutenant,  U.  S.  Navy. 


INSTRUMENTS    EMPLOYED    IN   NAVIGATION. 

FORin   E. 

(for  meteorological  data.) 


33 


riYDKUliKAI'HlU    (JF^ICK,     IViKTKOKUl.UUICAL    Uii. 

U.  S.  S. on  passage  from to 

["AKTMKIMT. 

-  i8— . 

> 

G 

in 

6 

Lat,        Long. 

AT  NOON. 

Winds. 

Mercurial  Barometer, 
inches. 

Range. 

Fahrenheit's  Thermom- 
eter. 

State  of  Weather. 

1 

o 

u 
o 

c 

Particula 
Nature  ( 
Wind. 

Dry  Bulb. 
Max.        Min. 

Wet  Bulb. 
Max.       Min. 

" 

Remarks  : 

Compiled  - 


i8-,  by . 


U.  S.  Navy. 


FORm  II. 

(for  meteorological  data.) 

Hydrographic  Office,  Meteorological  Department. 
U.  S.  S. at  anchor  in .     Lat. ,  Long.  - 


Winds, 

Mercurial  Barometer, 
inches. 

Range. 

Fahrenheit's  Thermom- 
eter. 

w 
a 

H 

<: 

b 
O 
U 
H 

< 
H 

Mean  Direc- 
tion. 

Mean  Force. 

Particular 
Nature  of 
Wind. 

Date. 

Dry  Bulb. 
Max.        Min. 

Wet  Bulb. 
Max.      Min. 

- — 

^ 

( 

Remarks  :  Give  bearings  (magnetic)  and  description  of  anchorage. 

Compiled ,  i8— ,  by ,  [/.  S.  Navy. 

3   B 


34 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION. 


Log  of  the  United  States  Ship 

> 

J?ate,            Gum 

On  passage  from  Acapulco,  Mexico,  t 

WINDS. 

BAROM- 
ETER. 

TEMPER- 
ATURE. 

0 

>> 

x^ 

-u 

t/i 
-a 

3    . 
0  ^ 

i 

.       . 

1 

Hour. 

•4-t 

.s 

t5 

r— * 

3 

M 

"3 

pq 

3 

^1 

DO 
V.  2 

f  clear 
loths. 

the  Se 

f  the 
s  und 
h. 

t/1 

C 

_c 

"ij 

^ 

•t-) 

■"  >, 

0     >^ 

0—  (J 

1 

c 

s 
0 
U 

0 

Q 

Si 

0 

>> 

<u 

(U 

h-1 

-4-» 

1h 

< 

State  of 

s 

c/3 

1 

Prop.  0: 
State  of 

Record 
vessel 
of  wat 

A.M. 

Pt. 

I 

7 

4 

N.N.KiE. 

N.W. 

6-7 

30.14 

58 

58 

S3 

61 

b.  c.  q. 

cu.  nimb. 

3  H.R. 

Sail  alone. 

2 

8 

0 

(< 

6-9 

30.  I4I58 

5853 

61 

2      • 

( 

Double    reefed 

3 

7 

0 

<( 

7-8 

30.  10  58 

5853 

61 

5 

{ 

topsails,  fore 

4 

6 

0 

<C 

6-8 

30.  1058 

5853 

61 

4 

i 

topmast  stay- 

5 

5 

0 

(C 

6-8 

30.  io|58|  5853 

62 

5 

t 

sail,  and  cour- 

35° N. 
134°  21' 

6 

4 

6 

N.  E.  by  N. 

5-7 

30.10J58  5852 

62 

4 

t 

ses. 

7 

4 

2 

N.  E.:|N. 

4-7 

30.101581  5852 

62 

3     • 

t 

■f 

W. 

§ 

4 

0 

N.  E.  f  N. 

4 

30.13581  5853 

62 

3 

( 

1 

9 

4 

2 

(I 

3 

30.16591  5954 

62 

I 

i 

10 

3 

0 

N.  E. 

4-7 

30.  1459J  5954 

62 

I 

( 

Turned  out  all 

II 

4 

0 

N.N.E.iE. 

4 

30.0959  5954 

62 

0.  c.q.  r. 

0 

a 

reefs,  and  set 

Noon. 

4 

0 

(( 

4 

30.  06 

59  59 

54 

62 

b.cp.q. 

2      " 

to'gallant  sails 
and  royals. 

Took  in  royals. 

Distance  run  by  Log  since  preceding  Noon 130  knots      4  tenths. 

Latitude  by  D.  R.  at  Noon North       35^  30'       " 

m 

Longitude  by  D.  R.  at  Noon West       133^'  57'       " 

■ 

Latitude  by  Observation  at  Noon  © North       35^  10'       " 

a 

Longitude  by  Chronometer  from  Forenoon  Observations  © West       134°  01'       " 

■ 

Square  S  Current  during  the  time  0.4  knot  per  hour,  setting  to  the  S.  by  W. 
2S.     ^  Variation  of  the  Compass  by  Amplitude  0  observed  at  Sunrise..                      °       '       " 

V 

^|l 

Variation  of  the  Compass  by  Azimuth  ©  observed  at  8  a.  m.  (in 

35'^  2' N.,  134^  30' W.)..'. Easterly  15°    0'       " 

Water  exnended  during  the  Drecedinp'  ia.  hours. .      ^60  frallons. 

Water during  the  preceding  24  hours  . ... " 

W' 

Water  remaining  on  hand  fit  for  use  at  Noon 5j  130       " 

1 

Coal  consumed  during  the  preceding  24  hours tons.             lbs. 

■ 

Cnnl  remainincr  on  hand  nf  Nonn  . 

{ 

56    " 

* 

P.M. 

I 

6 

4 

N.N.E.iE. 

N.  W. 

4-5 

1^30.04 

59 

5f 

54 

62 

0.  c.  p.  q. 

cu.  nimb. 

0 

H.R. 

2 

6 

6 

N.  E.  byN. 

<( 

5 

ii-30.oo 

59 

58 

54 

62 

0.  c.  p. 

0 

a 

3 

6 

2 

N.W.  by  W. 

5^ 

Ii:30.00 

59 

58 

55 

62 

(( 

0 

ct 

4 

7 

4 

5-6 

1^30.00 

59 

59 

55 

62 

it 

0 

Cf 

5 

6 

4 

4-6 

ii30.oo 

59 

59 

55 

62 

0.  c.  d.  q. 

0 

i( 

6 

5 

4 

4-6 

I  i- 30.  00 

60 

59 

55 

62 

ii 

0 

M. 

Took    in   and 

7 

7 

6 

4-6 

I  i  30.  00 

60 

58 

55 

61 

b.cp.q. 

3 

<( 

furled  to'gal- 

§ 

8 

4 

4-6 

1^30.00 

61 

5855 

61 

(( 

3 

<( 

lant  sails. 

9 

7 

4 

6 

\\  29.  96 

61 

585561 

(( 

5 

it 

10 

7 

0 

6 

11-29.96 

61 

5955161 

0.  c.  q. 

0 

a 

II 

6 

0 

5-6 

1^29.93 

61 

595660 

(( 

0 

<< 

Mid. 

7 

0 

W.  S.  W. 

6 

li  29. 89 

61 

59  56  60 

0.  c.  r.  q. 

0 

(( 

Longitude  by  Chronometer  from  Afternoon  Observations  © °      '       " 

T  r\r\  rrj  f  iirl^i   \^\T   i '\\Y'i\^'\c\xnf^\f*Y   Trom    i)  W^P  I'vn  t  loti  Q    — 

^                              0      '      II 

i_<OIlgIluUC    \)\    V^lirUIlUlIlCLCI     llUlll    vy  1J.>CI  VttL10Ii:>    — 

Variation  of  the  Compass  by  Amplitude  observed  at  Sunset 0       /       /' 

Variation  of  the  Comoass  bv at . 

0 

/      // 

W      t4  A  A  44  \t^^mf  A  A       V*'  A          b  A&^^        ^it^^tj  4&*  fc.^*^^^  *i^        P-'     T                                                                  '  ~                                                           ™ 

■ 

\ 

INSTRUMENTS    EMPLOYED    IN    NAVIGATION.  35 

under  the ^ommand  of  ,   U.  S.  Navy^ 

San  Francisco,  California,  Saticrday^  yanuary  22,  1876. 

RECORD  OF  THE  MISCELLANEOUS  EVENTS  OF  THE  DAY. 


From  midnight  to  4  a.  m. : 

Wind  steady  in  direction,  but  variable  in  force  ;  always  strong,  but  at  intervals  lilowing  in  heavy  squalls. 
Weather  boisterous  and  damp;  partly  cloudy :  bright  starlight  at  times.  Heavy,  rough  sea  from  Nw'd. 
Ship  pitching  3^'  to  5*-^  and  rolling  12^  to  22^^  each  way — a  kind  of  corkscrew  motion.  Steering  a  course 
N.NE.  ^2  E.  per  standard  compass.     Density  of  sea- water, . 


From  4  to  8  a.  m. : 

Wind  slightly  moderating  during  watch — otherwise  state  of  wind,  weather,  sea,  and  motion  of  ship  the 
same  as  during  preceding  watch.     Steering  "  full  and  by."     Density  of  sea-water .     ****** 


From  8  to  meridian : 

Wind  steady  iu  force  and  direction.  One  hour  of  heavy  squalls — three  of  moderate.  Cloudy,  cool,  and 
raw,  with  light  rain  and  showers.  Pitch,  2  '  to  4'-^ — roll,  10^  to  13^',  each  way.  Course — "full  and  by."  At 
8  shook  reefs  out  of  topsails  and  set  to'gallant  sails  and  royals.  Reduced  sail  frequently  to  squalls.  Density 
of  sea-water, .     ****** 


.From  meridian  to  4  p.  m. : 

Wind  fresh  and  steady ;  moderate  squalls.     Cloudy,  raw,  and  showery.     Sea  going  down,  and  motion  of 
ship  easy.     Course — "  full  and  by."     Density  of  sea- water, .     ****** 


From  4  to  6  p.  m. : 

W'ind,  weather,  squalls,  and  sea  the  same  as  during  preceding  watch.     Steering  a  course — NE.  by  N. 
per  st'd  c.     At  5  furled  to'gallant  sails.     Density  of  sea-water,  .     ****** 


From  6  to  8  p.  m. : 

Wind  and  weather,  squalls  and  sea  the  same  as  during  preceding  watch.     Course — N.  E.  by  N.  per  c. 
Density  of  sea-water, . 


From  8  to  midnight : 

A  very  fresh,  steady  breeze.     Moderate  squalls.     Cloudy  and  damp — rainy  toward  the  end  of  watch 
Course — N.  E.  by  N.  per  c.     Density  of  sea-water, .     ***»#* 


36 


INSTRUMENTS    EMPLOYED    IN   NAVIGATION. 


Log  of  the  United  States  Ship 


,  Rate,  Guns, 

On  passage  from  Acapulco,  Mexico, 


130°  W 
36°  J5' 


Hour. 


A.M. 
I 

2 

3 
4 

5 
6 

7 

8 

9 

lO 

II 
Noon. 


t3 


11 


3 
o 
U 


N.  E.byN, 


N.  E. 

N.  E.  by  N, 

N.  E.iN. 

N.  E.iN. 

N.E. 


WINDS. 


S 

o 


West. 

W.  by  S. 

N.  by  W. 
N.W. 

N.W.byN, 

N.W. 


7 
7 
7 
7 
6-7 

6-7 
6 
6-8 
6-8 
6-7 
6-7 
6-8 


Pt, 
li 
li 
li 
li 
li 
li 
li 
li 
li 
li 
li 
li 


BAROM- 
ETER. 


in 

o 

C 


.d 
M 


29. 
29. 
29. 
29. 
29. 
29. 
29. 
29. 
29. 
29. 
29. 
29. 


83 
80 
70 
67 

65 
70 

71 

72 

85 
85 
85 
85 


TEMPER 
ATURE. 


3 

Q 


fQ 


5856, 

5857 
5858: 
5858 

5856: 
5854 
57:53: 


57 
55 
55 
55 
55 


53 

5'! 

5° 
50| 


in 


o.  c.  q. 
o.  c.  r. 

o.  c.  q.  r. 

o.  c.  p.  q. 

o.  c.  q. 


b.c. 
b.c.p.q. 


13 
3    • 

O    "> 


o 


nimb. 


cu.  nimb. 


o 

i-t 


OJ 


O 

■4-« 

OJ 


H.R 


Square 
28. 


Distance  run  by  Log  since  preceding  Noon 165  knots      o  tenths. 

Latitude  by  D.  R.  at  Noon North      36°  11'       " 

Longitude  by  D.  R.  at  Noon West      130°  53'       " 

Latitude  by  Observation  at  Noon  © North      36°  03'       " 

Longitude  by  Chronometer  from  Forenoon  Observations  0 West      131°  14'       " 

Current  during  the  time  0.3  knot  per  hour,  setting  to  the  S.  S.  W. 

Variation  of  the  Compass  by  AmpHtude  0  observed  at  Sunrise. .  °  " 

Variation  of  the  Compass  by  Azimuth  0  observed  at  8  a.  m.  in 

35°  59'  N.,  131^36'  W Easterly  14O  30'       " 

Water  expended  during  the  preceding  24  hours 360  gallons. 

Water during  the  preceding  24  hours " 

Water  remaining  on  hand  fit  for  use  at  Noon 4,  770       " 

Coal  consumed  during  the  preceding  24  hours tons.  lbs. 

Coal  remaining  on  hand  at  Noon 86     "  " 


P.M. 

I 

6 

0 

2 

5 

0 

3 

5 

0 

4 

4 

0 

5 

6 

0 

6 

7 

0 

7 

5 

4 

8 

5 

4 

9 

5 

0 

10 

6 

0 

II 

7 

0 

Mid. 

6 

4 

N.  E.  by  N, 


N.  E.  by  E. 

iE. 
N.  E.  by  E. 

E.  N.  E. 

N.  E.  by  E. 

N,  E.  i  E. 

N.  E.  i  E. 

N.E. 

N.  E.  byN. 


N.W. 

6-8 

H 

29.85 

56 

54 

50 

60 

b.  C.  p.  q. 

cu.  nimb. 

4 

(( 

8 

H 

29.8655 

54  50 

60 

0.  c.  p.  q. 

0 

it 

8-9 

H 

29-8755 

54 

48 

60 

<( 

0 

N.W.byN. 

7-8 

H 

29.9255 

53 

47 

60 

<( 

5 

(( 

7-8 

i^ 

29-  83  55 

52147 

60 

b.  c.  q. 

4 

It 

9-7 

H 

29.8755 

50I46 

60 

(( 

ii 

3 

ii 

7 

H 

29. 90  55 

5046 

60 

<c 

5 

it 

7 

H 

29.  88  55 

5246 

60 

c< 

'< 

5 

It 

5-7 

H 

29. 92  55 

53|47 

60 

b.c.p.q.h. 

5 

5-7 

H 

29-  92  55 

53 

47 

bo 

b.  c.  q. 

5 

(( 

5-7 

H 

29-  90  55 

53 

47 

bo 

ii 

6 

N.W. 

5-7 

H 

29-9055 

53 

48 

60 

11 

7 

H.R, 


Longitude  by  Chronometer  from  Afternoon  Observations  0 ° 

Longitude  by  Chronometer  from  Observations  ^jc ° 

Variation  of  the  Compass  by  Amplitude  observed  at  Sunset ° 

Variation  of  the  Compass  by at o 


•S  c 

43   C 


•ss-g 


-P  V. 


o 


>  o 


Sail  alone. 

Courses,  top 
sails,  and  fore 
topmast   stay- 
sail. 

Furled  the  miz. 
topsail. 

Doub'  J     reefed 
the  .ops"  is. 


Treble  reefed  the 
topsails  and  sin- 
gle reefed  the 
foresail. 


i 


INSTRUMENTS    EMPLOYED    IN    NAVIGATION.  37 

under  the  command  of  ,    U.  S.  Navy^ 

to  San  Francisco,  California^  Sunday,  yanuary  23,  1876. 

RECORD  OF  THE  MISCELLANEOUS  EVENTS  OF  THE  DAY. 

From  midnight  to  4  a.  m. : 

Wind  strong,  but  unsteady  in  force  and  direction — a  succession  of  heavy  and  moderate  squalls.  Cloudy, 
wet,  and  raw.  Rough  sea  from  Nw'd.  Course — NE.  by  N.  Very  rapid  fall  of  0.16  inch  in  barom.  At  3.30 
took  in  and  furled  mizzen  topsail.     Density  of  sea-water, . 


From  4  to  8  a.  m. : 

Wind  generally  freshening,  but  unsteady — blowing  in  heavy  and  moderate  squalls.  Heavy  sea  from 
Nw'd.  Ship's  motion  a  combination  of  pitch  and  roll,  both  deep,  but  easy.  Cloudy  and  raw.  Course-  -NE. 
by  N.  for  3  hours,  then  N.E.     At  5.30  double-reefed  the  topsails.     Density  of  sea-water, . 


From  8  a.  m.  to  meridian : 


Wind  strong,  steady  in  direction,  but  blowing  in  squalls,  both  heavy  and  moderate.     Rough  sea.     Blue 
sky  and  clouds.     Course — "full  and  by."     Density  of  sea-water, — 


»         *        3f        ^        #        * 


From  meridian  to  4  p.  m. : 

Blowing  a  gale — steady  in  direction,  but  fitful  and  squally  in  force.  At  times  blue  sky  and  clouds,  again 
entirely  overcast,  showery,  and  cool.  Rough  swell  from  Nw'd.  Course — "full  and  by."  At  I  o'clock  took 
a  third  reef  in  topsails  and  single-reefed  the  foresail.     Density  of  sea-water,  . 


I 


From  4  to  6  p.  m.  : 

Wind,  weather,  sea,  and  course  the  same  as  during  preceding  watch.     Ship  rolling  and  pitching  deeply. 
Density  of  sea-water,  . 


From  6  to  8  p.  m. : 

Wind  slightly  moderating  and  more  steady  in  force  and  direction.     Weather  clear  and  pleasant.     Sea 
rough.     Moderate  squalls  of  wind.     Course — "full  and  by."     Density  of  sea-water, . 


From  8  p.  m.  to  midnight : 

Wind  strong,  steady  in  direction,  but  squally  in  force — a  series  of  heavy  and  moderate  squalls.  Weather 
clear,  cool,  and  boisterous.  At  8.30  had  a  heavy  squall  of  wind  accompanied  with  large  hail.  Course — "ful/ 
and  by."     Density  of  sea-water, . 


38 


THE    SAILINGS. 


CHAPTER    III. 

THE   SAILINGS. 

Art.  106.  Upon  leaving  a  port  to  conduct  a  ship  to  another  port  the  first  things  to  determine  are  the 
Irack,  or  course,  and  distance  between  the  ports  ;  but  since  it  is  impossible,  owing  to  various  obstacles,  such  as  winds 
and  currents,  to  pursue  a  premeditated  course,  it  becomes  necessary  then  to  determine  at  any  time  the  ship's  plar." 
from  the  course  and  distance  sailed,  in  order  to  establish  a  new  course  and  to  calculate  anew  the  distance. 

Art.  lOy.  The  Navigator  has  choice  of  two  tracks,  either  the  R/iiiiiil),  or  the  Great  Circle,  and  depending 
upon  the  one  chosen  is  the  sailing  called  Rhumb  Sailing,  or  Great  Circle  Sailing. 

The  earth's  surface  may  l:ie  considered  either  as  an  extended  plane  or  as  a  spherical  surface,  which  distinc- 
tions give  rise  to  the  terms  Plane  Sailing  and  Spherical  Sailing. 

Art.  lOS.  In  considering  a  ship's  position  at  sea  with  reference  to  any  other  place,  either  one  left  or  one 
to  be  steered  for,  five  things  are  involved:  COURSE,  DISTANCE,  DIFFERENCE  OF  LATITUDE,  Departure,  and 
Difference  of  Longitude. 

In  practice,  two  problems  arise,  viz  : 

1st.  Course  and  distance,  from  a  given  Latitude  and  Longitude  known,  to  find  the  Latitude  and  Longitude 
of  another  place. 

2d.  Latitudes  and  Longitudes  of  two  places  given  to  determine  Course  and  Distance  between  them. 

The  solutions  of  these  problems  are  called  "  Sai/in^s." 

1.— PLANE  SAILING. 


Art.  109.    When  the  earth's  surface  is  considered  as  a  plane  surface 

in  Art.  io8  are  involved : 
Course,  Distance,  Difference 
of  Latitude,  and  Departure. 

The  solution  of  the  prob- 
lems of  Plane  Sailing  require 
an  application  of  the  rules 
of  Plane  Trigonometry ;  and 
under  this  head  are  treated 
Current  Sailing  and  Traverse 
Sailing. 

The  abbreviations  and 
signs  used  henceforward  will 
be  found  on  the  page  facing 
Chap.  I,  page  i. 

Art.  IIO.  In  Fig.  30 
T  and  T'  are  two  places  on 
the  earth's  surface;  TT',  the 
rhumb-line,  or  theloxodrome 
between  them. 

C.  represent  T'T«,the  Course. 
Dist.  represent  T'T,  the  Distance. 

D.  L.  represent  T;/'  =  T';/,  the  Difference  of  Latitude. 
Dep.  represent  T«,  in  Latitude  of  T, 

T'«',  in  Latitude  of  T', 

LL',  in  Middle  Latitude,  the  Departure. 

D.  Lo.  represent  MM',  the  Difference  of  Longitude. 

L.  represent  TM,  the  Latitude  of  T   ?-(- when  North. 

L'  represent  T'  M',  the  Latitude  of  T'  \  —  when  Soutli. 

Lo.  represent  the  Longitude  of  T    ^  -j-  when  West. 

Lo'  represent  the  Longitude  of  T'  5  —  when  East, 


four  of  the  five  elements  mentioned 


Fig. 


30- 


Let 


Hence 

D.  L.  =  L'  —  L. 
L'        =  L.  +  D.  L. 


D.  Lo.  =  Lo'  —  Lo. 
Lo'       =  Lo.  +  D.  Lo. 


paying  attention  to  the  signs  or  names  of  Latitudes  and  Longi- 
tudes. 

Art.  111.  In  Plane  Sailing,  the  curvature  of  the  Earth 
being  neglected,  the  t-iang!e  ccMitaining  these  elements  becomes 
a  right-plane  triangle,  F"ig.  31  ;  the  rhumb,  TT',  a  straight 
line. 

In  this  triangle — 

Dist.,  the  distance,  is  the  hypotenuse. 

Dep.,  the  departure,  one  side. 

D.  L.,  the  difference  of  latitude,  the  other  side. 

<'.,  the  course,  is  the  angle  formed  by  1).  L.  and  Dist. 


THE    SAILINGS. 


39 


From  this : 


CosC.  -. 


SinC. 


Dist.' 

Dep. 

Disi. 


TanC  —  ^^P- 


and 


D.  L.  =  Dist.  cos  C. 
Dep.  =  Dist.  sin  C. 
Dep.    =  D.  L.  tan  C, 


Dep.,  being  regarded  as  the  departure  in  either  latitude. 

Art.  112.  The  solution  of  this  right  plane  triangle  for  different  values  of  C.  and  Dist.  gives  corresponding 
livalues  for  D.  L.  and  Dep.  These  being  tabulated,  form  a  Tablk  ok  Right  Triangles,  or,  as  it  is  termed  in 
I  Navigation,  a  Traverse  Table. 

i  Taule  I,  in  this  work,  gives  the  values  of  D.  L.  and  Dep.  for  each  unit  of  Dist.  from  i  to  300,  and  for  each 

I  quarter-point  (2^  49')  of  C. 

Table  2  gives  the  values  of  D.  L.  and  Dep.  for  each  unit  of  Dist.  from  i  to  300,  and  for  each  degree  of  C. 
Art.  113.    Referring  again  to  the  plane  triangle,  Fig.  31,  the  solutions  of  the  various  cases  of  Plane  Saihng 
may  be  shown  in  the  following  Table  : 


Case. 

Given. 

Required. 

Solutions. 

I 

Course  and  distance. 

Difference  of  latitude- 
Departure  

D.  L.  =  Dist,  cos  C.       Log.  D.  L.  =  log  Dist.  +  log  cos  C. 
Dep.   =  Dist.  sin  C.        Log.  Dep.  =  log  Dist.  -f  log  sinC. 

Distance  . 

Dist.    —   ^"-^                Log  Dist.    —  logD.  L.       log  cos  C. 
COS.  C.                                                               " 

Dep.    =  D.  L.  tan  C.       Log  Dep.   =  log  D.  L.  -f  log  tan  C. 

j      of  latitude. 

Departure 

3 

Course  and  departure. 

Distance 

Difference  of  latitude. 

Dist.    =    .J^                 Log  Dist.    =  log  Dep.  —  log  sin  C. 
D.  L.  —  /^^P;                 Log  D.  L.  —  log  Dep.  —  log  tan  C. 

i 

Course  - 

Cos  C.  —  ^•.  ^"                Log  cos  C.  —  log  D.  L.  —  log  Dist. 
Dep.    =  Dist.  sin  C.       Log  Dep.   =  log  Dist.  +  log  sin  C. 

^     1      ence  of  latitude. 

Departure 

T^ictonr^i^    nrtA     r1*Ai-vnvf 

Course . 

Sin  C.  —  ^^P*                 Log  sin  C.  —  log  Dep.  —  log  Dist. 
D.  L.  —  Dist.  cos  C.      Log  D.  L.  =  log  Dist.  +  log  cos  C. 

5 

ure. 

Difference  of  latitude. 

6 

Difference  of  latitude 
and  departure. 

Course 

Distance  ... . 

Tan  C.  =  ^^P"                 Log  tan  C.  —  log  Dep.  —  log  D.  L. 
Dist.     —  ^^^P;-                Log  Dist.  —  log  Dep.  —  log  sin  C. 

Problems  of  Plane  Sailing  may  lie  solved  by  direct  inspection  of  the  Traverse  Table,  or  solved  as  problems  of 
Plane  Trigonometry,  using  the  tables  of  logarithms  of  numbers  and  logarithmic  functions  of  angles,  Tables  42 
and  44. 

Case  I. 
Coiost'  and  distanc-  sailed  ghieii,  to  Jin  d  tlu-  difft-rence  of  latitude  and  departure  from  the  meridian. 

A  ship,  from  the  latitude  of  49°  57'  N.,  sails  S.  W.  by  W.  244  miles ;  required  the  latitude  she  is  in,  and  h« 
departure  from  the  meridian  sailed  from. 

Given,  Dist.  =  244,  C.  =  5  points  =  56'-^  15'. 
To  find  D.  L.  and  Dep. : 

BY   computation. 

D.  L.  =  Dist.  cos  C. 

Dist.   =        244         log        2.38739 

C.        =56^15'  log  cos  9. 74474 


D.  L.  =     135.6         log        2.13213 

Dep.  =  Dist.  sin  C. 

Dist.  =        244         log        2.38739 

C.        =56°  15'  log  sin  9.91985 


Dep. 


202.9  log  2.30724 


40  THE    SAILINGS. 

Since  L'  =  L  -j-  D,  L.,  and  in  this  case  since  the  ship  sails  southerly,  D.  L.  is — 

L.       =  +  49°  5/ 
D.L.  =  —   2    i6 


L'       =      47    41  N. 


BY  INSPECTION. 


In  Table  i  find  the  course  =  5  points  at  the  bottom  of  the  page,  and  in  the  column  marked  Dist.  look  for  244, 
opposite  which,  in  the  columns  marked  Dep.  and  Lat.,  at  the  bottom  of  the  page,  will  be  found 

Si 
D.  L.  =  I35'.6  Dep.  =  202.9 

which,  being  applied  in  the  same  manner  as  above,  will  give 

L.'  =47041'  N. 

Case  II. 
Course  and  difference  of  latitude  given,  to  find  the  distance  run,  and  departure  from  the  7neridian. 

A  ship  runs  S.  E.  by  E.  from  \°  45'  north  latitude,  and  then,  by  observation,  is  in  o'^  31'  south  latitude; 
required  her  distance  and  departure. 

In  this  case,  as  the  ship  has  crossed. the  equator,  the  sum  of  the  two  latitudes,  i^  45'  .and  o"^  31',  is  the  differ, 
ence  of  latitude,  2°  16'  =  136  miles. 

Given,  D.  L.  =  136,  C.  =  5  points  =  56°  15'. 

To  find  Dist.  and  Dep. : 


BY  COMPUTATION. 
Dep.  =  D.  L.  tan  C.  Dist. 


D.  L. 

cos  C. 


D.  L.  =       136  log        2.13354  2.13354 

C.        =56^x5'         log  tan  o.  1 75 1 1         log  cos  9. 74474 


Dep.   =    203.5  ^05        2.30865 

Dist.   =    244.8  ■  log        2.38880 

BY   INSPECTION. 

Entering  Table  I  with  course  =  5  points,  find  in  Lat.  column  136,  and  opposite  will  be  found  Dist.  =  245, 
Dep.  =203.7. 

Case  III.  f 

Course  and  departure  from  the  meridian  given,  to  find  the  distance  and  difference  of  latitude. 

If  a  ship  sails  N.  E.  by  E.  j{,  E.  from  a  port  in  3°  15'  south  latitude,  until  she  departs  from  her  first  meridian 
203  miles,  required  the  distance  sailed  and  the  latitude  she  is  in. 


Given,  C  =  5^  points  =  64°  41 '  15",  L.  =  3°  15'  S.,  Dep.  =  203. 
To  find  D.  L.,  L',  and  Dist.  : 


BY   COMPUTATION. 

D.  L.  -  ^^P:,Dist.-  °"P:,L' 
tan  C.                   sin  C. 

=  L.  +  D.  L. 

Dep.   =               203         log        2.30750 
C.        =64°4i'i5''         logtano.32517 

2.30750 
log  sin  9.95616 

p.  L.  =                 96         log         1.98233 
Dist.   =            224.6 

log        2.35134 

L.        =-3°  15' 
D.  L.  =  +  i     36 

1 


L'       =      I     39S. 

BY    INSPECTION. 

Entering  Table  i  with  C.  =  5^  points  and  Dep.  ==  203,  find  D.  L.  =  96,  Dist. ^=  224.5. 


THE    SAILINGS.  41 

Case  IV. 
Distance  and  difference  of  latitude  i^iven,  to  fimt  the  course  and  departure. 

Suppose  a  ship  sails  244  miles,  between  the  south  and  the  east,  from  a  port  in  2°  52'  south  latitude,  and  then, 
.  by  observation,  is  in  ^"^  oS'  south  latitude;  what  course  has  she  steered,  and  what  departure  has  she  made  ? 

From  the  latitude  by  observation,  5"^  08',  take  2"-'  52',  the  latitude  left;  the  remainder,  2^  16'  ^=  136  miles,  is 
the  differer.ce  of  latitude. 

Given,  Dist.  =  244,  D.  L.  =:  136. 
To  find  C.  and  Dep. 


Course,  S.  E.  by  E. 


BY   COMPUTATION. 

Cos  C.  = 

D.  L. 

Dist. 

Dep.  =  Dist.  sin  C. 

D.L. 
Dist. 

=      .36 
=      244 

log 
log 

2-13354 
2-38739 

log        2.38739 

C. 

=  56'  08 

log  cos 

9.74615 

log  sin  9.91925 

Dep. 

=  202.6 

log         2.30664 

BY    INSPECTION. 


Seek  in  Table  i  or  Table  2  until  Lat.  =  136  is  found  opposite  Dist.  ■=  244  in  one  of  the  following  columns, 
on  the  same  line  will  be  found  in  the  third  column  the  value  of  Dep.  =  202.9,  and,  since  Lat.  and  Dep.  corre 
spond  with  the  names  at  the  foot  of  their  columns,  the  course  =  5  points  will  be  found  at  the  bottom  of  the  page 

Case  V. 

Distance  and  departure  given,  to  find  the  course  and  difference  of  latitude. 

Suppose  a  ship  sails  244  miles  between  the  north  and  west,  from  the  latitude  of  32^  25'  north,  until  her  deparl 
ure  is  203  miles ;  what  course  has  she  steered,  and  what  latitude  is  she  in  ? 

Given,  Dist.  =  244,  Dep.  =  203,  L.  =  32*^  25'  N. 
To  find,  C,  D.  L.,  and  L'. 

BY   COMPUTATION. 

r-  Sin  C.   =  2?^         D.  L.  =  Dist.  cos  C. 

\  Dist. 

Dep.  =:        203        log        2.30750 

Dist.  =        244        log        2.38739        log        2.38739 

C.       =56018'         log  sin  9.92011         log  cos  9.74417 

D.L.=     135-4  N.  log        2.13156 

L.       =  32°  25'  N. 
D.  L.  =    2    15  N. 


Course,  N.  W.  by  W. 


I 


L'      :=34     40  N. 


BY    INSPECTION. 


Seek  in  Table  i  or  Table  2  until  opposite  244  in  Dist.  column  is  found  Dep.  =  203  in  one  of  the  following 
columns,  in  the  third  column  will  be  found  D.  L.  =;  135.6,  and  in  accordance  with  the  proper  names  of  the  coluams 
will  be  found  at  the  bottom  of  the  page  Course,  N.  W.  by  W.     Table  i. 

Case  VI. 

Difference  of  latitude  and  departure  given,  to  find  the  course  and  distance. 

A  ship  sails  between  the  north  and  west  till  her  difference  of  latitude  is  136  miles,  and  her  departure  is  03 
miles ;  required  her  course  and  distance. 

Given,  D.  L.  =  136,  Dep.  =203. 
To  find  C.  and  Dist. 

BY  COMPUTATION. 

Dep. 
Sin  C. 

log        2.30750 


BY  COMI 

'UTATION 

Tan  C. 

Dep. 
D.  L. 

Dist. 

Dep.  =        203 
D.  L.  =        136 

log 
log 

2.30750 
2-13354 

C.       =  56°  11'         log  tan  0.17396        log  sin  9.91951 

r  XT   ^v   .     Av       ^'^^-  ^      ^"'4-3  H'        2.38799 

Course,  N.  W.  by  W. 


42 


THE    SAILINGS. 


Traverse  Table. 


t 


BY  INSPECTION. 

Seek  in  the  tables  till  the  given  difference  of  latitude  and  departure  are  found  together  in  their  respective 
columns  ;  then  against  them  will  be  the  distance  in  its  column,  and  the  course  will  be  found  at  the  top  of  that  table 
if  the  departure  be  less  than  the  difference  of  latitude,  otherwise  at  the  bottom. 

Thus,  with  the  difference  of  latitude  136,  and  the  departure  203,  enter  the  tables,  and  these  numbers  will  be 
found  to  correspond  nearly  to  5  points,  or  N.  W.  by  \V.  course,  and  a  distance  equal  to  244  miles. 

The  solution  of  the  various  cases  of  Plane  Sailing  by  "Construction  "  will  be  readily  understood  by  a  knowl- 
edge of  the  use  of  the  Plane  Scale,  «S:c.,  and  adapting  the  right  triangle  to  the  values  of  the  several  elements  forming 
each  Case. 

Traverse  Sailing. 

Al*t>  1 14*  A  Traverse  is  an  irregular  track  which  a  ship  makes  by  sailing  on  several  different  courses,  and 
the  problem  involved  in  Traverse  Sailing  is  this : 

To  reduce  several  courses  and  distances  to  a  single  course  and  distance,  and  to  find  the  corresponding  differences  of 
latitude  and  departure. 

Art.  115.  The  method  of  solving  this  prolilem,  or  working  the  traverse,  is  as  follows  : 
Make  a  Traverse  Table  consisting  of  six.  columns ;  name 
them  Course,  Distance,  N.,  S.,  E.,  W.  ;  begin  at  the  left  hand 
and  write  the  courses  and  distances  in  their  respective  columns. 
Find  the  difference  of  latitude  and  departure  for  each  of  the 
courses  by  Table  i  or  2,  and  write  them  in  their  proper  col- 
umns ;  /  c,  when  the  course  is  southerly,  the  difference  of  latitude 
must  be  written  in  the  column  S. ;  when  northerly,  in  the  column 
N. ;  the  departure,  when  westerly,  in  the  column  W. ;  when 
easterly,  in  the  column  E.  Add  the  differences  of  latitude  in 
each  column,  subtract  ihe  lesser  sum  from  the  greater,  which 
difference  will  be  the  difference  of  latitude  of  the  same  name  as 
the  greater. 

Do  the  same  with  the  departures. 

With  the  difference  of  latitude  and  the  departure  thus  found, 
the  course  and  distance  made  good  will  be  found  as  in  Case  VI, 
Plane  Sailing.* 

Example  i.  A  ship  sails  S.  S.  E.  15  miles;  S.  E.  34  miles; 
W.  by  S.  16  miles  ;  W.  N.  W.  39  miles;  S.  by  E.  40  miles:  re- 
quired the  course  and  distance  made  good. 

Place  all  these  courses,  distances,  &c.,  in  the  traverse  table;  then  add  up  all  the  westings,  eastings,  north- 
ngs,  and  southings,  separately,  and  set  down  their  respective  sums  at  the  bottom  of  each  column  ;  and  as  the  west- 
ing IS  greater  than  the  easting,  subtract  the 
easting  therefrom ;  the  difference,  14.2,  shows 
that  the  ship's  departure  is  so  much  west  of 
her  first  meridian. 
Again,  the  southing  being  greater  than  the  north- 
ng,   subtract  the  northing  from  it,  and  the  remainder, 
65.3,  shows  how  far  the  ship  is  to  the  southward  of  her 
first  place 

The  difference  of  latitude  =  65.3  and  the  depart- 
ure =  14.2  give  (Table  i  or  2)  Course  S.  by  W.,  and 
distance  =  67  miles. 

Or,  by  computation — 

D.  L.  =       d^.T.        log         1.81491 
log         1. 15229 


Courses. 

Dist. 

Diff.  of  Lat. 

Departure. 

N. 

S. 

E. 

W. 

S.  S.  E.         15 

S.  E.           34 

W.byS.    1     16 

W.  N.  W.       39 

S.  by  E.        40 

14.9 

13-9 
24.0 

3-1 
39-2 

5-7 
24.0 

7.8 

15-7 
36.0 

From  sum  take 

14.9 

80.2 
14.9 

37.5 

Si-7 
37-5 

Remainder.- 

65-3 

14.2 

65-3 

14.2 


=  12^ 


16'         log  tan  9.33738 
66.8 


log 
log 
log 


1. 15229 

sin  9.32728 


.82501 


Suppose  the  ship  had  left  latitude  41°  10'  N.,  by 
applying  the  difference  of  latitude  =  —  65.3  will  give 
latitude  arrived  at  40"  05'  N. 

Example  2.  A  ship  from  Mount-Desert  Rock,  in 
the  latitude  of  43^^  50'  N.,  sails  for  Cape  Cod,  in  the 
latitude  of  42^^  3'  N.,  its  departure  from  .the  meridian 
of  Mount-Desert  Rock  being  supposed  to  be  84  miles 
west ;  but,  by  reason  of  contrary  winds,  she  is  obliged 
to  sail  on  the  following  courses,  viz:  South  10  miles, 
W.  S.  W.  25  miles,  S.  W.  30  miles,  and  W.  20  miles. 
Required,  the  bearing  and  distance  of  the  two  places, 
the  course  and  distance  sailed  by  the  ship,  and  the  bear- 
ing and  distance  of  her  intended  port. 


BY   PROJECTION. 

Latitude  of  Mount-Desert  Rock, 
Latitude  of  Cape  Cod, 

Difference  of  latitude. 


43' 
42 


050' 
3 


N. 
N. 


I    47  =  107  miles. 


*  This  method  of  reducing  compound  courses  to  a  single  one  is  perfectly  accurate  in  sailing  on  a  plane,  and  is  nearly  so  in  ' 
sailing  a  short  distance  on  the  spherical  surface  of  the  earth  ;  and  though  in  this  case  it  is  liable  to  a  small  error  in  high  latitudes, 
yet  in  general  the  rule  is  sufficiently  accurate  for  deducing  the  several  courses  and  distances  sailed  in  one  day  to  a  suigle  <  ourse 
and  distance. 


i 


THE    SAILINGS. 


43 


Let  C  represent  Mount-Desert  Rock ;  draw  the  meridian  CK,  which  make  equal  to  107  miles  the  difference  of 
ititude  between  the  two  places,  and  perpendicular  thereto  the  line  FE,  equal  to  the  departure  84  miles  ;  then  is 
•the  place  of  Cape  fod.  \N  ith  the  chord  of  6o'  sweep  alx.ul  the  centre,  C,  a  cncle,  S.  W.,  to  represent  the 
'nmmss  and  upon  it  note  tlie  various  courses  sailed.  The  first  course  bcint;  south,  the  distance,  10  miles,  is  set 
ff  from  C  toward  F  ui.on  the  meridian,  and  this  point  represents  the  place  of  the  ship  after  saihng  her  hrst  course; 

.  ^    }  ■  _       _^  1     1:  .. .    _,.    :„    tl,,.    1^.1    ovor.ii->l/>     \-i  /     VV     S    VV     ■?C  nines 


ontinue  setting  off  the  various  courses  and  distances  as  in 


the  last  example,  viz,  W.  S.  W.  25  miles,  .S.  W.  30 


liles'and  WesT  20  miles,  to  the  point  A;  then  will  A  represent  the  place  of  the  ship  after  sailing  these  courses. 
oin'cE  AC,  AE;  draw  AB  perpendicular  to  the  meridian  CF,  and  AD  parallel  thereto;  then  will  AC,  =  76.2 
,iles,  be  the  distance  made  good ;  AE  =  69.1  miles,  the  distance  of  Cape  Cod  from  the  ship;  CK,  the  distance  of 
lie  two  places  =  136  miles;  ACB  =  5/^  3^',  the  course  made  good;  EAD  =  16^  34',  the  course  to  Cape  Cod, 
nd  ECF,  the  course  from  Mount-Desert  Rock  to  Cape  Cod  =  ^S-  8',  &c. 


BY   COMPUTATION. 


D.  L.  =      107 
Dep.   =        84 


log 
log 


2.02938 

1.92428 


C.        =  38°  8'        log  tan  9.89490 

Dist.    =      136 
Course  to  Cape  Cod,  S.  38-  8'  W.  from  Mount  Desert. 

BY   INSPECTION. 


log  1.92428 

log  sin  9.79063 
log        2.13365 


The  difference  of  latitude  and  departure  for  the  several  courses  being  calculated,  by  Case  I,  Plane  Sailing, 


and  arranged  in  the  traverse  table,  it  appears  that  the  difference 
of  latitude  made  good  by  the  ship  is  40.8  miles,  and  the  depart- 
ure 64.3  miles;  then,  by  Case  VI,  Plane  Sailing,  these  numbers 
are  found  to  correspond  to  a  course  of  S.  57°  36'  W.,  and  dis- 
tance 76.2  miles. 

Subtract  the  difference  of  latitude  made  good  by  the  ship, 
40.8  miles,  from  the  whole  difference  of  latitude,  107  miles,  and 
there  remain  66.2  miles,  which  is  the  difference  of  latitude  be- 
tween the  ship  and  Cape  Cod.  In  the  same  manner,  by  subtract- 
ing the  ship's  departure,  64.3  miles,  from  the  whole  departure, 
84  miles,  there  remain  19.7  miles  for  the  departure  between  the 
ship  and  Cape  Cod.  With  this  difference  of  latitude  66.2,  and 
departure  19.7,  the  bearing  of  Cape  Cod  is  found,  by  Case  VI, 
Plane  Sailing,  S.  16*^  34'  W.,  and  its  distance  69.1  miles. 


Current  Sailing. 


Traverse  Table. 


Courses. 

Dist. 

Diff.  of  Lat. 

1 
Departure.    ; 

N. 

S. 

E. 

W.    1 

1 

South. 

W.  S.  W. 

S.  W. 

W. 

10 

25 

30 
20 

10.  0 

9.6 

21.2 

23.1 

21.2 

20.  0 

Diff.  of  lat. . . 

40.8 

Dep... 64.  3 

Art.  116.    When  a  ship  sails  through  a  sea  in  which  there  is  a  current,  the  effect  will  be  to  set  her  in  a 

certain  direction  and  at  a  certain  rate.     It  may  be  reduced  to  a  case  of  Traverse  Sailing  '^Y  considering  the  jW 
and  drij 
The  me 


1  direction  and  at  a  certain  rate,  it  may  dc  reciuceci  10  a  cubc  ui  iiavcia..  oaiii..g  .j_y  ^^..0..^....^,  ...v,-.. 
'■ift  of  the  current  as  a  separate  course  and  distance,  and  a  traverse  worked  to  obtain  the  combined  result, 
lethod  of  treating  currents  will  be  described  under  the  head  '■'■Navigating  the  Ship." 


» 


2.— SPHERICAL  SAILING. 


Art.  11 '7.  In  Plane  Sailing  the  earth's  surface  has  been  considered  an  extended  plane,  and  the  relations 
considered  between  Course,  Distance,  Difference  of  Latitude,  and  Departure  from  the  meridian. 

As  lonfT  as  the  distance  sailed  over  is  small  this  supposition  is  comparatively  correct,  but  as  soon  as  the  Ditter- 
ence  of  Longitude  enters  into  consideration,  then  the  surface  of  the  earth  must  be  regarded  as  spherical,  and  new 
problems  arise  embracing  the  five  elements,  viz  :  Course,  Distance,  Departure,  Difference  of  Latitude, 
and  Difference  of  Longitude.  ^  ^^  ,         •■ 

Under  the  head  of  SPHERICAL  Sailing  are  to  be  treated  Parallel,  Middle  Latitude,  Mercator  s,  and 
Great  Circle  Sailings. 

Parallel  Sailing. 


Art.  11§.    When  a  ship  sails  due  East,  or  West,  on  a  parallel  of  latitude,  the  distance  sailed 
and  the  course  =  90'^.  ^ 

The  problem  involved  is  to  determine  the  relations  between — 

L.,  the  latitude  of  the  parallel. 

Dep.,  the  departure,  and 

D.  Lo.,  the  difference  of  longitude. 

In  Fig.  32  let  T  and  T'  be  two  places,  P  the  adjacent  pole,  TT'  the  arc  of  the  paral-  o 
lei  of  latitude  through  the  two  places,  MM'  the  corresponding  arc  of  the  equator  inter- 
cepted between  their  meridians  PM  and  PM'. 

Then  TT'  =  Dep.,  the  departure  on  the  parallel  whose  latitude  is  TCM  =  OTC,  and 
whose  radius  is  OT  =  r.  ,     1       rrr 

MM'  =  D.  Lo.,  the  arc  of  the  equator  which  is  the  measure  of  MPM  ,  the  differ- 
ence of  longitude  of  the  meridians  PM  and  PM'. 

The  radius  of  the  equator  CM  =  CT  =  R. 

TT'  and  MM'  are  similar  arcs  of  two  circles,  and  are  therefore  proportional  to  the 

radii  of  the  circles. 

TT'    :  MM'      =  OT  :  CM,  or 
Dep.  :  D.  Lo.  =  r  :  R. 


departure, 


44  THE    SAILINGS. 

In  the  right  triangle  COT —  ,li 

OT 
Cos  CTO  =  ^^,  or 

Cos  L.      =      ;  hence, 
K. 

;■  ^  R  cos  L. 

Hence,  the  radius  of  a  parallel  of  latitude  is  equal  to  the  radius  of  the  equator  multiplied  by  the  cosine  of  the  latitude. 

Substituting  this  value  of  r  in  the  proportion 

Dep.  :  D.  Lo.  =  R.  cos  L.  :  R. 
Dep.  :  D.  Lo.  =  cos  L.  :  i  or, 

Dep.     =  D.  Lo.  cos  L.         and, 
D.  Lo.  =  Dep.  sec  L. 

Case  I. 

The  difference  of  longitude  between  two  places  in  the  same  parallel'  of  latitude  being  given,  to  find  the  distance  betwedk 

them. 


1 


Suppose  a  ship  in  the  latitude  of  49°  30'  N.  or  S.,  sails  directly  east  or  west,  until  her  difference  of  longi- 
tude be  3"^  30' ;  required  the  distance  sailed. 

L.  =  49^  30'  log  cos.  9.81254 

D.  Lo.  =       210  log  2.32222 

Dep.  =  Dist.     =     136.4  log         2.13476 

BY   INSPECTION. 

Find  the  latitude  among  the  degrees  in  Table  2,  and  in  the  distance  column  the  difference  of  longitude 
opposite  to  which,  in  the  column  of  latitude,  will  be  the  distance  required. 

In  the  present  example  the  latitude  is  49"  30' ;  and  as  the  table  is  only  calculated  to  single  degrees,  we  mu^ 
find  the  numbers  in  the  tables  of  49"^  and  50'^',  and  take  the  mean  of  them ;  the  former  is  137.8,  the  latter  135.0,  tl 
mean  of  which  is  the  sought  distance  or  departure,  136.4.  J 

Case  II.  -     ^ 

The  distance  between  two  places  on  the  same  parallel  of  latitude  given,  to  find  their  difference  of  longitude. 

Suppose  a  ship  in  the  latitude  of  49*^  30'  N.  or  S.,  and  longitude  36^'  40'  W.,  sails  directly  west  136.4  miles: 
required  the  difference  of  longitude,  and  longitude  in. 


L.         =49°  30'  log  sec.  0.18746 

Dep.     =    136.4  log         2.13481 

D.  Lo.  =       210  log         2.32227 

Lo.       =  36°  40'  W. 
D.  Lo.  =   3    30  W. 

Lo'       =40    10  W, 

BY    INSPECTION. 


I 


Look  for  the  latitude  among  the  degrees,  as  if  it  was  a  course,  and  the  departure  in  the  column  of  latitude; 
against  which  will  stand  the  difference  of  longitude  in  the  distance  column. 

Thus,  in  the  course  49^,  we  must  seek  for  136.4  in  the  latitude  column,  and  we  find  it  corresponds  to  the  dis- 
tance 208;  and  in  the  course  50"-,  we  find  it  nearly  corresponds  to  212;  half  the  sum  of  208  and  212  is  210,  which 
is  the  sought  difference  of  longitude. 

This  method  of  Saihng  was  resorted  to  in  days  when  the  means  of  determining  the  longitude  were  not  reliable, 
and  it  was  the  practice  to  make  the  parallel  sought,  and  then  run  on  a  due  east  or  west  course. 

Middle  Latitude  Sailing. 

Art.  119*    When  a  ship  follows  a  course  obliquely  across  the  meridian,  two  methods  are  in  use  for  calcu-jl 
lating  the  difference  of  longitude,  Mercator's  Sailing  and  Middle  Latitude  Sailing;   the  former  of  which  would  be  ■' 
perfectly  accurate  if  the  meridional  differences  of  latitude  were  carried  to  a  sufficient  number  of  decimals.     The 
latter  is  but  an  approximation,  though  sufficiently  accurate  for  short  runs  and  for  a  day's  work;  in  calculating  large  ^ 
distances  it  is  liable  to  error.  _  1 

Ai't.  120.    Middle  Latitude  Sailing  regards  the  departure  as  the  distance  between  the  meridian  leftj 
and  the  meridian  arrived  at  on  the  middle  parallel  of  latitude — 

Mid.  L.  =  X  (L.  +  L'). 

and  there  is  involved  the  following  problem  : 

Given  the  course  and  distance  and  the  latitude  lefty  to  find  the  difference  of  longitude. 

By  Plane  Sailing — 

D.  L.  :=  Dist.  cos  C.         Dep.  :=  Dist.  sin  C. 

L'  =  L.  +  D.  L.  :  Mid.  L.  —  >^  (L.  +  L')  =  L  +  ^^  D.  L. 


THE    SAILINGS. 


45 


id  by  Parallel  Sailing — 
ince 


D.  Lo.  =  Dep.  sec.  Mid.  L. 

Dep.     =  Dist.  sin  C 

D.  Lo.  r=  Dist.  sin  C.  sec.  Mid.  L. 


Art.  121.    From  these  equations  the  following  Table  is  formed,  which  contains  all  the  rules  necessary  for 
)lving  the  various  cases  of  Middle  Latitude  SaiHng : 


Given. 

To  find. 

Solutions. 

Both  latitudes  and 
longitudes. 

Departure . 

Dep.     =D.  Lo.  X  cos  Mid.  L. 

Tan.  C.  =  Dep.    ~  D.  L.  or'tan  C.  =  (cos  Mid.  L.X  D.  Lo.)  -~  D.  L. 

Dist.      =  sec  C.  X  D.  L.  or  Dist.  =  Dep.  -^  sin  C. 

I 

Course 

Distance . . . . 

Both  latitudes  and 
departure. 

Course  ... ... 

Tan  C.  =  Dep.  -f-  D.  L.               '' 

Dist.      ^  Dep.  -f-  sin  C. 

D.  Lo.  =  Dep.  ~  cos  Mid.  L. 

2 

Distance 

Difference  of  longitude 

3 

One  latitude,  course, 
and  distance. 

Difference  of  latitude. 

Departure 

Difference  of  longitude 

D.  L.    =  Dist.  X  cos  C. 
Dep.      =  Dist.   X  sin  C. 
D.  Lo.  =  Dep.    X  sec  Mid.  L.  or  (Dist.  X  sin  C  X  sec  Mid.  L.) 

Both  latitudes  and 
course. 

Departure 

Dep.      =  D.  L.  X  tan  C. 

Dist.      —  D.  L.  —  cos  C. 

4 

Distance 

Difference  of  longitude 

D.  Lo.  =  Dep.    X  sec  Mid.  L.  or  D.  L.  X  tan  C  X  sec  Mid.  L. 

5 

Both  latitudes  and 
distance. 

Course 

Departure 

Difference  of  longitude 

Cos  C.  =  D.  L.  -f-  Dist. 

Dep.      =  Dist.    X  sin  C. 

D.  Lo.  =  Dep.   X  sec  Mid.  L. 

6 

One  latitude,  course, 
and  departure. 

Difference  of  latitude. 
Distance 

Difference  of  longitude 

D.  L.    =  Dep.  -r-  tan  C. 
Dist.      =  Dep.  -f-  sin  C. 
D.  Lo.  =  Dep.    X  sec  Mid.  L. 

7 

One    latitude,  dis- 
tance, and  depart- 
ure. 

Difference  of  latitude.;  D.  L.    =  Dist.    X  cos.  C. 

Art.  132.    The  assumption  that 

Mid.  L.  =  ^(L. +  L') 

5  sufficiently  accurate  for  small  distances,  but  where  great  precision  is  desirable  there  must  be  applied  a  small  cor- 
action  to  the  Middle  Latitude  which  is  given  in  the  following  Table : 


This  Table  contains  the  correction,  in  minutes,  to  be  added  to  the   Middle  Latitude  to  obtain  the  cor- 
rected Middle  Latitude. 

Mid. 
Lat. 

Difference  of  Latitude. 

Mid. 
Lat. 

IP 

0 
0 
0 
0 
0 
0 
0 
0 
0 

2c 

30 

40 

5° 

6° 

70 

8° 

9^ 

10° 

12° 

14° 

16° 

18° 

200 

o 

15 
i8 

21 

/ 

2 

1 

3 
0 
2 

/ 

5 
4 
4 

7 
6 

5 

/ 

9 
8 

7 

/ 

12 
ID 

9 

15 

13 
12 

1 

18 
16 

15 

1 

26 

23 
21 

36 

32 
29 

/ 

47 
41 
37 

59 
52 
47 

/ 

72 
64 
58 

0 

15 
18 

21 

24 
30 

35 
40 

45 
50 

2 

2 
2 

3 

0 

3 

5 
5 
4 

7 
6 
6 

8 

II 

10 
10 

14 

13 
12 

20 
18 
18 

27 
25 
24 

35 
32 
32 

44 
41 
40 

54 
50 
49 

24 
30 
35 

2 

2 
2 

3 

3 
4 

5 

5 
5 

6 

6 
7 

8 
8 
9 

10 
II 
II 

13 

13 
14 

18 

19 
20 

^1 
26 

28 

32 
36 

41 

43 
46 

50 

53 
57 

40 
45 
50 

5? 
58 
60 

0 
0 
0 

2 

2 

3 
3 
3 

4 
4 
4 

6 

6 
6 

8 
8 
9 

10 
II 
II 

13 

14 
14 

16 

22 

24 
26 

31 

33 
35 

40 

43 
46 

49 
52 
57 

51 

63 

68 

72 

55 
58 
60 

62 
64 
66 

0 
0 
0 

2 

2 

2 

3 
3 
4 

5 
5 
5 

7 
7 
8 

9 
10 
II 

12 

13 
14 

18 

19 
20 
22 

27 
29 
32 

37 
40 

43 

62 
67 

72 

77 

83 
90 

62 
64 
66 

68 
70 
72 

0 
0 
0 

2 

2 

3 

4 
4 
5 

6 
6 
7 

8 
9 

ID 

12 

13 
14 

15 
16 
18 

19 
21 

23 

24 
26 
29 

34 
38 
42 

47 
58 

62 
68 
76 

79 
88 

98 

99 
no 

124 

68 
70 
72 

This  Table  is  to  be  entered  at  the  top  with  the  difference  of  the  two  latitudes,  and  at  the  side  with 
the  middle  latitude  :  under  the  former,  and  opposite  to  the  latter,  is  the  correction,  in  minutes,  to  be 
added  to  the  middle  latitude,  to  obtain  the  corrected  middle  latitude. 

46 


THE    SAILINGS. 


An.  133.  In  order  to  be  accurate,  the  Middle  Latitude  should  be  used  only  when  the  latitudes  are  of  the 
same  name.  If  of  different  names  and  the  distance  small,  the  departure  may  be  assumed  equal  to  the  difference 
of  longitude  since  the  meridians  are  sensibly  parallel  near  the  ecjuator.  But  if  the  distance  is  great,  the  two  por- 
tions of  the  track  on  opposites  of  the  equator  may  be  treated  separately. 

Case  I. 

The  latitudes  and  longitudes  of  two  places  given,  to  find  their  hearing  and  distance. 

Required,  the  l)earing  and  distance  between  Cape  Cod  light-house,  in  the  latitude  of  42°  3'  N.,  longitude 
70"  4'  W.,  and  the  island  of  St.  Mary  (one  of  the  Western  Islands),  in  the  latitude  of  36'^  59'  N.,  and  longitude 
250  10'  W. 


Cape  Cod's  latitude, 
St.  Mary's  latitude. 

Difference  of  latitude, 
In  miles, 


42°    3'  N. 
36    59  N. 


42°    3' 
36    59 


Longitude, 
Longitude, 


5      4 
60 


Sum, 

Middle  latitude, 


304 


79 


39    31 


70° 
25 

4' 
10 

W. 

w. 

44    54 
60 

BY   COMPUTATION. 


D.  L. 


D.  L.  = 
D.  Lo.  = 
Mid.  L. 


Dep.  =  D.  Lo.  cos  Mid.  L.        Tan  C 
Dist.  —  D.  L.  sec  C. 
304  ar.  CO  log  7.5 1 713        log 


Difference  of  longitude,  2,694  miles, 
cos  Mid.  L.  X  D.  Lo. 


2694 


39°  31' 


log        3.43040 
log  cos  9.88730 


log  3-43040 

log  cos      9.88730 


2.48287 


Dep.        =      2078        log        3.31770 
C.  =81041' 


Dist.        =      2102  miles 
Bearing,  S.  81' '  41'  E.,  or  E.  %  S.  nearly. 


log  tan      0.83483        log  sec  0.83970 
log        3-32257 


BY  INSPECTION. 


Look  for  the  middle  latitude  as  if  it  was  a  course  in  Plane  Sailing,  and  the  difference  of  longitude  in  the  dis- 
tance column,  opposite  to  which,  in  the  column  of  latitude,  will  stand  the  departure ;  having  the  difference  of 
latitude  and  departure,  the  course  and  distance  are  found  (as  in  Case  VI,  Plane  Sailing)  by  seeking  in  Table  2,  with 
the  ditierence  of  latitude  and  departure,  until  they  are  found  to  agree  in  their  respective  columns  ;  opposite  to 
them  will  be  found  the  distance  in  its  column,  and  the  course  will  be  found  at  the  top  of  that  table,  if  the  departure 
be  Icis  than  the  difference  of  latitude,  otherwise  at  the  bottom. 

Thus,  with  one-tenth  of  the  difference  of  longitude  269.4  or  269,  enter  Table  2,  and  oppo.-ite  to  it,  in  the  distance 
column  of  the  tables  of  39^  and  40^,  find  209.1,  and  206.1  in  the  latitude  column;  now,  the  middle  latitude  being 
nearly  39J4'  ,  take  the  mean  of  these,  207.6,  for  the  departure,  which,  being  multiplied  by  10,  gives  the  whole 
departure  2076.  Again,  enter  Table  i  with  one-tenth  of  the  departure  207.6,  and  one-tenth  of  the  difference  of 
latitude  30.4,  and  find  that  they  agree  nearly  to  a  course  of  7j4^  points,  and  a  distance  of  210,  which,  multiplied  by 
10,  gives  the  sought  distance,  2,100  miles,  nearly. 

Case  II. 

Both  latitudes  and  departiire  from  the  meHdian  given,  to  find  the  course,  distance,  and  difference  of  longitude. 

A  ship  in  the  latitude  of  49°  57'  N.,  and  longitude  of  15'  16'  W.,  sails  southwesterly  till  her  departure  is  194 
miles,  and  latitude  in  47°  18'  N.     Required,  the  course,  distance,  and  longitude  in. 


Latitude  left. 
Latitude  in. 

49°  57'  N. 
47    x8  N. 

Difference  of  latitude, 

2    39  =  159  miles. 

Sum  of  latitudes. 
Middle  latitude, 

97    15 
48    38 

BY  computation. 

Tan  C.  =  Dep.  -^  D.  L.        Dist.  =  Dep.  - 

i-  sin  C.         D.  Lo.  = 

=  Dep.  -h  cos  Mic 

D.  L.       =         159        log        2.20140 

Mid.  L.  =  480  38' 

Dep.        =         194        log        2.28780 

log        2.28780 

log  cos  9.82012 
log        2.28780 

C.             =  50"  40'         log  tan  0.08640 

log  sin  9.88844 

Dist.        =     250.8  miles. 

D,  Lo.     =     293.5  =   4°  54'  W. 

\jo.          =                  15    16  W. 

log        2.39936 

log        2.46768 

Lo'          =!                  20    10  W. 

Course,  S.  50°  40'  W. 

K'' 


THJii    ISAlLiJSG«,  47 

,»  2Y  INSPECTION. 

With  the  (lifTercnce  of  latitude  and  departure,  find  the  course  and  distance  (as  in  Case  VI  of  Plane  Sailing) 
by  seeking  in  Table  2  until  the  difference  of  latitude  and  tleparture  are  found  to  correspond,  against  which,  in  the 
distance  column,  will  he  the  distance ;  and  if  the  departure  be  less  than  the  difference  of  latitude,  the  course  will  be 
found  at  the  top  of  that  table,  otherwise  at  tlie  bottom. 

Then  take  the  middle  latitude  as  a  course  and  find  the  departure  in  the  latitude  column ;  the  number  corre- 
sponding in  the  distance  column  will  be  the  difference  of  longitude. 

In  the  present  example,  with  the  difference  of  latitude  159,  and  the  departure  194,  we  find  that  the  nearest 
numbers  to  these  are  15S.0  and  195.  i,  standing  together  over  51"^^',  against  the  distance  251  ;  whence  the  course  by 
inspection  is  S.  51"-^  W.,  and  the  distance  251.  Then,  taking  as  a  course  49"^  (which  is  the  nearest  to  the  middle 
latitude  48^^  38'),  seek  for  the  departure  194  in  the  latitude  column  ;  the  nearest  number  is  194.2  ;  opposite  to  this, 
in  the  distance  column,  is  296,  for  the  difference  of  longitude;  this  value  differs  a  little  from  that  found  by  loga- 
rithms, owing  to  the  miles  of  middle  latitude  neglected  ;  for  if  we  were  also  to  find  the  difference  of  longitude  for  the 
middle  latitude  48^,  and  proportion  for  the  minutes,  the  result  would  come  out  nearly  the  same  as  by  Icgarithms. 

Case  III. 
One  latitude,  course,  and  distance  given,  to  find  the  difference  of  latitude  and  difference  of  longitude. 

A  ship  in  the  latitude  of  42°  30'  N.,  and  longitude  58°  51'  W.,  sails  S.  E.  by  S.  300  miles;  required  the  lati- 
tude and  longitude  in. 

BY  COMPUTATION. 

C.  =  33°  45'        log  cos  9  91985        log  sin  9-74474 
Dist.         =       300         log         2.47712         log         2.47712 

D.  L.       =    249.4         log         2.39697 

Dep.         =     166.7  log         2.22186         log         2.22186 

Mid.  L.    =  40°  26'  log  cos  9.88148 

D.  Lo.     =       219  ^  log         2.34038 

L.       =42'-^3o'N.  Lo.       =58^"5i'\V. 

D.  L.  =    4      9   S.  D.  Lo.  =    3    39  E. 


L'       =38    21    N.  Lo'       =55    12  W. 

BY  INSPECTION. 

With  the  course  and  distance,  find  the  difference  of  latitude  and  departure  (as  in  Case  i  of  Plane  Sailing),  by 
finding  the  given  course  at  the  top  or  bottom  of  the  tallies,  either  among  the  points  or  degrees ;  in  that  page,  and 
opposite  to  the  distance  taken  in  its  column,  will  stand  the  difference  of  latitude  and  departure  in  their  columns. 
Then  take  the  middle  latitude  as  a  course,  and  find  the  departure  in  the  latitude  column;  against  it,  in  the  distance 
column,  will  stand  the  difference  of  longitude. 

Thus,  under  the  course  three  points,  or  S.  E.  by  S.,  and  against  the  distance  300,  stand  the  difference  of  lati- 
tude 249.4,  and  the  departure  166.7.  With  the  middle  latitude  40'^  26',  or  40°,  as  a  course,  and  the  departure 
166.7,  lound  in  the  latitude  column,  find,  in  the  distance  column,  the  difference  of  longitude  218. 

Case  IV. 
Both  latitudes  and  course  given,  to  find  the  departure,  distance,  and  difference  of  longitude. 

Suppose  a  ship  sailing  from  a  place  in  the  latitude  of  49^^  57'  N.,  and  longitude  of  30^^'  W.,  makes  a  course  good 
of  S.  39*-  W.,  and'then,  by  observation,  is  in  the  latitude  of  47°  44'  N. ;  required  the  distance  run,  and  the  longi- 
tude in. 

Latitude  from,  49°  57'  N. 

Latitude  by  observation,  47    44  N. 


Difference  of  latitude 

2    13 
60 

-.        133 

Sum  of  latitudes, 

97^  41' 

Middle  latitude. 

48    51 

BY   COMPUTATION. 

Mid.  L.  =48^51' 
D.  L.      =         133 
C.           =        39"' 

log        2.12385 
log  tan  9.90837 

log         2.12385 
log  COS  9.89050 

log  COS 

;  9.81825 

Dep.       =^    I07-7 

log        2.03222 

log 

2.03222 

Dist.       =     171. 1 
D.  Lo.     =     163.7  = 
Lo.         = 

=  2'    44'W. 
30      0  W. 

log        2.23335 

log 

2.21397 

Lo'         =  32    44  W, 


48  THE    SAILINGS. 

BY  INSPECTION. 

Find  the  course  among  the  points  or  degrees  (in  Table  I  or  2,  as  in  Case  II,  Plane  Sailing),  and  the  differ, 
ence  of  latitude  in  its  column,  against  which  will  stand  the  distance  and  departure  in  their  columns ;  then  take  the 
middle  latitude  as  a  course,  and  find  the  departure  in  the  latitude  column,  against  which,  in  the  distance  column, 
will  stand  the  difference  of  longitude. 

Thus,  with  the  course  39°,  and  the  difference  of  latitude  133,  enter  Table  2,  the  nearest  number  in  the  table  is 
132.9,  which  corresponds  to  the  distance  171,  and  to  the  departure  107.6  miles. 

Then,  with  the  middle  latitude  48°  51',  or  49°,  as  a  course,  enter  Table  2,  and  seek  for  the  departure  107.6, 
in  the  latitude  column,  which  corresponds  to  the  distance  164,  or  the  difference  of  longitude. 

Case  V. 

Both  lafitudes  and  distance  given,  to  find  the  course,  departure,  and  difference  of  longitude. 

Suppose  a  ship  sails  300  miles  northwesterly  from  a  place  in  the  latitude  of  37°  N.,  and  the  longitude  of 
32°  16'  W.,  until  she  is  in  the  latitude  of  41*^  N.;   required  her  course  and  longitude  in. 

Latitude  left,  37°  o'  N,  37°  o'  N. 

Latitude  in,  41    o  41    o 

Sum,  78    o 

Middle  latitude,  39    o 

Difference  of  latitude,  240 

BY  COMrUTATION. 


37° 

0' 

N 

41 

0 

4 

0 

60 

Mid.  L.  =       39° 
D.  L.      =       240 
Dist.       =       300 

log         2.38021 
log         2.47712 

log          2.47712 
log  sin  9.77812 

log  cos 

9.89050 

c.       =36°  52' 

log  COS  9.90309 

Dep.       =       180 

log         2.25524 

log 

2.25524 

D.  Lo.    =   231.6  = 
Lo.         = 

=    30  52'  W. 

32    16 

log 

2.36474 

Lo'         = 

36      8  W. 

BY  INSPECTION. 

Find  the  course  (as  in  Case  IV,  Plane  Sailing)  by  seeking  in  Table  2  till  against  the  distance  taken  in  its 
column  is  found  the  difference  of  latitude  in  one  of  the  following  columns ;  adjoining  to  it  will  stand  the  departure; 
which,  if  less  than  the  difference  of  latitude,  the  course  is  to  be  found  at  the  top  of  the  table,  but  if  greater,  at  the 
bottom ;  then  take  the  middle  latitude  as  a  course,  and  find  the  departure  in  the  column  of  difference  of  latitude, 
against  wliich,  in  the  distance  column,  will  stand  the  difference  of  longitude. 

Thus,  the  distance  300,  and  the  difference  of  latitude  240,  are  found  to  correspond  nearly  to  a  course  of  37°, 
and  a  departure  of  180.5  ;  then,  taking  the  middle  latitude  39°  as  a  course,  seek  the  departure  180.5,  in  the  latitude, 
column,  corresponding  to  which,  in  the  distance  column,  is  the  difference  of  longitude  232. 


Case  VI. 
One  latitude,  course,  and  departure  given,  to  find  the  difference  ofi  latitude,  distance,  and  difference  of  longitude. 


I 


A  ship  in  the  latitude  of  50"  10'  8.,  and  longitude  of  30°  00'  E.,  sails  E.  S.  E.  until  her  departure  is  160  miles; 
required  her  distance  sailed,  and  latitude  and  longitude  in. 


log         2.20412 
log  sec  0.19849 


BY   COMPUTATION. 

c. 

Dep. 

=  67030' 
=         160 

=       66.3 
=     173.2 

=  50"  43' 

log 
log 

log 

tan 

O.3S278 
2.20412 

log  sin 
log 

log 

9.96562 
2.20412 

D.  L. 
Dist. 
Mid.  L. 

1. 82 134 

2.23850 

D.  Lo 

=     252.7 

L. 
D.  L 

L' 

Mid, 

L.  = 

50^^ 
I 

'  10'  s. 
6 

Lo. 
D.  L.o 

Lo' 

=  30°    0'  E 
=    4    13 

51 

50 

16  s. 
43 

=  34    13  E 

BY   INSPECTION. 

2.40261 


Find  the  course  among  the  points  or  degrees.  Table  i  or  Talkie  2  (as  in  Case  III,  Plane  Sailing),  and  the 
departure  in  its  column,  corresponding  to  which,  in  the  columns  of  distance  and  difference  of  latitude,  will  be  found 
the  distance  and  difference  of  latitude  respectively;  then,  with  the  middle  latitude  as  a  course,  seek  the  departuie 
in  the  column  of  latitude,  corresponding  to  which,  in  the  distance  column,  will  stand  the  difference  of  longitude. 


THE    SAILINGS. 


49 


j  Thus,  ester  Tabie  i,  above  E.  S.  E.,  or  6  points,   and  seek  for  the  departure   i6o,  the  nearest  to  which  is 

!;  159.8;   the  corresponding  numbers  give  the  distance  173,  and  the  difference  of  latitude  66.2  rriles. 

Enter  Table  2  with  tlie  middle  latitude  50^  43',  or  (51°  nearly)  as  a  course,  and  seek  for  the  departure  160,  in 
the  latitude  column,  opposite  to  which,  in  the  distance  column,  will  be  found  the  difference  of  longitude  254  miles, 
nearly. 

Case  VII. 

One  latitude,  distance  sailed,  and  departure  from  the  meridian  given,  to  find  the  course,  difference  of  latitude,  and 

difference  of  longitude. 

A  ship  in  the  latitude  of  49°  30'  N.,  and  longitude  of  25°  o'  W.,  sails  southeasterly  215  miles,  until  her 
departure  from  the  meridian  is  167  miles;   required  the  course  steered,  and  the  latitude  and  longitude  the  ship  is  in. 


Dist.       =        215         log 
Dep.       =         167        log 


BY   COMPUTATION. 

2.33244        log        2.33244 
2.22272 


log        2.22272 


c. 


—  enO  cK' 


50"^  58'         log  sin  9.89028        log  cos  9.79918 

2.13162 


D.  L.     =2 
L.          =49 

15   S.  =  135.4                      log 

30  N. 

L'          =47 

Mid.  L.  =48 

D.  Lo.  =    4 
Lo.         =  25 

15  N. 
23 

12  £.  =  251.5 
0  W. 

Lo'         =  20 

48  w. 

BY   INSPECTION 

log  sec  0.17774 
log         2.40046 


As  in  Case  V,  Plane  Sailing,  tind  the  course  by  seeking  in  Table  2  till  against  the  distance,  in  its  column,  is 
found  the  given  departure  in  one  of  the  following  columns,  adjoining  to  which,  in  the  other  column,  will  be  the 
difference  of  latitude,  which  if  greater  than  the  departure  the  course  will  be  at  the  top,  but  if  less  the  course  will 
be  found  at  the  bottom.  Then  take  the  middle  latitude  as  a  course,  and  find  the  departure  in  the  column  of  differ- 
ence of  latitude,  against  which,  in  the  distance  column,  will  be  found  the  difference  of  longitude. 

Thus  the  dista..ce,  215,  and  the  departure,  167,  are  found  nearly  to  correspond  to  a  course  of  51°,  and  a  differ- 
ence of  latitude  of  1 35.3 ;  then  with  the  middle  latitude,  48^,  as  a  course,  enter  the  table  and  seek  for  the  departure, 
167,  in  the  latitude  column ;  the  distance  corresponding,  250,  is  the  difference  of  longitude  nearly. 

Mercator's  Sailing. 

Art.  134.  The  principles  of  Middle  Latitude  Sailing  already  enunciated  answer  the  requirements  of  the 
Navigator  for  small  distances,  or  in  cases  where  the  difference  of  latitude  is  small  in  comparison  with  the  differ- 
ence of  longitude  ;  but  when  large  differences  of  latitude  and  longitude  r» 
are  involved,  especially  in  high  latitudes,  that  method  is  liable  to  great 
error. 

To  satisfy  such  cases  resort  must  be  had  to  the  Mercator  princi- 
ple, which  is  explained  in  Art.  63,  Chap.  II,  Part  I. 

From  the  principle  of  that  projection  there  exists  the  following 
relation : 

D.  Lo.  =  Dep.  sec  L. 

or,  in  words,  t/ie  meridians  being  parallel,  arcs  of  parallels  of  latitude 
are  shoion  as  equal  to  corresponding  arcs  of  the  equator ;  each  bei^tg  ex- 
panded in  the  proportion  of  the  secant  of  its  latitude  to  I. 

The  lengths  of  small  portions  of  the  meridian  thus  increased,  ex- 
pressed in  minutes  of  the  equator,  are  called  meridional  parts ;  see 
Art.  66.  The  meridional  parts  computed  for  every  minute  of  latitude 
from  o'-  to  90^  form  the  Table  of  ^Meridional  Parts  {Table  t,)  by  means  jyjj 
of  which  a  Mercator's  chart  may  be  constructed  and  all  cases  of  Mer- 
cator's Sailing  be  calculated.  With  the  assistance  of  Table  3  the  rules 
of  Plane  Trigonometry  answer  for  the  solution  of  all  the  problems. 

Art.  ltiS'5.  In  the  triangle  ABC  the  angle  ACB  represents  the 
course,  C. ;  side  AC  represents  the  distance,  Dist. ;  side  EC  repre- 
sents the  true  difference  of  latitude,  D.  L. ;  AB  represents  the  depart- 
ure, Dep.;  then,  corresponding  to  BC,  the  Table  of  Merid.  Parts,  or 
Increased  Latitudes,  gives  EC,  the  meridional  difference  of  latitude  w,- 
and,  completing  the  right  triangle  CEF,  EF  will  represent  the  differ- 
ence of  longitude,  D.  Lo. 

The  principles  of  Plane  Sailing  can  be  deduced  from  the  triangle 
ABC,  and  from  the  triangle  FEC  is  derived  the  characteristic  principle 
of  Mercator's  Sailing. 

Tan  ECF 


B 


Since 


D.  Lo. 


EF 
EC 

w  X  tan  C. 


Fig.  33. 


Art.  126.    To  find  the  arc  of  the  expanded  meridian  intercepted  lietween  any  two  parallels,  or  the  meridional 
difference  of  latitude,  when  both  places  are  on  the  same  side  of  the  equator,  subtract  the  meridional  parts  of  the 

4    B 


50 


THE    SAILINGS. 


lesser  latitude  from  the  meridional  parts  of  the  greate.%  the  remainder  will  be  the  meridional  difference  of  latitude; 
but  if  the  places  are  on  different  sides  of  the  equator,  the  sum  of  the  meridional  parts  will  be  the  meridional  differ- 
ence of  latitude. 

Art.  137.  When  the  bearing  is  large,  or  near  90°;  /.  <?.,  when  the  difference  of  longitude  is  greater  than 
the  difference  of  latitude,  the  method  of  Middle  Latitude  Sailing  should  be  preferred  to  Mercator  Sailing.  F"or 
accuracy,  the  proper  middle  latitude  should  be  greater  than  the  mean  of  the  latitudes;  hence,  the  Tabic  in  Art.  122 
should  be  used,  but  ordinarily  the  mean  will  suffice. 

Art.  12s.  The  various  cases  of  Mercator's  Sailing  are  given  in  the  following  Table,  with  the  formula;  for 
their  solutions;  and  each  case  is  thereafter  exemplified  by  a  practical  question: 


Case. 

Given. 

To  find. 

Solutions, 

I 

Both  latitudes  and  longi- 
tudes. 

Course 

Tan  C.  =:  D,  Lo,  -^  m. 
Dist,     =  sec  C,    X  D.  L. 
Dist.      =  D.  L.    —  cos  C. 
Dep.     =  D.  L.    X  tan  C. 
Dep.      =  (D,  L,  X  D.  Lo. )  -i-  m. 

Distance  .... .... 

Departure 

2 

Both  latitudes  and  depar- 
ture. 

Course 

Tan  C,  =  Dep.  •    -^  D.  L, 
Dist.     =  D.  L.    X  sec  C. 
Dist.     =  Dep.     ^  sin  C, 
D,  Lo.  =  m.          X  tan  C. 
D,  Lo,  =  (Dep.   X  m.  ^  D,  L. 

Distance 

Difference  of  longitude 

3 

One  latitude,  course,  and 
distance. 

Departure 

Dep.      =  Dist.      X  sin  C. 
D.  L.    =  Dist.      X  cos  C. 
D.  Lo.  =  m.          X  tan  C. 

Difference  of  latitude 

Difference  of  longitude 

4 

Both  latitudes  and  course. 

Distance  . .. 

Dist.      =  D.  L.    —  cos  C. 
Dep.     =  D,  L.     X  tan  C, 
D,  Lo.  =  m.          X  tan  C. 

Departure 

Difference  of  longitude 

5 

Both   latitudes   and  dis- 
tance. 

Course 

Departure .. 

Cos  C.  =  D.  L.    —  Dist. 
Dep.      =  Dist.      X  sin  C. 
D.  Lo.  :=  m.          X  tan  C. 

Difference  of  longitude 

6 

One  latitude,  course,  and 
departure. 

Difference  of  latitude 

Distance 

D    L.    =Dep.      -l-tanC, 
Dist.      =  Dep.     -:-  sin  C, 
D.  Lo.  =  m.          X  tan  C. 
D.  Lo.  =  (Dep.    X  m.)  -7-  D.  L. 

Difference  of  longitude 

7 

One    latitude,    distance, 
and  departure. 

Course  

SinC,    =  Dep.     —Dist. 

D.  L.     =  Dist.      X  cos  C. 

D.  Lo.  =  m.          X  tan  C. 

D.  Lo.  =  (Dep.    X  m.)  —  D.  L. 

1 

Difference  of  latitude 

Difference  of  longitude 

I 


Case  I, 

T^  latititdes  and  longitudes  of  hvo  places  given,  to  find  the  direct  course  and  distance  betiveen  them. 

Required  the  bearing  and  distance  from  Cape  Cod  light-house,  in  the  latitude  of  42°  03'  N.  and  longitude 
70*^  04'  W.,  to  the  island  of  St.  Mary,  one  of  the  Western  Islands,  in  the  latitude  of  36°  59'  N,  and  longitude  of 
250  10'  W, 

BY   COMPUTATION, 


L. 


=  42^  03'  N, 
=  36    59  N, 


Merid,  parts  2770.4 
Merid.  parts  zyjT-^ 


Lo. 
Lo' 


=  70^ 

=  25 


4'W. 
10 


D.  L, 


5      4 
304 

L.    = 


D. 

m.  = 

D,  Lo.  = 

C.  = 


304 
392.8 
2694 


log 
log 


392.8 


2.59417 
3-43040 


44    54 
2694 


81^  42'         log  tan  0.83623 


Dist.      =        2106 
Course,  S,  81"  42'  E, 


D.  Lo. 

log        2.48287 

log  sec  0.84056 
log        3-32343 


THE    SAILINGS. 


51 


BY   INSPECTION. 

With  the  meridional  difTercnce  of  latitude  and  the  difference  of  longitude  used  as  difference  of  latitude  and 
departure,  tind  the  course  by  inspecting  Table  2  corresponding  to  those  numbers ;  with  this  course  and  the  proper 
ditlerence  of  latitude,  timl  the  correspontling  distance. 

Thus,  one-tenth  of  the  meridional  difference  of  latitude  and  difference  of  longitude  are  found,  by  interpolation, 
to  agree  nearly  to  a  course  of  Si*^  30';  this  course  and  the  proper  difference  of  latitude  are  found  to  correspond  to 
a  distance  of  2,165  '"'les.  differing  somewhat  from  the  distance  found  by  computation,  owing  to  the  neglect  of  a 
few  minutes  In  the  course. 

Case  II. 

Both  Itjtittidcs  and  titc  departure'  ghwn,  to  find  the  course,  distaiirc,  and  difference  of  longitude. 

A  ship  in  the  latitude  of  49  '  57'  N.  and  longitude  of  15"^  16'  W.  sails  southwesterly  until  her  departure  is  197 
miles,  and  then,  by  observation,  is  in  the  latitude  of  47^^  18'  N. ;  required,  her  course,  distance,  and  longitude  in. 

BY  COMPUTATION. 


159 
197 

239-9 

51^  06' 

253-2 
297.2 

4°  57' 
15    16 

L 
L 

W. 
W. 

w. 

.  =  49°  57'        M< 
'=47    18         M( 

irid.  parts  3452.2 
;rid.  parts  3212.3 

=                239.9 
log        2.20140 

log  sec  0.20207 

log 
log; 

log 

D.  L.    = 

Dep.     = 

2    39         m- 

log        2.20140 
log        2.29447 

m.          ^ 
C.          = 

log  tan  0.09307 

BY   INSPE( 

2.3S003 
tan  0.09307 

Dist.     = 
D.  Lo.  = 

Lo.        = 

log        2.40347 

CTION. 

2.47310 

Lo'        = 

20    13 

Find  the  course  by  Plane  Sailing,  Case  VI,  by  seeking  in  the  tables  with  the  proper  difference  of  latitude  and 
departure  till  they  are  found  to  agree  in  their  respective  columns,  corresponding  to  which  will  be  the  distance  in  its 
column,  and  the  course  will  be  found  at  the  top  of  that  column  if  the  departure  is  less  than  the  proper  difference 
of  latitude,  otherwise  at  the  bottom ;  with  the  same  course  find  the  meridional  difference  of  latitude  in  the  latitude 
column,  corresponding  to  which,  in  the  departure  column,  will  be  the  true  difference  of  longitude. 

Thus,  with  the  difference  of  latitude  and  departure  159  and  197,  find  the  course  51"",  and  the  distance  253;  in 
the  same  table,  opposite  to  half  of  the  meridional  difference  of  latitude  I20,  find  the  departure  148.0,  which,  being 
multiplied  by  2,  gives  the  difference  of  longitude  296  miles,  nearly. 


Case  III. 
One  latitude,  course,  and  distance  given,  to  find  the  difference  of  latitude  and  difference  of  longitude. 


A  ship  in  the  latitude  of  42°  30'  N.,  and  longitude  of  58^  51' W.,  sails  S.  W.  by  S.  300  miles;  required  the 
latitude  and  longitude  in. 

BY    COMPUTATION. 


I 


c. 

Dist. 

=  3-3°  45' 
=        300 

=    4°    9'  S.  = 
=  42    30  N. 

log  cos  9.91985 
log        2.47712 

log  tan 

log 
log 

9.82489 

D.  L. 
L. 

249.4   log        2.39697 
Merid.  parts  =  2806.7 

Merid.  parts  =  2480. 7 

326.0 

=    217.8 

L' 
m. 
D.  Lo. 

=  38    21  N. 
=    3°38'W. 

2.51322 
2.33811 

Lo. 


Lo' 


58  51  w. 


=:  62      29  W. 


BY  INSPECTION. 


As  in  Case  I,  Plane  Sailing,  find  the  course  at  the  top  or  bottom  of  the  tables,  either  among  the  points  01 
degrees,  and  in  that  page,  opposite  the  distance,  will  be  fourd  the  difference  of  latitude  and  departure  in  their 
respective  columns.  Then,  in  the  same  table,  find  the  meridional  difference  of  latitude,  in  the  latitude  column; 
corresponding  to  which,  in  the  departure  column,  will  be  the  difference  of  longitude. 

Thus,  under  the  course  S.  \V.  by  S.,  or  3  points,  and  ojiposite  the  distance  300,  stands  the  difference  of  latitude 
249.4.  Then,  under  the  same  course,  find  half  of  the  meridional  ditlerence  of  latitude  in  the  latitude  column, 
against  which  stands  108.9,  in  the  departure  column;  which,  multiplied  by  2,  gives  217.8,  the  difference  of  longi- 
tude. 


52  THE    SAILINGS. 

Case  IV. 
Both  latitudes  and  course  given,  to  find  the  distance  and  difference  of  longitude . 

A  ship  from  the  latitude  of  49°  57'  N.,  and  longitude  of  30"  W.,  sails  S.  39°  W.,  till  she  arrives  in  the  latitude 
of  47°  44'  N. ;  required  the  distance  run,  and  longitude  in. 

BY   COMPUTATION. 


L.         =  49°  57'  N.  Merid.  parts,  3452.2 

L'        =47    44  N.  Merid.  parts,  3250.7 


D.  L.  ^ 

2    13 

:   133         m.    = 

201. 

5 

C.          =     39° 
D.L.     =     133 

log  cos  9.89050 
log        2.12385 

log  tan 

9.90837 

m.          =     201.5 

— 

log 

2.30428 

Dist.      =     1 71. 1 
D.  Lo.  =    2°  43' 
Lo.        =30      0 

W. 
W. 

w. 

= 

log        2.23335 

163.2 

log 

2.21265 

Lo'        =32    43 

BY 

INSPECTION. 

As  in  Case  II,  Plane  Sailing,  find  the  course  among  the  points  or  degrees,  and  the  proper  difference  of  lati- 
tude in  its  column,  adjoining  to  which  will  be  the  distance  and  departure  in  their  respective  columns;  then,  in  the 
same  table,  find  the  meridional  difference  of  latitude  in  the  latitude  column,  adjoining  to  which,  in  the  departure 
column,  will  be  the  difference  of  longitude. 

Thus,  under  the  course  39°,  and  opposite  the  difference  of  latitude  133  (the  nearest  to  which  is  132.9),  stand 
the  distance  171,  and  the  departure  107.6;  in  the  same  table,  opposite  the  meridional  difference  of  latitude  201.5, 
found  in  the  latitude  column,  stands  163.2,  in  the  departure  column,  which  is  the  difference  of  longitude,  as  before. 

Case  V. 

Both  latitudes  and  distance  given,  to  find  the  course  and  dififcrence  of  longitude. 

A  ship  from  the  latitude  of  37  "  N.,  and  longitude  of  32"  16'  W.,  sails  300  miles  northwesterly,  until  she  is  in 
the  latitude  of  41*^  N.;  required  the  course  steered,  and  longitude  in. 

BY   COMPUTATION. 


L.        =  370  N. 
L'        =41    N. 

Merid. 
Merid. 

parts,  2378.8 
parts,  2686.5 

D.   L.  =     4O  :=  240 

miles. 

m.   = 

307-7 

D.  L.    =     240 
Dist.     =     300 

log 
log 

log  cos 

2.38021 
2.47712 

m.          =     307.7 

c.       =36^52' 

9.90309 

log         2.48813 
log  tan  9.87501 

D.  Lo.  =    3    51  W.  = 
Lo.       =32    16  W. 

230.7 

log        2.36314 

Lo'        =36    07  W. 
Course,  N.  W.  ^  N. 

BY 

INSPECTION. 

As  in  Case  IV,  Plane  Sailing,  seek  in  the  table  till  against  the  distance,  taken  in  its  column,  is  found  the  giren 
difference  of  latitude  in  one  of  the  following  columns;  adjoining  to  it  will  stand  the  departure,  which,  if  less  than 
the  difference  of  latitude,  the  course  will  be  found  at  the  top,  otherwise  at  tlie  bottom;  in  the  same  table  find  the 
meridional  difference  of  latitude  in  the  latitude  column,  adjoining  to  which,  in  the  departure  column,  will  stand  the 
difference  of  longitude. 

Thus,  the  distance  300,  and  the  difference  of  latitude  240,  are  found  to  correspond  to  a  course  of  37°,  and  a 
departure  of  180.5  >  ^^'^  'i^  the  latitude  column,  opposite  half  the  meridional  difference  of  latitude,  153-8,  stands  I16 
in  the  departure  column,  which  doubled,  gives  the  difference  of  longitude  232. 

Case  VI. 

One  latitude,  course,  and  departure  given,  to  find  the  distance,  dififcrence  of  latitude,  and  difference  of  longitude. 

A  ship  from  the  latitude  of  50°  10'  S.,  and  longitude  of  30"  E.,  sails  E.  S.  E.  until  her  departure  is  160  miles; 
required  the  distance  sailed,  and  the  latitude  and  longitude  in. 


THE    SAILINGS.  53 


BY  COMPUTATION. 


c. 

Dep. 

=  67030' 
=     160 

=     173-2 
=    1°    6'S. 

log  sin  9.96562 
log        2.20412 

log  tan  0.38278 
log        2.20412 

logt 

an  0.38278 

Dist. 
D.  L. 

log        2.23850 
=                  66.3 

log         I. 82134 

L. 

=  50    10  S. 

Merid.  parts 

3472.4 

L' 

=  51    16  S. 

Merid.  parts 

3576.4 

m. 

= 

104.0 

log 

2.01703 

D.  Lo. 
Lo. 

=   4°  II'  E. 
=  30      0  E. 

— 

251. 1 

log 

2.39981 

Lo' 

=  34    II   E- 

BY   INSPECTION. 

As  in  Case  III,  Plane  Sailing,  find  the  course  either  in  Table  i  or  Table  2,  and  the  departure  in  its  column, 
corresponding  to  which  will  stand  the  distance  and  difference  of  latitude  in  their  respective  columns  ;  in  the  same 
table  find  the  meridional  difference  of  latitude,  in  the  latitude  column,  corresponding  to  which,  in  the  departure 
column,  will  be  found  the  difference  of  longitude. 

Thus,  over  the  course  E.  S.  E.,  or  6  points,  and  against  the  departure  160,  stands  the  distance  173  miles,  and 
the  difference  of  latitude  66.2  miles.  Again,  in  the  same  table,  find  the  meridional  difference  of  latitude  104,  in 
the  latitude  column,  opposite  to  which,  in  the  departure  column,  stands  the  difference  of  longitude  251.3  miles. 

Case  VII. 

One  latitude,  distance  sailed,  and  departure  given,  to  find  the  course,  difference  of  latitude,  and  difference  of  longitude. 

A  ship  in  the  latitude  of  49°  30'  N.,  and  the  longitude  of  25°  W.,  sails  southeasterly  215  miles,  making  167  miles 
departure ;  required,  the  course  steered  and  the  latitude  and  longitude  in. 

BY  COMPUTATION. 

Dist.    =       215        log        2.33244        log        2.33244 
Dep.   =        167        log        2.22272 

C.  =  50'  58'        log  sin  9.89028        log  cos  9.79918        log  tan  0.0911 1 

D.  L.  =    2    15   S.  ^  135-4        log        2.13162 
L.        ='49    30  N.         Merid.  parts  3410.6 

L'        =  47    15  N.        Merid.  parts  3207.9 

m.        =  202.7  l°g        2.30685 

D.Lo.^   4°  10'  E.  =  250.0  log        2.39796 

Lo.      =  25      o  W. 

Lo'      =  20    50  W. 

Course  =  yp  58'  =  S.  E.  ;^  E. 

BY   INSPECTION. 

Find  the  course  and  difference  of  latitude,  as  in  Case  V,  Plane  Sailing,  by  seeking  in  Table  2,  till  the  distance 
and  departure  are  found  to  correspond  in  their  respective  columns,  adjoining  to  which,  in  the  column  of  latitude, 
will  be  found  the  true  difference  of  latitude,  which,  if  greater  than  the  departure,  the  course  will  be  found  at  the 
top,  but  if  less,  the  course  will  be  found  at  the  bottom ;  with  this  course  seek  the  meridional  difference  of  latitude 
in  the  latitude  column,  adjoining  to  which,  in  the  departure  column,  will  be  found  the  difference  of  longitude. 

Thus,  the  distance  215,  and  the  departure  167,  are  found  to  correspond  to  a  course  of  about  51"^,  and  a  differ- 
ence of  latitude  135.3.  Find  in  this  table  one-half  the  meridional  difference  of  latitude  101.3,  opposite  to  which, 
in  the  departure  column,  stands  125.1 ;  this  doubled  gives  250.2  for  the  difference  of  longitude,  nearly. 

Great  Circle  Sailing. 

Art.  129.    As  has  been  already  shown,  the  great  advantages  of  Mercator's  Sailing  are 

1st.  Being  able  to  indicate  the  ship's  track  by  merely  placing  a  straight-edged  ruler  on  the  chart  and  drawing 
a  line  between  the  ports  of  departure  and  destination,  and  reading  directly,  by  means  of  a  parallel  line  to  the  nearest 
compass-rose,  the  course ;  or,  if  from  accidental  circumstances  the  ship  is  thrown  off  the  course  at  any  period  of 
the  voyage,  to  immediately  determine  the  new  one. 

2d.  The  ability  to  foresee  the  whole  of  the  track  ahead,  and  thus  to  know  whether  there  are  such  obstacles  in 
the  way  as  dangers,  land,  or  shoals. 

Art.  ]  30.  That  method  of  sailing  answers  every  purpose  for  short  voyages  or  within  the  tropical  regions; 
but,  in  the  present  day  of  long  voyages  and  great  competition,  much  time  and  distance  can  be  saved  by  resorting 
to  the  Great  Circle  track,  or  to  a  compromise  between  it  and  the  Rhuvtb  track,  called  a  Composite  track. 

The  great  obstacle  which  once  existed  against  the  practice  of  Great  Circle  Sailing,  viz,  the  determination  of 


54 


THE    SAILINGS. 


the  longitude,  a  necessary  element  in  the  calculations,  no  longer  exists.  Again,  the  great  labor  of  determininj 
various  points  and  pricking  them  off  on  a  Mercator  Chart,  drawing  througli  tliem  a  free-liand  curve,  is  obviatec 
by  the  use  of  charts  upon  which  all  great  circles  are  represented  as  straight  lines ;  hence,  as  with  a  rhumb  line  oi 
the  Mercator's  Chart,  the  entire  track  may  be  seen  and  obstacles  thereby  avoided. 

Hence,  there  are  two  advantages  in  favor  of  the  great-circle  track  over  the  rhumb-track;  the  difference  o 
distance  and  the  great  ratio  in  which  it  increases  in  high  latitudes  and  between  places  separated  by  many  degree; 
of  longitude  ;  and  the  difference  of  time  saved  on  a  voyage  by  a  proper  application  of  the  principles  of  the  grea 
circle.  These  advantages  apply  especially  to  steamers,  which  can  so  readily  adopt  the  constant  changes  of  course 
necessary. 

Art.  131.    To  further  illustrate  the  advantage  to  sailing  vessels,  refer  to  the  case  shown  in  Fig.  34. 

Suppose  AB  to  be  the  rhumb -line  between  the  ports  A  and  B;  course,  W.  by  S. ;  ACB  to  be  the  great-circle 
course,  vV.  by  N. ;  and  the  wind 
to  come  from  the  intermediate 
point  West. 

If  the  ship  sailed  within  6 
points  of  the  wind,  and  by  fol- 
lowing the  Mercator  track  she 
would  be  put  on  the  starboard 
tack,  and  therefore  sail  7  points 
away  from  the  direct  course, 
and,  after  running  100  miles, 
would  be  but  20  miles  nearer  the 
destination ;  whereas,  if  put  on 
the  port  tack,  a  course  would 
be  made  within  5  points  of  the 
direct  course,  and  a  gain  of  56 
miles  made  in  100  miles  run. 

Should  the  wind  be  from 
the  points  indicated  by  the  Mer- 
cator course,  W.  by  S.,  and  the 
ship  on  the  starboard  tack,  a 
course  would  be  made  at  right 
angles  to  the  direct  course,  and 
therefore  no  distance  gained; 
gained  in  100  miles  run. 

It  is  possible  in  high  latitudes  that  a  ship  may  have  such  a  wind  as  to  sail  close-hauled  on  one  tack  on  the 
rhumb-line  and  yet  be  nearing  the  port  better  by  sailing  on  the  other  tack,  or  12  points  from  the  rhumb-course. 

Art.  133.  In  order  to  make  simple  the  operation  of  laying  down  the  great-circle  track,  and  that  the  whole 
track  may  be  seen  in  advance,  Godfray  constructed  his  chart,  and,  to  make  it  answer  all  requirements,  supplemented 
it  with  a  diagram,  which  will  give,  by  inspection,  the  various  courses,  and  the  distance  to  be  run  on  each,  in  such 
manner  as  to  keep  within  )^  of  a  point  of  the  constantly-changing  course  of  the  great  circle. 

The  Chart  is  constructed  on  the  Central  ox  Gnomonic  projection,  so  that  all  great  circles  appear  as  straight  lines. 
The  Pole  is  made  the  centre  of  projection,  the  parallels  of  latitude  being  shown  as  a  series  of  concentric  circles,  the 
radius  of  any  parallel  being  equal  to 

r  cot  L., 

in  which  r  is  the  radius  of  the  parallel  of  45°.  The  meridians  are  shown  as  straight  lines  cutting  each  parallel  into 
360  equal  parts  ;  one  of  them  being  selected  as  the  prime  meridian,  the  coast  lines  are  traced  in  by  the  co-ordinates 
(Latitude  and  Longitude)  of  different  points. 

TJie  charts  extend  only  to  the  20th  parallel,  for  these  reasons  :  Great-circle  charts  are  not  needed  for  the  inter- 
tropical regions  Ijecause  the  difference  of  distance  between  the  tracks  by  the  great  circle  and  by  the  rhumb  is  so 
small  that  the  Mercator  Chart  will  answer  every  purpose;  and,  again,  the  existence  of  the  trade-winds  and  the 
doldrums  controls  the  choice  of  the  route  within  their  belts ;  besides,  the  Pole  being  assumed  as  the  centre  of  pro- 
jection, the  magnitudes  of  the  circles  increase  rapidly  in  low  latitudes,  becoming  infinite  at  the  equator.  Should 
any  other  point  than  the  pole  be  selected  as  the  centre  of  projection  the  parallels  of  latitude  would  be  represented 
as  liyperbolas,  or  ellipses. 

Art.  133.  The  Course  and  Distance  Diagram  consists  of  a  series  of  concentric  curves  corresponding 
to  the  parallels  of  latitude,  bounded  by  a  horizontal  and  a  vertical  line;  the  degrees  of  latitude  are  marked  on  the 
vertical  line,  and  the  distances  from  the  highest  latitude  on  the  horizontal  line  at  intervals  of  100  nautical  miles,  and 
through  the  various  points  of  division  are  drawn  horizontal  and  vertical  lines  over  the  whole  figure.  These  are 
again  intersected  by  32  curved  lines, _  the  spaces  between  marked  in  points  and  quarter-points  for  the  determination 
of  the  courses.  These  spaces  are  alternately  light  and  shaded,  and  the  curves  so  traced  as  to  give  the  nearest 
quarter-point.  They  are  exact  for  the  middle  of  each  space,  and  the  separation  between  a  light  and  a  shaded  space 
corresponds  to  the  intermediate  eighth-point. 


Fig.  34. 

a  course  on  the  port  tack  would  be  within  4  points  of  the  direct  course,  and  71  miles 


Art.  134.   Rules  for  using  the  Chart  and  Diagram  Problem. 


I 


Given  the  latitudes  and  the  longitudes  of  the  place  of  the  ship  and  her  port  of  destination,  to  find  the  courses  and  di 

tances  to  be  run  on  the  great-circle  track. 

Find  the  ship's  place  on  the  chart  and  join  it  by  a  straight  line  with  the  port  of  destination.  This  will  be  the 
great-circle  track. 

Note  the  direction  of  the  track  near  the  ship's  place,  /.  c.,  whether  from  N.  or  S.,  toward  E.  or  W. 

Note  also  the  highest  latitude  of  the  ship's  track,  i.  e.,  the  latitude  of  the  place  where  it  approaches  nearest  to 
the  Pole. 

Now  refer  to  the  Diagram,  and,  along  the  horizontal  line  corresponding  to  the  highest  latitude,  find  the  point 
where  it  intersects  the  curve  corresponding  to  the  latitude  of  the  ship.  This  point,  \vhich  may  be  called  the  shi/i's 
place  on  the  Diagram,  will  fall  in  one  of  the  light  or  shaded  places,  and  will  indicate  the  course  to  be  steered  in 
points  and  quarter-points  from  N.  or  S.,  toward  E.  or  \\'.,  as  previously  found;  and  at  the  same  time  its  [xjsitioii 
relatively  to  the  vertical  lines  will  give  the  distance  from  the  highest  latitude  in  miles. 


THE    SAILINGS.  55 

Determine  how  far  the  ship  must  be  run  on  the  course  thus  found,  and  this  will  be  done  by  proceeding  along 
the  horizont^  line  which  represents  the  ship's  course  on  the  I  )iagram,  going  toward  the  increasing  or  decreasing 
latitudes  as  the  track  on  the  chart  will  indicate,  until  tlie  light  or  shaded  space  corresponding  to  the  next  quarter- 
point  is  reached.  The  difference  between  the  corresponding  numbers  at  the  top  of  the  Diagram  will  he  the  dis- 
tance to  be  run  on  that  first  course,  or,  more  easily,  measure  the  distance  with  a  pair  of  compasses,  and  apply  it  to 
the  scale  of  nautical  miles  attached  to  the  Diagram;  and  in  the  same  manner  determine  the  distances  to  be  run 
upon  the  succeeding  courses.  .        ,      ,.  .  , 

Having  determined  the  distance  of  the  ship  from  the  /ng/iist  latitude,  determme  the  distance  from  that  point  to 
the  port  of  destination  in  the  same  manner ;  and  the  sum  of  the  two  distances  when  the  highest  latitude  falls 
between  the  two  places,  their  difference  when  it  does  not,  will  be  the  distance  from  one  place  to  the  other. 

Since  it  is  almost  impossible  to  keep  the  ship  on  the  exact  track  during  the  entire  voyage,  the  first  two  or 
three  courses  will  be  sufficient,  and  ihe  whole  operation,  being  so  simple  and  rapid,  had  better  be  repeated  each 
day  with  the  new  position  of  the  ship. 

Art.  135.    The  following  Example  will  illustrate  the  application  of  the  rule : 

To  find  the  courses  and  distances  on  a  great  circle  from  Cape  Agidhas,  the  southern  extremity  of  Africa,  Lat. 
34°  50'  ^■■>  Long.  20°  E.,  to  Perth,  Australia,  Lat.  31°  57'  '5'. ,  Long.  115°  53'  E. 

Having  drawn  the  track  on  the  chart,  it  will  be  seen  that  the  highest  latitude  is  44°  45',  and  that  the  track  is 
a  practicable  one. 

Now  refer  to  the  Diagram  and  find  the  point  where  the  horizontal  line  through  44^°  is  crossed  by  the  curve 
of  35^,  the  latitude  of  Agulhas.  This  point  falls  on  the  light  space  corresponding  to  t^)^  points.  Hence,  the 
first  course  is  S.  5J4^  points  E.,  or  S.  E.  by  E.  ^  E.,  and  the  corresponding  distance  is  2,130  miles  from  the  highest 

latitude. 

Then,  proceeding  along  the  horizontal  line  toward  the  highest  latitude,  measure  the  breadths  of  the  successive 
light  and  shaded  spaces  and  the  following  series  of  courses  and  distances  will  be  obtained: 

Miles. 


Miles. 

S.  SX^  points  E 43 

S.  5!^  points  E 253 

S.  i%  points  E 235 

S.  6      points  E 220 

S.  ex  points  E...... 208 

S.  (^Yz  points  E 197 


S.  6^  points  E 188 

S.  7      points  E 181 

S.  T%  points  E 176 

S.  7;4  points  E 173 

S.  >]%  points  E 171 

East 85 


Miles. 

N.  7      points  -E 181 

N.  6X  points  E 188 

&c.,  &c.,  &c., 


The  highest  latitude  being  now  reached,  the  ship  will  have  to  go  through  the  same  courses  in  an  inverse  order; 
but,  as  is  evident  from  the  chart,  the  courses  will  now  run  between  North  and  East,  and  the  series  will  be — 

Miles. 

East - 85 

N.  734:  points  E 171 

N.  ^y2  points  E 173 

N.  •}%.  points  E 1 76 

until  the  latitude  of  Perth  is  reached,  which,  as  the  Diagram  shows,  will  be  at  2,465  miles  from  the  highest  latitude. 
The  total  distance  is  therefore  4,595  miles,  which  is  204  miles  less  than  by  Mercator,  and  the  first  course  by  Mer- 
cator  would  be  N.  88^  E.,  differing  nearly  3  points  from  that  by  great  circle. 

Composite  Sailing. 


Art.  136.  Whenever  the  great  circle  by  passing  too  close  to  the  Pole  becomes  too  dangerous,  owing  to  the 
ice,  &c.,  resort  must  be  had  to  some  maximum  parallel  (the  selection  depending  upon  the  season  of  the  year  and 
the  Navigator's  knowledge).  Then  the  track  will  consist  of  a  part  of  that  parallel  and  the  parts  of  two  great  circles 
which  touch  it,  and  which  pass,  one  through  the  ship's  place  and  the  other  through  the  port  of  destination.  On  the 
great-circle  chart  the  track  will  be  shown  by  the  two  straight  lines  drawn  from  the  two  places  tangent  to  the  circle 
of  highest  latitude  and  the  part  of  this  circle  between  the  points  of  contact.  This  combination  of  Great  Circle  and 
Parallel  Sailing  is  called  Composite  Sailing.  o        i  c     t 

Art.  137.    E.XAMPLE.  A  ship  in  Lat.  30"  .V.,  Long.  18°  W.,  is  bound  to  Melbourne,  Lat.  38^  49   S.,  Long. 

'^    Mark  the  ship's  place  on  the  chart,  and  draw  the  great-circle  track.     It  will  be  found  to  reach  77>^^  South,  and 
is  consequently  impracticable.     Suppose  55*^  to  be  the  highest  latitude  decided  upon. 

Since  the  highest  latitude  is  known,  the  courses  and  distances  can  at  once  be  found  by  the  Diagram. 
The  intersection  of  the  horizontal  line  through  55^  with  the  parallel  of  the  ship's  place,  30^  falls  on  the  course 
3l^  points  at  a  distance  of  3,140  miles. 

Hence,  the  first  course  is  S.  3^  points  E.,  or  S.  E.  X  S-  ,        ,         .    .    .       ■,   x.  .  .1.      -u- 

And,  by  examining  the  distances  at  which  the  changes  of  course  take  place,  it  is  found  that  the  ship  must  run 
305  miles  on  this  course,  then  330  miles  on  the  course  S.  4  points  E.,  &c.;  but,  to  see  whether  these  courses  are 
practicable  or  not,  reference  must  be  had  to  the  chart.  ,      ^        ,         ,     ,  ■   ^    r  ^ 

Erom  the  ship's  place  draw  a  straight  line  tangent  to  the  latitude  circle  of  55°,  and  mark  the  point  of  tangency 
O-  From  Melbourne  draw  a  straight  line  tangent  to  the  same  circle  at  0.  These  two  straight  lines  and  he 
intercepted  part  of  the  parallel  from  Qio®  constitute  the  Composite  track ;  the  portion  from  Q  io  ^  being  due 
Enst 

' '  The  lengths  of  the  two  parts  from  the  ship  to  O  and  from  ®  to  Mell^ourne  may  be  deterniined,  as  before,  by 
the  Diagram.     The  portion  of  the  parallel  from  Q  to  ®  is  found  by  the  usual  rules  for  Parallel  Sailing. 

The  total  distance  will  be  found  to  be  7,003  miles,  being  400  miles  longer  than  the  direct  great-circle  track, 
and  1,130  miles  shorter  than  the  rhumb-track.  ,       i.      1  111         o      / 

The  difference  between  the  first  course  from  the  ship  to  Q  and  the  course  by  rhumb  would  be  35  14  ,  or 
nearly  '^%  points. 


56 


THE    SAILINGS. 


Art.  138.    Raper's  Method  of  drawing  the  great-circle  track  is  to  find  the  course  from  each  place  to  tht 
other  and  lay  off  both  of  these  courses  on  the  Mercator  chart,  then  to  find  the  "  tnax it/mm  separation  in  latitude  ' 

jp  and  draw  through  this  point  a  line  parallel  to  the  rhumb-line 

between  the  two  places.  Having  these  three  points,  the  track 
can  be  approximately  drawn  by  hand. 

Art.  139.    Problem, — To  fittd  the  courses  and  the  distancei 
between  the  places  and  the  vertex, 

^JS  The  Courses.— In  Fig.  35  let  A  and  B  be  the  two  places ; 

AVB  the  arc  of  the  great  circle  joining  them ;  V  the  vertex 
of  the  great -circle  track;   P  the  pole. 

P  A.B  =  C,  will  be  the  course  from  A  to  B. 

PBA  =:  C,  will  be  the  course  from  B  to  A. 

APB  =  D.  Lo.,  will  be  the  difference  of  longitude. 

L.      =90  —  PA,  the  latitude  of  A. 

L'      =  90  —  PB,  the  latitude  of  B. 


Then 


By  Napier's  Analogies- 


Tan  y2  (c  +  c) 

Tan  >^  (C  —  C) 


cos 


(L'-L.) 


sin  }^  (L'  +  L.) 

sin  X  (L'  —  L.) 
cos  }i  (L'  +  L.) 


cot  14  D,  Lo. 


cot  l4  D.  Lo. 


C.  =  X(C'-f  C). 


(C 


L.)  is  numerically  the  half-sum,  and 


C.) 
C'  =  >^(C'  +  C)  +  X(C'-C.) 

"When  the  two  places  are  on  opposite  sides  of  the  equator,  ^  ( L'  — 
}4  (L'  +  L. )  the  half-difference  of  the  two  latitudes. 

Example.   To  find  the  courses  on  the  great  circle  between  St.  Helena,  in  Lat.  15^  55'  S.,  Long.  5^  44'  W., 
and  Cape  Horn,  in  Lat.  55*^  59'  S.,  Long.  67°  16'  W. 

C.  =  course  from  St.  Helena  to  Cape  Horn. 

C'  =  course  from  Cape  Horn  to  St.  Helena. 

;^(L'  +  L.)  =  350  57' 
>^  (L'  —  L.)  =  2o  2 
)4.  D.  Lo.        =  30    46 


L. 

:^ 

15° 

55' 

L' 

= 

55 

59 

L'  +  L 

1.  =^ 

71 

54 

L'  — L 

r.  =: 

40 

4 

D.  Lo. 

= 

61 

32 

J^(L'-f 

-L.)  = 

35°  57' 

'A  (L'  - 

-L.)- 

20 

2 

J4  D.  Lo.   = 

30 

46 

>^(C'-f 

■  C.)  = 

69 

36 

;^(C'- 

■C.)  = 

35 

24 

C. 

= 

34 

12 

log  cosec  0.23130 
log  cos  9.97289 
log  cot      0.22524 

log  tan      0.42943 


log  sec  0.09177 
log  sin  9.53475 
log  cot  0.22524 


or 
or 


S.  34°  12'  W. 

N.  75      o   E. 


log  tan  9.85176 


1st. 


2d. 


=  105      o 

Art.  140.    The  Distance. 
sinK(C'  +  C.) 


Tan  y.  Dist, 


sin>^  (C  — C.) 


tan 


(L'-L.) 


Tan  A  Dist.  =  ''^%-^-,+^l\  cot  ^  (L'  +  L.) 


cos 


(C'-C.)' 


Use  the  first  formula  when  %  (L'  -|-  L. )  is  near  o,  and  consequently  y  (C  +  C.)  near  90° ;  the  second  when 
y  (L'  —  L. )  and  consequently  %.  (C'  —  C. )  are  near  o. 

In  the  foregoing  example  either  formula  may  be  used,  but  the  balance  is  in  favor  of  the  second. 


X(C'  +  C.)  =69036' 
X(C'-C.)  =35  24 
K(L'  +  L.)      =35    57 


log  cos  9.54229 
log  sec  0.08877 
log  cot  0.13954 


^  Dist.  =  1832'=  30    32         log  tan  9.77060 
Distance  =  3,664  miles. 

To  Jind  the  Vertex. 

Art.  141.  When  the  course  shaped  on  the  great  circle  from  each  place  is  less  than  90°  (reckoning  both 
courses  from  the  nearest  pole)  the  vertex  falls  between  the  two  places ;  when  one  of  the  courses  exceeds  90'-'  the 
vertex  falls  outside  the  arc  joining  them. 

FORMULAE. 

For  the  Latitude : 

Cos  Lv  =  cos  L  sin  C.      or 

Cos  Lv  =  cos  L'  sin  C 
For  the  Longitude : 


Tan  D.  Loy  = 
Tan  D.  Loy 


cot  C. 


sin  L. 

cot  C^ 
sin  L' 


or 


THE   SAILINGS. 


57 


n  the  foregoing  example — 

C. 
L. 

=  34°  12' 

=  15    55 

log  sin  9. 74980 
log  cos  9.98302 

log  cot  0.16775 
log  sin  9.43813 

Lv 

D.  Lov 
Lo. 

=  57    17 
=  79    27  W. 

=    5    44  W. 

log  cos  9. 73282 

log  tan  0.72962 

Lov 


85    1 1  W. 


To  find  the  maxirmim  separation  in  Latitude. 

Art.  142.  If  the  two  places,  A  and  B,  are  on  the  same  side  of  the  equator,  the  ship  on  the  great  circle 
track  between  them  is  always  in  a  higher  latitude  than  if  following  the  rhumb  course ;  hence,  since  both  tracks 
coincide  at  their  extremities,  there  must  be  some  point  on  the  great  circle  at  which  its  distance  from  the  rhurnl)  line, 
measured  on  a  meridian,  is  greater  than  at  any  other  point.     This  point  is  at  the  maximum  separation  in  latitude. 

When  the  two  places  are  on  opposite  sides  of  the  equator  there  are  two  points  of  maximum  separation  in  lati- 
tude, one  to  the  northward  of  the  rhumb  line  in  North  latitude,  the  other  to  the  southward  of  the  rhumb  line  in 

South  latitude.  ,      r  n    1 

Tlie  point  of  maximum  separation  necessarily  falls  between  the  places.  When  the  vertex  also  falls  between 
the  places  the  point  of  maximum  separation  falls,  between  the  vertex  and  the  place  most  distant  from  this  in  longi- 
tude.    If  the  two  places  are  in  equal  latitudes  the  vertex  and  point  of  maximum  separation  in  latitude  coincide, 

FORMULiE. 


Find  the  position  of  the  vertex  and  the  rhumb  course. 
For  the  latitude  Lm — 

Cos  Lm 


cos  Ly 


sin  course  (rhumb) 
For  longitude,  D.  Lon,,  the  difference  of  longitude  between  the  vertex  and  point  of  maximum  separation- 

r,.     T^   ,  cos  course  (rhumb) 

Sin  D.  Lom  =^ T^ 

sm  Lv 

In  the  foregoing  example — 

Rhumb  course  —  Cr  =  50°    3^ 
Lv=57     17 
log  sin  9.88457         log  cos  9.80762 
log  cos  9.73278         log  sin  9.92498 


Cr 
Lv 


:5o°    3' 
^57    17 


Lm        =  45    10  S. 
D.Lom=49    45 
Lo„ 


log  cos  9.84821 


:85       IlW. 


log  sin  9.88264 


LOr 


35    26  W. 


Art.  143.    To  find  the  point  of  intersection  E  of  the  great  circle  with 
the  equator,  when  the  two  places  A  and  B  are  on  opposite  sides. 

In  Fig.  36— 

Let  Lo.  =  rtE,  the  longitude  of  A  from  E. 

Let  Lo'  :=  /'E,  the  longitude  of  B  from  E. 

Let  D.  Lo.  =  Lo'  —  Lo.,  the  difference  of  longitude  of  B  from  A, 

Let  L.  =  Latitude  of  A. 

Let  L'  =  Latitude  of  B. 


From  the  right  triangles  AE«  and  BEi5 — 

Tan  E. 


Fig.  36. 


or. 


Tan  E.  = 


tan  k.a tan  B3 

sin  Ea       sin  E<^ 

tan  L.       tan  L' 


whence, 
and 

By  Plane  Trig., 

But 
and  put 

then 


sin  Lo.      sin  Lo" 

sin  Lo.      tan  L. 
sin  Lo'       tan  L' 

sin  Lo'  -f-  sin  Lo. tan  L'  -f-  tan  L. 

sin  Lo'  —  sin  Lo.       tan  L'  —  tan  L. 

Tan  ^  (Lo'  +  Lo.)  ^  sin  (L'  +  L.) 
Tan>i(Lo'  — Lo.)       sin  (L' —  L.) 


D.  Lo. 

X 


Lo'  —  Lo., 

K  (Lo'  4-  Lo.); 


Tan 


Lo. 
Lo' 


sin  (L'  +  L.)  ,  -r^   -,       /  V 

X  —  ^  D.  Lo. 
.jr-\-  'AD.  Lo. 


58  THE    SAILINGS. 

Find  X  from  formula  (i)  and  Lo.,  or  Lo'  from  (2),  or  (3),  and  apply  Lo.  or  Lo'  to  the  longitude  of  A  or  B  to 
ascertain  the  longitude  of  E,  the  intersection  of  the  great  circle  with  the  equator.  Attention  must  be  paid  to  the 
sign  or  name  of  L.,  L',  Lo.  and  Lo'. 

Example.  Given  two  points,  one  in  Lat.  40°  N.,  Long.  70°  W.,  and  the  other  in  Lat.  30°  S.  and  Long.  io° 
W.,  to  find  the  intersection  of  the  great  circle  with  the  equator. 

L'  =  +  40° 

L,  ^=  —  30 

L'  +  L.  :=       10        '       log  sin      9.23967 

L'  —  L.  =       70  log  cosec  0.02701 

^  D.  Lo.  =       30  log  tan      9.76144 


X  ^65'       log  tan      9.02812 

Lo'  =       36      5  corresponding  to  longitude  of  B. 

Long,  of  B  =       70     o 

Long,  of  E  ^       33    55  in  Lat.  0°. 

Example.   Given  two  places,  one  in  Lat.  40°  N.,  Long.  70°  W.,  the  other  in  Lat.  50°  N.  and  Long.  10°  W., 
to  project  the  great-circle  track  between  them. 

For  the  Courses. 


L.  =  40° 
L'  =50 

N.            L'  +  L.  = 
N.            L'  —  L.  = 

90° 
10 

>^(L' 

+  L.)  =  45C    0' 
-L.)=    5      0 
Lo.      =30      0 

log  cosec  0.1 505 1 
log  cos     9-99834 
log  cot      0.23856 

log  sec  O.I 505 1 
log  sin  8.94030 
log  cot  0.23856 

>^(C'  +  C.)  =  67    43 
;^(C'-C.)=i2      3 

log  tan     0.38741 

log  tan  9.32937 

G.  =  N.  550  40'  E.          C  =  N.  79 

0  46'  W. 

The  Distance. 

X(C'  +  C.)  =  67 

y,  (c'-c.)  =  i2 

;^(L'  +  L.)  =  45 

Yz  Dist.          =  12 
Distance  =  2,544 

0  43'                               log 

3                       log 
0                        log 

72'  =21°  12'         log 
miles. 

cos  9.57885 
sec  0.00968 
cot  0.00000 

tan  9.58853 

The  Vertex. 

L. 

C. 

=  40°    0' 
=  55    40 

=  50    46  N. 

,Ov  =46    44  E. 

=  70      0  W. 

log  cos  9.88425 
log  sin  9.91686 

log  sin  9.80807 
log  cot  9-83442 

Lv 
D.  I 
Lo. 

log  cos  9.801 II 

log  tan  0.02635 

Lot        =23    16  W. 

The  Maximum  Separation  in  Latitude. 


Rhumb  C. 
L, 

=  76° 
=  50 

=  49 
=  17 

=  23 
=  40 

44/ 
46 

28 

14  W. 
16  W. 
30  w. 

log  sin  9.98825 
log  cos  9.80105 

log  cos  9.36075 
log  sin  9.88906 

L,„ 
D.  Lo„ 

LOy 

Lo,„ 

log  cos  9.81280 

log  sin  9.47169 

Draw  on  the  chart  the  rhuml)-line  connecting  the  two  places  ;  lay  off  the  courses  N.  55°  40''  E.  and  N.  79°  46' 
W.  Through  the  point  of  maximum  separation  draw  a  line  parallel  to  the  rhumb-line,  and  through  the  three 
points  trace  the  curve,  which  will  be  approximately  the  great  circle-track. 

E.XAMPLE.  Give  two  places,  one  in  Lat.  40°  N.  and  Long.  70°  W.,  the  other  in  Lat.  30°  S.  and  Long.  10° 
W. ;  to  project  the  great-circle  track  passing  through  them. 

The  Courses. 

L.  =  30°  S.  L'  +  L.  10° 

L'  =  40    N.  L'  —  L.  70 

^(L'  +  L.)=  5"^  o'  log  cosec  1.05970  log  sec  0.00166 
>i(L'  — L.)  =  35  o  log  cos  9-9133^  log  sin  9.75859 
j4  D.  Lo.       =30      o         log  cot      0.23856        log  cot  0.23856 


^(C'  +  C.)  =  86    29         log  tan      1.21162 

>^(C'-C.)  =  44    55  log  tan  9.99881 

C.  =  N.  41°  34'  W.  C  =  .S.  480  36'  E. 


THE   SAILINGS. 

The  Distance. 

\A  (C  +  C.)  =  86^'  29'  log  sin      9-999 '8 

>^(C'  — C.)  =  44    55  log  cosec  0.15115 

^(L'  — L.)  =  35      o  log  tan      9-^4523 

yi  Dist.  =      2682'  =  44"  42'         log  tan     9-99556 

Distance  =  5,364  miles. 

The  Vertex. 

L'  =    40°    o'  log  cos  9.88425         log  sin  9.80807 

C  =    48    36  log  sin  9.87513         log  cot  9.94528 

L'v        =    54    56  log  cos  9.75938 

D.  Lov=    53    54  W.  logtano.13721 

Lo'        =70      o  W. 

Lov       =123    54  W. 

Point  of  Intersection  with  the  Equator. 

L'  +  L.        =10°    o'         log  sin      9.23967 

L' L.        =70      o         log  cosec  0.02701 

^  D.  Lo.     =30      o         log  tan      9.76144 

X  ^65  log  tan      9.02812 

Lo'  =36      5  ,  corresponding  to  Long,  of  B. 

Long,  of  B.  =  70      o 

Long,  of  E.  =  33    55  ,  in  Lat.  o^ 


59 


-^0 


The  Course  at  the  Equator. 

y^  (L'  +  L.)  =  20°  o'  log  cosec  0.46595  log  sec  0.02701 
i^(L'_L.)  =  20  o  log  cos  9.97299  log  sin  9.53405 
y.  D.  Lo.        =18      3  log  cot      0.48694        log  cot  0.48694 

i/(C'  +  C.)=83    14         log  tan      0.92588 

^  ( C  —  C. )  =  48    10  log  tan  0.04800 

Course  =35      4 

Nortli  maxiiiiuin  separation  in  Latitude, 

Qi^  —    39°  42'  log  sin  9.80534        log  COS.  9.88615 

Lv  =    54    56  log  COS  9.75931         log  sin.  9  91301 

L'm  =    25    55  N.         log  cos  9.95397 

D.  Lo'nw  =70      3  E  log  sin  9-97314 

Lo'v  =123    54  W. 

Lo'n,         =    53    51  W. 

South  maximum  separation  in  Latitude. 

Cr  =  37°  24'  log  sin  9.78346         log  cos  9.90005 

Lv  =54    56  log  cos  9.75931         log  sin  9.91301 

L„,  =  18    56  log  cos  9.97585 

D.  Lon,v  =  76    04  W.  log  sin  9.98704 

Lov  =  56    05  E. 

I^om         =  19    59  W. 
Having  the  five  points :  the  two  places,  the  intersection  with  the  equator,  and  the  two  points  of  maximum 

separation  in  latitude,  the  great  circle  may  be  traced.  .,        ■     ,    ^    .„,;  c     i  ^.,„   ^c^o  f     tn  nrn 

Example.   Given  one  place  in  Lat.  40°  S.,  Long.  20-  E.,  and  another  in  Lat.  40°  S.,  Long.  80    E.,  to  pro- 

ject  the  great-circle  track. 

The  Course. 

yt  (L'  +  L.)  =  400  o'  log  cosec  0,19193 
y  {L' —  L.)  =  o  o  log  cos  0.00000 
y  D.  Lo.         =30      o  log  cot      0.23856 

^(C'  +  C.)  =  69    38  log  tan     0.43049 

C.  =  S.  69    38'  W.         C  =  S.  69-  38  E. 


60  THE    SAILINGS. 


The  Distance. 

%.  (C  +  C.)  =  69°  38' 

log  cos  9.54161 

>^  (C  -  C.)  =    0      0 

log  sec  0.00000 

Y  (U  +  L.)  =  40     0 

log  cot  0.07619 

yi  Dist.           =      1352'  =  22°  32' 

log  tan  9.61780 

Distance,         =      2704  miles. 

The  Vertex,  also  the  tnaximum  i 

•epa 

■ration  in  Latitua 

L.     =  40^^    0'             log 

cos 

9.S8425 

C.     =  69    38              log 

sin 

9.97196 

Lv    =  44    06  S.          log 

cos 

9.85621 

Lov  =50      0  P2. 

I 


NAVIGATING    THE    SHIP. 


61 


CHAPTER   IV. 

NAVIGATING    THE    SHIP. 
TAKING  THE  DEPARTURE. 

Art*  144.  Upon  clearing  the  land,  the  first  step  previous  to  shaping  the  course  and  commencing  the  log 
is  to  fix  the  ship's  position,  or,  in  other  words,  taking  the  departure. 

The  position  of  the  ship  may  be  referred  to  some  well-known  point  of  land,  or  conspicuous  object,  whose 
latitude  and  longitude  are  tabulated,  either  by  a  compass  bearing,  or  an  astronomical  bearing,  and  an  estimated  or 
calculated  distance  ;  then  the  reverse  of  the  bearing  and  the  distance  entered  in  the  log-book  as  the  first  course  and 
distance  run. 

Art.  145.  I.  By  a  Sint.i.e  Bearing  and  Distance.— The  bearing  of  the  point  of  land  or  conspicuous 
object  being  observed  by  the  Azimuth  Compass,  the  reverse  of  the  reading  entered  in  the  log-book  as  the  first 
course  subject  to  the  same  compass  corrections  of  variation  and  de- 
viation as  all  other  compass  courses — using  the  deviation  corre- 
sponding to  the  course  of  the  ship  at  the  time  the  bearing  was 
taken. 

The  distance  to  be  estimated  by  the  Navigator  and  entered  as 
distance  run.  This  estimation  is  liable  to  error,  and  may  be  consid- 
ered sufficiently  accurate  when  the  distance  is  small ;  but,  when 
great,  the  error  becomes  too  large,  and  resort  must  be  had  to  a  more 
accurate  method. 

Art.  146.  2.  By  two  Bearings  of  the  same  object. — 
If  the  ship's  track  lay  along  the  land,  take  the  bearing  of  the  object 
and  note  the  angle  between  it  and  the  direction  of  the  ship's  head. 
After  the  ship  has  run  on  the  same  course  to  change  the  bearing  sev- 
eral points,  note  the  same  angle  again. 

Then,  in  Fig.  37,  there  are  known  the  angles  CBA  and  CAB; 
consequently  ACB,  and  the  side  AB,  being  the  distance  run  in  the  \  \(;i 

interval,  to  find  the  distance  AC  or  BC. 


By  Plane  Trigonometry, 


BC; 


AC  =  ' 


AB  sin  CAB 
sin  ACB 

AB  sin  CBA 
sin  ACB 


Example.  A  point  of  land,  C,  bore  from  the  ship's  first  position  E.  N.  E. ;  after  running  25  miles  N.  by  W. 
it  bore  S.  E. ;  required,  the  distance  of  the  ship  from  the  point  of  land  at  the  time  of  the  last  bearing. 


AB    =25 

log            1-39794 

CAB  =    7  points  =  78°  45' 

logsm      9.99157 

CBA  =    3  pomts  =  33    45 

ACB  =    6  points  =  67    30 

log  cosec  0.03438 

BC     =  26.5  miles 


log 


1.42389 


Then  the  departure  will  be  entered  as  a  course  N.  W.,  and  distance  run  26.5  miles. 

Art.  147.  Should  either  angle  be  found  equal  to  a  right  angle,  or  the  bearing  at  right  angles  to  the  course, 
the  distance  may  be  found  by  direct  inspection  of  the  Traverse  Tables ;  using  the  angle  at  the  other  observation  as 
a  Course  and  the  Distance  run  as  a  Diff.  Lat.,  the  corresponding  Dep.  will  be  the  distance  of  the  object  at  the  90^ 
bearing.  As  has  been  explained  before,  the  Traverse  Table  is  but  a  Table  of  Right  Triangles,  so  that  all  similar 
problems  may  thus  be  solved  by  direct  inspection. 

The  errors  liable  to  become  involved  in  this  method  will  arise  only  from  observation  of  the  compass  bearings, 
and  the  most  favorable  application  will  be  when  the  triangle  is  equilateral.* 


Solution  by  Inspection  of  Table  5. 

Art.  148.  The  solution  of  this  problem  may  be  facilitated  by  the  use  of  Table  5^  and  5^.  The  course 
and  distance  must  be  first  corrected  for  leeway  and  current,  and  then  if  the  bearings  are  in  points  use  Table  ^A ; 
if  in  degrees.  Table  5^?. 

RULE. 

Multiply  the  distance  run  in  the  interval  between  taking  the  bearings  by  the  two  numbers  found  in  the  table 
under  the  "Difference  between  the  course  and  first  bearing,"  and  opposite  the  "  Difference  between  the  course 
and  second  bearing;"  the  greater  product  is  the  distance  of  the  object  wh'en  the  second  bearing  was  taken;  the 
other  is  its  distance  when  abeam. 

In  the  foregoing  example  the  "  Difference  between  the  course  and  first  bearing"  being  7  points,  "Difference 

*  If  the  ship  continues  on  the  course  until  the  2d  bearing  =  the  ist  bearing  ■\-  the  Diff.  between  the  course  and  the  ist  bear- 
ing ;  in  other  words,  until  the  angle  between  the  two  bearings  —  the  angle  between  the  course  and  ist  bearing:  the  triangle 
A(  H  (Fig.  37)  becomes  an  isosceles  triangle  and  HC  =  AH,  or  the  distance  from  the  position  of  the  second  bearing  =  the  dis 
tance  run  between  the  two  bearings. 


62  NAVIGATING   THE    SHIP. 

between  the  course  and  second  bearing"  13  points,  the  corresponding  numbers  in  Table  ^A  are  found  to  be  1.06 
and  0.59,  which,  multipHed  by  25,  the  distance  run,  will  give  26.5  and  14.75,  '^e  distances,  respectively,  at  times  of 
taking  second  bearing  and  when  the  object  was  abeam. 

Art.  149.  3.  By  Cross  Bearings. — When  the  ship  is  so  located  that  bearings  may  be  taken  of  two  promi- 
nent objects  (located  on  the  chart)  differing  nearly  90°,  this  method  is  sufficiently  accurate  to  define  the  position  of 
the  ship. 

Observe  the  (rue  Dearings  of  two  points  of  land,  drawing  lines  through  them  on  the  chart  corresponding  to 
the  bearings,  and  the  place  of  the  ship  will  be  at  the  point  of  intersection. 

If  the  angle  denoting  the  difference  of  bearings  varies  much  from  a  right  angle,  the  position  will  be  uncertain, 
for  the  reason  that  a  small  error  in  the  bearing  will  produce  a  large  one  in  tlie  distance. 

Art.  150.  4.  By  Bearings  and  Distances  of  three  Ubjecis. — When  it  becomes  necessary  to  define 
the  ship's  position  with  great  accuracy  and  there  can  be  observed  three  prominent  and  known  points  on  shore, 

resort  must  be  had  to  this  method. 

Let  A,  B,  and  C,  in  Fig.  38,  be  three 

fixed  objects  on  shore,  and  from  the  ship 

at  D  suppose  the  angles  CDB  and  ADB 

were  found  :=  40°  and  60°. 

(^  With  the  complement  of  CDB  =  50°, 

draw  the  lines  BE  and  CE ;  the  point  of 
intersection  will  be  the  centre  of  a  circle, 
on  some  point  of  whose  circumference  the 
ship  must  be.  Then,  with  the  comple- 
ment of  the  angle  ADB  =:  30^,  draw  the 
lines  AF  and  BF,  meeting  at  F,  which 
point  will  be  the  centre  of  another  circle, 
P         ^  ^  on  some  point  of  whose  circumference  the 

*  "'  ■  ship  must  be.     D,  the  point  of  intersec- 

tion of  the  circumferences  of  the  two  circles,  will  be  the  position  of  the  ship. 

Should  either  of  the  angles  exceed  90°,  the  excess  of  the  angle  over  90°  must  be  laid  off  on  the  side  of  the  line 
joining  the  two  stations  opposite  to  that  on  which  the  ship  lies. 

It  is  evident  that  this  method  will  be  defective  when  the  centres  E  and  F  are  near  each  other  and  the  two 
circles  nearly  coincide. 

Art.  151.    5.  By  Soundings. — Under  some  circumstances,  where  the  depth  of  water  is  not  great  and 

varies  gradually  with  the  distance  from  the  land,  the  ship's  position  may  be  approximately  determined  by  soundings. 

Art.  15S.    6.  Astronomically. — When  a  Sumner  line  maybe  observed  nearly  at  right  angles  to  the 

bearing  of  a  prominent  object  on  shore,  the  intersection  of  the  two  will  give  accurately  the  position  of  the  ship 

(see  Chap.  IX,  Part  II). 


SHAPING  THE  COURSE. 


Art.  153.  Having  taken  the  departure,  the  course  must  then  be  shaped,  and  from  that  moment  the  run  by 
log  must  be  determined.  Having  decided  upon  the  track,  whether  by  rhumb  or  by  great  circle,  the  true  or  the 
magnetic  course  may  be  taken  from  the  chart ;  if  the  latter,  allowance  must  be  made  for  the  deviation  for  that  direc- 
tion of  the  ship's  head  to  obtain  the  compass  course.  If  sailing  in  a  known  current  there  should  be  deduced  and 
allowed  a  proper  amount  for  it.  Should  the  wind  be  ahead  and  the  ship  under  sail,  that  tack  must  be  chosen  upon 
which  the  greatest  distance  will  be  made  good  toward  the  port  of  destination ;  and,  if  sailing  on  the  great  circle, 
that  track  must  be  chosen  which  lies  nearest  the  track. 


til 


THE  DAY'S  W^ORK. 


! 


Art.  1 54.  The  days  work  is  the  operation  of  computing  from  the  data  expressed  in  the  log-book  the  ship's 
run  for  twenty-four  hours  preceding  each  noon.  The  term  is  usually  restricted  to  the  dead  reckoning ;  and  the 
data  given  are  the  latitude  and  longitude  at  the  preceding  noon  (by  observation),  the  compass  courses,  the  distance 
run  on  each  course,  the  variation  of  the  compass,  the  deviation  for  each  direction  of  the  ship's  head,  the  leeway, 
the  set  and  drift  of  currents  if  any  accurately  known,  the  force  and  direction  of  the  wind,  state  of  sea,  sail  carried, 
i.\:c. ;  to  find  the  latitude  and  longitude  by  dead  reckoning,  the  true  course  and  distance  made  good,  and  the 
compass  bearing  and  distance  of  the  port  of  destination,  or  that  point  toward  which  the  ship  is  to  be  directed  dur- 
ing the  coming  twenty- four  hours. 

Strictly  speaking,  the  day's  work  includes  all  the  computations  the  Navigator  must  make  each  day,  the  results 
of  which  are  entered  in  the  log-book,  but  that  portion  to  be  described  here  will  be  limited  to  the  dead  reckoning. 

Art.  155.  The  method  of  keeping  the  log-book  has  been  already  described,  and  to  illustrate  the  method  of 
computing  the  day's  work  the  run  shown  in  the  columns  of  Form  Z,  Art.  98,  Chap.  II,  Part  I,  will  be  taken. 

Rules  for  working  a  dayi's  7Vork. 

1.  Correct  the  several  courses  sailed*  for  variation  and  leeway,  and  enter  them  in  a  traverse  table,  and  oppo- 
site to  each  course  place  the  distance  run  on  that  course,  found  by  summing  up  the  knots  and  fathoms  sailed  by 
the  ship  on  that  course.  Find  in  Table  i  or  2  the  difference  of  latitude  and  departure  corresponding  to  each  course 
and  distance,  and  set  them  in  their  respective  columns;  then  the  difference  between  the  sums  of  the  northings  and 
southings  will  be  the  difference  of  latitude  made  good,  of  the  same  name  with  the  greater;  and  the  difference 
between  the  sums  of  the  eastings  and  westings  will  be  the  departure  made  good,  of  the  same  name  with  the  greater 
quantity. 

2.  Seek  in  Table  i  or  2  until  the  above  difference  of  latitude  and  the  departure  are  found  together  in  their 
respective  columns ;  opposite  to  tiiese  will  be  the  distance  made  good,  and  at  the  top  or  bottom  of  the  jiage, 
according  as  the  departure  is  less  or  greater  than  the  difference  of  latitude,  will  be  found  the  course. 

*  The  set  and  drift  of  a  current  (if  there  be  any)  is  to  be  reckoned  as  a  course  and  distance,  and  on  the  first  day  after  losing 
sight  of  the  land  the  bearing  and  distance  of  it  are  to  be  taken  into  account. 


»  NAVIGATING    THE    SHIP.  63 

3.  If  the  latitude  from  which  the  ship's  departure  is  taken,  or  yesterday's  latitude,  I)e  of  the  same  name  as 
the  difference  of  latitude,  add  them  togeliier ;  hut  if  of  different  names,  take  their  difference  ;  the  sum  or  remainder 
will  be  the  present  latitude  of  the  same  name  as  the  greater. 

4.  Find  the  middle  latitude  between  the  latitude  of  yesterday  and  this  day,  which  take  as  a  course  in  Table  2, 
and  seek  for  the  departure  in  the  column  of  difference  of  latitude ;  then  will  the  distance  corresponding  be  the  dif- 
ference of  longitude,  of  the  same  name  as  the  departure. 

5.  If  the  longitude  in  yesterday  be  of  the  same  name  as  the  difference  of  longitude,  add  them  together;  l)ut 
if  of  different  names  take  their  difference;  the  sum  or  remainder  will  be  the  longitude  in,  of  the  same  name  as  the 
greater. 

Example.  At  noon,  January  22d  (see  Form  Z,  Chap.  II,  Part  I),  in  Lat.  35^  10'  N.,  Long.  134  '  01'  W. ; 
variation,  15^^  E.  ;  deviation  from  E.  to  N.  E,  ^  point  E. :  to  determine  Lat.  and  Long,  by  D.  R.  at  noon  of 
January  23d. 

By  inspection  of  the  columns  it  will  be  seen  that  the  sliip  was  on  the  port  tack  during  the  entire  day,  and, 
owing  to  wind  and  sea,  making  an  average  leeway  of  i  '4  points  easterly.  Hence,  the  total  correction  to  be  applied 
to  the  compass  courses  to  obtain  the  true  courses  will  be  3  points  easterly. 

Then  form  the  following  abstract : 


Distances. 

Compass  courses. 

Correction. 

True  courses. 

6.4 

136.0 

12.0 

4.6 

6.0 

N.  2^  E. 
N.  3      E. 
N.  4      E. 
N.  3K  E. 
N.  3X  E. 

3  points  E . . 

do 

do  ..... 

....do  

do 

N.  sy^  E. 
N.  6      E. 
N.   7      E. 
N.  6K  E. 
N.  6%  E. 

From  this  abstract  arrange  the  Traverse  Table,  and  in  Table  i  find  the  corresponding  differences  of  latitudes 
and  the  departures. 


Courses. 

Distances. 

N. 

S. 

E. 

W. 

N.  sVz  E. 

6.4 

3-0 

5-6 

N.  6      E. 

136-0 

52.0 

125.6 

N.  6>^  E. 

4.6 

1-3 

4.4 

N.  6X  E. 

6.0 

1-5 

5-^ 

N.  7      E. 

12.0 

2.3 

II. 8 

D.  L.  =:  60.1  N.  Dep.  =  153.2  E. 

L.  ==  35°  10'  N. 

D.  L.     =1    GO  N. 


L.  =  36    10  N. 

Mid.  L.  =  35    40 

Entering  Table  2  with  35°  40'  as  a  course,  and  Dep.  =  153.2,  in  column  Lat.,  there  will  be  found  in  Dist. 
column  D.  Lo.  ^^  188'. 

Lo.        =  134^    I'  W. 
D.  Lo.  =      3      8   E. 


Lo'        =130    53  W. 

Entering  Table  2  with  D.  L.  =  60.  i  and  Dep.  =  153.2  the  distance  made  good  will  be  founa  Dist.  =  165 
miles,  and  the  course  C.  ^=  b?P,  or  N.  6  points  E. 
Hence,  at  noon  January  23d, 

Lat.  D.  R.,      36^3  10'  N, 

Long  D.  R.,  130    53  W. 

™    Having  obtained  the  Lat.  and  Long,  by  observation,  the  difference  will  show  the  set  and  drift  of  current,  being 
careful  to  eliminate  the  combined  errors  of  steering,  estimating  leeway,  and  logging. 
In  this  case  the  Lat.  and  Long.,  by  observation,  are — 


By  comparing  with  position  by  D.  R. — 


Lat.        36°  03'  N. 
Long.  131     14  W. 

D.  L.    =    7'  S. 
D.  Lo.  =21   W. 


From  which  the  bearing  and  distance  between  positions  by  Obs.  and  by  D.  R.  are  found  to  be- 

Dist.  =  22  miles. 

C       =  S.  71-  W.,  or  W.  S.  W.  %  W. 


64 


NAVIGATING    THE    SHIP. 


i 


The  port  of  destination  being  San  Francisco,  the  new  course  and  distance  may  be  taken  directly  from  the  chart 
by  inspection,  or  computed  by  the  proper  rules  of  Mid.  Lat.,  or  Mercator's  Saihng. 

San  Francisco,  Lat.        37°  48'  N. 
Long.    122    21   W. 

Mid.  Lat.  =  36°  56' 

D.  Lo.       =       533' 

Dep.  ==       425' 

D.  L.         =       105' 

C.  =        76^,  or  E.  N.  E.  ^  E.  (true). 

Dist.  =        440  miles. 


By  Mercator's  Sailing : 


L.  =  360    3' 
L'=37    48 


Merid.  parts  2308.2 
Merid.  parts  2439.0 


130.8 


m.         =     130.8 
D.  Lo.  =        533 

C.  =  76°  13' 

D.  L.    =        105 


log 
log 


2.11661 
2.72673 


log  tan  0.61012 


Dist.     =     440.7 

Course,  E.  N.  E.  ^  E.  (true). 


log  sec  0.62297 
log         2.021 19 

log         2.64416 


MAKING  THE  LAND. 


Art.  156.  Every  precaution  and  forethought  should  be  observed  as  the  ship  draws  near  the  land;  and 
the  careful  Navigator  will  be  on  the  lookout  for  the  many  evidences  of  the  proximity  of  land,  such  as  the  shoal- 
ing of  the  water,  the  change  of  color  of  the 
water,  the  change  of  temperature  of  the  sur- 
face-watei^  the  presence  of  land-birds,  &c.  As 
soon  as  the  land  is  made,  the  ship's  position 
should  be  laid  off  on  the  chart  by  reckoning  and 
verified  by  bearings  of  well-defined  points,  if 
any  in  view. 

Should  there  be  any  uncertainty  in  the 
longitude,  there  may  at  times  be  wisdom  in  mak- 
ing the  latitude  of  the  point  required  and  then 
running  on  the  parallel.  But  the  invariably  safe 
plan  will  be  to  locate  the  ship  on  a  Sumner's 
line,  and  know  to  a  certainty  the  relative  bear- 
ing of  the  land,  which  will  determine  the  course 
to  be  pursued  even  in  the  thickest  weather.  Of 
course,  due  regard  must  always  be  had  for  the 
soundings. 

Suppose,  for  instance,  a  ship  approaching 
the  land  in  thick  weather  is  to  make  the  point 
A,  Fig.  39.  By  an  observation  the  ship  has 
been  located  on  the  ///w  of  position,  CDBE  (see 
Chap.  IX,  Part  2),  which  is  plotted  upon  the 
chart.  On  the  line  of  bearing,  AB,  measure  the 
distance  from  A,  and  run  that  distance  on  a 
course  parallel  to  the  line  of  bearing,  and  then 
follow  carefully  the  course  parallel  to  the  line  of 
position  toward  the  land  or  point  required,  keep- 
ing tlie  lead  going.  Of  course,  it  will  be  known 
by  the  soundings  tlie  approximate  position  of 
the  ship,  as  in  Fig.  39,  whether  between  B  and 
E,  or  outside  of  B. 

There  must  be  considered  also  the  cur- 
rents, the  time  of  tide,  as  well  as  all  other  facts  laid  down  in  the  Sailing  Directions,  without  a  diligent  study  of 
which  no  careful  Navigator  would  approach  a  coast  in  either  good  or  bad  weather. 


^ 


I 

i 


NAUTICAL    ASTRONOMY. 


CHAPTER   I. 


DEFINITIONS. 

Art.  1l57.  That  branch  of  Navigation  which  relates  to  the  determination  of  a  ship's  place  at  sea  by  observations 
the  heavenly  bodies,  or  Celo-Navigation,  requires  a  knowledge  of  the  rules  and  principles  of  Nautical  Astronomy. 
—  An  observer  upon  the  surface  of  the  earth  appears  to  view  the  heavenly  bodies  as  if  they  were  situated  upon 
the  surface  of  a  vast  hollow  sphere,  of  which  his  eye  is  the  centre.  This  sphere  appears  to  have  a  motion  of  rota- 
tion about  an  axis  passing  through  the  observer's  eye,  parallel  to  the  earth's  axis.  In  reality,  we  know  that  this 
apparent  vault  has  no  existence,  and  we  can 
tlierefore  determine  only  the  relative  directions 
of  the  heavenly  bodies,  not  their  distances  from 
each  other  or  from  the  observer. 

Art*  158.  But  by  adopting  an  imagin- 
ary spherical  surface  of  an  arbitrary  radius, 
the  eye  of  the  observer  being  at  the  centre, 
the  places  of  the  heavenly  bodies  can  be  pro- 
jected upon  this  Celestial  Concave  at  points 
where  the  lines  joining  them  with  the  centre 
intersect  the  surface  of  the  sphere. 

Let  C,  in  Fig.  40,  be  the  position  of  the 
observer's  eye,  CS  and  CS'  the  radii  of  two 
concentric  spheres ;  then,  if  X,  Y,  and  Z  be 
three  heavenly  bodies,  it  matters  not  ''o  which 
of  the  spheres  their  positions-  be  referred, 
either  to  .r,  r,  and  z  in  the  smaller,  or  x'  v', 
'and  z'  in  the  larger,  forming  the  spherical 
triangle  .rj-r:,  or  x'v'z'.* 

But  since  the  centre  of  the  earth  should 
be  the  point  from  which  all  angular  distances 
should  be  measured,  the  observer,  by  trans- 
ferring himself  there,  will  find,  projected  on 
the  celestial  concave,  not  only  the  heavenly 
bodies,  but  the  imaginary  points  and  circles  of 
the  earth's  surface.  The  actual  position  of 
the  observer  on  the  surface  will  be  projected 
in  a  point  called  the  zenith  ;  the  meridians  and 
equator  will  also  be  projected 


Fig.  40. 


Art.  159.  \Mth  regard  to  the  motion  of  the  various  points  and  circles  projected  on  the  celestial  concave, 
it  must  be  considered  that  those  dependent  upon  the  observer's  position  have  a  different  motion  from  those  which 
remain  the  same,  no  matter  from  where  viewed. 

It  would  be  well,  therefore,  to  imagine  an  inner  spherical 
surface  connected  rigidly  with  the  earth  on  which  (Fig.  41) 
are  projected — 

Z,  the  zenith  of  the  observer's  position; 

HCH',  the  horizon ; 

ZPX,  the  observer's  meridian; 

PG,  the  Greenwich  meridian. 

On  the  outer  surface  are  projected  all  the  points  and 
circles  which  are  independent  of  the  observer's  position.  This 
outer  surface  is  to  be  considered  as  revolving  diurnally  about 
its  axis,  PP',  carrying  with  it  all  the  various  points  and  circles. 

Art.  160.  Spherical  Astronomy  treats  of  the  direc- 
tions of  the  heavenly  bodies  as  they  are  imagined  to  be  pro- 
jected upon  the  celestial  concave,  and  it  embraces  the  prob- 
lems which  arise  from  the  diurnal  motion,  and  also  those 
which  arise  from  the  annual  motion  so  far  as  it  affects  the  ap- 
parent positions  of  the  heavenly  bodies,  or  their  directions 
from  the  standard  points  of  reference. t 

Art.  161.  In  order  to  define  the  position,  or  location, 
of  a  point  or  points  in  sjjace,  a  system  of  lines,  angles,  or 
planes,  or  a  combination  of  these,  is  used,  to  refer  it  or  them  to 
some  fixed  line  or  plane  adopted  as  the  primitive ;  and  the  lines 
or  planes  referring  to  the  standard  are  called  co-ordinates. 

For  instance,  in  Fig.  42  is  explained  the  system  of  recti- 
linear co-ordinates  for  a  plane. 

A  fixed  line,  FE,  is  chosen^  and  a  definite  point,  C,  in  it  as  the  orit^in. 

Then,  the  position  of  a  point.  A,  is  defined  by  CB  =  x,  the  distance  from  the  origin,  C,  to  the  foot  of  perpen- 
dicular,  let  fall  from  A  on  FE;  and  by  AB  =y,  the  length  of  the  perpendicular. 


3  B 


*  Reed's  Naval  Science. 


+  Chauvenet. 


65 


66 


NAUTICAL   ASTRONOMY. 


D 


The  distance  x  is  called  the  abscissa,  and  y  the  ordinate. 

Assuming  two  intersecting  right  lines  FE  and  HI  as  standard  lines  of  reference,  the  location  of  the  point  A  is 

defined  by  regarding  the  distances  measured  to  the  right  hand  of  HI  and  above  FE  2iS  positive  ;  those  to  the  left 

■rr  hand  of  HI  and  below  FE  as  tiegative. 

An  exemplification  of  this  sys- 
tem is  found  on  the  chart,  on  which 
FE  is  represented  by  the  equator,  HI 
by  the  prime  meridian ;  the  co-ordi- 
nates X  and  )' being  the  longitude  and 
latitude  of  the  point  A. 

Art.  162.  Great  Circle  Co- 
ordinates. — The  great  circle  is  to  the 
sphere  what  the  straight  line  is  to  the 
plane;  hence,  in  order  to  define  the 
position  of  a  point  on  the  surface  of  a 
sphere,  some  great  circle  must  be 
selected  as  the  primary,  and  some 
particular  point  of  it  selected  as  the 
origin. 

Thus,  in  Fig.  43,  which  repre- 
sents the  case  of  a  sphere,  some  fixed 
great  circle,  CBQ,  is  selected  as  the 
axis,  and  called  the  primary ;  and  a 
point,  C,  chosen  as  the  origin.  Then 
to  define  the  position  of  any  point  A, 
the  abscissa  x  =  the  distance  from  C 
to  the  point  B  where  the  secondary 
great  circle  through  A  intersects  the 
primary ;  the  ordinate  y  =  the  dis- 
tance of  A  from  the  primary  meas- 
ured on  the  secondary : 


JE 


Fig.  42. 


a:  =  CB. 


JJ/rrrAB. 


In  the  case  of  the  earth  the  primary  selected  is  the  Equator  (its  plane  being  perpendicular  to  the  Earth's  axis), 
on  which  are  measured  the  abscissae ;  and  upon  the  secondaries  to  it  are  measured  the  ordinates  of  all  points  on 

the  earth's  surface.  The  initial  point  on  the  equator  for  reference  is  determined 
by  the  prime  7)ieridian  chosen.  Hence,  as  before  explained,  East  longitudes  and 
North  latitudes  are  called  positive.  West  longitudes  and  South  latitudes  are  called 
negative. 

Art.  163.  Polar  .System  of  Co-ordinates. — There  is  a  second  system  of  co- 
ordinates for  a  plane. 

A  fixed  point,  P,  is  selected,  called  the  Pole,  and  a  line  PP',  a  given  fixed  line 
through  it,  called  the  Initial  Line. 

Suppose  a  line  to  revolve  around  the  point  P,  marking  out  an  angle,  which  is 
reckoned  positive  wlien  the  revolution  is  opposite  to  the  hands  of  a  watch,  ttegative 
when  in  the  same  direction  as  the  watch  hands.  The  revolving  line  is  called  the  Ra- 
dius Vector;  the  angle  is  called  the  Polar  Angle. 

Hence,  the  position  of  the  point  A  is  defined  by  the  length  of  the  radius  vector, 
-p,    -^  PA,  and  the  polar  angle,  ZPA. 

■  ^^'  '  Art.  164.    Tliis  system  may  be  applied  to  the  surface  of  a  sphere  by  conceiving 

the  sphere  to  be  generated  by  the  revolution  of  a  semicircle  about  its  diameter. 

Suppose  the  semicircle  PZP'  (Fig.  45)  to  start  in  a  revolution  about  its  diameter,  starting  from  an  initial  posi- 
tion which  is  defined  as  PZP',  the  sphere  PQP'(y  will  be  generated ;  the  extremity  P  of  the  diameter  corre- 
sponds to  the  point  P  of  the  plane,  and 
the  fixed  great  circle,  PZP',  to  the  fixed 
line  PP'  of  the  plane.  And,  in  the 
same  manner,  the  position  of  the  point 
A  on  the  surface  of  the  sphere  will  be 
defined  by  the  co-ordinates  PA,  the 
radius  vector,  and  ZPA,  the  polar  angle. 
In  the  case  of  the  sphere,  the  angle 
.P  ZPA,  or  the  polar  angle,  is  measured 
by  the  arc  ZX  of  the  circumference 
(see  Fig.  44),  and  the  distance  on  the 
radius  vector  to  A  may  be  taken  from 
the  pole  P  as  PA,  or  by  its  complement 
AX  from  the  circumference. 

Hence  it  may  be  seen  that  from  the 
properties  of  the  sphere  the  two  corre- 
sponding systems   of    great-circle    co- 
ordinates and  polar  co-ordinates  may 
be  interchanged. 
Art.  165.    Therefore,  by  applying  these  principles  to  the  celestial  concave,  there  are  three  systems  of  co- 
ordinates, according  to  the  circle  adopted  as  the  primary  and  the  point  used  as  an  origin. 
These  systems  are — 

1.  Altitude  and  Azimuth. 

2.  Declination  and  Hour  Angle. 

3.  Declination  and  Right  Ascension. 


Fig. 


44. 


NAUTICAL   ASTRONOMY. 


67 


1— ALTITUDE  AND  AZIMUTH. 

Al't.  166.    In  this  system  the  primary  circle  is  the  Jiorizon.     An  observer  in  changing  his  position  on  the 
,  surface  of  the  earth  changes  his  zenith,  but  the  pole  of  the  heavens  remains  fixed  ;  hence,  the  object  of  this  system 
is  to  connect  the  zenith  with  the  fixed  pole,  by  observations  of  the  heavenly  bodies.     The  horizon  is  chosen  as  the 
primary  circle  because  its  pole  is  the  zenith. 

And,  since  the  object  is  to  connect  the  zenith  with  the  pole,  the  great  circle  passing  through  both  being  sec- 
ondary to  the  horizon,  affords  by  its  intersec- 
tion  the  point  of  origin  for  co-ordinates.  ^ 

This  secondary  great  circle  is  the  celes- 
tial meridian,  and  intersects  the  horizon  in 
two  points,  named  the  North  and  South 
points,  and  the  one  adjacent  to  the  elevated 
pole  is  the  one  selected  as  the  origin. 

Art.  167.  Fig.  46  will  illustrate  the 
meaning  of  the  terms  used  in  reference  to  the 
horizon. 

The  eye  of  an  observer  on  the  surface  of 
the  earth  is  always  at  a  certain  elevation,  as 
at  A,  which  gives  a  larger  view,  not  only  of 
the  earth's  surface,  but  also  of  the  heavens, 
than  if  the  eye  were  on  the  surface.  Tan- 
gents to  the  surface  from  the  eye  continued 
to  the  celestial  concave  will  give  the  small 
circle  hrli,  which  is  the  terrestrial  horizon, 
and  a  small  circle  of  the  celestial  concave 
^V//',  which  is  the  Sensible  or  Visible  Hori- 
zon of  the  Heavens.  Since  this  Sensible  Ho- 
rizon varies  according  to  the  elevation  of  the 
observer's  eye,  it  is  evident  that  it  cannot 
serve  as  the  primary  circle  for  a  system  of  co- 
ordinates. By  passing  a  plane  through  the 
common  centre  of  the  earth  and  the  celestial 
concave  parallel  to  the  plane  of  the  Sensible 
Horizon,  there  is  obtained  the  Rational  or 
Celestial  Horizon,  HR,  which  is  the  required 
great-circle  axis  for  this  system  of  co-ordi- 
nates. |\[" 

Considering  the  earth's  radius  to  be  zero,  ^         ^ 

as  compared  with  a  supposed  infinite  radius  '  ^  • 

of  the  celestial  concave,  the  Sensible  and  Celestial  Horizons  may  be  regarded  as  coinciding,  provided  the  eye  of 
the  observer  is  on  the  surface  of  the  earth.  A  tangent  plane  at  that  point  would  form  a  great  circle,  which  can 
never  be  if  the  eye  is  at  an  elevation. 

The  vertical  line  is  a  straight  line  perpendicular  to  the  plane  of  the  horizon  at  the  position  of  the  observer. 
The  two  points  of  its  interception  with  the  celestial  concave  are  the  poles  of  the  horizon,  and  are  named  the  Zenith 
and  N'adir,  the  first  above  the  horizon  at  Z,  the  second  below 
the  horizon  at  N.  (Fig.  46). 

Art.  168.  Fig.  47  is  a  stereographic  projection  of 
the  sphere  upon  the  plane  of  the  rational  horizon,  NWSE, 
the  projecting  point  being  the  nadir ;  hence,  the  zenith  is 
represented  at  Z. 

The  secondaries  to  the  horizon  are  called  vertical  circles, 
or  circles  of  altitude ;  any  place,  O,  being  selected  on  the 
surface  of  the  sphere,  the  vertical  circle  passing  through  it 
will  be  projected  into  the  straight  line  ZH,  since  all  vertical 
circles  pass  through  the  zenith  and  nadir. 

The  celestial  meridian  is  that  vertical  circle  whose  plane 
coincides  with  the  plane  of  the  terrestrial  meridian,  hence 
passes  through  the  Zenith  and  the  pole,  cutting  the  horizon 
in  two  points,  called  the  N^orth  and  South  points  of  the 
horizon. 

Since  the  object  of  this  system  is  to  connect  the  Zenith 
with  the  pole  this  plane  gives  the  point  of  origin,  and  that 
point  of  intersection  with  the  horizon  adjacent  to  the  ele- 
vated pole  is  chosen. 

The  line  of  intersection  of  the  plane  of  the  celestial 
meridian  with  the  plane  of  the  horizon  is  the  meridian  line 
NZS. 

The  vertical  circle,  which  is  perpendicular  to  the  me-  « 

ridian,  is  the  prime  vertical  WZE.     The  line  of  intersection  „ 

of  its  plane  with  that  of  the  horizon  is  the  east  and  west  47* 

line,  and  the  points  of  meeting  the  sphere  are  the  east  and  7!.>est  points  of  the  horizon. 
%       Art.  169.   The  co-ordinates  of  this  system  are  as  follows  : 

The  Azimuth  of  a  heavenly  body  is  the  arc  of  the  horizon  intercepted  between  the  vertical  circle  passing 
through  the  body,  and  the  point  of  origin.  It  is  reckoned  toward  east  or  west,  according  as  the  body  is  east  or  west 
of  the  meridian,  hence  through  iSc-.  It  is  defined  by  prefixing  the  letter  denoting  the  point  of  origin,  and  affix- 
ing the  letter  denoting  the  direction  in  which  the  azimuth  is  reckoned,  as  N.  6o'-  E.,  or  S.  120^  E. 

The  azimuth  of  the  point  O  will  be  NH,  or  SH.     Sometimes,  when  the  body  is  in  the  horizon,  it  is  referred 


68 


NAUTICAL    ASTRONOMY. 


to  the  east  or  west  points,  and  that  measure  called  the  Amplitude.  A  body  in  the  horizon,  whose  azimuth  is 
N.  60°  E.,  would  have  an  amplitude  of  E.  30°  N.     WH  would  be  the  amplitude  of  O  in  the  horizon. 

The  Altitude  of  a  heavenly  body  is  the  arc  of  the  vertical  circle  passing  through,  intercepted  between  the 
body  and  the  horizon.     The  altitude  of  the  point  O  is  HO. 

Regarding  this  system  of  co-ordinates  as  a  polar  system,  the  initial  position  of  the  radius  vector  is  the  meridian 
line,  and  the  co-ordinates  will  be  the  angle  at  the  Zenith  NZH,  or  SZH,  and  the  Zenith  distance  OZ,  which  is  the 
complement  of  the  altitude. 

2.— DECLINATION  AND  HOUR  ANGLE.  -m 

Art.  lYO.    In  this  system  the  primary  circle  is  the  Equator.     It  is  that  great  circle  nf  the  sphere,  VVQE" 
(Fig.  47),  whose  plane  is  perpendicular  to  the  axis  of  the  earth,  and  therefore  coincides  with  the  Earth's  equator. 
This  circle  is  also  called  the  Equinoctial,  for  when  the  sun  in  his  path  appears  to  pass  the  two  points  of  inter- 
section with  the  equator  the  days  and  nights  are  equal  all  over  the  earth. 

Great  circles,  secondary  to  the  Equinoctial,  are  called  Circles  of  Declination,  and  also  Hour  Circles.  POD  is 
the  Declination,  or  Hour  Circle,  passing  through  the  body  O.  _ 

Small  circles,  parallel  to  the  equator,  are  called  Parallels  of  Declination.  \ 

Art.   171.    The  co-ordinates  of  this  system  are — 

1.  Declination,  which  is  the  distance  of  a  heavenly  body  from  the  equinoctial  measured  in  a  circle  of  decli- 
nation. 

2.  Hour  Angle,  which  is  the  angle  at  the  pole  of  the  celestial  concave,  between  the  declination  circle  of  the 
heavenly  body  and  the  celestial  meridian.  The  hour  angle  is  measured  by  the  arc  of  the  equinoctial,  intercepted 
between  the  declination  circle  and  the  celestial  meridian.  J 

OD  is  the  declination  of  tlie  body  O,  and  DPZ  is  the  hour  angle,  or  the  arc  QD.  * 

The  point  of  origin  is  generally  taken  to  be   that  point  of  intersection  of  the  equinoctial  with  the  meridian 

which  is  above  the  horizon,  and  the  hour  angle,  reckoned  in  the  same  direction  in  which  the  celestial  sphere  has  its 

apparent  diurnal  motion,  from  east  to  west,  and  from  0°  to  360°,  or  from  o''  to  24^. 

The.  polar  distance  of  a  heavenly  body  is  often  used,  and  it  is  the  arc  of  the  hour  circle  intercepted  between  the 

pole  and  the  body.     PO  is  the  polar  distance  of  O.     Polar  distances  are  reckoned  from  the  poles  through  iSC^, 

and  named  North  or  South,  according  to  the  name  of  the  pole  from  which  reckoned.     It  is  sometimes  convenient 

to  distinguish  North  polar  distances  as  -\-  and  South  polar  distances  as  ^. 

3.— DECLINATION  AND  RIGHT  ASCENSION.  T 

Art.  172.    In  this  system  the  primary  circle  is  the  same  as  in  the  second,  the  Equinoctial;  and  one  of  the 

co-ordinates  the  same,  the  Declination.  The  second  co-ordinate  is  also  measured  on  the  equator,  but  not  from  the 
point  of  o-igin  which  would  be  suggested  at  first  thought.  Since  the  plane  of  the  celestial  equator  coincides  with 
that  of  the  terrestrial  equator,  it  would  seem  that  the  point  of  the  celestial  concave  corresponding  to  the  intersec- 
tion of  the  earth's  prime  meridian  with  its  equator  should  be  the  point  of  origin.  But  this  point  remains  in  rigid 
connection  witli  the  earth  while  the  stars  and  heavenly  bodies  revolve  with  the  celestial  concave ;  hence,  an  origin 
must  be  chosen  which  shall  be  independent  of  the  earth,  and  revolving  in  diurnal  motion  with  the  celestial  concave. 

The  earth  has  a  motion  of  revolution  about  the  Sun  annu- 
ally in  an  elliptical  orbit,  and  in  consequence  of  this  motion 
the  Sun  appears  to  perform  the  circuit  of  the  heavens,  and 
his  apparent  path  is  a  great  circle  upon  the  surface  of  the 
celestial  concave. 

This  circle  is  called  the  ECLIPTIC. 
CVT  represents  the  ecliptic  in  Fig.  48. 
The  axis  of  the  earth  being  inclined  at  an  angle,  which 
may  be  considered  constant,  with  the  plane  of  her  annual 
orbit,  the  ecliptic  crosses  the  equator  in   two  points  at  an 
angle  called  tlie  obliquity  of  the  ecliptic. 

The  points  wliere  the  ecliptic  and  the  equator  intersect 
are  called  the  eqitiiwctial points,  or  tlie  equinoxes. 

The  vernal  equinox,  V  in  the  figure,  is  the  point  through 
which  the  sun  passes  from  the  southern  to  the  northern  celes- 
tial hemisphere,  and  the  autumnal  equinox  the  point  through 
which  he  passes  from  the  northern  side  of  the  equator  to  the 
southern. 

The  solstices  are  the  points  of  the  ecliptic  90°  distant  from 
the  equinoxes,  and  are  called  summer  and  winter  solstices. 

Art.  173.  The  origin  of  this  system  of  co-ordinates  is 
the  vernal  equinox,  V  in  the  figure,  and  is  called  the  First 
Point  of  Aries. 

Then,  the  second  co-ordinate  of  this  system,  Right  As- 
cension, is  the  arc  of  the  equinoctial  intercepted  between 
the  declination  circle  of  the  heavenly  body  and  the  vernal  equinox,  and  is  reckoned  from  the  vernal  equinox  east- 
ward from  0°  to  360°,  or  from  o''  to  24''. 

The  co-ordinates  of  O,  according  to  this  system,  are  its  declination,  OD,  and  its  right  ascension,  VD,  or  the 
angle  VPD. 

Art.  174.  There  is  a  fourtli  system  of  co-ordinates  used  by  astronomers  in  which  the  ecliptic  is  the  primary 
circle  and  the  vernal  equinox  the  point  of  origin.  The  co-ordinates  are  the  Celestial  Latitude  and  Longitude.  The 
latitude  is  measured  on  secondaries  to  the  ecliptic,  called  circles  of  latititde,  and  the  longitude  is  the  arc  of  the 
ecliptic  intercepted  between  the  vernal  equinox  and  the  circle  of  latitude  passing  through  the  body,  and  is  reckoned 
eastward  from  0°  to  360°. 

OL  is  the  celestial  latitude  of  O  and  VL  its  longitude. 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY - 


69 


CHAPTER    II. 


INSTRUMENTS  USED  IN  NAUTICAL  ASTRONOMY 


1.— THE  SEXTANT. 

Art.  ITS.  The  most  important  of  the  nautical  instruments  for  the  purposes  of  the  Navigator  is  the  Sextant, 
owing  to  its  small  dimensions,  its  adaptability,  and  its  great  degree  of  accuracy,  although  it  cannot  be  expected  to 
give  results  as  accurate  as  those  attained  by  fixed  instruments,  but  sufficiently  accurate  for  Navigation. 

Fig.  49  represents  the  common 
form  of  the  Sextant.  The  frame  is  of 
brass;  the  graduated  arc,  AA,  inlaid 
in  the  brass,  is  usually  of  silver,  some- 
times of  gold  or  of  platinum. 

The  divisions  of  the  arc  are  usu- 
ally lo'  each,  which  are  subdivided  by 
the  Vernier  to  lo". 

The  handle,  H,  by  which  it  is 
held  in  the  hand,  is  of  wood.  The 
mirrors,  M  and  w,  are  of  plate-glass, 
silvered.  The  upper  half  of  the  glass 
m  is  left  without  silvering,  in  order 
that  the  direct  rays  from  a  distant  ob- 
ject may  not  be  intercepted. 

To  give  greater  distinctness  to  the 
images,  a  small  telescope,  E,  is  placed 
in  the  line  of  sight ;  it  is  supported  in 
a  ring,  K,  which  can  be  moved  by  a 
screw  in  a  direction  at  right  angles  to 
the  plane  of  the  sextant,  whereby  the 
axis  of  the  telescope  may  be  directed 
either  toward  the  silvered  or  the  trans- 
parent part  of  the  mirror.  This  motion 
changes  the  plane  of  reflection,  which, 
however,  always  remains  parallel  to 
the  plane  of  the  sextant ;  the  use  of 
the  motion  being  merely  to  regulate 
the  relative  brightness  of  the  direct 
and  the  reflected  images. 
The  vernier  is  read  by  means  of  a  glass,  R,  attached  to  an  arm  which  turns  upon  a  pivot,  S,  and  is  carried 
"upon  the  index-bar. 

The  index-glass,  M,  or  central  mirror,  is  secured  in  a  brass  frame,  which  is  firmly  attached  to  the  head  of  the 
index-bar  by  screws.  This  glass  is  generally  set  perpendicular  to  the  plane  of  the  sextant  by  the  maker  with  no 
adjusting  screws;  other  instruments  have  an  adjusting  screw  at  the  back  of  the  mirror,  to  be  used  in  order  to 
replace  the  mirror  in  a  perpendicular  plane,  if  by  accident  it  has  been  displaced. 

The  fixed  mirror,  m,  is  usually  called  the  horizon-glass,  being  that  through  which  the  horizon  is  observed  in 
taking  altitudes.  It  is  usually  provided  with  screws,  by  which  its  position  with  respect  to  the  plane  of  the  sextant 
may  be  rectified. 

At  P  and  Q  are  colored  glasses  of  different  shades,  which  may  be  used  separately  or  in  combination  to  shield 
the  eye  from  the  intense  light  of  the  sun. 

In  order  to  observe  with  accuracy  and  make  the  images  come  precisely  in  contact,  a  tangent-sarzo,  B,  is  fixed 
to  the  index,  and  by  this  it  can  be  moved  with  greater  regularity  than  l)y  hand,  but  this  screw  does  not  act  until 
the  index  is  fixed  by  the  screw  C  at  the  back  of  the  sextant.  Care  must  be  taken  not  to  force  the  tangent-screw, 
when  it  arrives  at  either  extremity  of  its  arc. 

When  the  index  is  to  be  moved  any  considerable  quantity,  the  screw  C  must  be  loosened ;  and  when  the  index 
is  brought  nearly  to  the  division  required,  the  screw  C  must  be  tightened,  and  then  the  index  moved  gradually  by 
the  tangent-screw. 

Besides  the  telescope,  E,  the  instrument  is  usually  provided  with  an  inverting  telescope,  I,  and  a  tube  without 
glasses,  F;  also,  rings  with  colored  glasses  to  put  on  the  eye-end  of  the  telescope  as  a  substitute  for  the  shades, 
P  and  Q,  to  eliminate  any  possible  errors  which  might  arise  from  non-parallelism  of  their  surfaces. 

Art.  I'S'G.    The  Principle  of  the  Sextant. — The  principle  of  Optics  applied  to  the  Sextant  is  this  : 
"  The  angle  between  the  first  and  the  last  directions  of  a  ray  which  has  undergone  two  reflections  in  the  same 
plane  is  equal  to  twice  the  inclination  of  the  reflecting  surfaces  to  each  other." 

To  demonstrate  this  principle,  let  I  and  H,  in  Fig.  50,  be  two  reflecting  surfaces  perpendicular  to  the  plane  of 
representation,  IN  a  perpendicular  to  I,  HN"  and  IN'  perpendicular  to  H.     These  perpendiculars  are  parallel  to 
the  plane  of  representation  and  the  angle  NIN'  =  A  is  the  angle  of  inclination  of  the  surfaces  I  and  H. 
A  ray,  SI,  is  reflected  at  I,  in  the  direction  IH,  making  the  angle  SIN  ^=  NIH. 
IH  is  reflected  again  at  H  in  the  direction  HE,  making  IHN"  =  N"HE. 

If  IS"  is  parallel  to  HE,  then  S'lN'  =  NTH  =  IHN",  and  SIS"  =  E  is  the  angle  between  the  first  and  the 
last  directions  of  the  ray  SIHE,  which  has  undergone  two  reflections  at  I  and  H  respectively. 

SI  and  IH  are  in  a  plane  passing  through  IN  perpendicular  to  I;  IH,  HE,  and  its  parallel,  S"I,  are  in  a  plane 
passing  through  HN"  and  IN'  perpendiculars  to  H.  These  lines  are  all  in  the  same  plane  parallel  to  the  plane  of 
representation  when  the  incident  ray  SI  is  parallel  to  that. 


.70 


INSTRUMENTS   EMPLOYED   IN   NAUTICAL   ASTRONOMY. 


or 


In  this  case — 


SI  also  intersects  HE  at  E  and 


Fig.  50. 

SIS"  =  SIH  —  S"IH 

=  2NIH  — 2N'IH 
=  2  NIN' 
E  =  2  A. 

SEH  =  SIS"  =  E. 


third 
and 


But  if  SI  is  not  parallel,  SIH  and  IHE  are  in  different  planes,  which  intersect  in  IH;  and  if  SIS"  is  in  a 
[  plane,  which  intersects  the  first  in  SI  and  the  second  in  S"I,  then,  by  Geometry— 


SIS"  >  SIH  —  S"IH 
NIN'>NIH  — N'lH. 


No  comparison  can  be  made  without  discussing  the  trihedral  angles  or  their  corresponding  spherical  triangles. 
The  result  would  be — 

SIS"  <  2  NIN' 
E       <2  A. 


or 


Art.  IW.  To  apply  this  to  the  sextant,  let  I  represent  the  index-glass  attached  to  lA,  the  index-arm,  and 
constructed  so  that  they  revolve  together  around  the  axis  at  I  perpendicular  to  the  plane  of  the  instrument;  GAB 
is  a  graduated  limb  in  the  plane  of  the  instrument  whose  centre  is  at  I,  each  half-degree  of  this  arc  reading  as  i^; 
H,  the  horizon  glass  attached  to  the  frame;  EH,  the  line  of  sight,  either  through  a  telcbcope  or  through  a  sight- 
vane,  directed  toward  the  object,  S'.  The  eye  of  an  observer  in  this  line,  and  turned  toward  H,  would  see  S' 
.directly  through  the  transparent  part  of  the  horizon-glass  and  an  object,  S,  by  the  reflected  ray,  IHE. 

If  the  index  arm  and  glass  are  moved  so  that  two  objects  S  and  S'  appear  to  coincide,  then  (S'  being  so  dis- 
tant that  IS"  may  be  regarded  as  directed  to  S') — 

SIS"  =  SIS'  =  E 

is  the  angular  distance  of  S  and  S'  at  I,  the  centre  of  the  instrument. 


INSTRUMENTS  EMPLOYED  IN  NAUTICAL  ASTRONOMY.  71 

If  O  is  ^e  reading  of  the  limb  when  the  two  mirrors  are  parallel,  and  A  the  reading  when  S  and  S'  appear  to 
coincide,  the  arc  OA  of  the  limb  measures  the  inclination  of  the  mirrors,  and  the  difference  of  the  reading  is  the 
angle  E. 

Art*  178.    The  theory  of  the  instrument  requires  the  following  conditions,  viz: 

1st.  The  two  surfaces  of  each  mirror  and  shade  glass  must  be  parallel  planes ; 

2d.  The  graduated  arc,  or  limb,  should  be  a  plane,  and  with  its  vernier  accurately  divided ; 

3d.  The  axis  should  be  at  the  centre  of  the  limb,  and  perpendicular  to  its  plane ; 

4th.  The  index  and  horizon  glasses  should  be  perpendicular,  and  the  line  of  sight  parallel,  to  the  plane  of  the 
limb. 

The  1st,  2d,  and  3d  are  carefully  attended  to  by  the  maker ;  they  admit  of  being  tested  and  any  deviation 
found,  but  only  by  well-devised  observations.  The  complete  theory  provides  formulse  for  ascertaining  their  defects 
and  the  corrections  of  such  errors. 

The  4th  indicates  the  principal  adjustments  to  be  made  by  the  observer. 

ADJUSTMENTS   OF  THE   SEXTANT, 

Art.  lyO.  1st.  Adjustment  0/  the  Index-Glass. — The  reflecting  surface  of  this  glass  must  be  perpendicular 
to  the  plane  of  the  sextant.  In  order  to  test  this,  set  the  index  near  the  middle  of  the  arc;  then,  placing  the  eye 
very  nearly  in  the  plane  of  the  sextant,  and  near  the  index-glass,  observe  whether  the  arc  seen  directly  and  its 
reflected  image  in  the  index-glass  appear  to  form  one  continuous  arc;  if  so,  the  glass  is  perpendicular  to  the  plane 
of  the  sextant ;  if  the  reflected  image  appears  to  droop  from  the  arc  seen  directly,  the  glass  leans  backward ;  if  it 
seems  to  rise,  the  glass  leans  forward. 

The  adjustment  is  made  by  the  screws  at  the  back  of  the  mirror. 

Al'tt  1S0«  2d.  Adjustment  of  the  Horizon-Glass. — This  mirror  should  also  be  perpendicular  to  the  plane  of 
the  sextant.  The  index-glass  having  been  adjusted,  if  by  revolving  it  by  means  of  the  index-arm  there  is  found 
one  position  in  which  it  is  parallel  to  the  horizon-glass,  then  the  latter  must  also  be  perpendicular  to  the  plane  of 
the  sextant.  In  order  to  test  this  put  in  the  telescope  and  direct  it  toward  a  star ;  move  the  index  until  the 
reflected  image  appears  to  pass  the  direct  image.  If  one  passes  directly  over  the  other  the  mirrors  must  be 
parallel.  If  one  passes  on  either  side  of  the  other  the  horizon-glass  needs  adjustment,  which  is  accomplished  by 
means  of  the  screws  attached. 

The  sea-horizon  may  also  be  used  in  the  following  manner  :  Hold  the  sextant  vertically  and  bring  the  direct 
and  the  reflected  images  into  coincidence.  Then  incline  the  sextant  until  its  plane  makes  but  a  small  angle  with 
the  horizon  ;  if  then  the  images  still  coincide  the  glasses  are  parallel ;  if  not,  the  horizon-glass  needs  adjustment. 

Al't.  1  81.  3d.  Adjustment  of  the  Telescope. — In  measuring  angular  distances,  the  line  of  sight,  or  axis  of 
the  telescope,  must  be  parallel  to  the  plane  of  the  instrument,  as  a  deviation  in  that  respect,  in  measuring  large 
angles,  will  occasion  a  considerable  error.  To  avoid  this,  a  telescope  is  made  use  of,  in  which  are  placed  two  wires, 
parallel  to  each  other,  and  equidistant  from  the  centre  of  the  telescope;  by  means  of  these  wires  the  adjustment 
may  be  made  in  the  following  manner :  Screw  on  the  telescope,  and  turn  the  tube  containing  the  eye-glass  till  the 
wires  are  parallel  to  the  plane  of  the  instrument;  then  select  two  objects,  as  the  sun  and  moon,  whose  angular 
distance  must  not  be  less  than  90°,  because  an  error  is  more  easily  discovered  when  the  distance  is  great ;  bring 
the  reflected  image  of  the  sun  exactly  in  contact  with  the  direct  image  of  the  moon,  at  the  wire  nearest  the  plane  of 
the  sextant,  and  fix  the  index ;  then,  by  altering  a  little  the  position  of  the  instrument,  make  the  objects  appear  on 
the  other  wire ;  if  the  contact  still  remains  perfect,  the  axis  of  the  telescope  is  in  its  right  situation ;  but,  if  the 
limbs  of  the  two  objects  appear  to  separate  or  lap  over,  at  the  wire  which  is  farthest  from  the  plane  of  the  sextant, 
the  telescope  is  not  parallel,  and  it  must  be  rectified  by  turning  one  of  the  two  screws  of  the  ring  into  which  the 
telescope  is  screwed  and  fixed,  having  previously  unturned  the  other  screw;  by  repeating  this  operation  a  few 
times  the  contact  will  be  precisely  the  same  at  both  wires,  and  the  axis  of  the  telescope  will  be  parallel  to  the 
plane  of  the  instrument. 

Art.  182.  4th.  The  Index  Correction. — Having  made  the  preceding  adjustments,  it  is  necessary  to  find  that 
point  of  the  arc  at  which  the  zero  of  the  vernier  falls  when  the  two  mirrors  are  parallel ;  for  all  angles  measured 
by  the  sextant  are  reckoned  from  that  point.  If  this  point  be  to  the  left  of  the  actual  zero  of  the  limb  by  a  quantity, 
r,  all  readings  will  be  too  great  by  r ;  if  it  is  to  the  right  of  the  actual  zero  all  readings  will  be  too  small  by  the 
same  quantity. 

If  desirable  that  the  reading  should  be  zero  when  the  mirrors  are  parallel,  the  zero  of  the  vernier  must  be 
placed  on  zero  of  the  arc ;  and  then,  by  means  of  the  adjusting  screws  of  the  horizon-glass,  move  that  glass  until 
the  direct  and  reflected  images  of  the  same  object  coincide. 

The  adjustment  is  unnecessary  since  the  correction  to  be  applied  to  the  readings  can  always  be  determined, 
and,  as  a  general  rule,  greater  accuracy  will  be  attained  if  the  instrument  has  an  index  correction  to  be  observed 
anew  at  the  time  of  taking  every  observation. 

Art.  183.    The  Index  Correction  is  found  as  follows  : 

1st.  By  a  Star. — Bring  the  direct  and  reflected  images  of  a  Star  into  coincidence,  and  read  off  the  arc.  The 
index  correction  is  numerically  equal  to  this  reading,  and  is  positive  or  negative  according  as  the  reading  is  on  the 
right  or  left  of  the  zero.     This  method  may  be  used  with  the  sea-horizon,  but  not  with  great  precision. 

2d.  By  the  Sun. — Measure  the  apparent  diameter  of  the  Sun  by  first  bringing  the  upper  limb  of  the  reflected 
image  to  touch  the  lower  limb  of  the  direct  image ;  and,  again,  by  bringing  the  lower  limb  of  the  reflected  image 
to  touch  the  upper  limb  of  the  direct  image. 

Denote  the  readings  in  the  two  cases  by  r  and  r' ;  then,  if  S  =  apparent  diameter  of  the  sun,  and  R  =  the 
reading  of  the  sextant  when  the  two  images  are  in  coincidence, 

r  =  R  +  S, 
^^  =  R  —  S, 
whence  R  =  ^(r-|--^)>  and  the  index  correction  is 

JT  =  —  R. 

Hence  the  following  rule : 

If  the  reading  in  either  case  is  on  the  arc,  mark  it  with  the  negative  sign;  if  off\^t  arc  (on  the  extra  arc), 
mark  it  with  \h^  positive  sign;  then  the  index  correction  is  one-half  the  algebraic  sum  of  the  two  readings. 


72  INSTRUMENTS   EMPLOYED   IN   NAUTICAL   ASTRONOMY. 

For  example — 

On  the  arc  —  31'  20" 

Offthearc  +  33   10 

+    I   50 
•^  =    o  55 
It  is  seen  that  c         1/  /  j\ 

hence,  if  the  observations  are  good,  it  will  be  found  that  one- half  the  algebraic  difference  of  the  readings  is  equal  to 
the  Sun's  diameter  as  given  in  the  Ephemeris  on  the  day  of  observation.  But,  in  order  that  this  should  be  correct, 
the  sun's  horizontal  diameter  should  be  measured  to  avoid  the  effect  of  refraction. 

If  required  to  obtain  the  index  correction  with  great  precision,  the  mean  of  a  number  of  measures  of  the  sun's 
horizontal  diameter  should  be  taken. 


THE   VERNIER. 


\ 


d 

0 

— 



— ■ 

— 

3 

— 

— 

4 



— 

e 

, 

— 

8 



— 

I 

, 

JU> 

— 

•— 

Art.  184.    The  arc  of  a  sextant  is  usually  divided  into  120°  to  150°,  and  each  degree  into  six  equal  parts  of  1 
10'  each;   the  ^«'«;Vr  enables  us  to  read  the  fractional  parts  of  the  subdivisions  of  the  arc. 

The  vernier  IS  an  index  for  reading  off  the  graduated  scale  or  limb  of  an  instrument,  by  which  aliquot  parts  of 
the  smallest  spaces  into  which  the  scale  or  limb  is  divided  are  measured.  It  consists  of  a  piece  similar  to  the  scale 
or  arc  to  be  read,  and  along  which  it  slides.  The  length  of  this  piece  is  made  such  as  to  include  exactly  some  par- 
ticular number  of  divisions  of  the  scale ;  it  is  then  divided  into  a  number  of  equal  parts,  differing  by  one 
from  the  number  of  divisions  in  that  part  of  the  scale  with  which  it  coincides.  There  are,  hence,  two 
*'''~3;;n*'  forms  of  vernier,  according  as  the  number  of  divisions  in  it  is  one  less  (Fig.  51)  or  one  greater  (Fig.  52) 
than  in  the  corresponding  length  of  the  scale.  Now,  if  the  two  extremities  of  the  vernier  be  made  to 
coincide  with  certain  lines  of  graduation  of  the  scale,  then  it  is  evident  that  none  of  the  intermediate 
lines  of  the  vernier  will  coincide  with  those  of  the  scale.  The  first  division  of  the  vernier  will  exceed 
or  fall  short  of  the  first  of  the  intermediate  divisions  of  the  scale  by  a  certain  space,  the  second  will 
exceed  or  fall  short  by  twice  this  space,  the  third  by  three  times  this  space,  and  so  on  to  the  last,  which 
will  exceed  or  fall  short  by  a  whole  division.  Hence,  the  space  by  which  the  first  division  of  the  vernier 
exceeds  or  falls  short  of  that  on  the  scale  will  be  that  fraction  of  a  division  of  the  scale  whose  numera- 
tor is  unity,  and  denominator  the  number  of  divisions  in  the  vernier.  If,  therefore,  from  the  position  < 
in  which  the  extremity  of  the  vernier  coincides  with  a  line  of  graduation  of  the  scale,  we  retreat  or  push 
Fig.  51.  forward  the  vernier  through  the  above  space,  its  next  line  of  graduation  will  coincide  with  the  next  line, 
on  the  scale;  if  we  retreat  or  push  it  through  another  such  space,  the  next  line  will  coincide,  and  so  on.  Con-^ 
versely,  if  we  see  any  line  of  the  vernier  coinciding  with  one  of  the  scale,  we  know,  by  counting  the  number  of 
lines  from  the  end,  how  many  spaces  it  has  been  moved  from  its  first  position,  or  tell  this  by  inspection  if  the 
extreme  line  of  the  vernier  is  marked  zero  and  the  rest  I,  2,  3,  &c.     Hence,  if  the  index-point  or  zero-line  do  not 

— exactly  coincide  with  a  line  of  graduation  of  the  scale,  we  have  only  to  carry  the  eye 

.10  6°       ^^   along  the  vernier  till  we  mark  some  lines  of  division  which  are  coincident ;  the  num- 

*"^^^i4/f//MJMj^^4U^  ber  of  this  division  on  the  vernier  will  give  that  fraction  of  a  division  of  the  scale  by 

L^ '"*!' — ^- — J         which  the  zero  point  is  distant  from  the  preceding  line  of  graduation  on  the  scale. 

■^     ■"*  In  the  first  kind  of  vernier,  where  the  number  of  divisions  falls  short  by  one  of  the 

Fig.  52.  number  of  divisions  in  the  corresponding  length  of  the  scale,  the  vernier  has  to  be 

numbered  backward,  or  in  a  direction  contrary  to  that  of  the  scale.  This  disadvantage  is  counterbalanced  by  the 
great  size  and  consequent  clearness  of  the  division  of  the  vernier ;  and  this  was  the  form  originally  proposed  by 
the  inventor.  It  is  that  which  is  sometimes  applied  to  the  scale  of  the  barometer.  The  barometer  scale  (Fig.  51) 
is  divided  into  inches  and  tenths ;  and  the  vernier  being  in  length  W  of  an  inch,  and  divided  into  ten  equal  parts, 
measures  hundredths  of  an  inch.  The  verniers  used  for  scientific  barometers  is  of  the  second  kind,  and  in  general 
twenty-five  vernier  spaces,  equal  twenty-four  of  the  scale  spaces,  which  are  each  half  a  tenth,  or  five  hundredths  of 
an  inch ;  therefore,  the  difference  between  one  of  the  vernier  and  one  of  the  scale  is  two-tenths  of  a  hundred,  or 
two  thousandths  of  an  inch.  Thus,  in  the  marine  barometer,  reading  .002  of  an  inch,  the  short  divisions  on  the 
scale  correspond  to  .05  of  an  inch,  the  long  divisions  on  the  vernier  to  .01,  and  its  short  divisions  to  .002  of  an 
inch.  The  limb  of  the  sextant,  and  similar  astronomical  instruments,  is  read  by  a  vernier  of  the  second  kind  (Fig. 
52).  Suppose  the  limb  to  be  cut  to  a  third  part  of  a  degree,  or  20',  then,  if  the  length  of  the  vernier  be  equal  to  ; 
19  of  these  divisions,  and  is  divided  into  20  equal  parts,  by  its  means  we  are  enabled  to  read  off  ^j  of  each  division  ' 
of  the  limb,  or  to  measure  angles  truly  to  i'.  This  is  according  to  the  simple  form  of  the  vernier.  In  instruments 
for  measuring  angles  it  is  convenient  that  the  vernier  should  be  divided  into  60  equal  parts,  so  as  to  enable  us  to 
read  off  to  the  same  number  of  seconds  as  the  limb  is  graduated  into  minutes.  This  could  be  effected  by  making  it 
in  length  equal  to  59  divisions  of  the  limb;  but  then,  if  the  limb  is  highly  graduated,  the  cutting  would  be  minute, 
and  the  reading  by  the  vernier  not  clearly  distinguishable.  The  difficulty  is  obviated  as  follows :  The  vernier  is 
made  in  length  equal  to  |(«  X  60)  —  I  \  divisions  of  the  limb  (where  ;/  is  an  integer),  but  still  dividing  it  into  60  ■ 
equal  parts  instead  of  {n  X  60).  Thus,  let  the  limb  be  graduated  to  10' ;  take  n  =  2,  then  the  length  of  the  ver- 
nier will  be  119  of  the  divisions  of  the  limb  (10'  each).  Now,  if  the  vernier  were  divided  into  120  (2  X  60)  equal 
parts,  it  would  enable  us  to  read  to  j^ji  of  10' ;  but  this  is  unnecessary  and  inconvenient.  It  is  therefore  divided 
into  60  equal  parts  only,  and  enables  us  to  read  to  -^^  of  10'.  or  to  10". — HarbonVs  Glossary.  ; 

To  measure  the  angular  distance  between  the  sun  and  the  moon.  1 

Art.  1§5.  Screw  on  the  telescope  and  place  the  threads  parallel  to  the  plane  of  the  instrument;  turn  down 
one  or  more  of  the  dark  glasses,  according  to  the  brightness  of  the  sun ;  then  hold  the  sextant  so  that  its  plane 
may  pass  through  the  sun  and  moon ;  if  the  sun  be  to  the  right  hand  of  the  moon,  the  sextant  is  to  be  held  with 
its  face  upward;  if  to  the  left  hand,  the  face  is  to  be  held  downward;  with  the  instrument  in  this  position,  look 
directly  at  the  moon  through  the  telescope,  and  move  the  index  forward  till  the  sun's  image  is  brought  nearly  into 
contact  with  the  moon's  nearest  limb ;  then  fix  the  index  by  the  screw  under  the  sextant,  and  make  the  contact 
perfect  by  means  of  the  tangent-screw;  at  the  same  time,  move  the  sextant  slowly,  making  the  axis  of  the  telescope 
the  centre  of  motion;  by  this  means  the  objects  will  pass  each  other  and  the  contact  be  more  accurately  made; 
observing  that  the  point  of  contact  of  the  limbs  must  always  be  observed  in  the  middle  between  the  parallel  wires. 
The  observation  being  thus  made,  the  reading  will  be  the  instnii/iental  distance  of  the  nearest  limbs  of  the  sun  and 
moon ;  by  applying  the  index  correction  the  obserT'rd  distance  will  be  given. 


INSTRUMENTS   EMPLOYED   IN   NAUTICAL   ASTRONOMY. 


73 


To  measure  the  distance  betiveen  the  moon  and  a  star. 

Art.  1§6.  Turn  down  one  of  the  screens,  if  the  moon  is  bright,  and  direct  the  plane  of  the  instrument 
■  through  both  objects,  with  its  face  upward,  if  the  moon  is  to  the  right  of  the  star;  but  if  to  the  left,  the  face  is  to 
be  held  downward ;  look  at  the  star  through  the  telescope  and  transparent  part  of  the  horizon-glass,  and  move  the 
index  till  the  moon's  image  appears  nearly  in  contact  with  the  star ;  fasten  the  index,  move  the  sextant  round  the 
axis  of  the  telescope,  as  in  measuring  the  distance  of  the  sun  and  moon,  and  turn  the  tangent-screw  till  the  coinci- 
dence of  the  star  and  the  cnlighlcued  or  round  liiitb  of  the  moon  is  perfect ;  observing  that  the  point  of  contact  of 
the  limb  of  the  moon  and  star  must  always  be  in  the  middle  between  the  parallel  wires.  The  observation  being 
thus  made,  tlie  index  will  point  out  the  distance  of  the  enlightened  limb  of  the  moon  from  the  star,  whether  it  be 
the  farthest  or  nearest  limb.  This  reading  will  be  the  instrumental  distance  of  the  moon  and  star,  and  by  applying 
the  index  correction  the  ohsoi'cd  distance  will  be  given. 

Art.  ISy,  It  facilitates  the  observations  of  lunar  distances  to  set  the  index  approximately  upon  the  angular 
distance  before  commencing  the  observation.  This  may  be  found  from  the  Ephemeris,  bearing  in  mind  that  this 
distance  in  the  case  of  the  sun  and  moon  must  be  diminished  by  the  sum  of  their  semidiameters  (say  32');  and  in 
the  case  of  the  moon  and  a  planet,  or  star,  it  is  to  be  diminished  or  increased  by  the  moon's  semidiameter  (say 
16'),  according  as  the  bright  limb  is  nearer  to  or  fai'ther  from  the  star  than  the  moon's  centre.  This  proceeding 
is  aJso  a  check  against  the  mistake  of  employing  the  wrong  star. 

.    To  measure  the  altitude  of  a  celestial  object  frojn  the  sea  horizon. 

Art.  1S§.  Direct  the  telescope  toward  that  part  of  the  horizon  which  is  beneath  the  object;  move  the  index 
nntil  the  image  of  the  object  reflected  in  the  sextant-mirrors  is  brought  to  touch  the  horizon  at  the  point  immedi- 
ately under  it.  To  determine  this  point,  the  observer  should  move  the  instrument  around  to  the  right  and  left,  and 
at  the  same  lime  vibrate  it  about  the  sight-line,  taking  care  to  keep  the  object  in  the  middle  of  the  field  of  view ; 
the  object  will  appear  to  sweep  in  an  arc,  the  lowest  point  of  which  must  be  made  to  touch  the  horizon  by  a  suit- 
able motion  of  the  tangent-screw. 

2.— THE  ARTIFICIAL  HORIZON. 

Art.  189.  The  artificial  Iwrizon  is  a  small,  rectangular,  shallow  basin  of  mercury,  over  which  is  placed  a 
roof,  consisting  of  two  plates  of  glass  at  right  angles  with  each  other,  to  protect  the  mercury  from  agitation  by  the 
wind.     The  mercury  affords  a  perfectly  horizontal  surface,  which  is  at  the  same  time  an  excellent  mirror. 

If  MN,  in  Fig.  53,  is  the  hori- 
zontal surface  of  the  mercury;  SB  a  ray 
of  light  from  a  celestial  object,  incident 
to  the  surface  at  B ;  BA  the  reflected 
ray ;  then  an  observer  at  A  will  receive 
the  ray  BA  as  if  it  proceeded  from  a 
point  S',  whose  angular  depression, 
MBS',  below  the  horizontal  plane  is 
equal  to  the  altitude,  MBS,  of  the  ob- 
ject above  that  plane.  If,  then,  SA  is  a 
direct  ray  from  the  object  parallel  to 
SB,  an  observer  at  A  can  measure  with 
the  sextant  the  angle  SAS'  =  SBS'  = 
2SBM,  by  bringing  the  image  of  the 
object  reflected  by  the  index-glass  into 
coincidence  with  the  image  S'  reflected 
by  the  mercury  and  seen  through  the 
horizon-glass.  The  instrumental  meas- 
ure corrected  for  index  error  will  be 
double  the  apparent  altitude  of  the  star. 

The  sun's  altitude  will  be  measured 
by  bringing  the  lower  limb  of  one  image 
to  touch  the  upper  limb  of  the  other. 
Half  the  corrected  instrumental  reading 
will  be  the  apparent  altitude  of  the  sun's 
lower  or  upper  limb,  according  as  the 
nearest  or  farthest  limbs  of  the  direct 
and  reflected  images  were  brought  into 
contact. 

In  observations  of  the  sun  with  the 
artificial  horizon  the  eye  is  protected  by 
a  single  dark  glass  over  the  eye-piece  of 
the  telescope,  thereby  avoiding  the  errors 
that  might  possibly  exist  in  the  dark 
glasses  attached  to  the  frame  of  the  sex- 
tant. 

The  glasses  in  the  roof  over  the 
mercury  should  be  made  of  plate-glass, 
with  perfectly  parallel  faces.  If  they  are 
at  all  prismatic,  the  observed  altitude 
will  be  erroneous.  The  error  may  be 
remov£d  by  observing  a  second  altitude 
with  the  roof  reversed,  and,  in  general, 
by  taking  one-half  of  a  set  of  observations  VIG.  53. 

with  the  roof  in  one  position  and  the  other  half  with  the  roof  reversed ;  or  this  error  may  be  avoided  by  substituting 
for  the  two  plates  of  glass  a  covering  of  ordinary  mosquito-netting  when  the  atmosphere  is  comparativeiy  calm. 


74 


IJJSTRUMEKTS   EMPLOYED   IN   NAUTICAL   ASTRONOMY. 


Instead  of  the  mercurial  horizon,  a  glass  plate  is  sometimes  used  standing  upon  three  screws,  by  means  o! 
which  it  is  levelled,  a  small  spirit-level  being  used  to  test  its  horizontality.  The  lower  surface  of  the  plate  is  black- 
ened, so  that  the  reflection  of  the  celestial  object  takes  place  only  at  the  upper  surface. 


3— THE  CIRCLE  OP  REFLECTION. 

Art.  190.  The  Circle  of  Refection  was  invented  by  the  celebrated  Professor  Mayer,  of  Groningen,  and  has 
since  been  greatly  improved  by  the  Chevalier  De  Borda,  Mr.  Troughton,  and  Mr.  Mendoza  y  Rios.  In  its  present 
improved  state  it  has  a  decided  superiority  over  the  sextant,  in  measuring  the  distance  of  the  moon  from  the  sun 
or  a  star,  on  account  of  its  correcting,  in  a  great  measure,  the  errors  arising  from  a  faulty  division  of  the  limb, 
want  of  parallelism  in  the  surfaces  of  the  mirrors  and  colored  glasses,  and  entirely  avoiding  the  error  which  might 
arise  in  a  sextant  from  the  mirrors  not  being  parallel  when  the  index  is  on  o. 

Fig.  54  represents  the 
Circle  of  Reflection  as  given 
by  De  Borda,  and  also  a  sec- 
tion of  the  same  instrument, 
marked  with  the  same  letters 
of  reference.  The  principal 
parts  of  this  instrument  are : 
the  circular  limb,  LMV;  the 
central  index,  EF  ;  the  hori- 
zon-index, MD;  the  central 
glass  or  mirror,  A ;  the  ho- 
rizon-glass or  mirror,  B;  the 
telescope,  GH  ;  the  colored 
glasses,  3,  4;  the  handle,  5; 
the  ventelle,  6 ;  and  the  ad- 
justing tool,  7. 

The  liiiib  of  the  instru- 
ment, LMV,  is  a  complete  cir- 
cle of  metal,  and  is  connected 
with  a  perforated  central  plate 
by  six  radii ;  it  is  divided 
into  720°,  because  of  the 
double  reflection ;  each  de- 
gree is  generally  divided  into 
three  equal  parts,  and  the 
division  is  carried  to  minutes, 
or  lower,  by  means  of  the 
verniers  of  the  two  indices. 

The  t-ivo  indices  are  mov- 
able round  the  same  axis, 
which  passes  exactly  through 
the  centre  of  the  instrument; 
the  central  index,  EF,  car- 
ries the  central  mirror,  A; 
and  the  horizon-index,  MD, 
carries  the  telescope,  GH, 
and  the  horizon-mirror,  B; 
both  indices  are  furnished 
with  verniers  and  tangent- 
screws  at  O  and  N. 

The  central  mirror.  A, 
is  placed  on  the  central  in- 
dex immediately  above  the 
centre  of  the  instrument ; 
the  plane  of  this  mirror 
makes  an  angle  of  about  30° 
with  the  middle  line  of  the 
index,  and  is  adjusted  per- 
pendicular to  the  plane  of 
the  instrument  by  means  of 
the  screws  placed  on  the 
back  part  of  the  frame  of  the 
mirror. 

The  horizon-glass,  B,  is 
placed  on  the  horizon-index, 
near  the  limb,  so  as  to  inter- 
fere as  little  as  possible  with 
the  rays  proceeding  from  ob-  '^  ^^'  54' 

jects  situated  on  the  opposite  side  of  that  index  with  respect  to  the  central  mirror.  The  horizon-glass  is  adjusted 
perpendicular  to  the  plane  of  the  instrument,  in  a  similar  manner  to  that  of  the  horizon-glass  of  a  sextant ;  and  in 
some  circles  this  mirror  is  movable  about  an  axis  perpendicular  to  the  plane  of  the  instrument;  by  this  means  tht 
situation  with  respect  to  the  telescope  may  be  adjusted. 

The  telescope,  GH,  attached  to  the  other  end  of  the  horizon-index,  is  an  astronomical  one,  inverting  the  observed 
ubjects,  and  has  two  parallel  wires  in  the  common  focus  of  the  glasses,  distant  from  each  other  between  2  and  3 
degrees.  These  wires,  at  the  time  of  observation,  must  be  placed  parallel  to  the  plane  of  the  instrument ;  to  effect 
this,  marks  are  made  on  the  eye-piece  and  on  the  tube  at  G,  and,  by  making  them  coincide,  the  wires  may  be 


6 


INStRtlMEKTS   EMPLOYED   IN   NAUTICAL   ASTRONOMY.  75 

brought  to  their  proper  position.  The  telescope  may  be  raised  or  depressed  by  two  screws,  I,  K,  so  as  to  be 
directed  to  any  part  of  the  horizon-glass ;  and,  by  means  of  the  graduations  on  the  two  standards  i,  k,  the  tele* 
.  scope  may  be  rendered  parallel  to  the  plane  of  the  instrument. 

There  are  two  sets  of  colored  glasses  (3,  4),  each  set  usually  containing  four  glasses  of  different  shades;  the 
glasses  of  the  large  set  (4),  which  are  placed  before  the  central  mirror  at  a,  a,  should  have  each  about  half  the 
degree  of  shade  with  which  the  corresponding  glasses  (3)  of  the  other  set,  placed  at  C,  are  tinged,  because  the  rays 
from  the  luminous  object  pass  twice  through  the  colored  glass  placed  before  the  central  mirror,  and  only  once 
through  the  other.  The  glasses  placed  at  a,  a  are  kept  tight  in  their  places  by  small  pressing  screws  at  their  ends, 
or  by  slides  passing,  in  front,  through  perforations  in  the  stems  of  their  frames ;  when  fixed  for  observation,  they 
make  an  angle  of  about  85^  with  the  plane  of  the  instrument ;  by  this  means  the  image  from  the  colored  glass  is 
■  not  reflected  to  the  telescope.  When  the  angle  to  be  measured  is  between  5°  and  35°,  one  of  the  large  set  is  to  be 
fixed  at  a,  a  :  in  other  cases,  one  of  the  small  set  is  to  be  placed  in  the  socket  C.  The  reason  of  using  the  large 
glass  is  this  :  when  the  small  glass  is  placed  at  C  it  intercepts  the  direct  light  of  the  luminous  object,  in  its  passage 
toward  the  central  mirror,  if  the  object  happens  to  be  situated  within  the  angular  space  included  by  the  lines  from 
the  centre  A,  by  the  sides  of  the  frame  of  the  glass  placed  at  C.     This  is  avoided  by  using  the  large  glasses. 

The  handle  (5)  is  of  wood,  and  is  fixed  to  the  back  of  the  instrument,  immediately  under  the  centre.  By  this 
it  is  held  during  the  time  of  observation. 

The  ventelle  (6)  is  used  in  terrestrial  observations  to  diminish  the  light  of  the  object  seen  directly,  to  render 
it  equal  in  brightness  to -that  of  the  object  seen  by  reflection ;  this  is  performed  by  putting  the  ventelle  in  the  socket 
D,  and  raising  or  depressing  it  till  the  objects  appear  of  equal  brightness. 

There  are  two  adjusting  tools,  of  the  form  represented  in  7 ;  they  are  exactly  of  the  same  size,  and  their  height 
is  nearly  equal  to  that  of  the  central  mirror ;  they  may  be  used  in  adjusting  the  central  mirror  perpendicular  to  the 
plane  of  the  instrument,  and  in  making  the  axis  of  the  telescope  parallel  to  that  plane. 

The  instrument,  as  we  have  now  described  it,  is  the  same  as  it  was  left  by  De  Borda.  Mr.  Troughton  has 
since  suggested  the  improvement  of  fixing  to  the  horizon-index  the  arc  WSPR,  and  providing  it  with  two  sliding 
pieces,  U,  X,  in  order  to  facilitate  the  fixing  the  indices  at  their  proper  angles  with  each  other  in  taking  successive 
observations.  When  the  central  and  horizon  glasses  are  parallel,  the  central  index  covers  the  space  SP  of  the  arc, 
and  the  spaces  SW,  PR  are  each  divided  into  degrees  from  S  to  W  and  from  P  to  R,  and  numbered  o  at  S  and 
P,  and  continued  to  130°  toward  W  and  R.     The  use  of  this  arc  and  sliding  pieces  will  be  explained  hereafter. 

That  ingenious  mathematician  and  navigator,  Mr.  Mendoza  y  Rios,  has  further  improved  the  circular  instru- 
ment by  the  substitution  of  a  circular  ring  (moving  round  the  centre  of  the  instrument,  over  or  adjacent  to  the 
limb  TjNIV)  for  a  vernier,  instead  of  those  attached  to  the  indices  by  De  Borda ;  and,  by  fixing  this  circular  vernier 
alternately  to  each  of  the  indices,  it  serves  as  a  vernier  for  both,  and,  after  any  number  of  observations,  gives  the 
compound  motion  of  both  indices ;  and  thus  double  the  number  of  distances  are  obtained  by  this  instrument  that 
can  be  obtained  by  De  Borda's  circle  with  the  same  number  of  observations.  Mr.  Rios  has  also  improved  the 
form  of  the  handle  for  holding  the  instrument. 

Adjustments  of  the  Circle  of  Reflection. 

Art.  191*  Before  entering  upon  an  explanation  of  the  adjustments  of  this  instrument,  it  will  be  proper  to 
premise  that  there  are  three  different  methods  of  observing  the  angular  distance  of  two  objects  with  this  instru- 
ment, viz,  (i)  by  what  is  called  an  observation  to  the  right,  (2)  by  an  observation  to  the  left,  and  (3)  by  a  cross 
observation. 

An  observation  to  the  right  is  that  when  the  object  whose  image  is  to  be  reflected  and  the  central  mirror  are 
On  the  same  side  of  the  telescope;  an  observation  to  the  left,  when  the  object  to  be  reflected  and  the  central  mirror 
are  on  opposite  sides  of  the  telescope,  which,  in  both  cases,  is  supposed  to  be  directed  to  the  other  object ;  and  a 
cross  obserz'ation  is  a  combination  of  the  forementioned  observations,  the  first  being  generally  taken  to  the  left  and 
the  second  to  the  right. 

The  adjustments  of  a  circle  consist  in  placing  the  mirrors  perpendicular  to  the  plane  of  the  instrument,  and  in 
making  the  axis  of  the  telescope  parallel  to  that  plane.  These  are  all  the  adjustments  necessary  in  measuring  an 
angular  distance  by  cross  observations ;  but  if  one  observation  only  be  taken  to  the  right  or  to  the  left,  it  will  be 
necessary  to  find  the  division  on  which  the  horizon-index  must  be  placed  to  make  the  horizon-glass  parallel  to  the 
central  glass  when  the  central  index  stands  on  o.  These  adjustments  are  similar  to  those  of  a  sextant;  but  a  par- 
ticular explanation  of  each  will  here  be  given. 

1st.   To  set  the  central  glass  perpendicular  to  the  plane  of  the  instrument. 

This  adjustment  may  be  made  by  placing  the  eye  in  front  of  the  central  glass  at  L  a  little  above  the  plane  of 
the  instrument,  and  observing  if  the  reflected  image  of  that  part  of  the  limb  nearest  the  eye  appears  to  make  one 
continued  circular  line  with  the  parts  of  the  limb  toward  T,  seen  to  the  right  and  left  of  the  central  glass ;  for,  in 
this  case,  the  glass  is  perpendicular  to  the  plane  of  the  instrument;  otherwise,  it  must  be  adjusted  by  means  of  the 
screws  till  the  two  images  coincide.  * 

By  examining  this  adjustment  in  different  parts  of  the  limb,  it  will  be  known  if  the  limb  be  in  the  same  plane. 
If  any  difference  should  be  found,  the  central  glass  must  be  so  fixed  that  the  reflected  image  of  the  limb  may  appear 
as  much  above  the  direct  image  in  some  places  as  below  it  in  others. 

2d.   To  set  the  horizon-glass  perpendicular  to  the  plane  of  the  instrument. 

"  The  central  glass  being  previously  adjusted,  and  the  telescope  directed  to  the  line  separating  the  silvered  ftom 
the  transparent  part  of  the  horizon-glass,  hold  the  instrument  nearly  vertical,  and  move  either  index  till  the  direct 
and  reflected  image  of  the  horizon,  seen  through  the  telescope,  coincide  ;  then  incline  the  instrument  till  it  is  nearly 
horizontal,  and,  if  the  images  do  not  separate,  the  horizon-glass  is  perpendicular  to  the  plane  of  the  instrument ; 
but  if  they  do  separate,  the  position  of  the  glass  must  be  rectified  by  means  of  the  screws  in  its  pedestal. 

*  When  the  instrument  is  furnished  with  adjusting  tools  this  adjustment  may  be  made  in  the  following  manner :  Set  the 
tools  on  opposite  parts  of  the  limb  at  T  and  L ;  place  tne  eye  at  c,  at  nearly  the  same  height  as  the  upper  edge  of  the  tools,  so 
that  part  of  the  tool  at  T  may  be  hid  by  the  central  glass ;  move  the  central  index  till  the  reflected  image  of  the  tool  nearest  the 
eye  appears  in  the  central  glass  at  the  side  of  the  other  tool  seen  directly  ;  then,  if  the  upper  edges  of  the  tools  are  apparently  in 
the  same  straight  line,  the  central  glass  is  peq^endicular  to  the  plane  of  the  instrument ;  otherwise,  its  position  must  be  adjusteo 
by  the  screws  at  the  back  of  the  frame. 


76  INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 

This  adjustment  may  be  also  made  by  directing  the  sight  through  the  telescope  to  any  well-defined  object; 
then  if,  by  moving  the  central  index,  the  reflected  image  passes  exactly  over  the  object  seen  directly,  the  glass  is 
perpendicular;  otherwise,  its  position  must  be  adjusted  by  means  of  the  screws  attached  to  the  pedestal  of  the 
glass. 

A  planet  or  star  of  the  first  magnitude  will  be  a  good  object  for  this  purpose.  If  the  sun  is  used,  one  of  the 
colored  glasses  must  be  placed  at  C  and  another  at  D. 

3(/.   To  make  the  axis  of  the  telescope  parallel  to  the  plane  of  the  instrument. 

The  telescope  may  be  raised  or  depressed  by  means  of  two  screws  attached  to  the  standards  /,  k  (2),  and  pass- 
ing through  two  pieces  of  brass  connected  with  the  tube  of  the  telescope.  On  each  of  these  pieces  is  a  mark  or 
index,  by  which  the  telescope  is  to  be  adjusted;  for,  by  bringing  the  indices  to  the  same  mark  on  each  standard, 
the  telescope  will  be  parallel  to  the  plane  of  the  instrument.* 

A,th.   To  find  that  division  to  which  the  horizon-index  must  be  placed  to  render  the  mirrors  parallel  when  the  central 

index  is  on  o.  x 

Place  the  central  index  on  o ;  direct  the  telescope  to  the  horizon-glass,  so  that  the  line  joining  the  silvered 
and  transparent  parts  of  that  glass  may  appear  in  the  middle  of  the  telescope ;  hold  the  instrument  vertically,  and 
move  the  horizon-index  till  the  direct  and  reflected  horizons  agree,  and  the  division  shown  by  the  horizon-index  will 
be  that  required. 

This  adjustment  may  also  be  made  by  measuring  the  diameter  of  the  sun  in  contrary  directions  ;  thus,  the  central 
index  being  fixed  on  o,  place  a  dark  glass  at  C  and  another  at  D;  direct  the  telescope  (through  the  transparent  part 
of  the  horizon-glass)  to  the  sun,  and  move  the  horizon-index  till  his  reflected  image  appears  in  the  telescope; 
bring  the  upper  edge  of  the  direct  image  to  coincide  with  the  lower  of  the  other,  and  note  the  angle  shown  by  the 
index ;  then,  by  moving  the  horizon-index,  bring  the  lower  edge  of  the  direct  image  to  coincide  with  the  upper 
edge  of  the  reflected  one,  and  note  also  the  angle  pointed  out  by  the  index  ;  half  the  sum  of  these  two  angles  will 
be  the  point  of  the  limb  where  the  horizon-index  must  be  placed  to  render  the  mirrors  parallel.  Thus,  if  the  index, 
in  the  first  observation,  is  on  473°  30',  and,  in  the  second,  on  474°  34',  the  half  sum  of  the  two,  474°  2',  will  be 
the  point  where  the  horizon-index  must  be  placed  to  make  the  mirrors  parallel. 

Art.  193.    To  obscnu-  the  meridian  altitude  of  any  celestial  object,  either  by  an  observation  to  the  right  or  to  the  left. 

The  method  of  observing  the  meridian  altitude  of  an  object  with  a  circle  is  exactly  similar  to  that  with  a  quad- 
rant or  sextant.  The  central  index  must  be  fixed  on  o,  and  the  horizon-index  on  the  point  which  renders  the  two 
mirrors  parallel ;  then  the  altitude  may  be  taken  either  by  an  observation  to  the  right  or  to  the  left ;  but  the 
former  method,  in  which  the  large  colored  glasses  are  not  necessary,  is  in  general  to  be  preferred,  because  these 
large  glasses  are  more  liable  to  cause  an  error  in  the  observation  than  the  small  ones. 

If  an  observation  to  the  right  is  to  be  taken,  a  small  dark  glass  must  be  placed  at  C,  if  the  object  be  bright; 
then  hold  the  instrument  in  the  right  hand,  in  a  vertical  position ;  move  the  central  index,  according  to  the  order 
of  the  divisions  of  the  limb,  till  the  reflected  image  of  the  object,  seen  in  the  telescope,  nearly  touches  the  direct 
image  of  the  horizon ;  tighten  the  index  by  the  screw  at  the  back  of  the  instrument ;  make  the  contact  complete 
in  the  middle,  between  the  parallel  wires  of  the  telescope,  by  the  tangent-screw,  and  by  sweeping,  exactly  in  the 
same  manner  as  when  observing  with  a  quadrant,  and  the  central  index  will  point  out  the  altitude  of  the  object. 

If  an  obseii'ation  to  the  left  is  taken,  and  the  object  be  bright,  a  large  dark  glass  must  be  placed  at  a,  a,  if  the 
altitude  be  between  5°  and  35°,  otherwise  a  small  glass  at  C;  hold  the  instrument  in  the  left  hand,  in  a  vertical 
position ;  move  the  central  index  contrary  to  the  order  of  the  divisions,  and  bring  the  reflected  image  in  contact 
with  the  horizon  as  above ;  the  angle  shown  by  the  central  index,  being  subtracted  from  720°,  will  be  the  sought 
altitude. 

In  both  these  methods  of  observing  the  meridian  altitude  of  an  object,  the  circle,  the  radius  of  which  is  only 
5  inches,  will  hardly  be  so  accurate  as  a  good  sextant  of  a  larger  radius  ;  but,  by  the  help  of  a  well-regulated  watch, 
the  meridian  altitude  may  be  obtained.  Toy  the  circle,  to  a  much  greater  degree  of  accuracy  than  by  a  sextant,  by 
observing  in  the  following  manner :  A  few  minutes  before  the  object  passes  the  meridian,  begin  to  observe  the  alti- 
tude by  cross  observations  (in  the  manner  to  be  described  in  the  next  article),  and  note  the  time  of  each  observa- 
tion by  the  watch ;  continue  to  observe  till  a  few  minutes  after  the  object  has  passed  the  meridian ;  then  the  angles 
shown  by  the  central  index,  being  divided  by  the  whole  number  of  observations,  will  give  the  approximate  merid- 
ian altitude ;  the  correction  to  be  applied  to  it  to  obtain  the  true  meridian  altitude  may  be  found  by  means  of  Tables 
26  and  27,  by  a  method  which  will  be  explained  hereafter,  when  treating  of  finding  the  latitude  by  a  single  altitude 
of  the  sun. 

In  this  article  the  meridian  altitude  only  has  been  spoken  of,  though  it  is  evident  that  the  method  is  applicable 
to  an  object  not  on  the  meridian;  but,  in  this  case,  the  cross  observations,  which  give  to  the  circle  all  its  advan- 
tages, may  be  used,  and  the  mean  of  the  altitudes  taken  instead  of  a  single  altitude.  This  method  is  peculiarly 
adapted  to  the  taking  of  altitudes  for  regulating  a  watch ;  for  this  reason  it  will  be  particularly  explained  in  the 
following  article : 

Art.  193.     To  lake  altitudes  of  the  sun,  or  any  celestial  object,  by  cross  observations,  for  regulating  a  watch. 

Fix  the  central  index  on  o,  and  if  the  object  be  bright,  and  the  altitude  between  5°  and  35'^,  place  a  large 
colored  glass  before  the  central  glass  at  a,  a,  otherwise  a  small  one  at  C ;  hold  the  instrument  in  the  left  hand,  in 

*  If  you  suspect  that  the  marks  on  the  standards  are  inaccurate,  you  may  examine  them  in  the  following  manner:  Lay  the 
circle  horizontally  on  a  table ;  place  the  two  adjusting  tools  on  opposite  parts  of  the  limb,  at  T  and  L  ;  and,  at  about  12  or  15  feet 
distance,  let  a  well-defined  mark  be  placed  so  as  to  be  in  the  same  straight  line  with  the  tops  of  the  tools  ;  then  raise  or  lower 
the  telescope  till  the  mark  is  apparently  in  the  middle  between  the  two  wires ;  then  the  axis  of  the  telescope  will  be  parallel  to 
the  plane  of  the  instrument,  and  the  difference  (if  any)  between  the  divisions  pointed  out  by  the  indices  on  the  graduation  of 
the  standards  /,  k  (2),  will  be  the  error  of  the  indices,  and,  this  bemg  known,  it  will  be  easy,  in  future  adjustments,  to  make 
allowance  for  it. 


I 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 


77 


Times  of  obs. 

A"-  gle. 

4'i  20'"  0* 
4  21   10 
4  22  15 
4  23   0 
4  24  45 
4  25  30 

6)60  24' 

6)26   16  40 

4  22  47 

10   4 

a  vertical  portion ;  move  the  horizon-index  till  the  image  of  the  reflected  object  be  brought  in  complete  contact 
with  the  horizon,  in  the  middle  between  the  two  parallel  wires  of  the  telescope,  as  directed  in  the  preceding  article, 
and  note  the  time  of  ol)servation  I^y  the  watch ;  then  fasten  the  horizon-index ; 
hold  the  instrument  in  the  right  hand,  in  a  vertical  position;  move  the  central 
index  according  to  the  order  of  the  divisions  till  the  reflected  image  be  again  brought 
into  complete  contact  with  the  horizon*  as  above,  and  note  the  time  of  observation. 
Then  half  the  sum  of  the  times,  and  half  the  angle  shown  by  the  index,  will  be 
a  mean  time,  and  a  mean  altitude  corresponding  thereto. 

If  greater  accuracy  be  required,  the  observation  must  be  repeated,  setting  out 
from  the  points  where  the  indices  then  are,  and  observing  in  the  same  manner  by 
moving  first  the  horizon-index,  then  the  central  one ;  continue  taking  as  many  of 
these  cross  observations  as  are  judged  necessary,  and  note  the  times  of  each  obser- 
vation ;  then  the  sum  of  the  times,  divided  by  the  whole  number  of  observations, 
will  be  a  mean  time ;  and  the  angle  shown  by  the  central  index,  divided  by  the 
i  number  of  observations,  will  be  a  mean  altitude  corresponding  thereto.  Thus,  if 
six  observations  were  taken,  and  the  times  noted  as  in  the  adjoined  table,  the  angle 
shown  by  the  index  being  60^'  24',  the  mean  time  would  be  obtained  by  dividing  the  sum  of  the  times,  26*'  16'" 
40%  by  6,  and  the  mean  altitude  by  dividing  60"-^  24'  by  6;  therefore,  the  mean  time  would  be  4''  22™  47^  ancl 
the  mean  altitude  corresponding  10-  4'. 

Art."  194.     To  measure  the  distance  behveen  the  sun  and  moon  by  a  circular  instrument. 

The  instrument  being  well  adjusted,  fix  the  central  index  on  o,  and,  if  the  object  be  bright,  place  a  small  dark 
glass  at  C ;  hold  the  instrument  so  that  its  plane  may  be  directed  to  the  objects  with  its  face  downward  when  the 
sun  is  to  the  right  of  the  moon ;  otherwise,  with  its  face  upward ;  direct  the  sight  through  the  telescope  tc  the 
moon ;  move  the  horizon-index,  according  to  the  order  of  the  divisions  of  the  limb,  till  the  reflected  image  of  the 
sun  appears  in  the  telescope,  and  the  nearest  limbs  of  the  sun  and  moon  are  almost  in  contact;  fasten  the  index, 
and  make  the  coincidence  of  the  limbs  perfect,  in  the  middle  between  the  two  parallel  wires  of  the  telescope,  by  means 
of  the  tangent-screw  of  the  horizon-glass,  and  note  the  time  of  observation ;  then  invert  the  instrument,  and  move 
the  central  index,  according  to  the  order  of  the  divisions  of  the  \\\\\h,  by  a  quantity  equal  to  twice  the  arc  passed 
over  by  the  horizon-index  (or  twice  the  distance  of  the  sun  and  moon);  direct  the  plane  of  the  instrument  to  the 
objects;  look  directly  at  the  moon,  and  the  sun  will  be  seen  in  the  field  of  the  telescope;  fasten  the  central  index, 
and  make  the  contact  of  their  nearest  limbs  complete,  in  the  middle  between  the  two  parallel  wires  of  the  telescope, 
by  means  of  the  tangent-screw  of  the  central  index,  and  note  the  time  of  observation ;  then  half  the  arc  shown  by 
the  central  index  will  be  the  distance  of  the  nearest  limbs  of  the  sun  and  moon,  and  half  the  sum  of  the  times  will 
be  the  mean  time  of  observation. 

Having  finished  these  two  observations,  two  others  may  be  taken  in  the  same  manner,  setting  out  from  the 
points  where  the  indices  then  are,  and  moving  first  the  horizon-index,  then  the  central  index:  proceed  thus  till  as 
many  observations  as  are  judged  necessary  be  taken,  always  observing  that  the  number  of  them  be  even;  tlien  the 
angle  shown  by  the  central  index  (or  that  angle  increased  by  720"^  or  1440^,  &c.,  if  the  index  has  been  moved  once 
or  twice,  &c.,  round  the  limb),  being  divided  by  the  whole  number  of  observations,  will  give  the  mean  distance; 
and  the  sum  of  all  the  times,  divided  in  like  manner,  will  be  the  mean  time  of  the  observation. 

Art.  If>f3.    To  measure  the  distance  between  the  moon  and  star  by  a  circular  instrument. 

Fix  the  central  index  on  o,  and,  if  the  moon  be  bright,  and  the  distance  between  5°  and  35°,  place  a  large 
green  glass  before  the  central  mirror  at  <?,  a,  otherwise  a  small  one  at  C ;  hold  the  instrument  so  that  its  plane 
maybe  directed  to  the  objects  with  its  face  downward  when  the  moon  is  to  the  right  of  the  star,  otherwise  with  its 
face  upward;  direct  the  sight  through  the  telescope  to  the  star ;  move  the  horizon-index,  according  to  the  order  of 
the  divisions  of  the  limb,  till  the  reflected  image  of  the  moon  appears  in  the  telescope,  and  the  enlightened  limb  of 
the  moon  be  nearly  in  contact  with  the  star ;  fasten  the  index,  and  make  the  coincidence  perfect,  in  the  middle 
between  the  parallel  wires  of  the  telescope,  by  means  of  the  tangent-screw  belonging  to  that  index,  and  note  the 
time  of  observation  ;  then  invert  the  instrument,  and  move  the  central  index,  according  to  the  order  of  the  divis- 
ions of  the  limb,  by  a  quantity  equal  to  twice  the  arc  passed  over  by  the  horizon-index;  direct  the  plane  of  the 
instrument  to  the  objects ;  look  directly  at  the  star,  and  the  moon  will  be  seen  in  the  field  of 
the  telescope ;  fasten  the  central  index,  and  make  the  contact  of  the  enlightened  limb  of  the 
moon  and  the  star  complete,  in  the  middle  between  the  two  parallel  wires  of  the  telescope, 
by  means  of  the  tangent-screw  of  that  index,  and  note  the  time ;  then  half  the  arc  shown  by 
the  central  index  will  be  the  distance  of  the  star  from  the  enlightened  limb  of  the  moon,  and 
half  the  sum  of  the  times  will  be  the  mean  time  of  observation ;  these  two  observations 
being  completed,  others  may  be  taken  in  the  same  manner,  according  to  the  directions  above 
given  for  measuring  the  distance  of  the  sun  from  the  moon. 

In  continuing  to  take  these  cross  observations  by  a  circle  furnished  with  the  arc  WSR, 
and  slides  U,  X,  it  will  be  very  easy  to  bring  the  reflected  image  into  the  field  of  the  telescope  ; 
but  if  the  instrument  is  not  thus  furnished,  it  will  be  often  diflicult  to  bring  the  image  into  the 
field  of  the  telescope,  and  much  time  will  be  lost,  and  the  observations  rendered  tedious  by 
that  means  ;  to  remedy  this,  a  small  table  of  the  angles,  at  which  each  index  should  be  placed, 
ought  to  be  made  before  beginning  the  observation ;  this  table  is  easily  formed,  as  follows :  Find  roughly,  accord- 
ing to  the  directions  heretofore  given,  the  point  at  which  the  horizon-glass  must  be  placed  to  be  parallel  to  the  cen- 
tral glass,  when*  the  central  index  is  on  o ;  then  find  what  point  of  the  arc  the  horizon-index  stands  upon,  after 

*  The  arc  described  on  the  limb  by  the  central  index  will  be  equal  to  twice  the  altitude  of  the  object,  or  twice  the  angle  passed 
over  by  the  other  index  ;  if  more  cross  observations  be  taken,  each  of  the  indices,  when  moved,  will  describe  an  arc  equal  to 
double  the  altitude  of  the  object ;  the  same  is  to  be  observed  in  measuring  anv  other  angular  distance.  If  the  instrument  is  fur- 
nished with  the  arc  WSR,  and  sliding  pieces  U,  X,  you  must  bring  the  slide  X'to  the  central  index,  after  taking  the  first  observa- 
tion tc  the  left,  and  place  the  slide  U  at  the  same  degree,  on  the  arc  SVV,  that  X  is  on  the  arc  PR ;  then,  in  the  next  observation, 
the  central  index  is  to  be  brought  to  touch  the  slide  U  ;  in  the  next  observation  to  the  left,  the  slide  X  is  to  be  brought  to  the 
central  index ;  and  so  on  for  the  other  observations.  Thus,  by  means  of  the  slides,  the  indices  may  be  placed  at  nearly  their 
proper  angles  with  each  other  at  the  beginning  of  the  observation,  which  will  save  considerable  time.  After  being  thus  fixed, 
the  contact  must  be  completed  by  means  of  the  tangent-screw  of  the  index,  which  is  to  be  moved. 


Central 

Horizon- 

Index. 

Index. 

QO 

525 

108 

633 

216 

21 

324 

129 

432 

237 

540 

c^C. 

c\:c. 

78  INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 

measuring  the  first  distance,  as  directed  above ;  the  difference  between  these  two  points  will  be  the  angular  dis. 
tance  of  the  objects  ;  the  double  of  this  distance,  being  successively  added  to  o°,  and  to  the  angle  pointed  out  by 
the  horizon-index  after  the  first  observation,  will  give  the  points  of  the  arc  where  the  indices  must  be  placed  at 
the  2d,  3d,  4th,  &c.,  observations.  Thus,  if  the  point  of  parallelism  is  471°,  and  the  point  where  the  horizon- 
index  is  at  the  first  observation  is  525°,  the  difference,  or  54^,  will  be  the  angular  distance ;  the  double  of  this, 
or  108°,  being  added  to  525°,  gives  633°,  which  is  the  point  of  the  arc  where  that  index  must  be  placed  at  the  third 
observation;  633°  added  to  108'-' gives  741°,  or  21'-'  (because  the  divisions  recommence  at  720°),  which  is  the 
point  where  the  index  must  be  placed  at  the  fifth  observation,  &c.,  as  in  the  adjoined  table.  The  central  index 
being  at  first  on  0°,  after  the  second  observation  it  will  be  on  108^;  at  the  fourth,  on  108°  +  108°  =:  216°;  at 
the  sixth,  on  216^  -f"  108°  =  324°,  &c.  Thus,  by  constantly  adding  108"^,  or  twice  the  distance  of  the  objects, 
the  angles  at  which  the  indices  must  be  placed  will  be  obtained ;  and  by  fixing  them  at  these  angles,  the  reflected 
image  will  be  brought  into  the  field  of  view  without  any  trouble.  * 


4.— THE   PORTABLE   TRANSIT. 


I 


Art.  196«  The  portable  transit  histrument,  although  of  no  service  while  actually  on  board  ship,  is  a  neces- 
sary adjunct  to  a  Navigator's  outfit  under  certain  circumstances,  while  engaged  in  special  scientific  duty,  for  the 
purpose  of  regulating  chronometers,  and  also  for  the  establishment  of  secondary  meridians,  as  will  be  explained 
hereafter. 

It  is  an  instrument  for  determining  the  time  of  a  star's  transit  over  any  given  vertical  circle ;  hence,  it  is 
necessary  that  the  motion  of  the  telescope  should  be  confined  to  the  vertical  plane.  It  may  be  mounted  in  any 
vertical  plane,  but  is  chiefly  used  in  the  plane  of  the  meridian,  or  in  the  prime  vertical;  in  the  first,  for  determin- 
ing the  local  time ;  in  the  second,  for  determining  the  latitude  of  the  place  of  observation. 

When  spoken  of  simply  as  the  "  transit  instrument"  it  is  usually  understood  to  be  in  the  meridian. 

Although  it  admits  of  some  variety  of  form,  a  general  description  will  be  given  here  of  the  one  used  in  the 
Coast  Survey  (made  by  Wiirdemann,  of  Washington),  with  also  the  general  principles  for  its  use,  and  the  adjust- 
ments.! 

Fig.  55  represents  an  instrument  with  a  telescope  of  26  inches  focal  length,  with  2  inches  aperture,  and  ordi- 
narily used  with  a  magnifying  power  of  40. 

The  peculiar  feature  of  this  instrument  is  its  folding  frame,  PP,  which  takes  the  place  of  the  piers.  It  is 
made  of  iron,  and  as  light  as  possible  consistent  with  due  strength  and  stability.  The  screws  //being  removed, 
the  inclined  supports//  fold  in  against  the  upright  ones,  and  then  the  latter  fold  down  upon  the  horizontal  frame; 
and  the  whole  frame  can  be  put  into  a  box.  The  box  is  deep  enough  to  receive  the  telescope  also.  The  instru- 
ment can  thus  be  conveniently  transported  and  soon  set  up  on  a  temporary  foundation,  Q.  The  frame  is  approxi- 
mately leveled  by  the  foot-screws  SSS. 

A  diagonal  eye-piece,  E,  is  necessary  for  observing  stars  at  high  altitudes. 

T  is  the  telescope  tube,  connected  at  M  with  the  conical  portions  NN  of  the  horizontal,  or  rotation,  axis. 
This  axis  is  hollow,  and  terminates  in  two  steel  cylindirical  pivots,  which  rest  in  V's,  at  VV. 

In  the  ]irincipal  focus  of  the  objective,  at  7n,  is  the  reticule,  consisting  of  five  or  seven  parallel  threads ;  these 
are  parallel  to  the  vertical  plane  of  the  telescope  and  perpendicular  to  its  optical  axis ;  and  also  of  two  horizontal 
threads  at  right  angles  to  the  former.  These  threads,  and  the  images  of  stars  in  their  plane,  are  observed  with 
the  eye-piece  E.  The  eye-tube  is  moved  out  and  in  by  a  rack  and  pinion,  r,  to  bring  the  threads  precisely  into 
the  focus  of  the  object-glass.  The  star  is  made  to  traverse  the  field  between  the  horizontal  threads,  and  the  eye 
is  kept  directly  in  front  of  each  thread  in  succession  by  means  of  a  slide  moved  by  hand. 

'\\\&  finder  F  consists,  1st,  of  a  small  graduated  circle,  4  inches  in  diameter,  permanently  attached  to  the 
telescope;  2d,  of  a  spirit-level,^,  attached  to  an  arm  which  revolves  about  the  centre  of  the  circle.  This  arm 
carries  a  vernier  and  has  a  clamp  and  a  fine-motion  screw  at 7^  When  the  vernier  reads  0°  the  axis  of  the  level  is 
parallel  to  the  optical  axis  of  the  telescope ;  hence,  if  the  vernier  is  set  to  0°,  and  the  telescope  is  revolved  until 
ihe  bubble  stands  in  the  middle  of  the  tube,  the  optical  axis  will  be  horizontal.  If  the  vernier  is  then  set  at  any 
other  given  reading  R,  the  telescope  revolved  until  the  bubble  stands  in  the  middle  of  the  tube,  the  angle  of  incli- 
nation of  the  telescope  to  the  horizon  will  be  equal  to  R.  The  altitude  of  a  star,  whose  transit  is  to  be  observed, 
is  known  from  its  declination  and  the  latitude  of  the  place  of  observation,  and  it  is  usually  necessary  to  prepare  for 
the  observation  by  setting  the  telescope  at  the  proper  altitude  by  means  of  the  finder.  At  A  and  B  are  clamp  and 
fine-motion  screws,  by  means  of  which  the  telescope  is  fixed  and  accurately  set  at  any  zenith  distance. 

The  inclination  of  the  rotation  axis  is  measured  with  a  striding  level,  which  is  applied  to  the  pivots  VV.  The 
feet  of  the  level  have  also  the  form  of  V's.  The  striding-level  is  filled  with  ether,  hermetically  closed,  and  sup- 
plied wiih  a  chamber  to  regulate  the  length  of  the  bubble  at  all  temperatures. 

The  illuminating  lamps  are  shown  in  their  position.  Their  light  is  thrown  into  the  axis  in  nearly  parallel 
lines  by  means  of  a  lens  in  the  lantern  opposite  the  middle  point  of  the  flame,  the  flame  being  nearly  in  the  focus 
of  the  lens. 

Art.  IDT.  Adjustment  of  the  instnunent. — The  stone  pier,  block  of  wood,  or  other  support  for  the  transit 
may  be  set  approximately  in  position  with  regard  to  the  meridian  by  means  of  a  compass-needle,  the  magnetic 
declination  being  known  and  allowed  for.  The  top  of  the  pier  is  leveled  and  the  frame  of  the  instrument  placed  in 
position,  so  that  the  transit-axis  coincides  as  near  as  may  be  with  the  plane  of  the  prime-vertical;  the  adjusting- 
screws  of  the  Y's,  both  for  horizontal  and  vertical  motion,  are  placed  nearly  in  the  middle  of  their  position ;  the 
striding-level  is  carefully  adjusted  and  the  transit-axis  of  the  telescope  leveled.  The  threads  are  then  placed  in 
the  focus  of  the  eye-piece  and  set  vertical.  The  telescope  is  adjusted  to  sidereal  focus.  The  adjustment  for  colli- 
mation  may  be  effected  by  means  of  a  distant  object  or  by  means  of  a  collimating-telescope,  the  axis  being  reversed 
in  its  Y's  during  the  operation.  This  method  suffices  for  the  portable  instrument,  and  gives  a  first  approximation, 
to  be  afterward  tested  and  perfected  Ijy  means  of  transits  of  stars. 

The  local  time  may  readily  be  obtained,  by  the  use  of  a  sextant,  with  an  accuracy  within  a  fraction  of  a  minute, 
and  the  latitude  may  be  found  either  by  a  map  or  by  the  same  instrument,  the  nearest  minute  of  arc  being  suffi- 
cient.    For  the  purpose  of  placing  the  transit  in  position,  a  small  altitude  and  azimuth  instrument  may  also  very 

*  If  the  distance  of  the  object  varies  during  the  observation,  these  angles  will  require  correction  as  you  proceed  with  the 
vjbservations.  Thus,  if  the  distance  was  increasing,  aiTd  at  the  sixtli  observation  it  was  found  that  the  central  index  was  on  326° 
instead  of  324°,  the  increase  being  2°,  you  must  add  2°  to  the  rest  t)f  the  numbers  on  the  table,  and  place  the  horizon  index,  at 
the  seventh  observation,  on  i2ij°  +  2°  =  '3^°!  '^"'^  ^^^  central  index,  at  the  eighth  observation,  at  432°  +  2°  r=  434°,  &c. 

t  For  a  full  discussion  Chauvenet's  Spherical  and  Practical  Astronomy  may  be  referred  to,  or  the  publications  of  the  Burean 
of  Navigation,  Navy  Department,  or  those  of  the  Coast  Survey. 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL   ASTRONOMY. 


79 


advantageously  be  used  for  ascertaining  with  sufficient  approximation  the  local  time,  latitude,  and  direction  of 
the  meridian.  To  point  the  telescope  to  a  star  when  cuhiiinating,  and  supposing  the  finder  to  read  zenith-dis- 
tances, we  have  for  a  star  ^  ^  of  the  zenith  Z^^L^D  —  r,  where  the  upper  sign  refers  to  southern  and  the 


I 


Fig.  55. 


80 


INSTRUMENTS    EMPLOYED    IN   NAUTICAL   ASTRONOMY. 


lower  sign  to  northern  stars  with  respect  to  the  zenith ;  the  refraction,  r,  may  generally  be  neglected.  The  index- 
error  of  the  finder  may  readily  be  removed  by  pointing  to  a  known  star  and  keeping  it  between  the  horizontal 
threads  when  transiting,  for  which  position  the  finder  is  to  be  made  to  show  the  correct  setting.  The  chronometer- 
time  of  the  transit  of  a  slow-moving  (polar)  star  is  next  computed,  the  telescope  pointed  to  it,  and  the  star  bisected 
with  the  middle  thread  at  the  computed  time  of  culmination,  making  use  of  the  slow  azimuth-motion  of  the  Y,  or, 
if  need  be,  by  shifting  the  frame  of  the  instrument.  The  axis  having  been  leveled,  we  next  set  for  and  observe 
two  close  zenith-stars,  one  north,  the  other  south  of  it,  and  with  clamp  east  and  clamp  west,  from  which  we  obtain 
a  very  close  approximation  of  the  chronometer-correction  on  sidereal  time.  The  process  of  bisecting  a  circumpolar 
star  may  then  be  repeated,  using  the  azimuth-screw  only  for  this  adjustment,  after  which  the  telescope  will  gener- 
ally be  found  sufficiently  near  in  the  plane  of  the  meridian  to  admit  of  commencing  the  regular  series  of  observations. 

Art.  19S.  Method  of  obscn<ation. — Generally,  a  series  of  observations  commences  with  transits  of  stars 
selected  to  furnish  instrumental  corrections,  then  follow  transits  of  so-called  time-stars;  and  the  night's  work  is 
concluded  by  again  observing  stars  of  the  character  first  named. 

The  deviation  from  horizontality  of  the  transit-axis  is  determined  by  level-readings,  for  each  star,  if  possible, 
and  the  inequality  of  pivots  is  to  be  allowed  for.  The  value  of  a  division  of  the  striding-level  is  ascertained  by 
any  of  the  methods  explained  in  connection  with  the  zenith-telescope,  and  the  effect  of  temperature  is  to  be  allowed 
for,  if  sensible. 

The  collimation  is  ascertained  by  observing  one-half  of  the  number  of  stars  with  clamp  east  or  west;  then 
reversing  the  telescope  and  observing  the  remaining  half,  clamp  west  or  east;  or  we  may  specially  observe  for 
collimation,  noting  the  transits  of  a  close  circumpolar  star  over  one-half  of  the  threads,  then  reversing  the  telescope 
and  noting  the  remaining  transits  over  the  same  threads  now  presented  in  the  reverse  order;  it  is  well  to  note  the 
state  of  the  level  during  each  transit. 

The  deviation  in  azimuth  is  obtained  from  observations  of  stars  differing  considerably  in  decHnation  (some- 
times  called  high  and  low  stars),  but  little  in  right  ascension,  or  from  observations  of  two  close  circumpolar  stars, 
one  culminating  above  the  other  below  the  pole,  and  having  a  difference  of  right  ascension  not  differing  much  from 
twelve  hours.  It  is  not  safe  to  rely  on  the  stability  of  the  instrument  and  the  constancy  of  the  rate  of  the  chro- 
nometer by  observing  the  same  star  at  upper  and  lower  culminations  immediately  following.  Knowing  the  read- 
ing of  the  azimuth-screw  for  any  two  states  of  the  instrument  in  which  the  azimuthal  deviation  has  been  determined, 
the  value  of  one  division  of  its  micrometer-head  becomes  also  known.  It  is  desirable  that  the  sum  of  the  azimuthal 
corrections  for  the  circumzenith-stars  nearly  balance,  and  that  for  any  two  zenith-stars  the  mean  of  the  tangents  of 
their  declinations  equals  the  tangent  of  the  latitude ;  the  deduced  chronometer-correction  will  then  be  free  of  any 
error  in  azimuth. 

If  more  than  one  observer  engages  in  the  same  series  of  observations,  their  personal  equation  must  be  ascer- 
tained. 


Art.  199.  Fig.  56  represents  a  modified  form  of  the  portable  transit,  the  "broken-backed"  or  prismatic, 
instrument,  which  is  rapidly  coming  into  favor  owing  to  the  great  facility  with  which  it  can  be  used.  It  is  either  a 
zenith  telescope,  or  a  transit  instrument,  and  possesses  the  excellent  feature  of  permitting  the  striding-level  to  rest 
at  all  times  on  its  axis. 

The  explanation  already  given  of  the  straight  transit  will  suffice  for  an  understanding  of  this  instrument  with 
a  study  of  the  figure. 

Art.  200.  Table  48  gives  a  list  of  stars  selected  for  the  determination  of  time  with  the  portable  transit. 
Other  lists  of  stars  are  to  be  found  in  the  American  and  British  Nautical  Almanacs,  the  Connaissance  des  Temps, 
the  Berlin  Star  List,  and  others. 

5.— THE  CHRONOMETER. 

Art.  301.  The  okivnomrter  is  simply  a  correct  time-measurer  and  differs  from  an  ordinary  watch  by  having 
the  force  of  its  main-spring  rendered  uniform  by  means  of  a  variable  lever.  Owing  to  the  fact  that  on  a  sea  voyage 
a  chronom.eter  is  exposed  to  many  changes  of  temperature  by  changing  climate,  &c.,  it  is  furnished  with  an  expan- 
sion balanee,  formed  of  a  combination  of  metals  of  different  expansive  qualities,  such  as  brass  and  st«;el,  which 
produces  the  required  compensation. 


I 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 


81 


i  Against  accidental  causes  of  irregularity  the  chronometer  can  be  guarded  by  proper  treatment,  by  regular  and 
'systematic  winding,  by  being  stowed  in  boxes  lined  with  soft  cushions,  and  by  being  hung  in  gimbals. 

Since,  however,  it  is  not  possible  to  make  a  perfect  instrument,  one  which  will  be  uninfluenced  by  the  dis- 
turbing causes  incident  to  a  sea  voyage,  it  becomes  the  duty  of  the  Navigator  to  determine  the  ei'ror  and  to  keep 
watch  upon  the  variable  rate  of  the  instrument. 

Art.  202.  The  error  of  the  chronometer  on  mean  time  at  any  place  is  the  difference  between  the  time  indi- 
'cated  by  the  clironometer  and  the  mean  time  at  that  place. 

The  amount  the  chronometer  gains  or  loses  daily  is  the  daily  rate. 

Tlie  indications  of  a  chronometer  at  any  given  instant  require  a  correction  for  the  accumulated  error  to  that 
instant ;  and  this  can  be  found  if  the  error  is  known  for  any  given  time  together  with  the  daily  rate. 

The  methods  of  finding  these  quantities  will  be  given  hereafter. 

Art.  203.    StooiHige  and  transportation. — Chronometers  should  be  stowed  on  board  ship  as  near  the  centre 
of  motion  as  possible,  in  boxes  with  as  many  divisions  as  there  are  instruments  to  be  provided  for;  the  sides  and 
i  bottoms  of  the  divisions  should  be  cushions   stuffed  with  horse-hair,  so  that  each  chronometer  may  be   tightly 
wedged  in.     This  piecaution  is  to  overcome,  as  far  as  possible,  the  effects  of  vibration  and  concussion. 
I  They  should  be  stowed  with  the  XII  and  VI  marks  in  parallel  lines,  not  only  for  convenience  of  comparison, 

but  that  they  may  all  be  similarly  affected  by  "the  local  magnetic  attraction  of  the  ship's  iron.  Their  lids  should  be 
removed  and  a  fearnaught  cover  substituted,  with  a  flap  for  each  instrument,  thus  avoiding  shocks  from  accidental 
falling  of  lids  and  affording  a  convenient  method  of  regulating  temperature.  The  flaps  also  facilitate  the  opera- 
tion of  comparing,  for  by  keeping  all  covered  but  the  standard  and  the  one  being  compared  with  it  the  sound  is 
deadened. 

Since  the  principal  cause  of  deviation  of  chronometers  is  change  of  temperature,  regard  should  be  had  in 
1  selecting  a  place  for  them,  that  it  should  be  of  as  nearly  as  possible  uniform  temperature. 

^Vhen  transporting  by  hand  the  chronometer  should  be  clamped,  for  if  left  free  to  move  in  the  gimbals  it  will 
be  more  liable  to  bad  results  from  the  violent  oscillations.  If  permitted  to  run  down,  the  balance-wheel  should  be 
hghtly  wedged  with  bits  of  cork. 

Art.  204.    Winding. — Chronometers  are  made  to  run  either  eight  days  or  forty-eight  hours,  and  should  be 
'  wound  every  seventh  day,  or,  in  the  case  of  the  latter,  daily,  which  will  allow  twenty-four  hours  if  through  any 
cause  the  winding  should  not  be  done  at  the  specified  time. 

Although  chronometers  are  wound  with  a  given  number  of  half-turns  (which  number  should  be  displayed  over 
each  instrument),  after  completing  this  accurate  number  the  winding  should  be  continued  gently  until  the  key  is 
felt  to  butt. 

In  winding  box-chronometers,  the  chronometer  is  taken  firmly  in  the  left  hand  and  inverted  carefully  in  its 
gimbals,  the  key  inserted,  and  turned  with  the  right  hand,  being  careful  to  ease  back  the  slide  which  covered  the 
keyhole,  and  returning  the  instrument  to  its  natural  position.  The  chronometers  should  be  wound  consecutively 
and  always  in  the  same  order  to  prevent  omissions,  and  a  farther  precaution  taken  to  inspect  the  indicators  to  see  if 
all  have  been  wound. 

Art.  205.  Comparison. — Some  one  instrument  is  selected  as  the  standard,  the  best,  as  near  as  can  be 
judged,  and  with  this  all  others  are  compared  daily  after  winding.  Box-chronometers  are  made  to  beat  half- 
seconds,  and  in  comparisons  it  will  be  found  that  the  beats  of  two  instruments  are  nearly  synchronous,  and  this 
fraction  of  a  beat  must  be  estimated  by  the  ear,  which  can  be  done  without  difficulty  within  a  half  beat,  or  a  quarter 
of  a  second ;  but  considerable  practice  is  necessary  to  estimate  within  o^.  i  with  eertainty. 

A  record  should  be  made  and  retained  of  the  comparisons,  which  will  furnish  a  graphic  history  of  the  perform- 
ance of  each  instrument. 

For  convenience'  sake  the  standard  may  be  distinguished  by  the  letter  Z,  and  the  others  by  the  letters  A,  B, 
C,  &c.,  as  far  as  they  extend  in  number. 

The  error  and  daily  rate  are  —  if  the  chronometer  is  fast  and  gaining;  -\-  \{  slotu  and  losing. 

Art.  206.    The  following  form  represents  a  convenient  method  of  recording  comparisons. 


Max.  Ther. 


MiN.  Ther. 


Date. 

Letter  and 
No. 

Standard. 

Chronometers. 

■ 

Differences. 

Second 
differences. 

1879. 
Wednesday,  Apiil  9  . . . . 

A 

777 
15 

1509 
C 

775 
D 

1304 

//.     m.     s. 
I      25     0 

30 
26     0 

30 

h.   m.      s. 
I     4     0.0 

041      4. 5 

II   41   38.0 

I    13  21.5 

h.    m,      s. 
0     21     0.0 

0  44  25.5 

1  44  22. 0 
0     13     8.5 

Thursday,  April  lO 

A 

111 
B 

1509 
C 

1304 

I      30     0 

30 
31     0 

30 

I       9      2.  0 

0  46       1.5 
II    46    23.0 

1  18    22.5 

0     20  58.0 

0  44  28.  5 

1  44  37-0 
0     13     7-5 

s, 

—  2.0 

+    3.0 

+  15.0 

—  1.0 

The  second  differences  expressed  in  the  last  column  are  the  daily  rates  in  case  the  standard  Z  does  not 
change. 

6   B 


82  INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 

When  taking  observations  the  chronometers  should  not  be  taken  from  the  box,  but  a  hack-watch  or  pocket 
chronometer  used  to  note  the  times ;  careful  comparisons  taken  before  and  after  the  observation  in  order  to  reduce 
the  time  noted  to  the  corresponding  chronometer  time. 

Art.  207.  The  practical  benefit  of  a  system  of  daily  comparisons  is  that  a  guard  may  be  kept  on  the  steadi- 
ness of  the  rates  of  the  instruments.  For  instance,  take  the  case  of  the  chronometer  marked  A ;  the  record  gives 
the  daily  values  of  Z  —  A.  If  the  daily  rates  happened  to  be  the  same,  Z  —  A  would  remain  a  constant  quantity '• 
if,  as  IS  the  general  rule,  the  rates  were  different,  Z  —  A  would  vary  by  a  quantity  equal  to  the  algebraic  difference 
of  their  rates  ;  if  the  rates  remained  uniform  the  second  difference  would  remain  constant ;  therefore,  if  the  second 
difference  should  not  remain  uniform  it  would  show  the  rate  of  Z,  of  A,  or  of  both  was  changing,  and  in  case  there 
is  a  third  chronometer  it  may  be  useful  in  pointing  out  which  one  of  the  other  two  was  going  astray. 

Having  three  chronometers,  the  record  gives  daily  Z  —  A  and  Z  —  B,  whence  from  those  two  quantities  there 
may  be  found  A  —  B  or  B  —  A.  Hence,  if  the  second  difference  of  the  daily  value  of  A  —  B  remained  constant 
while  Z  —  A  was  irregular,  it  is  fair  to  presume  that  the  rate  of  chronometer  Z  was  altering.  The  same  course  of 
reasoning  may  be  carried  out  for  any  number  of  instruments.  Of  course,  with  but  three  instruments,  a  direct 
comparison  can  be  readily  made  between  A  and  B ;  but,  in  case  of  a  larger  number,  this  system  is  almost  abso- 
lutely essential. 

It  must  be  noted  that,  for  the  purposes  of  comparison,  it  is  best  to  consider  the  standard  Z  fast  of  all  other 
chronometers,  no  matter  what  may  be  the  actual  indications ;  and  also  that  all  the  chronometers  may  be  treated  in 
a  uniform  manner,  considered  either  2\\fast  or  all  slmo  of  local  mean  time,  regard  then  being  had  for  the  algebraic 
signs  of  the  quantities.  , 

Art.  20§.  Each  chronometer  should  be  accompanied  with  a  record  from  the  Observatory  showing  the  daily 
rates  for  mean  temperatures  for  each  lo'-^",  say,  from  40^  to  100°  Fah.  ;  then,  with  a  maximum  and  minimum  ther- 
mometer in  the  chronometer-case,  the  actual  temperature  of  the  preceding  day  is  recorded  as  soon  as  the  case  is 
opened  for  winding  in  the  morning.  Then,  referring  to  the  tabulated  record  of  observed  daily  rates  accordino-  to 
temperature,  the  rate  for  the  preceding  day  is  found  by  inspection,  and,  applying  this  according  to  its  sign  to^'the 
sum  of  the  accumulated  daily  rates  up  to  the  previous  day,  there  will  be  found  the  whole  amount  of  the  accumu- 
lated rate  on  the  given  day,  to  be  applied  as  a  correction  to  the  primary  error.  Although  the  rates  may  differ  with 
lapse  of  time,  &c.,  it  is  more  than  likely  that  the  differences  of  rates  for  corresponding  temperatures  will  remain 
the  same  or  nearly  so. 

The  proper  methods  of  determining  chronometer  errors  and  rates,  and  for  carrying  "traveling"  rates  will  be 
given  hereafter.  .  /    o  &  j 

6.— THE  NAUTICAL  ALMANAC.  \, 

Art.  209.  The  first  part  of  the  "American  Ephemeris  and  Nautical  Almanac"  is  especially  prepared  for 
the  use  of  Navigators,  and  therefore  adapted  to  the  meridian  of  Greenwich. 

It  contains  the  Ephemeris  of  the  Sun  and  Moon ;  the  distances  of  the  Moon  from  the  centres  of  the  Sun  and  \ 
the  four  most  conspicuous  planets,  and  from  certain  fixed  stars ;  the  Ephemeris  of  the  planets  Venus,  Mars,  Tupi-  '• 
ter,  and  Saturn ;  and  the  mean  places  of  a  large  number  of  the  principal  fixed  stars.     In  a  supplement  it  gives 
tables  for  finding  the  latitude  of  a  place  by  altitudes  of  the  Pole  Star,  the  same  as  Table  28. 

Art.  210.  Time.— Astronomers  make  use  of  several  different  kinds  of  time,  dependent  upon  certain  defined 
points,  the  Centre  of  the  Sim,  an  imaginary  point  called  the  Mean  Sun,  and  the  First  Point  of  Aries,  or  the 
Vernal  Equinox. 

Art.  211.    Transit. — The  instant  when  any  point  of  the  celestial  sphere  is  on  the  meridian  of  the  observer, 
either  that  half  containing  the  zenith  or  that  containing  the  nadir  is  called  the  transit  of  that  point,  also  the  inerid-  " 
lan  passage,  or  the  culmination.     When  on  the  half  of  the  meridian  containing  the  zenith,  it  is  designated  as  the 
upper  transit ;  when  on  the  half  containing  the  nadir,  the  louier  t7-ansit. 

Art.  2 12.  Diurnal  time  is  the  hour-angle  of  those  points  which  are  chosen  to  define  it,  and  the  unit  of 
time  IS  the  period  between  two  successive  transits  over  the  same  branch  of  the  meridian.  This  unit  is  called  a  Day. 
It  is  divided  into  24  equal  parts  called  Hours,  which  are  subdivided  into  Minutes  and  Seconds. 

Art.  213.    Solar  time  is  measured  by  the  daily  motion  of  the  Sun,  and  is  designated  as  Appai'eiit  time. 

Apparent  time  is  the  hour-angle  of  the  centre  of  the  actual  sun.  An  apparent  solar  day  is  the  interval  of  time 
between  two  successive  transits  of  the  sun's  hour-circle  over  the  same  meridian.  Apparent  noon  is  when  the  sun's 
hour-ciicle  coincides  with  the  celestial  meridian.  This  is  the  most  natural  and  direct  measure  of  time,  and  the  unit 
of  time  adopted  by  the  Navigator  at  sea  is  the  apparent  solar  day.  Apparent  noon  is  the  time  when  the  latitude 
can  be  most  easily  and  readily  determined,  and  the  ordinary  method  of  determining  the  longitude  involves  a  calcu- 
lation to  deduce  the  apparent  time  first. 

Art.  214.  But,  since  the  intervals  between  the  successive  returns  of  the  sun  to  the  same  meridian  are  not 
equal,  apparent  time  cannot  be  taken  as  a  standard.  The  apparent  day  varies  in  length  from  two  causes:  1st,  the 
sun  does  not  move  in  the  equator,  that  great  circle  perpendicular  to  the  axis  of  rotation  of  the  heavens,  but  in  the 
ecliptic;  2d,  that  the  sun's  motion  in  the  ecliptic  is  not  uniform.  At  times  the  sun  describes  an  arc  of  57'  of  the 
ecliptic;  at  other  times,  an  arc  of  61'  in  a  day.  At  the  points  where  the  ecliptic  and  equinoctial  intersect  the 
inclination  is  23°  27',  and  at  the  solstices  they  are  parallel. 

Art.  215.  To  avoid  the  irregularity  of  time  caused  by  the  want  of  uniformity  in  the  sun's  motion,  a  ficti- 
tious sun,  called  the  Mean  Sun,  is  supposed  to  move  in  the  equator  with  a  uniform  velocity,  which  is  the  mean 
velocity  of  the  true  sun  in  the  ecliptic;   in  other  words,  its  motion  in  right  ascension  is  strictly  uniform. 

In  order  to  estabhsh  a  connection  between  the  two  suns,  it  is  necessary  to  imagine  a  sul'sidiary  sun  starting 
with  the  true  sun  and  moving  uniformly  in  the  ecliptic  with  the  average  motion  of  the  true  sun,  returning  with  it 
to  the  perigee.  When  this  subsidiary  sun  crosses  the  first  point  of  Aries,  the  mean  sun  is  supposed  to  be  with  it 
at  that  point,  and  thence  to  commence  its  uniform  motion  in  the  equinoctial. 

Art.  216.  Mean  time  is  the  hour-angle  of  the  mean  sun.  A  mean  day  is  the  interval  between  two  suc- 
cessive transits  of  the  mean  sun  over  the  meridian.  Mean  noon  is  the  instant  when  the  mean  sun's  hour-circle 
coincides  with  the  meridian. 

Mean  time  is  perfectly  equable  in  its  increase,  and  at  certain  times  agrees  with  apparent  time ;  then  again  it 
IS  in  advance,  at  other  times  behind  it.  Mean  time  lapsing  uniformly,  is  measured  by  the  clocks  in  ordinary  use, 
and  the  chronometers  used  by  Navigators  are  regulated  to  it.  < 

Art.  217.    The  difference  between  apparent  and  mean  time  is  called  the  Equation  of  tinie.     By  means  of     . 
it  apparent  time  is  changed  to  mean  time  or  the  reverse.     Thus,  if  the  apparent  time  be  given,  the  corresponding 


i 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 


83 


limean  time  w?l  be  found  by  adding  or  subtracting  the  equation  of  time  according  to  the  precept  at  the  head  of  the 
t  cohimn  in  which  it  is  found  on  Page  I  of  the  Nautical  Ahnanac.     If  the  mean  time  be  given,  the  apparent  time  is 
found  by  applying  the  etpiation  of  time  as  directed  by  the  precept  on  Page  II. 

Art«  218.    SiJtira/  ti/iic  is  measured  by  the  daily  motion  of  the  stars;  or,  as  it  is  used  by  Astronomers,  by 
the  daily  motion  cf  that  point  of  the  equator  which  is  the  origin  of  the  co-ordinate's  right  ascension  and  declina- 
\  lion,  the  vernal  equinox ;  hence. 

Sidereal  time  is  ihe  hour-angle  of  the  First  Point  of  Aries. 

A  sidereal  day  is  the  interval  between  two  successive  transits  of  the  First  Point  of  Aries  across  the  same  me- 
.)  ridian. 
I  Sidi-ira!  noon  is  the  instant  the  hour-circle  of  the  First  Point  of  Aries  coincides  with  the  celestial  meridian. 

In  order  to  connect  sidereal  time  with  mean  time  an  element  is  calculated  and  tabulated  in  the  Nautical  Alma- 
nac, the  Sidt'ira/  Thiic  of  Mean  A'oon,  which  is  also  the  J\igk/  Asri'iisioit  of  ike  Mean  Sun. 

Art.  tll9.  Civil  Time. — The  eivil  day,  according  to  the  customs  of  society,  commences  at  midnight  and 
comprises  twenty- four  hours  until  the  following  midnight.  The  hours  are  counted  from  o  to  12  from  midnight  to 
noon;  then,  again,  from  o  to  12  from  noon  to  midnight.  Thus  the  civil  day  is  divided  into  two  periods  of  twelve 
hours  each,  the  first  of  which  is  marked  A.  M.  (Ante  Meridiem),  the  last  is  marked  P.  M.  (Post  Meridiem). 

Art.  320.  The  astronomical  or  solar  day  commences  at  noon  of  the  civil  day  of  the  same  date.  It  com- 
prises twenty-four  hours,  reckoned  from  o  to  24,  from  noon  of  one  day  to  noon  of  the  next. 

Astnntoniieal  time  (apparent  or  mean)  is  the  hour-angle  of  the  sun  (apparent  or  mean)  reckoned  on  the  equator 
westward  thrcughout  its  entire  circumference  from  o''  to  24''. 

The  r/rv'/day  begins  twelve  hours  before  the  astronomical  Aa,y,  and  an  understanding  of  this  is  the  only  guide 
necessary  for  converting  one  kind  of  time  to  the  other.     For  instance, 

Civil  time  January  9,  2  a.  m.,  is  Astronomical  time  January  8*^  14''. 

Civil  time  January  9,  2  p.  m.,  is  Astronomical  time  January  9'^  2ii. 

Art.  221. —  Time  at  different  meridians. — The  hour-angle  of  the  sun  at  any  meridian  is  called  the  local 
(solar)  time. 

The  hour  angle  of  the  sun  at  the  same  instant  is  the  corresponding  Greenwich  time. 

The  difterence  between  the  local  time  at  any  meridian  and  the  Greenwich  time  is  equal  to  the  longitude  of 
that  place  from  Greenwich  (that  being,  as  before  stated,  the  prime  meridian  for  American  Navigators),  expressed 
in  time.     This  may  be  readily  reduced  to  arc  by  observing  that 


4"  =  360^ 

jO   —^m 

I"  =  I50 

I'    =4^ 

I'"  =  15' 

I"  =tV« 

1=  =  15" 

Art.  222.  The  difference  between  the  local  times  of  any  two  meridians  is  equal  to  the  difference  of  longi- 
tude of  those  meridians. 

In  comparing  corresponding  times 
of  different  meridians  the  most  easterly 
meridian  may  be  distinguished  as  that  at 
which  the  time  is  greatest,  or  the  latest. 

In  Fig  57  if  PM  and  PM'  be  the 
celestial  meridians  of  two  places ;  PS, 
the  declination  circle  through  the  sun ; 
PG,  the  Greenwich  meridian ;  then 

Tg  =  the  Greenwich  time  =  GPS. 

Tm  =  the  corresponding  local  time 
ac  all  places  on  the  meridian  PM  =  MPS. 

Tm'  =  the  corresponding  local  time 
at  all  places  on  the  meridian  PM'  =  M'PS. 

Lo.  =  west  longitude  of  meridian 
PM  =  GPM. 

Lo'  =  east  longitude  of  meridian 
PM'  ==  GPM' ;  then, 

Lo  =  Tg  —  Tm. ;  Lo'  r=Tm'  —  Tg, 
or  Tg  —  Tm',  observing  that  east  longi- 
tudes are  to  be  regarded  as  negative. 


M'PS—  MPS 

Tra'    —  Tm    =  Lo' 


M'PM         } 

J        >  the  difference  of  longitude  of  the  two  meridians. 


Both  local  and  Greenwich  times,  or  Tm  and  Tg,  in  the  above  formukie,  are  supposed  to  be  reckoned  westward 
always  from  their  respective  meridians  and  from  o'"  to  24I' ;  in  other  words,  Tg  and  Tm  are  the  astronomical  times 
which  sliould  be  used  in  all  astronomical  computations. 

'Ihe  formula  Lo.  =  Tg  —  Tm  is  true  for  any  kind  of  time,  solar  or  sidereal;  or,  in  general  terms,  Tc;  and 
'Im  are  the  hour  angles  of  any  point  of  the  sphere  at  the  two  meridians  whose  difference  of  longitude  is  Lo.  S 
may  be  the  sun  (true  or  mean)  or  the  vernal  equinox. 

Since  nearly  every  computation  made  by  the  Navigator  is  dependent  upon  some  data  from  the  Nautical 
Almanac,  the  first  operation  necessary  is  to  deduce  from  the  local  time  the  corresponding  Greenwich  date,  either 
exact  or  approximate,  and  the  Greenwich  time  should  invariably  be  expressed  astronomically. 
L        The  formula  is — 

Tg  =  Tm  -f-  Lo. , 

remembering  that  west  longitudes  are  positive,  east  longitudes  are  negative. 

Hence  the  following 

Rule.  Having  expressed  the  local  time  astronomically,  add  the  longitude  if  west,  subtract  it  \{  east ;  the  result 
IS  the  corresponding  Greenwich  time. 


84  INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY.  ! 

Example.    In  longitude  8i°  15'  W.  tlie  local  time  is,  1879,  April,  15"^  10''  17"  30^  a.  m. ;  required,  theGreea  : 
wich  time. 

Loral  Ast.  time,  April,  14^  22'^  17'"  30^ 

Longitude,  4.      5    25       o  •  j 


Greenwich  time,  15     3   42 


f 


Example.    In  longitude  81°  15'  E.  the  local  time  is,  August,  5*^  2''  10'"  30^  p.  m. ;  required,  the  Greenwich 
time. 

Local  Ast.  time,  ^'^    2'^  10'"  30^ 

Longitude,  —     5    25       o 

Greenwich  time,  4     20    45     30                                                               ? 

Example.    In  longitude  17°  28'  W.  the  local  time  is,  May,  r'  3''  10'"  p.  m.  ;  required,  the  Greenwich  time. 

Local  Ast.  time,  i''  3'^  10"'    o** 

Longitude,  +1      9     52 


time. 


Greenwich  time,  i    4    19     52 

Example.    In  longitude  125°  30'  E.,  the  local  time  is,  May,  i'^  8"  10"'  30^  a.  m. ;  rcijuired,  the  Greenwich' 

Local  Ast.  time,  April,     30''  20''  io">  30^ 
Longitude,  —      8    22       o 


Greenwich  time,  30    11    48     30 

From  the  formula  Tg  =  Tm  -|-  Lo. 

is  derived  Tm  ^  Tg  —  Lo., 

so  that  it  will  be  seen  that  to  find  the  corresponding  local  time  for  a  Greenwich  time  the  above  process  muj 
simply  be  reversed.  1 

Since  all  observations  at  sea  are  referred  to  chronometers  regulated  to  Greenwich  mean  time,  and,  as  thest 
instruments  are  usually  marked  on  the  dial  from  o''  to  I2'\  it  becomes  necessary  to  distinguish  whether  it  is  a.  m. 
or  p.  m.  at  Greenwich.  Therefore,  an  approximate  knowledge  of  the  longitude  and  local  time  is  necessary  to 
determine  the  Greenwich  date. 

Example.  In  the  approximate  longitude  5'^  W.,  about  ^^  30'!^  p.  m.  April  15th,  the  Greenwich  chronometer 
read  S^  25"',  and  was  fast  of  Gr.  time  3'"  15^;  required,  the  Gr.  Ast.  time. 


Approx.  local  time,       15'*  3'' 
Longitude,  approx.,  +         5 

30"' 
0 

Gr.  chro.,                     8''  25"'   0^ 
Corr.,                        —         3     15 

Approx.  Gr.  time,         15    8 

30 

Gr.  Ast.  time  15'^,       8    21    45 

Example.    In  longitude  5^  E.,  about  8  a.  m. 
5'';  required,  the  Gr.  Ast-  time. 

May  3d, 

the  Gr,  chro.  read  3''  15™  20",  and  was  fast  of  Gr.  ti 

Approx.  local  time.  May     2" 
Longitude,                         — 

20l» 

5 

Gr.  chro.,                   3''  15^  20» 
Corr.,                      —         3      15 

Approx.  Gr.  time,  2     15  Gr.  Ast.  time  2«i,       15  12       5 

Art.  333.  Reduction  of  the  Elements  in  the  A'antical  Almanac. — This  reduction  is  accomplished  by  Inter^ 
polatioti,  or  by  Proportional  Logarithms,  and  when  extreme  precision  is  required  the  second  differences  must  be 
employed. 

The  Ephemeris  is  computed  for  the  Greenwich  meridian,  and  contains  the  right  ascensions,  declinations,  equa- 
tions of  time,  iSrc,  for  given  equidistant  intervals  of  Greenwich  time.  Hence,  before  the  value  of  any  of  these 
quantities  can  be  found  for  a  given  local  lime,  it  is  necessary  to  determine  the  corresponding  instant  of  Greenwich 
time. 

Should  that  time  be  one  of  the  exact  instants  noted  in  the  Nautical  Almanac  for  the  value  of  the  required 
element,  nothing  more  is  necessary  than  to  employ  that  value.  But  if  the  time  falls  between  the  Almanac  times, 
the  required  quantity  must  be  found  by  interpolation. 

The  Almanac  contains  the  rate  of  change,  or  difference  of  each  of  the  principal  quantities  for  some  unit  of 
time.     And,  unless  great  precision  is  required,  the  first  differences  only  need  be  regarded. 

In  order  to  use  the  difference  columns  to  advantage,  the  Greenwich  date  should  be  expressed  in  the  same  unit 
of  time  for  which  the  difference  is  given.  Thus,  for  using  the  hourly  differences,  the  Greenwich  time  should  be 
expressed  in  hours  and  decimal  parts  of  an  hour;  when-using  the  differences  for  one  minute,  the  time  should  be  in 
minutes  and  decimal  parts  of  a  minute.  Or,  instead  of  using  decimal  parts,  some  may  j^refer  the  use  of  aliquot 
parts. 

It  may  be  observed  here  that,  since  the  quantities  in  the  Almanac  are  approximate  numbers,  given  to  a  certain 
unit,  any  interpolation  beyond  one  lower  order  than  that  unit  is  unnecessary  work.  And,  again,  computations  at 
sea  render  the  Greenwich  date  more  or  less  uncertain ;  therefore,  too  great  refinement  in  reducing  the  Almanac 
elements  will  produce  no  more  accurate  results  than  the  limit  stated 

Simple  interpolation  assumes  that  the  differences  of  the  quantities  are  proportional  to  the  differences  of  the 
times;  in  other  words,  that  the  differences  given  in  the  Almanac  are  constant;  which  is  never  the  case,  but  the 
error  arising  from  the  assumption  will  be  smaller  the  less  the  interval  between  the  times  in  the  Almanac.  Hence, 
those  quantities  which  vary  most  irregidarly  are  given  for  the  smallest  units  of  time;  as  the  variations  are  more 
regular  the  units  for  which  the  differences  are  given  increase. 


INSTRUMENTS    EMPLOYED    IN   NAUTICAL   ASTRONOMY. 


85 


I  Al*t«  324:>    Tojindftom  the  Nautical  Abnaitac  a  required  quantity  for  a  given  mean  time  at  a  given  place. 

Rule.    Express  the  given  mean  time  astronomically  and  find  the  corresponding  Greenwich  date. 
_     Take  from  the  Nautical  Almanac  for  the  nearest  preceding  mean-time  date  the  required  (juantity  and  the  corre- 
'sponding  "  Diff.  for  i''",  or  "  Diff.  for  i'"",  noting  the  name  or  sign  of  each. 

.Multiply  the  "Diff.  for  i''"  by  the  hours  and  parts  of  an  hour,  or  the  "Diff.  for  I"'"  by  the  minutes  and 
and  parts  of  a  minute,  of  the  remaining  Greenwich  time;  and  add  the  product  algebraically. 

If  the  given  Greenwich  time  is  nearer  a  subsequent  \}s\zxi  a  /r^'^r^'^?/;?^  Almanac  date,  it  may  be  convenient  to 
interpolate  back  from  the  subsequent  date. 

E.VAMi'LE.    For  the  local  mean  time,  1879,  April  16''  ii'>  55'"  30^  a.  m.,  in  Long.  81°  15'  W.,  find  the  follow- 
[jiing  quantities  from  the  Nautical  Almanac: 

Equation  of  Time 
Right  Ascension       \ 
Declination  !  of 

Horizontal  Parallax  [ 
Semidiameter  J 

Local  Ast.  time,  April, 
Longitude, 


the  Sun,  Moon,  and  Jupiter. 


ijd  2311  55m  30s 
+     5    25      o 


Gr.  mean  time,  April, 


16      5    20     30 
+  5"-34 


1.  Eq.  t.  at  mean  o'', 
Corr.  for  5i>.34, 

Eq.  t.  (+  to  m.  t.), 

2.  Sun's  R.  A.  at  o''  Gr., 
Corr.  for  +  5i'.34, 

Sun's  R.  A., 


+ 


10M5 


o     13-37 

ih  36m  5 IS. 7 7 

49'-4i 
I    37    41.18 


H.  D.,    + 

+ 


0^,604 
5-34 


+  3'-22 


H.D. 


+ 


9'- 252 
5-34 


+     49^41 


3.  Sun's  Dec.  at  Gr.  o",     +  10^     5'  30".! 
Corr.  for  +  5". 34,  + 


4    44"-3 


Sun's  Dec. 


10     10    14  .4 


4.  Moon's  R.  A.  Gr.  s'',       22''  14"'  39^29 


Corr.  for  -f  20"'.  5,       + 
Moon's  R.  A., 


38^ 


22    15     17.59 


5.  Moon's  Dec.  Gr.  5'',     —    7-^  59'  36".! 
Corr.  for  +  20"'.$,        -|- 


4    27". 2 


Moon's  Dec.  — 

6.  Moon's  H.  P.  Gr.  o^ 
Corr.  for  +  5^.34,         — 

Moon's  H.  P., 

7.  Moon's  S.  D.  Gr.  o^', 
Corr.  for  +  5^.34,         — 

Moon's  S.  D., 


7    55     8  .9 
55'  i3"-6 

7".2 

55     6  .4 

15'  4".7 
i".8 


15    2  .9 


8.  Jupiter's  R.  A.  Gr.  d^,      ii!^  26"^  35^-54 
Corr.  for  +  5". 34,  +  9^71 


Jupiter's  R.  A. 


22    26    45  .25 


9.  Jupiter's  Dec.  Gr.  o'',  —  10°  40'  28". o 

Corr.  for  +  5''.34,         +  53".6 

Jupiter's  Dec,                —  10     39  34  .4 

10.  Jupiter's  H.  P.  April  16,  i".6 

11.  Jupiter's  S.  D.  April  16,  16". 9 


H.  D. 


M.  D., 


+    53"-24 
+      5  -34 


+  284".30 


+ 


1^.8685 
20.5 


M.  D.,+     i3".032 
+    20  .5 


H.  D. 


+ 


267". 16 

i"-34 
5  -34 


H.  D.,  — 

+ 


7".  15 


o".34 
5  -34 


—      i".8i 


H.  D., 


1^819 

5-34 

9».7i 


H.  D.,  +    io".03 
+      5  -34 

+     53".6 


The  sign  +>  prefixed  to  hourly  differences  of  Dec,  indicates  that  the  body  is  moving  northward ;  —  indi- 
cates that  the  body  is  moving  southward. 

Art.  223.    Interpolation  by  Second  Differences.— ?i\\o\M.  greater -precision  be  required  than  that  attainable 
by  simple  interpolation  resort  must  be  had  to  the  reduction  for  second  differences. 

The  differences  between  successive  values  of  the  (pianlities  given  in  the  Nautical  Almanac  are  called  theyfrjJ 
differences ;  the  differences  between  successive  first  differences  are  called  the  secotui  differences.     Simple  interpola- 


86 


INSTRUMENTS    EMPLOYED    IN   NAUTICAL   ASTRONOMY. 


tion  which  satisfies  the  necessities  of  sea  computations  assumes  the  first  differences  to  be  constant,  but  if  the  varia. 
tion  of  the  first  differences  is  regarded  a  further  interpolation  is  required  for  the  second  difference. 

The  difference  for  a  unit  of  time  in  tlie  American  Nautical  Almanac  against  any  function  expresses  the  rate  at 
which  the  function  is  changing  at  that  precise  instant  of  Greenwich  time.  Now,  regarding  it  as  variable,  and  the 
second  difference  as  constant,  it  varies  uniformly  with  the  Greenwich  time ;  therefore  its  value  may  be  found  for 
any  intermediate  time  by  simple  interpolation. 

Hence,  the  following  rule  for  employing  second  differences : 

Rule.  Employ  the  interpolated  value  of  the  first  difference  which  corresponds  to  the  middle  of  the  interval 
for  which  the  correction  is  to  be  computed. 

Example.    For  the  Greenwich  date  1879,  April,  10^  i8'»  25'"  30%  find  the  Moon's  declination — 


Moon's  Dec,  April  10,  iS'^  —  26°  19'  41".! 
Corr.  for -|- 25"'.5,  +  2". I 


Diff.  I'",  +    o".o44 

Corr.  2d  Diff.,     -\-    o".039 


Moon's  Dec, 


26    19   39  .0 


+    o".o83 
+  25   -5 


2d  Diff.,   +o".i8i 
+  o",2i3 

+  o".o39 


\ 


+ 


.12 


The  Diff.  for  i'"  increases  in  i''  o".i8i;  the  half  of  the  interval  for  which  the  correction  is  to  be  computed  is 
25^.5  -f-  2  =:  12"'.  75  =:  o''.2i3;  the  value  of  the  first  difference  at  18''  12™  45^^  is  found  by  adding  to  o".044  its 
present  value  the  quantity  o."i8i  X  O.213  :=  o"o39.  Then  proceed  as  in  simple  interpolation  to  find  the  correc- 
tion from  this  new  quantity  for  25"'.  5. 

Art.  336.  Page  I  of  the  Calendar  contains  the  Apparent  Right  Ascension  and  Declination  of  the  Sun  and 
the  Equation  of  Time  for  each  Greenwich  apparent  noon. 

This  page  is  chiefly  used  when  the  sun  is  observed  in  the  meridian  and  the  local  apparent  time  is  o.  The 
longitude  from  Greenwich  expressed  in  time,  xiiucst,  is  at  that  instant  the  Greenwich  apparent  time,  or  time  after 
Greenwich  noon  ;  if  east,  it  is  time  before  Greenwich  apparent  noon.  The  longitude  is  therefore  employed  in 
reducing  the  quantities  on  this  page  to  apparent  noon  at  any  place. 

Art.  337.    To  find  tJie  right  ascension  and  declination  of  the  Sim,  and  the  equation  of  time  at  apparent  noon  of  a 

given  place,  or  zvhen  the  sun  is  in  the  meridian. 

Rule.  Take  the  quantities  from  Page  I  of  the  Calendar  for  Greenwich  apparent  noon  of  the  same  date  as  the 
local  date,  and  apply  a  correction  equal  to  the  hourly  difference  multiplied  by  the  hours  and  parts  of  an  hour  of  the 
longitude,  adding  or  subtracting  tlie  correction  as  the  numbers  in  the  Almanac  indicate,  for  a  time  after  noon  if 
the  longitude  is  -west;  for  a  time  before  noon  if  the  longitude  is  east. 

Example.  At  a  place  in  Long.  81°  15'  W.,  1879,  April  17,  find  the  sun's  right  ascension  and  declination, 
and  the  equation  of  time  at  apparent  noon. 


Long.  8 

lO  i^'  w.  =  -}-  5I1  25™ 

=  5'>-42 

R.  A.  at  Gr.  app.  d^, 
Corr.  for  +  5 ''.42, 

ih  40".  33S.95 
+     50^23 

H.  D., 

+ 

9^268 
S-42 

R.  A., 

I  41  24.18 

+ 

50^23 

Dec.  at  Gr.  app.  o'', 
Corr.  for  +  5''.42, 

-f-  10°  26'  42". 3 
+          4'  46".2 

H.  D., 

+ 
+ 

52".8o 
5  -42 

Dec, 

10    31   28  .5 

+ 

286".  18 

Eq.  t.  at  Gr.  app.  o'', 
Corr.  for  +  5''.42, 

0™  24S.46 
+      3^- 18 

H.  D., 

+ 
+ 

0^587 
S-42 

Eq.  t.  ( —  from  app.  t.),  o    27  .64 


+      3-^-i82 


Example.    At  a  place  in  Long.  81°  15'  E.,  1879,  April  17,  find  the  sun's  right  ascension  and  declination,  and^ 
the  equation  of  time  at  apparent  noon. 

Long.  81°  15'  E.  =:  —  5''  25"'  =  —  5i'.42 


R.  A.  at  Gr.  app.  o'', 
Corr.  for  —  5*^.42, 

jh  4o>"  33s.  95 
—     So''- 23 

I    39    43-72 

11. 

D., 

9s.  268 
-    S-42 

R.  A., 

-  50^23 

Dec.  at  Gr.  app.  d^, 
Corr.  for  —  5'' .42, 

+  10°  26'  42".3 
4'  46".2 

H. 

D., 

+    S2"-8o 
-     5   -42 

Dec, 

+  10    21    56  .1 

—  286".  18 

Eq.  t.  at  Gr.  app.  o"^, 
Corr.  for  —  5  '•42, 

0"'  24^46 
-      3^.18 

H. 

D., 

+  0B.587 
—  S-42 

Eq.  t.  (  —  from  app.  t.),  c     21  .28 


—  3M82 


INSTRUMENTS  EMPLOYED  IN  NAUTICAL  ASTRONOMY.  87 

Art.  22S>    Tojitid  the  nght  ascension  of  the  Mean  Sjinfor  a  gwen  time  and  place, 

Ihe  Sidtveal  time  of  Mean  Xoon  is  also  the  Right  Asceiision  of  tJte  Mean  Sun  at  Greenwich  7nean  noon,  and 
;  may  be  reduced  for  the  longitude,  or  to  any  Greenwich  mean  time,  by  interpolating  for  the  constant  hourly  dififer- 
I  ence  9^8565. 

Since  at  the  instant  of  mean  noon  at  any  place  the  right  ascension  of  the  mean  sun  is  equal  to  the  sidereal 
,  time,  a  Table  for  reducing  intervals  of  mean  solar  time  to  sidereal  time  maybe  used  to  facilitate  the  interpolations. 
'  Table  9  is  such  a  table,  and  Table  S  is  to  reduce  intervals  of  sidereal  to  solar  time. 

The  right  ascension  of  the  mean  sun  is  also  equal  to  the  right  ascension  of  the  true  sun  +  the  equation  of 
time,  using  that  sign  for  the  equation  of  time  indicated  for  its  application  to  mean  time. 

Art.  329*    To  find  the  local  time  of  the  moon's  transit  over  a  given  meridian. 

Page  IV  of  the  Calendar  gives  the  mean  time  of  the  moon's  transit  over  the  meridian  of  Greenwicli  for  each 
day.  This  mean  time  is  the  hour-angle  of  the  mean  sun  at  that  instant,  or  the  difference  of  the  right  ascensions 
of  the  moon  and  the  mean  sun.  If  this  difference  did  not  change,  the  mean  local  time  of  the  moon's  meridian 
passage  would  be  the  same  for  all  meridians ;  but,  as  the  right  ascension  of  the  moon  increases  more  rapidly  than 
that  of  the  sun,  the  moon  is  apparently  retarded  from  transit  to  transit,  at  an  interval  varying  from  40'"  to  66'", 
according  to  the  rate  of  the  moon's  motion.  The  difference  between  two  successive  transits  given  in  the  Nautical 
Almanac  is  the  retarJaiion  of  the  moon  in  passing  over  24''  of  longitude,  and  the  hourly  difference  given  is  the 
retardation  in  passing  from  the  Greenwich  meridian  to  the  meridian  i*^  in  longitude  from  Greenwich. 

Rule.  Take  from  the  Nautical  Almanac  the  mean  time  of  the  moon's  meridian  passage  for  the  given  astro- 
iti///ira/  date  and  apply  a  correction  equal  to  the  hourly  difference  multiplied  by  the  longitude  in  hours,  adding  the 
correction  when  the  longitude  is  7cvst,  or  subtracting  it  when  east. 

The  reduction  may  be  made  by  Table  11. 

Example.    Longitude  Si*^  15'  W.,  1879,  April  18,  find  the  time  of  the  moon's  meridian  transit. 

Long.  81°  15'  W.  =  +  5''  25"'  =  -f  5i».42 

Gr.  merid.  passage,  April  17,      21''  44'". 3  H.  D.,-|-  i"'.67 

Corr.  for  +  5^.42,  +  9'".!  +5-42 


L.  m.  t.  of  transit,  April  17,         21    53    .4  +  9'"-05 

The  same  rule  applies  to  Planets  whose  mean  times  of  transit  are  given  in  the  Nautical  Almanac. 
HxAMPLE.    Long.  81°  15'  E.,  1879,  April  18,  to  find  the  time  of  Jupiter's  meridian  passage. 

Long.  81'='  15'  E.  =  —  5'>  25™  =  —  5''. 42 

Gr.  merid.  passage,  April  17,  20''  43'". 6  H.  D.,  —  o"'.  13 

Corr.  for  —  5''.42,  +  o™.7  —  5    .42 


Local  ast.  t.  of  transit,  April  17,  20    44    .3  -\-  o"'.7o 

Al't.  230.     To  find  the  moon's,  or  a  planet's,  right  ascension  and  declination  at  the  time  of  transit  aiier  a  giveti 

meridian. 

Rule.  Find  the  local  time  of  transit  by  the  foregoing  rule  (Art.  229);  find  the  corresponding  Greenwich  time 
by  applying  the  longitude,  and  take  out  the  right  ascension  and  declination  for  this  Greenwich  time  from  the  Nau- 
tical Almanac. 

Art.  331.     To  find  the  Greenfinch  mean  time  of  a  given  lunar  distance. 

The  Nautical  Almanac  gives,  on  Pages  XIII  to  XVIII,  of  the  Calendar,  the  Lunar  Distances,  or  the  angular 
distances  of  the  moon  from  the  centre  of  the  sun,  from  the  four  larger  planets,  and  from  certain  fixed  stars,  as  they 
would  appear  to  an  observer  from  the  centre  of  the  earth.  They  are  given  for  every  third  hour  of  Greenwich 
mean  time,  beginning  at  noon  ;  tlie  dates  are  therefore  astronomical.  There  is  also  given,  between  each  two  suc- 
cessive distances,  \}i\ei proportional  logarithm  of  the  difference,  or  the  logarithm  of  the  seconds  of  time  in  which  the 
distance  changes  i". 

Al't.  233.  ^\ie.  proportional  logarithm  of  an  angle  expressed  in  hours,  (Sec,  is  the  logarithm  of  the  quotient 
of  3"^  divided  Ijy  that  angle;  that  of  an  angle  expressed  in  degrees,  &c.,  is  the  logarithm  of  the  quotient  of  3"^ 
divided  by  that  angle.     The  angle  is  to  be  reduced  to  seconds. 

Table  45  contains  these  proportional  logarithms  for  each  second  from  o''  to  3'',  or  0°  to  3°. 

Art.  333.  Since  the  intervals  of  time  are  as  great  as  3''  for  which  the  lunar  distances  are  given,  the  first 
differences  cannot  be  assumed  as  constant ;  and  the  time  found  by  using  first  differences  only  is  not  sufficiently 
exact ;  therefore  it  should  be  corrected  for  second  differences. 

To  facilitate  this  correction,  refer  to  Table  35  of  this  work,  or  to  Table  I,  Nautical  Almanac. 

Rule.  Find  in  the  Nautical  Almanac  the  two  distances  between  which  the  true  distance  falls,  take  out  the 
nearest  of  these,  the  hours  of  Greenwich  time  over  it,  and  the  P.  L.  of  Diff. 

Find  the  difference  between  the  true  distance  and  the  distance  taken  from  the  Almanac;  and  from  the  P.  L. 
of  this  difference  subtract  the  P.  L.  of  Diff.  taken  from  the  Almanac.  The  result  is  the  P.  L.  of  an  interval  of 
time  (Table  45)  to  be  added  \.o  the  hours  of  Greenwich  time  taken  from  the  Almanac,  when  the  «?;•//< 7- Almanac 
diitance  is  used;   to  be  subtracted  from  the  hours  of  Greenwich  lime  when  the  /rtA'r  Almanac  distance  is  used. 

To  correct  for  second  Diff.,  take  the  difference  between  the  P.  L.  of  Diff.  used  and  the  one  which  follows  it  in 
the  Almanac.  With  this  difference  and  the  first  correction  of  the  Greenwich  time  already  found  enter  Table  35 
(or  Table  I,  N.  A.)  and  take  out  the  corresponding  seconds,  which  are  to  be  added  X.o  the  approximate  Greenwich 
time  if  the  Prop.  Logs,  in  the  Almanac  are  decreasing ;  to  be  subtracted  \{  they  are  increasing. 


88 


INSTRUMENTS    EMPLOYED    IN   NAUTICAL   ASTRONOMY. 


i 


Example.    1879,  April  19,  the  corrected  distance  of  the  moon's  centre  from  Jupuer  was  38°  40'  45" ;  required^ 
the  Greenwich  time. 


Corrected  distance, 
Almanac  distance, 

Difference, 

Time  after  12'', 

Gr.  m.  t.,  April  19, 


12"    O™    O^ 


+      2     17      25 


38°  40'  45" 
37    34    15 

I      6   30 


P.L-,  -3153 
P.L.,  .4325 
P.  L.,  .1172 


14    17    25 
Example.    1879,  April  19,  the  corrected  distance  of  the  moon's  centre  from  the  sun's  centre  was  20°  o'  lo". 


Corrected  distance. 


20°     o'   10' 


Almanac  distance. 

6'>    0"*   o^ 

+  15    45 

—              7 

20    29      I 

P-L-, -3577 

Difference, 

Time  after  6"^, 
Corn  for  2d  Diff., 

28   51 

P.L.,  .7951 
P.  L.,  .4374 

Gr.  m.  t.,  April  19, 


7   5    38 


Art.  234.    Ti>  find  the  distance  of  the  moon  from  a  given  object  at  any  given  time. 

Rule,  Find  the  corresponding  Greenwich  time.  Find  two  consecutive  distances  in  the  Almanac  between 
which  the  Greenwich  date  falls.  Take  the  difference  of  the  distances.  Add  the  P.  L.  of  this  difference  of  dis- 
tances (Table  45)  to  the  P.  L.  of  the  excess  of  the  Greenwich  time  above  the  first  of  the  Almanac  times.  The 
sum  will  be  the  P.  L.  of  an  arc ;  which  arc  being  applied  to  the  distance  corresponding  to  the  first  Almanac  time 
with  its  proper  sign  will  give  the  required  distance. 

Example,  1879,  April  19,  in  Long.  81°  15'  W,,  at  S''  30'"  p,  m.,  required  the  distance  of  Mars  from  the 
Moon. 

Local  m.  t.,  April  19,         8''  30™ 
Longitude,  +  5    25 


Gr.  ast.  time,  April  19,     13    55 

1st  Almanac  distance  12^,                       48^  57'  36" 
2d  Almanac  distance  15'^,                      50    20   51 

Diff.,                                                           I    23    15 
Gr.  t.,  13'!  55'"  —  i2h  0™  =  ih  55™, 

P. 
P. 

L., 
L., 

.3349 
.1946 

Correction,                                              +    53    li 

P. 

L., 

•5^95 

Required  distance,                               49    50  47 

CONVERSION   OF   TIME. 


89 


CHAPTER   III, 


CONVERSION  OF  TIMES. 

Art.  335*    To  convert  mean  time  into  apparent  time,  or  apparent  time  into  mean  time, 

l^ULE.  Find  the  Greenwich  time  corresponding  to  the  given  local  time.  If  apparent  time  is  given,  find  the 
Greenwich  apparent  time  and  take  the  equation  of  time  from  Page  I  of  the  Calendar.  If  mean  time  is  given,  find 
the  corresponding  Greenwich  mean  time  and  take  the  equation  of  time  from  Page  II. 

Correct  the  equation  of  time  for  this  date  and  apply  it  according  to  its  proper  sign  to  the  given  time. 
Example.    1879,  April  21,  3''  5""  p.  m.  mean  time,  in  Long.  81°  15'  W. ;  required  the  apparent  time. 


L.  m.  t.,  April  21,        2>^    5" 
Long.,  +  5    25 


Gr.  m.  t., 


8   30 


Eq.  t.,  Gr.  m.  t.  o^,       i™  17^.61 
Corr.  for  +  8h.5,  +     4  .40 

Eq.  t.  +  to  m.  t.,  I    22  .01 

L.  m.  t.,  April  21,    s*^  5     o 


H.  D.,    +  o^5I8 
+  8-5 

+  4  -403 


L.  appt.,  April  21,    3   6   22 
Example.    1879,  April  3,  8"^  45'"  a.  m.,  apparent  time  in  Long.  81°  15'  E. ;  required  the  mean  time. 


L.  app.  t.,  April  2,       20''  45"' 
Long.,  _    5    25 

Gr.  app.  t.,  April  2,       1520 


Eq.  t.  Gr.  o''  appt., 
Corr.  for  +  i5''-33, 


3'"  42^46 
-     11-56 


H.  D.,   —    0^754 
+  15  -33 


II  .56 


Eq.  t.  +  to  app.  t.,  3     30  .90 

L.  app.  t.  April  2,     20'^  45       o 

L.  m.  t.,  April  2,       20    48     30  .9 

1  If  great  precision  is  required  the  variation  of  the  hourly  difference  should  be  taken  into  account,  and  the  H.  D. 

•  corrected  for  the  mean  of  the  interval  from  April  2,  o^  to  I5'^33. 

Art.  336*    To  ce^tverta  mean  solar  time  interval  into  a  sidereal  time  interval. 

The  conversion  of  an  interval  of  mean  solar  time  into  an  equivalent  of  sidereal  time,  or  the  reverse,  is  facili- 
I  tated  by  the  use  of  Tables  8  and  9. 
I  In  case  Tables  are  not  at  hand  the  conversion  may  be  made  by  the  following  formula : 

Let  T  represent  an  interval  of  time  expressed  in  mean  time. 

Let  S  represent  a  sidereal  time  interval. 

The  sidereal  year  =  366.25636  sidereal  days. 

=  365.25636  mean  solar  days. 


Hence, 


S      366.25636       ,  „„-_„-« 
—  =  ^- — ■'  /> -  z=  1.0027370, 

T      365.25636  '^'^ 


Therefore,    S  =  1.0027379  T  =  T  +  .0027379  T.     (i) 
T=  0.9972696  S  =  S  —  .0027304  S.     (2) 

If  in  ( I)  T  =  24'!  .  • .  S  =  24''  3"'  56^5553,  or  in  a  mean  solar 
day  sidereal  time  gains  on  mean  time  3"'  56.^5553.     In  i*"  of  mean    y 
time  the  gain  is  9^.8565. 

If  in  (2)  S  =  24''  .  • .  T  =  24''  —  3'"  558.9094,  or  in  a  sidereal 
day  mean  time  loses  on  sidereal  time  3"  55^.9094.  In  i^  of  sidereal 
time  the  loss  is  9^.8296. 

If  in  (i)  and  (2)  T  and  S  in  the  last  terms  be  expressed  in 
hours  and  decimal  parts  of  an  hour,  then 

S  =  T  +  9.8565  T 
T  =  S  —  9.8296  S 

By  which  the  reductions  may  be  made. 

Art.  SS?.    To  convert  mean  solar  time  at  a  given  place  into 

sidereal  time. 

Let  QMQ'  in  Fig.  58  represent  the  celestial  equator  of  which 
P  is  the  pole. 

QPQ',  the  celestial  meridian. 

V,  the  vernal  equinox.  FiG.  58. 

M,  the  position  of  the  mean  sun  west  of  the  meridian. 

QPV,"or  the  arc  QV,  =  the  sidereal  time  since  it  measures  the  time  elapsed  since  V  was  on  the  meridian. 


90  CONVERSION    OP    TIME. 

QM,  the  mean  time. 
,    VM,  the  right  ascension  of  the  mean  sun. 

Hence,  QV  =  QM  +  VM,  or 

Sid,  time  =  mean  time  -\-  R.  A.  of  the  mean  stm  — 

If  the  mean  sun  be  east  of  the  meridian  at  M'  then  the  mean  time  =  24''  —  M'Q, 

QV  =  VM'  —  M'Q,  or 

Sid.  time  =  R.  A.  mean  sun  —  (24''  —  mean  time) 
=  R.  A.  mean  sun  -j-  mean  time  —  24'' 

The  "Right  Ascension  of  Mean  Sun"  is  given  on  Page  II  of  the  Calendar  for  every  day  at  Greenwich  mean 
noon. 

Rule.  Find  the  corresponding  Gr.  m.  time.  Correct  the  right  ascension  of  the  mean  sun  by  Table  9,  or  by 
the  H.  p.  9^8565  for  the  Gr.  time.  Add  the  given  mean  time  to  the  corrected  R.  A.  mean  sun;  the  result  will 
be  the  sidereal  time  (rejecting  24'*  if  greater  than  24^^). 

Example.   In  Long.  81°  15'  W.,  1879,  April  22,  2''  m.  t.,  p.  m. ;  required  the  sidereal  time. 

L,  Ast.  t.,  April  22,       2^    o'"  o^  R.  A.  m.  sun,       2'^  o™  418.24 

Long.,  -j-  5    25     o  Corr.  for  7'' 25'",       i     13.10 

Gr.  m.  t.,  April  22,         7    25     o  L.  m.  t.,  200 .00 

Sid.  time,  4    i     54 .34 

Example.   In  Long.  75°  E.,  1879,  April  22,  4'^  a.  m.,  mean  time;  required,  the  sidereal  time. 

L.  Ast.  t.,  April  21,     i6i'  o™  o^  R.  A.  m.  sun,  April  21,  o'',     i^  56™  44^69 

Long.,  —500  Corr.  for  11'' Gr.  t.,  i     48.42 

Gr.  m.  t.,  April  21,     11    o    o  L.  m.  t.,  April  21,  16     o      o 


x-^ 


Sid.  time,  17    58     33.11 

Art.  33§.    To  convert  sidereal  time  at  a  given  place  into  mean  time. 

Rule  I.  Take  from  the  Nautical  Almanac  the  R.  A.  of  the  mean  sun  for  noon  of  the  given  astronomical  day. 
Reduce  it  for  the  longitude  of  the  place,  Table  9,  and  the  result  will  be  the  sidereal  time  of  local  noon.  Subtract 
this  time  from  the  given  sidereal  time  (adding  24*1  to  the  latter  if  necessary);  the  result  will  be  the  sidereal  interval 
from  noon.  From  this  interval  subtract  the  reduction  to  a  mean  time  interval,  Table  8.  Prefix  to  the  result  the 
given  astronomical  day. 

Rule  II.  The  last  column  on  Page  III  of  the  Calendar  contains  the  "Mean  Time  of  Sidereal  o'',"  or  24'* 
—  R.  a.  of  the  Mean  Sun.  It  may  be  reduced  to  any  meridian  by  interpolating  for  the  longitude,  or  to  any  Green- 
wich sidereal 'i\V[i&,  by  means  of  Table  8,  or  by  means  of  the  hourly  difference  —  9^.8296. 

Take  from  the  ISiautical  Almanac  for  the  given  astronomical  day  the  "  Mean  Time  of  Sidereal  o''"  and  reduce 
it  for  the  longitude  by  Table  8,  rememljering  that  the  reduction  is  siibtractive  in  west  longitudes,  additive  in  east 
longitudes.     The  result  is  the  mean  time  of  local  sidereal  noon. 

Add  to  this  the  given  sidereal  time  and  reduce  the  sum  for  the  given  sidereal  time.  Table  8,  or  by  —  9*'.8296 
X  the  hours  and  parts  of  an  hour  of  the  sidereal  time. 

It  must  be  noticed  in  advance  if  the  sum  of  the  mean  time  of  sidereal  0''  and  the  given  sidereal  time  is  greater 
than  24''.     If  greater  than  24'',  the  mean  time  of  sidereal  o''  must  be  taken  out  for  the  preceding  astronomical  day. 

Example.  1879,  April  22,  a.  m.,  at  a  place  in  Long.  75^  E.,  the  sidereal  time  is  17''  58'"  33";  what  is  the 
corresponding  mean  time  ? 

The  astronomical  day  is  April  21. 

Sid.  t.  of  Gr.  mean  o'',  April  21,  i''  56"'  44^.69 

Reduction  for  Long.  =  —  5''  (Table  9),  —  49  .28 

Sid.  t.  of  local  o'', 
Given  Sid.  time, 

Sid.  interval  from  noon. 

Red.  for  Sid.  interval  (Table  8), 

Local  mean  time — Ast.,  April  21,  16      o      o 

or  Civil,  April  22,  4''  a.  m. 

Example.  1879,  April  22,  p.  m.,  at  a  place  in  Long.  81°  15'  W.,  the  sidereal  time  is  4''  i"^  54";  what  is  the 
corresponding  mean  time? 

The  astronomical  day  is  April  22. 

Longitude  =  81°  15'  W.  =  +  5I'  25"'. 
By  Rule  II.— 

Mean  time  of  Gr.  Sid.  o'',  April  22  =  21''  55'"  42^62. 


I  55 
17  58 

55-41 
33 -oo 

16   2 
2 

37-59 
37-70 

CONVERSION    OF   TIME. 


91 


2ih  59'n38s.53 
53  -24 


21 

4 

58 

I 

45 
54 

.29 
.00 

2 

0 

39 
39 

.29 
•63 

The  sum  of  this  and  the  given  Siil.  time  being  greater  than  24*", 

Mean  lime  of  Gr.  Sid.  o'',  April  21, 
Red.  for  Long.  =  +  S**  25"'  (Table  8), 

Mean  time  of  local  Sid.  o'', 
Given  Sid.  time, 


Red.  for  4''  i"'  54"  (Table  8), 

Local  mean  time,  April  22,  200 

Art.  239.    Given  mean  or  apparent  time  at  a  given  place,  to  Jind  what  heavenly  bodywill  pass  the  meridian  the 

next  after  that  time. 

In  Fig.  59  VQ  represents  the  P 

,     celestial  equator ;    V,  the    vernal 
1 1    equinox;   M,  the  mean  sun;   S,  a 
celestial  body  passing  the  meri- 
dian PQ. 

QM  ^  mean  time  at  the  given 
place. 

VM  =  R.  A.  of  the  mean  sun. 
VQ  =  R.  A.  of  the  body  S  = 
Sidereal  time  =  R.  A.  of  the  me- 
ridian. 

VQ  =  VM  -f  QM,  or  Star's 
I;    R.  A.  =^  R.  A.  mean  sun  -j-  mean 
I  time. 

Hence,  knowing  the  local 
j  mean  time,  it  is  necessary  to  find 
I  the  "  R.  A.  of  the  meridian,"  or 

■  the  Sidereal  time    (Art.  237),  to       \  J{ 

find  the  time  when  any  heavenly     "y 
body  passes  the  meridian. 

Having  found  the  R.  A.  of 
the  meridian,  by  consulting  the 
Star  Catalogue  (Nautical  Alma- 
nac, Table  48),   the   star   whose 

R.  A.  is  next  greater  will  evidently  l\j^ 

be  the  next  principal  star  to  pass 
the  meridian. 

Example.    1879,  April  23,  at 


Fig.  59. 


V 


4  p.  m.  (nearly)  mean  time,  in  Long.  81°  15'  W. ;  what  N.  A.  star  will  pass  the  meridian  next  after  that  time? 

L.  m.  t.,  April  23,         4''     o"'  o^ 


Long. 
Gr.  m.  t.. 


+  5     25     o 


9     25 


R.  A.  mean  sun,  April  23,  Gr.  o'^, 
Red.  for  Gr.  m.  t., 
L.  m.  t., 

R.  A.  of  meridian, 


2''  4'"  3  7^- 80 
+       I     32 .82 
400 


6610  .62 


Nautical  Almanac,  1879, 


R.  A.  of  fi  Geminorum,  6^  15'"  38^.457. 


Sometimes  it  is  necessary  to  find  what  principal  fixed  stars  will  pass  the  meridian  between  certain  hours.  To 
do  this,  the  R.  A.  of  the  meridian  must  be  found  for  each  of  these  times,  and  the  stars  whose  right  ascensions  fall 
between  will  be  the  stars  required. 

Art.  240.     To  find  the  mean  time  of  the  meridian  passage  of  a  heavenly  body,  the  loftgitiide  of  the  place  being 

laicnon. 

The  Sun. — The  apparent  time  of  the  Sun's  meridian  passage  is  o*"  o'"  0%  and  to  find  the  mean  time  take  from 
Page  I  of  the  Calendar  the  equation  of  time  and  correct  it  for  longitude,  or  take  it  from  Page  II  and  correct  it  for 
the  Greenwich  mean  time.  If  the  equation  of  time  is  subtractive  from  app.  time,  it  is  to  be  subtracted  from  the 
number  of  days. 

A  Star. — Let  S,  Fig.  59,  be  the  star  on  the  meridian  PQ;   V,  the  vernal  equinox;  and  M,  the  mean  Sun. 


Then 
Hence 


QM  =  mean  time  required  ; 
VM  =  R.  A.  of  mean  sun ; 
VQ  =  R.  A.  of  the  star. 
QM  =  VQ  —  VM,    or 

Mean  time  =  R.  A.  of  star  —  R.  A.  of  mean  suru 


92 


CONVERSION    OF    TIME. 


Rule.  Take  from  the  Star  List  the  R.  A.  of  the  given  star  and  from  the  Almanac  the  R.  A.  of  the  mean  s  _ 
for  noon  of  the  given  day  (apparent  places).  From  the  R.  A.  of  the  star  (increased  if  necessary  by  24}^)  subtract 
the  R.  A.  of  the  mean  sun,  and  the  remainder  will  be  the  approximate  local  mean  time. 

From  this  get  the  Greenwich  time  by  applying  the  longitude,  and  with  the  Gr.  time  correct  the  R.  A.  of  the 
mean  sun. 

Then  subtract  the  corrected  R.  A.  of  the  mean  sun  from  the  R.  A.  of  the  star  and  the  remainder  will  be  the 
time  of  meridian  passage  of  the  star. 

Example.  At  what  time  will  Sirius  pass  the  meridian  of  a  place  in  Long.  81°  15'  W.  on  April  24,  1879,  Ast. 
date  ? 

R.  A.  of  Sirius,  April  24,        6''  39'"  49^.85 
R.  A.  mean  sun,  2      8     34  .35 


Approx.  local  m.  t.. 
Longitude, 

Gr.  m.  t.,  April  24, 

R.  A.  of  mean  sun. 
Red.  for  Gr.  m.  t. , 

Red.  R.  A.  of  mean  sun, 
R.  A.  of  Siriixs, 


4    31 

+  5   25 


15-50 
o 


+ 


9   56     15 
2h    8>"  34^35 


I 

37 

•95 

2 
6 

10 

39 

12 

49 

.30 
.85 

Meridian  passage,  April  24,     4    29    37  .55 

Example.   At  what  time  will  Antares  pass  the  meridian  of  a  place  in  Long.  10°  E.,  on  August  5,  1879,  Ast 
date? 


R.  A.  of  Antares,  Aug.  5, 
R.  A.  of  mean  sun,  Gr.  o'', 

Approx.  local  time, 
Long., 

Gr.  m.  t., 

R.  A.  mean  sun  o*", 
Red.  for  Gr.  m.  t.. 


i6'i  22™    3^.40 
8    54    39-76 

7  27    23  .64 
—  o  40      o 

6   47    24 

8h  54m  39s.  76 
+         I       6 .93 

8  55    46.69 
16   22      3  .40 


R.  A.  of  Antares, 
Meridian  passage,  Aug.  5,         7    26 
The  Moon  and  Planets.— See  Art.  229,  Chap.  II,  Part  II. 


16.71 


k 


HOUR    ANGLE. 


93 


CHAPTER  IV. 


HOUR  ANGLE. 


Art.  241.    The  hour  angle  of  a  heavenly  body  is  the  angle  at  the  pole  of  the  celestial  concave  between  the 

declination  circle  of  the  heavenly  body  and  the  celestial  meridian. 

It  is  measured  by  the  arc  of  the  celestial  equator  between  the  declination  circle  and  the  celestial  meridian. 

In  Fig.  60  let  P  be  the  pole  of  the  celes-  p 

tial  equator  VQM;  -~ 

PQ,  the  celestial  meridian  ;  and  i 

PiVI,  PS,  and  PV  declination  circles.  \i\- 

Let  PM  be  the  declination  circle  of  the 
mean  sun. 

PS,  the  dechnation  circle  of  other  heavenly 
bodies. 

V,  the  vernal  equinox. 

Then,  QPM,  or  QM,  is  the  hour  angle 
■  of  the  mean  sun. 

QPS,  or  QS,  the  hour  angle  of  the  celes- 
I  tial  body. 

QPV,  or  QV,  the  hour  angle  of  the  ver- 
nal equinox,  or  the  sidereal  time  =  R.  A.  of 
the  meridian. 

VS  is  the  R.  A.  of  the  star. 

VM  is  the  R.  A.  of  the  mean  sun. 


Art.  242.    To  find  the  hour  angle  of  the  Sim  for  a  given  time  and  place. 

Rule.  The  apparent  time  is  the  hour  angle  of  the  sun,  and  if  mean  time  is  given  apply  to  it  the  equation  of 
time  to  find  the  hour  angle.  It  is  reckoned  from  the  upper  meridian  westward  through  24''.  If  the  hour  angle  is 
required  east  of  the  meridian  it  is  negative^  and  equal  to  24'^  —  app.  time. 

Art.  243.    To  find  the  hour  angle  of  a  celestial  body  at  a  given  time  and  place. 

In  Fig.  60  QS  =  QV  —  VS,   or 

H.  A.  of  star  ^  sid.  time  —  R.  A.  star. 

QV  =  VM  +  QM, 

H.  A.  of  star  :=  R.  A,  mean  sun  -j-  mean  time  —  R.  A.  star. 


Rule.    To  the  given  mean  time  add  the  R.  A.  of  the  mean  sun  to  find  sidereal  time. 

From  the  sidereal  time  subtract  the  R.  A.  of  the  celestial  body  (increasing  the  sidereal  time  by  24''  if  neces- 
§aiy) ;  the  remainder  will  be  the  required  hour  angle  west  of  the  meridian. 

EX.A.MPLE.  In  Long.  Si'^  15'  W.,  1879,  April  25,  12''  10™  30"  mean  time,  find  the  hour  angles  of  the  Sun, 
Moon,  Venus,  and  Sirius, 


L.  m.  t.,  April  25,  I2'>  10'"  31 

Long.  +  5    25      < 

Gr.  m.  t.,  April  25,       17    35     3 

Eq.  t.,  +  2 

H.  A.  sun  or  appt.,        12    12 


II 


41 

Sid.  time, 
R.  A.  Moon, 

H.  A.  Moon, 

Sid.  time, 
R.  A.  Venus, 

H.  A.  Venus, 


Sid.  time, 
R.  A.  Sirius, 


R.  A.  mean  sun, 
Red.  Gr.  m.  t., 
Sid.  time, 

I4h  25"'  54^30 

5  45       8.64 

8  40    45  .66 

14I'  25"'  54^30 
4    28      3.17 

9  57    51  -13 

14I'  25"'  54^.30 

6  39    49.83 


I2h   lo'ii  30S 
2     12      30.91 

2    53-39 

14  25   54.30 


H.  A.  Sirius, 


7    46      4.47 


94 


HOUR   ANGLE. 


Art.  24:4;.   Given  the  hour  angle  of  a  heavenly  body  at  a  given  place  and  day,  to  Jind  the  local  mean  time. 
In  Fig.  60,  QPS  given  to  find  QPM,  or  QS  given  to  find  QM. 

QV  =  VS  +  QS 
Sid.  time  =  R.  A.  of  the  body  +  H.  A. 

Rule.  Add  the  hour  angle  of  the  body  to  its  right  ascension  and  the  result  will  be  the  local  sidereal  time. 
From  this  subtract  the  R.  A.  of  the  mean  sun  to  find  the  mean  time.  Should  the  sum  of  H.  A.  and  R.  A.  exceed 
24'!,  deduct  24''. 

If  the  longitude  of  the  place  is  given,  but  not  the  Gr.  time,  an  approximate  value  of  the  Gr.  time  must  be 
found  first,  using  a  value  of  the  R.  A.  deduced  from  this  approximate  time;  from  the  local  time  thus  found  deduce 
a  more  exact  value  of  the  Gr.  time  with  which  a  more  exact  value  of  the  R.  A.  may  be  found ;  repeating  the 
process  until  the  necessary  degree  of  precision  has  been  reached. 

It  is  evident  in  the  case  of  the  sun  that  the  hour  angle  is  at  once  the  apparent  time,  from  which  the  mean  time 
is  found  by  properly  applying  the  equation  of  time. 

Example.  At  a  place  in  Long.  8i-  15'  W.,  1879,  April  25,  the  hour  angle  of  Sirius  was  7''  46'"  4^47:  what 
was  the  local  mean  time? 


R.  A.  Sirius,  April  25, 
H.  A., 


Sid.  time, 

R.  A.,  mean  Sun, 

Diff., 

Red.  for  12^  13'"  23^39, 

Red.  for  Long.  -\-  5''  25'" 

Local  mean  time,  April  25, 


6b  39".  49^83 
7  46   4-47 


14  25  54.30 
2  12  30.91 


12  i: 


23-39 
2    O  .15 

o  53  -24 


12  10  30 


Example.    Same  place  and  date,  the  hour  angle  of  Venus  was  9''  57"'  51M3;  what  was  the  local  mean  time! 

Venus  merid.  passage,  April  25,        2''  ii"'.9 
II.  A.  Venus, 

Approx.  local  time, 
Long., 

1st  approx.  Gr.  t.,  April  25, 

R.  A.  for  1st  Gr,  t., 
H.A., 

Approx.  sid.  time, 

R.  A.  mean  Sun  for  1st  Gr.  t. 

Approx.  local  time, 
Long., 

2d  approx.  Gr.  time, 

R.  A,  for  2d  Gr.  t., 
H.A., 

Sid.  time, 

R.  A.  menn  .Sun  for  2d  Gr.  t., 


9   57 

.8 

12     9 

+  5   25 

•7 
.0 

17   34 

•7 

4''  28" 
9   57 

3' 
51 

04 
13 

14  25 
2    15 

54 
24 

17 
19 

12    10 

+  5   25 

30 
0 

17   35 

30 

4i>  28" 
9   57 

3^ 
51 

18 
13 

14   25 
2    15 

54 
24 

31 
•31 

Local  mean  time,  April  25,  12    10     30 

Example.    Same  place  and  date,  the  hour  angle  of  the  moon  was  8''  40"^  46^06;  what  was  the  local  mean  time  ? 

Moon's  merid.  passage,  April  25,  Gr.,      2''  59"' 
Corr.  for  longitude  -(-  5'^  25"^ 

Local  time  of  transit, 
H.A., 

Approx.  local  time, 

Long.,  -f 

ist  approx.  Gr.  time,  April  2^, 


2"  59" 
II 

'.3H.  D 
.6 

> 

+ 

2"M5 

5   -4 

3    10 
8   40 

•9 
.8 

II    .6 

"    51 

5    25 

•7 
.0 

17    16 

•7 

% 


HOUR    ANGLE.  95 

R.  A.  of  Moon  for  isl  Cr.  time,  5''  44'"  268.22 

H.  A.,  8    40     46  .06 

Appro.x.  .sid.  time, 

R.  A.  Mean  Sun  for  ist  CJr.  time, 

1st  approx.  local  time. 
Long., 

2d  approx.  (a",  time, 

R.  A.  for  2d  Gr.  time, 
H.A., 

Sid.  time, 

R.  A.  Mean  Sun,  (Jr.  time, 

Locsl  mean  time,  April  25,  12    10    31 


14 

2 

25 
15 

12.28 
21  .21 

12 

5 

9 
25 

51  -07 
0 

17 

34 

51  -07 

5' 
8 

45" 
40 

9"-43 
46  .06 

14 

2 

25 
15 

55-49 
24-31 

96 


COKRECTION   OF    OBSERVED    ALTITUDES. 


CHAPTER   V. 

CORRECTIONS  OF  OBSERVED  ALTITUDES. 


Art.  245.    The  true  altitude  of  a  heavenly  body  is  the  altitude  of  its  centre  as  if  it  were  measured  by  i 
observer  at  the  centre  of  the  earth. 

The  obsen'cd  altitude  of  a  heavenly  body  measured  at  sea  is  reduced  to  the  true  altitude  by  the  application  of 
the  following-named  corrections,  applied  in  the  order  given  :  || 

Index  Correction,  Dip,  Refraction,  Parallax,  and  Semi-diameter.  '  \ 

It  is  not  absolutely  necessary  in   ordinary  nautical  practice    to   observe  this   order,  but  to  attain  the  nearest 
degree  of  precision  correct  methods  should  be  observed. 

Art.  246.   Applying  the  Index  Correction  to  the  reading  of  the  instrument  gives  the  ohso-ved  altitude  of  the 
upper  or  lower  limb;  i 

Applying  to  this  the  Dip  gives  the  apparent  altitude  of  the  limb ;  ^ 

Applying  the  correction  for  Refraction  and  Parallax  gives  the  true  or  geocentric  altitude  of  the  limb ; 

Applying  the  Semi-diameter  according  to  the  limb  observed  gives  the  true  or  geocentric  altitude  of  the  centre.  ^ 

PARALLAX.  * 

Art.  247.    The  parallax  of  a  heavenly  body  is  in  general  terms  the  angle  between  two  straight  lines 
drawn  to  the  body  from  different  points.     But  in  Nautical  AsXxonomy  geocentric  parallax  is  alone  considered,  which 

is  the   difference   be- 
'^  tween    the    positions 

of  a  heavenly  body  as 
seen  from  the  centre 
of  the  earth  and  from 
a  point  on  its  surface 
at  the  same  instant. 

The  zenith  dis- 
tance of  a  body,  S 
(Fig.  6i),  seen  from 
A  on  the  surface  of 
the  earth  is  ZAS;  seen 
from  C  it  is  ZCS,  and 
parallax  is  the  differ- 
ence of  these  angles. 

ZAS  —  ZCS  =  ASC 

Parallax  in  alti- 
tude is  then  the  angle 
at  the  heavenly  body 
subtended  by  the 
radius  of  the  earth. 

If  the  heavenly 
body  is  in  the  hori- 
zon as  at  H',  the 
radius  being  at  right 
angles  to  AH'  sub- 
tends the  greatest  pos- 
sible angle  at  the  star 
for  the  same  distance, 
and  this  angle  is  called 
the  horizontal  paral- 
lax. The  parallax  is 
less  as  the  bodies  are 
farther  from  the  earth, 
as  will  be  evident  from 
the  figure. 

Let  par.  =;  par- 
allax in  altitude,  ASC. 

Z   =  SAZ,     ap-  I 
parent  zenith  distance 
(corrected  for  refrac- 
tion). 


Fig.  6i. 


R  =  AC,  the  radius  of  the  earth. 

D  ^  CS,  distance  of  the  object  from  the  centre  of  the  earth. 

Then  the  triangle  of  ASC  gives 

R  sin  Z    /  •         r*  *  /-« 
sm  par  := — ,  (since  SAC 


=  iSqC 


SAZ) 


If  the  object  is  in  the  horizon  at  H*',  the  angle  AII'C  is  the  horizontal  parallax,  and  denoting  it  by  H.  P.  the 


right  triangle  AH'C  gives 


sin  H.  P.  = 


R 
D 


CORRECTION    OF    OBSERVED    ALTITUDES. 


97 


¥ 


SubstitiUHig  this  value  of  —  in  the  above, 

sin  par.  =  sin  H.  P.  sin  Z. 
If /^  =  SAH',  the  apparent  altitude  of  the  heavenly  body,  then  Z  =  90°  —  A; 
hence,  sin  par.  =  sin  H.  P.  cos  /t. 

'         Since  par.  and  H.  P.  are  always  small  the  sines  are  nearly  proportional  to  the  angles ; 

lience,  par.  =  H.  P.  cos  /i. 

Table  16,  giving  the  "  Sun's  parallax  in  altitude"  for  each  5^^  or  10^,  is  computed  from  this  formula. 
The  Nautical  Almanac  gives  the  moon's  horizontal  parallax  for  each  noon  and  midnight  at  the  Greenwich 
imeridian ;  the  horizontal  parallaxes  of  Venus,  Mars,  Jupiter,  and  Saturn  for  every  ten  days. 


REFRACTION. 

Art.  34 S.  It  is  known  by  various  experiments  that  the  rays  of  light  deviate  from  their  rectilinear  course  in 
passing  obliquely  out  of  one  medium  into  one  of  a  different  density ;  and  if  the  density  of  the  latter  medium  con- 
tinually increases,  the  rays  of  light  in  passing  through  it  will  deviate  more  and  more  from  the  right  lines  in  which 
they  were  projected  toward  the  perpendicular  to  the  surface  of  the  medium. 

The  ray  of  light  before  entering  the  second  medium  is  called  the  hicidciit  ray;  after  it  enters  the  second 
medium  it  is  called  the  refracted  ray,  and  the  difference  of  directions  of  the  two  is  called  the  refraction. 

The  rays  of  light  from  a  heavenly  body  must  pass  through  the  atmosphere  before  reaching  the  eye  of  an 
■  observer  upon  the  surface  of  the  earth.     The  earth's  atmosphere  is  not  of  a  uniform  density,  but  is  most  dense 
I  near  the  earth's  surface,  grad- 
ually decreasing  in  density  to- 
ward its  upper  limit :  hence  the 
path  of  a  ray  of  light,  by  pass- 
ing from  a  rarer  into  a  continu- 
I  ally  increasing  denser  medium, 
'  becomes  a  curve,  which  is  con- 
cave toward   the    earth.     The 
last  direction  of  the  ray  is  that 
of  a  tangent  to  the  curved  path 
at  the  eye  of  the  observer,  and 
the  difference  of  the  direction 
of  the  ray  before  entering  the 
atmosphere  and  this  last  direc- 
tion is  called  the  refraction. 

Art.  249.  To  illustrate 
this,  let  MN  (Fig.  62)  repre 
sent  the  strata  of  the  earth's 
atmosphere ;  SB,  a  ray  from  a 
starS,  entering  the  atmosphere 
at  B,  is  bent  into  the  curve  BA; 
and  the  apparent  direction  of 
the  star  is  AS',  the  tangent  to 
the  curve  at  the  point  A;  and 
the  refraction  is  the  difference 
of  directions  of  the  lines  BS 
and  AS'. 

If  CAZ  is  the  vertical  line 
of  the  observer,  by  a  law  of 
Optics  the  vertical  plane  of  the 
observer  wliieh  contains  the 
tangent  AS'  must  also  contain 
the  whole  curve  BA  and  the 
incident  ray  BS.  Hence  re- 
fraction increases  tlie  apparent 
altitude  of  a  star  without  af- 
fecting its  azimuth. 

At  the  zenith  the  refraction 
is  nothing;  the  less  thr  altitude 
the  more  obliquely  the  rays 
enter  the  atmosphere  and  the 
greater  will  be  the  refraction. 
At  the.  horizon  the  refraction  is 
the  greate;!. 

Art.  250.    The  refrac- 
tion  for  a  mean  state  of  the 
atmosphere,  barometer  30'",  Fahr.  ther.  50°,  is  given  in  Table  20.     All  observed  altitudes  of  the  heavenly  bodies 
must  i,e  decreased  by  the  numbers  taken  from  that  Table  corresponding  to  the  observed  altitude. 

Since  the  amount  of  the  refraction  depends  upon  the  density  of  the  atmosphere,  and  the  density  varies  with 
the  i)rtssure  and  the  temperature,  which  are  indicated  by  the  barometer  and  ihermometer,  the  true  refraction  is 
found  by  applying  to  the  mean  refraction  of  Table  20  the  corrections  to  be  found  in  Tables  21  and  22.  These  arc 
deduced  from  Bessel's  formulae,  and  are  regarded  as  the  most  reliable  Tables  constructed. 

7  B 


Fig.  62. 


98 


CORRECTION    OF    OBSERVED    ALTITUDES. 


If  the  refraction  be  required  for  the  apparent  altitude  5°,  when  the  thermometer  is  at  20°  and  the  barometei- 
at  3oi».67 — 

The  mean  refraction  by  Table  20  is,  9'  52" 

The  correction  for  height  of  barometer  is,     +  13 
The  correction  for  the  temperature,  -(-  42 


True  refraction, 


ID    47 


There  is  sometimes  an  irregular  refraction  near  the  horizon,  caused  by  the  vapors  near  the  surface  of  the! 
earth,  and  the  only  method  of  avoiding  the  error  arising  from  this  source,  which  is  sometimes  very  great,  is  to  takC; 
the  observations  at  a  time  when  the  object  is  more  than  10°  above  the  horizon. 


DIP. 


li 


Art.  251.  Dip  of  the  horizon  is  the  angle  of  depression  of  the  visible  sea  horizon  below  the  true  horizon! 
arising  from  the  elevation  of  the  eye  of  the  observer  above  the  level  of  the  sea. 

In  Fig.  63  suppose  A  to  be  the  position  of  an  ob- 
server whose  height  above  the  level  of  the  sea  is  AB. 

CAZ  is  the  vertical  line  of  the  observer,  and  AH 
is  the  intersection  of  the  true  horizon  witii  the  verticalj 
plane  through  CAZ,  and  the  heavenly  body  .S  being  ob-! 
served.  Draw  ATH'  in  this  vertical  plane  tangent  to 
the  earth's  surface  at  T.  Disregarding  refraction,  T 
will  be  the  most  distant  point  of  the  surface  visible  from 
A.  If  the  vertical  plane  should  be  revolved  about  CZ! 
as  an  axis,  AH  would  generate  the  plane  of  the  true  or 
celestial  horizon,  AH'  would  generate  the  surface  of  a' 
cone  touching  the  earth  in  the  small  circle  called  the, 
visible  sea  horizon,  and  the  angle  HAH'  will  be  thel 
dip  of  the  horizon. 

Art.  2r52.  Owing  to  the  existence  of  terrestrial 
refraction  the  most  distant  visible  point  ff  the  earth's 
surface  is  more  remote  from  the  observer  than  the  point 
T  in  Fig.  63. 

The  path  of  a  ray  of  light  from  the  point  T  (Fig. 
64)  to  the  eye  at  A  is  the  same  as  that  of  a  ray  from  A 
to  T.  Supposing  a  ray  of  light  from  the  star  at  S  to 
pass  through  A  it  will  be  bent  from  its  right-lined 
course  and  be  tangent  to  the  earth's  surface  at  T.  But 
the  direction  in  which  the  observer  at  A  will  see  the 
point  T  will  be  AH',  the  tangent  at  A  to  the  curved 
path  AT.  The  true  dip  is  therefore  HAH'  (Fig.  64), 
which  is  less  than  thai  shown  in  Fig.  63.  || 

Tlie  Dip  of  the  horizon  given  in  Table  14  for  every  probable  height  of  the  observer,  expressed  in  feet,  is  cal-  I 
culated  with  regard  to  tlie  effect  of  terrestrial  refraction.  ^,_ 

Art.  253.  What  has  been  heretofore  said  about  the  dip  of  the  horizon  supposes  it  free  from  all  incum- 
brances of  land  or  other  objects ;  but,  as  it  often  happens,  when,  ships  are  saihng  along  shore,  or  are  at  anchor  in 
harbor,  that  an  observation  is  desired  when  the  sun  is  over  the  land,  and  the  shore  nearer  the  ship  than  th .  visi^ 
ble  sea-horizon  would  be  if  it  were  unconfined,  in  this  case  the  dip  will  be  different  from  tliat  of  Table  r4  and 

greater  the  nearer  the  ^hip  is  to  thai 
puint  of  the  shore  to  which  the  sun's 
image  is  brought  dow  n.  For  this  rea^ 
son  Table  15  has  been  inserted,  whicll 
gives  the  dip  at  different  heights  ofl 
the  eye  and  at  different  distances  of 
the  ship  from  the  land.  Tlie  table  is 
to  be  entered  at  the  top  with  the 
height  of  the  eye  of  the  observer 
above  the  level  of  the  sea  in  feet,  and 
in  left-hand  column  with  the  distance 
of  the  ship  from  the  land  in  nautical 
miles.  Under  the  former  and  oppo- 
site the  latter  stands  the  dip  which  is 
to  be  subtracted  from  the  altitude  ob- 
served instead  of  the  numbers  found 
in  Table  14. 

Art.  254.  The  distance  of  the 
land  requisite  in  finding  the  dip  from 
Table  15  may  be  found  nearly  in  the 
following  manner :  Let  two  observ- 
ers, one  placed  as  high  on  the  main- 
mast as  he  can  conveniently  be,  and 
the  other  on  the  deck  immediately 
beneath  him,  observe,  at  the  same  in- 
stant, the  altitude  of  the  sun  or  other 
object  that  may  be  wanted,  and  let  the 
height  of  the  eye  of  the  upper  observer  above  that  of  the  lower  be  measured  in  feet  and  multiplied  by  0.56 ;  then 
the  product,  being  divided  by  the  difference  of  the  observed  altitudes  of  the  sun  in  minutes,  will  be  the  distance  in 
sea  miles,  nearly. 


Fig.  64. 


CORRECTION   OF    OliSERVED   ALTITUDES. 


99 


Thus,  if  the  eye  of  the  upper  observer  was  68  feet  higher  than  that  of  the  lower,  and  the  two  observed  alti- 
liulcs  of  the  sun  20^'  o'  and  20^  12',  the  distance  of  the  land,  in  sea  miles,  would  be  3.2.  For  68  X  0.56  =  38.08, 
and  this,  being  divided  by  the  difference  of  the  two  observed  altitudes  of  the  sun,  12',  gives  3.2,  nearly.  Now,  if 
the  lower  observer  be  25  feet  above  the  level  of  the  sea,  the  dip  corresponding  to  this  height  and  the  distance  3.2 
miles  will  be  6',  which,  being  subtracted  from  2o^-  o',  leaves  19*^  54',  the  altitude  corrected  for  the  dip. 

The  dip  may  be  calculated,  in  this  kind  of  observations,  to  a  sufficient  degree  of  accuracy,  without  using  Table 
15,  in  the  following  manner:  Divide  the  difference  of  the  heights  of  the  two  observers,  in  feet,  by  the  difference 
of  the  observed  altitude,  in  minutes,  and  reserve  the  quotient.  Divide  the  height  of  the  lower  observer,  in  feet, 
by  this  reserved  number,  and  to  the  quotient  add  one-quarter  of  the  reserved  numlier,  and  the  sum  will  be  the  dip 
in  minutes  corresponding  to  the  lower  observer.  Thus  in  the  above  example,  -(i  ^  5.6  is  the  reserved  number, 
and  1.^  =  4.4;  to  this  add  one-fourth  of  5'.6  or  i'.4,  and  the  sum  will  be  the  dip  5'. 8,  or  nearly  6',  corresponding 
to  the  lower  observer,  being  the  same  as  was  found  by  the  table. 


SEMI-DIAMETER. 


Al*t>  335.  The  semi-dia7neter  of  a  heavenly  body  is  half  the  angle  subtended  by  the  diameter  of  the  visible 
disc  at  the  eye  of  the  observer.  For  the  same  body  the  semi-diameter  varies  with  the  distance  ;  thus,  the  difference 
of  the  svn's  semi-diameter  at  different  times  of  the  year  is  due  to  the  change  of  the  earth's  distance  from  the  sun: 
and  similarly  for  the  moon  and  the  planets. 

In  the  case  of  the  moon  the  earth's  radius  bears  an  appreciable  and  considerable  ratio  to  the  moon's  distance 
from  the  centre  of  the  earth ;  hence  the  moon  is  appreciably  nearer  to  an  observer  when  she  is  in  or  near  his  zenith 
than  when  in  or  near  his  horizon,  and  therefore  the  semi-diameter  besides  having  a  menstrual  change  has  a  semi- 
diurnal one  also. 

The  increase  of  the  moon's  semi-diameter  due  to  her  increase  of  altitude  is  called  her  augrnentation.  This 
reduction  may  be  taken  from  Table  18. 

The  semi -diameters  of  the  sun,  moon,  and  principal  planets  are  given  in  their  appropriate  places  in  the 
Nautical  Almanac 

Example.  The  observed  altitude  of  Sirius  was  25^  30'  30"  ;  index  corr.  —  i'  30"  ;  height  of  the  eye  above 
the  sea-level,  15  feet.      Required  the  true  altitude. 

Since  the  stars  are  at  such  a  distance  that  the  earth's  orbit  subtends  no  angle  at  the  star,  there  is  no  parallax 
to  be  considered. 

Observed  altitude. 
Index  corn. 


Dip  Table  14, 

Apparent  altitude. 
Refraction, 

True  altitude. 


25" 

3°' 

I 

30" 
30 

25 

29 

0 
48 

25 

25 

2 

12 

2 

25  2: 


10 


Example.    Observed    altitude  of  Venus  was  53'^  26'   10";   index  corr.  -|-  2'  30";   height  of  eye,  20  feet. 
Required  the  true  altitude. 

Observed  altitude. 
Index  corr.. 

Dip, 


Refraction, 

Parallax  in  alt.  Table  17,     -)- 

True  altitude,  53    23    38 


St 

26' 

10" 

+ 

2 

30 

53 

28 

40 

— 

4 

23 

53 

+ 

24 

17 

43 

4 

Example.  In  Lat.  30  '  22'  N.,  Long.  81  W.,  on  May  6,  1879,  at  8  p.  m.,  the  observed  altitude  of  the  moon's 
lower  limb  was  25-  30'  30";  Bar.,  30'".45 ;  Ther.,  70';  index  corr.,  —  i'  30";  height  of  the  eye,  20  feet. 
Required  the  true  altitude. 

L.  m.  t..  May  6,  8^    C"    o^ 

Long.  81^  W.,  +  5    24      o 

Gr.  m.  t..  May  6, 

Moon's  H.  P.  midnight,     61'  ii".3 
Corr.  for  +  i''.4. 


H.  P., 


Corr.  for  i''.4, 

S.  D., 

Aug.  Table  18, 

Aug'd  S.  D., 


6i'ii".3 
I  -3 

13  24   0 

H.  D.,  -  o".93 
+  I  -40 

61  10 

midnight. 

Corn,   —  I  .30 

16'  42".  I 
--    0  .4 

16  41  .7 
7  -o 

16  48  .7 


100 


CORRECTION    OF    OBSERVED    ALTITUDES. 


Observed  altitude, 
Index  corr., 


Dip, 


Aug.  S.  D., 

Apparent  altitude, 
Corr.  Table  24, 

Approx.  true  altitude, 


25^  30'  30" 
I    ^o 


25 

29     0 
4    23 

25 
+ 

^^  37 
16  48 

25 
+ 

41    25 
53     8 

26    34   33 


Example.    May  6,  1879,  the  observed  altitude  of  the  sun's  upper  limb  was  62°  10'  40"  ;  index  corr.,  +  3' 
height  of  the  eye.  25  feet.      Required  the  true  altitude. 


10' 


1 


Observed  altitude. 

62° 

10'  40 

Index  corr., 

+ 

3    10 

Dip, 

— 

4   54 

Par., 

+ 

4 

Ref., 

31 

S.  D., 

• — 

15   53 

True  altitude. 

61 

52  36 

FINDING    THE    TIME. 


101 


CHAPTER    VI 


FINDING    THE    TIME. 


RATING    THE    CHRONOMETER. 


Art.  256.  Since  the  chronometer  rarely  runs  for  any  length  of  lime  without  change  of  rate  from  various 
causes,  it  is  desirable  to  ascertain  a  new  rate  as  often  as  possible.  The  length  of  the  interval  should  depend  upon 
the  character  of  the  chronometer  and  the  degree  of  accuracy  required. 

In  certain  ports  which  are  in  telegraphic  communication  witli  the  principal  observatory,  a  time-ball  is  dropped 
at  some  defined  instant  of  time,  and  by  comparing  with  it  the  chronometer  reading  from  day  to  day,  and  by  apply- 
ing the  longitude,  the  error  as  well  as  the  rate  may  be  established. 

Careful  comjiarisons  with  a  well-regulated  sidereal  clock  in  the  vicinity  will  suffice  to  give  the  error  and  rate. 

If  unable  to  have  resort  to  either  of  these  methods,  recourse  must  be  had  to  astronomical  observations,  par- 
ticular care  l)eing  taken  to  obtain  observations  soon  after  a  sea  voyage,  since  the  rate  of  the  instrument  is  liaVjle  to 
change  materially  at  sei  from  several  causes,  the  chief  of  which  is  the  disturbance  from  magnetic  influences,  the 
XII  hour  mark  being  directed  to  all  points  of  the  horizon. 

BY  TRANSITS. 

Art.  357.  The  most  accurate  method  of  finding  the  chronometer  correction  on  shore  is  by  means  of  a 
transit  instrument  well  adjusted  in  the  meridian,  noting  the  times  of  transit  of  a  star  or  the  limbs  of  the  sun  across 
the  threads  of  the  instrument. 

At  the  instant  of  a  star's  passage  over  the  meridian  wire  note  the  time  by  the  chronometer.  The  star's  hour 
angle  at  the  instant  =  o^,  therefore  the  local  sidereal  time  is  equal  to  the  star's  right  ascension.  By  converting 
this  sidereal  time  into  the  corresponding  mean  lime  and  applying  the  longitude,  the  Greenwich  mean  time  of 
transit  is  given.     By  comparing  with  this  the  time  shown  by  chronometer  the  error  is  found. 

Example.  1879,  May  9  (Ast.  day),  in  Long.  44°  39'  E.,  observed  the  transit  of  Arcturus  over  the  middle 
wire  of  the  telescope  ;  the  time  noted  by  a  chronometer  regulated  to  Greenwich  mean  time  being  8''  5'"  33*'.5. 

R.  A.  Arcturus,  May  9  =  14''  lo"'  11^71  =  local  sid.  t.  of  transit. 


R.  A.  mean  sun,  May  9,  o'\ 

Red.  for  Long.  —  2^^  58'"  36^  (Table  9),    — 

Sid.  time  of  local  o'>, 
R.  A.  Arcturus, 


Sid.  interval  from  noon, 
Red.  for  interval  (Table  8), 

Local  time  (mean)  of  transit.  May  9, 
Longitude, 

Gr.  mean  time  of  transit. 
Chronometer  time  of  transit, 

Chronometer  fast. 


42' 
29 


.69 
-34 


-1 

14 

7 
10 

13  35 
II  .71 

II 

2 

I 

58.36 

48.61 

II 

—   2 

I 
58 

9-75 
36.0 

8 

8 

2 
5 

33-75 
33-50 

59-75 


Example.  1879,  May  10  (Ast.  day),  in  Long.  81°  15'  W.,  observed  the  transit  of  Spica  over  the  five  wires 
of  the  telescope ;  the  times  given  below  having  been  noted  by  a  chronometer  regulated  to  Greenwich  mean  time. 
Find  the  error  of  the  chronometer. 

f  First  wire,  3*' 3i"M4'.5 

I  Second  wire,  32     1 1  . 7 

Time  of  transit  over    ^  Meridian  wire,         32     39  .0 
I  Fourth  wire,  ^^       6.2 

l^  Fifth  wire,  33     33.6 


Mean  time  observed, 


39.0 


R.  A.  mean  sun.  May  10,  o'',  3''  li'"  39^24 

Red.  for  Long,  -f-  5"  25'"  (Table  9),      +  53  -39 


Sid.  time  of  local  o'', 

R.  A.  of  Spica  (local  Sid.  time), 

Sid.  interval  from  noon, 
Red.  by  Table  8, 

Local  mean  lime  of  transit.  May  10, 
Longitude, 

Gr.  mean  time  of  local  transit. 
Chronometer  time  of  transit, 

Chronometer  fast  of  Gr.  m.  t., 


3 
13 

12 
18 

32.63 
52.29 

10 

6 

I 

19  .66 
39.33 

10 

+  5 

4 

25 

40.33 
0 

15 

3 

29 

32 

40-33 
39 

58.67 


102  FINDING    THE    TIME. 

Art«  258.  By  observing  the  transit  of  one  limb  of  the  sun  over  the  meridian  wire  of  the  telescope,  and 
noting  the  time  by  the  chronometer,  its  error  may  be  determined. 

The  instant  of  transit  of  the  sun's  centre  is  appa7-ent  jioon.  On  page  I  of  the  Calendar  of  the  Nautical  Almanac 
is  given  the  "  Sidereal  lime  of  the  Semi-diameter  passing  the  Meridian,"  which,  added  to  the  time  of  the  transit  of 
the  first  limb,  or  subtracted  from  the  time  of  transit  of  the  second  limb,  will  give  the  chronometer  time  of  transit 
of  the  centre. 

By  noting  the  times  of  transit  of  both  limbs  the  mean  will  give  the  chronometer  time  of  transit  of  the  centre. 

Example.  1879,  May  10,  in  Long.  30^  W.,  observed  the  transit  of  the  first,  or  western,  limb  of  the  sun, 
noting  the  time  by  a  chronometer  regulated  to  Greenwich  mean  time  i^  58'"  7^.     Find  the  chronometer  error. 

Eq.  of  time,  May  10,  Gr.  app.  o'',  3"'  45^58  II.  H.,     +  0M09 

Corr.  for  Long.  -(-  2'',  -j-  o  .22  -f-  2 


Eq.  time  (  —  from  app.  t.),  3     45  .80  -j-  o.  218 

App.  time  of  transit  of  sun's  centre,       12''    o       o  .00 


I 

59 

13 

.6 

2 

0 

0 

II 

59 

13 

.6 

II 

56 

14 

.2 

Mean  time  of  transit  centre,  11     56     14.20 

Chro.  time  of  transit  of  W.  limb,  i'' 58'"    7^0 

Sid.  time  of  S.  D.  passing  the  merid.,  i       6  .6 

Chro.  time  of  transit  of  sun's  centre, 
Longitude  30°  W., 

Corresponding  local  time. 

Local  m.  t.  of  transit  of  sun's  centre, 

Chro.  fast,  2     59  .4 

Example.  1879,  June  25,  in  Long.  60°  E.,  observed  the  transit  of  both  limbs  of  the  sun  over  the  meridian 
wire  of  the  telescope,  noting  the  times  by  a  chronometer  regulated  to  Greenwich  mean  time.  Find  the  chronom- 
eter error. 

Transit  of  the  western  limb. 
Transit  of  the  eastern  limb, 

Chro.  time  of  app.  noon, 

Equation  of  time,  June  25,  Gr.,  o^, 
Corr.  for  Long.  —  4'',  ■ — 

Eq.  t.  (-f- to  app.  t.),  2     14.59  —2.128 

App.  time  of  transit. 

Mean  time  of  transit, 
Longitude, 

Gr.  m.  t.  of  local  transit, 
Chro.  time  of  transit, 

Chro.  fast,  2     56  .66 

Example.  1879,  July  23,  in  Long.  74°  W.,  observed  the  transits  of  the  sun's  limbs  over  the  five  wires  of  th; 
telescope,  noting  the  times  by  a  chronometer  regulated  to  Greenwich  mean  time. 


81' 
8 

4'"   2^5 
6    20 .0 

8 

16^72 
2.13 

5    11-25 
II.  I)., 

+  o\532 
—          4 

I2'i 

2 
0 

14 
0 

-59 

12 

4 

2 
0 

14 
0 

-59 

8 
8 

2 
5 

14 
II 

-59 
•25 

Western  limb:    ist  w're, 

5'' 

olll 

2^0 

2d  wire, 

3d  wire, 

4th  wire, 

5th  wire. 

Eastern  limb:     Ist  wire. 

3 
3 

4 
4 
5 

29  .0 

56.5 
24  .0 
51.0 
17.0 

2d  wire, 

3d  wire, 

4th  wire, 

5th  wire, 

1 

6 

7 

43-5 
II  .0 

38-5 
6  .0 

Chro.  time  of  app.  noon. 

5 

5 

3-85 

!3,  o'S                         6'"  1 38 
4''  56™,          +                 0 

-15 

.41 

H.  D., 

+  0^083 
+  4-93 

Eq.  of  time,  July  23,  o''. 


Eq.  t.  (+  to  app.  t.),  6     13  .56  +0  .41 

App.  time  of  transit. 

Mean  time  of  transit, 
Longitude, 

Gr.  m.  t.  of  local  transit, 
Chro.  t.  of  local  transit, 

Chro.  fast,  2     50  .29 


6 

12b    0 

13.56 
0 

12     6 

4    56 

13-56 
0 

17      2 

5      5 

13-56 
3-85 

FINDING    THE    TIME. 


103 


Art.  259.  Tn  tliis  method  of  rating  chronometers,  as  well  as  tlial  of  equal  altitudes,  stars  are  to  be  preferred, 
1:  partly  because  many  can  Ijc  chosen  during  the  same  night,  and  the  instrument  is  not  exposed  to  the  sun's  rays. 

Observations  of  tlie  moon  to  determine  time  cannot  be  relied  upon  for  accuracy. 

Having  obtained  an  error  for  the  chronometer,  the  ol:)servation  should  be  repeated  at  a  proper  interval  of  time 
for  a  new  error;   then  from  the  two  a  rate  can  be  determined. 

Should  the  transit  instrument  not  be  in  perfect  adjustment,  or  the  instrumental  corrections  uncertain,  a  suffi- 
i:  ciently  reliable  rate  can  be  determined  by  observations  of  the  same  star,  or  set  of  stars,  at  proper  intervals,  pro- 
vided the  instrument  has  lieen  left  undisturbed. 

An  approximate  rate  may  be  found  by  observing  the  disappearance  of  a  star  behind  a  well-defined  vertical 
edge  of  a  terrestrial  object,  regard  l)eing  had  that  the  position  of  the  eye  is  the  same  at  all  the  observations.  Stars 
siiould  be  selected  whose  right  ascensions  and  declinations  remain  constant  during  the  interval. 

BY  A  SINGLE  ALTITUDE. 

Art.  260.  This  problem  is  simply  how  to  find  the  mean  time  at  any  place ;  and,  by  comparing  this  time 
with  that  indicated  l)y  the  chronometer,  the  error  on  local  mean  time  is  given.  If  the  chronometer  is  regulated  to 
Greenwich  mean  time,  apply  the  longitude  to  the  local  mean  time  obtained  by  observation,  and  compare  with  this 
the  lime  noted  liy  chronometer. 

Art.  2<>1.  It  should  be  borne  in  mind  that  the  most  favorable  position  of  the  heavenly  body  for  time 
iliserv-ations  is  when  near  the  prime  vertical.  When  exactly  in  the  prime  vertical  a  small  error  in  the  latitude 
IKxluces  no  appreciable  effect.  Therefore  if  the  latitude  is  uncertain,  good  results  may  be  obtained  by  selecting 
lor  observation  stars  near  the  prime  vertical. 

Art.  262.  Observe  several  altitudes  of  a  heavenly  body  in  quick  succession,  noting  the  times  by  chronom- 
eter, or  liy  a  watch  compared  with  the  chronometer,  and  find  the  mean  of  the  altitudes  corresponding  to  the  mean 
of  the  times.  Condensing  the  observation  into  a  brief  interval  of  time  eliminates  the  error  caused  by  assuming 
that  the  altitude  varies  in  proportion  to  the  time. 

Correct  the  observed  altitude  for  instrumental  errors,  and,  if  a  double  altitude  observed  by  the  artificial  hori- 
zon, reduce  the  apparent  altitude  to  the  true  altitude. 

If  the  sun,  the  moon,  or  a  planet  is  observed,  the  declination  is  to  be  taken  from  the  Nautical  Almanac  for 
the  time  of  the  observation.  If  the  time  is  not  very  accurately  known,  the  first  hour-angle  found  will  be  an  approx- 
imate one  ;  the  declination  found 
by  this  new  value  of  the  time 
will  produce  a  more  exact  value 
of  the  hour-angle;  and  thus  pro- 
ceed until  a  sufficiently  precise 
value  is  determined. 

Art.  263.     Then  know- 
ing, in  Fig.  65, 

AO  =  //,  the  altitude  of  the 
object  O. 

DO  :=  d,  the  declination  of 
the  object  O. 

And  QZ  =:  L,  the  latitude 
of  the  place. 

There  are  given  in  the  as- 
troiwniical  triangle : 

POZ,  the  three  sides. 

ZO  =  Z,  the  zenith  distance 


Fig.  65. 
PO  =:  PD,  the  polar  distance  =  90°  —  d. 


=  90^ 


A. 


PZ  =  Co-L,  the  co-latitude 
To  find  the  angle 


90^  — 
OPZ 


/,  the  hour-angle  of  the  body  O ; 


which  may  be  found  from  the  formul 


Sin  }i  t. 

Eut  if  it  is  preferred  to  use 
(/,+  !.+  PD) 


=7(" 


sin  ^  (Z  +  (L  -  d))  sin  J^  (Z  -  (L  -  d))\ 


cos  L  cos  (/  ' 

the  altitude  instead  of  the  zenith  distance,  the  formula  becomes  by  letting  S  ^=  )4 


Sin 


t. 


-Ji 


cos  S  sin  (S  —  A)\ 


I) 
cos  L  sin  PD     / 


PD,  the  jxilar  distance,  is  always  reckoned  from  the  elevated  pole ;  the  latitude  is  regarded  positive ;  hence, 
no  attention  need  be  paid  to  the  signs  of  the  quantities  in  the  second  member  of  the  equation. 

If  a  star  is  the  body  observed,  the  hour-angle,  with  the  R.  A.  of  the  star,  gives  sidereal  time,  from  which  the 
mean  time  can  be  found.  If  th'e  sun  is  the  body  observed,  the  hour-angle  gives  the  apparent  time,  from  which  the 
mean  time  can  be  deduced. 

Example.  At  a  place  in  Lat.  30^^  25'  22"  N.,  Long.  5''  25'"  42"  W.,  April  20th,  1879,  the  following  double 
altitudes  of  the  sun  west  of  Ihe  meridian  were  observed  with  a  sextant  and  artificial  horizon,  the  times  being  noted 
by  a  chroKometer  regulated  to  Greenwich  mean  time : 

2i^. 


Chronometer. 

Sh 

23... 

29" 

•5 

23 

53 

•5 

24 

18 

•5 

24 

4' 

•5 

25 

9 
18 

■5 

8 

24 

•S 

90° 

89 


o' 

50 
40 

30 

20 
89   40 


Bar., 

30'n.0S 

Ther.  att., 

81" 

Ther.  ext.. 

76° 

(I.  C), 

-  34'    0" 

+  31     0 

L  C, 

—     I   -?o 

104 


i'lNDiNG  THE  Time. 


The  approximate  correction  of  the  chronometer  was  —  3™  10^. 
What  was  the  true  correction  ? 


Chro.  t., 

Chro.  corr.,          — 

8I1   24m  18 
3     10 

'.5         Dec, 
.0         Corr. 

for  8i>.35, 

d=z 

+  11O29'  i8".i         H.  D., 
+            7     9-7 

+   11    36   27  .8         Corr., 

+    5i"-46 
+      8  .35 

Approx.  Gr.  t. 

8    21       8 

•5 

+  429  -69 

(Eq.  t.), 

Corr.  for  +  8''. 35, 

+ 

I'"  4^.94 
4.48 

H.  D., 

+      0^536            S.  D.,   15' 
+      8.35 

57" 

Eq.  t.  (-f-  to  mean  t 

■), 

I    9.42 

+      4  -476 

Obs.  2  IJ 

I.e., 

890 

40'    0" 
I    30 

2)89 

38   30 

i  Mean,     58''. 5 
7-2  Bar.,         0 

44 

49    15 
0    55 

(  Tlier.,— 3    .0 
Par. 
S.  D. 

=  + 

7 
15    57 

A 
Z 

=        45 
=         44 

4    24 
55    3^ 

L 
d 

=  +  30" 
=  +   II 

25'  22" 
36   28 

log  sec 
log  sec 

log  sin 
log  sin 

0.06434 
0.00897 

9  72264 
9-35391 

Z 

=          18 
=         44 

48   54 
55    36 

Y  sum 

;^diff. 

=         31 
=         13 

52    «5 
3    21 

2)19.14986 

Eq.  t. 

—        2'' 

56'"  35-^0 
I      9  .4 

log  sin  Y 

t-    9  57493  (Column  P.  M., 

Tal)le  44). 

L.  in.  t. 
•      I^ong 

=        2 
=  +  5 

55    25  .6 
25    42  .0 

- 

Gr.  ni.  t. 
Chro.  t. 

=        8 
=        8 

21       7  .6 
24     18  .5 

Chro    fast, 

3     i:>.9 

Example.  At  a  place  in  Lat.  48°  41  S.,  Long.  69^  3'  E.,  observed  a  double  altitude  of  the  sun  west  of  the 
meridian  with  a  sextant  and  an  artificial  horizon  to  be  59^  3'  lo" ;  the  time  noted  by  a  chronometer  regulated  to 
(jreenwich  time  being  o''  4'"  21".     Index  correction,  • —  I'  30". 

Approx.  Gr.  t.,  Jan.  20th,  O''  4'"  21%  or  o''.072. 

Longitude,  =  —  4''  36™  12^ 


Dec, 

Corr.  for  01^.072,      + 


20°  8'  26".6 


P.  D. 


=  —  20    8   24 
=        69  51    36 


(Eq.  t.), 

Corr.  for  01^.072,     -f 


II"!  14860 
o  .05 


Eq.  t.  (-f  to  app.  t.),       II     14  .65 


2Q 

I.e. 


r 

Par. 
S.  D. 


59°  3'  10" 

—  1  30 

2)59  I  40 

29  30  50 

—  I  42 
+  8 
+  16  17 


H.  D.,  +  32".48 
+     o  .072 


+ 


.33 


H.  D.,  +     0^738 
-j-      o  .072 


+     o  .053 


h 


=  29   45   33 


FINDING   THE   TIME. 


105 


A 
L 

P.  D. 

= 

290  45'  33/' 
48    41      0 
69    51    36 

148    18      9 

log  sec 
log  cosec 

0.1 803 1 
0.02740 

S 

S  — /; 

= 

74     9     5 
44    23    32 

log  cos 
log  sin 

9-43631 
9.84483 

2)19.48885 

t 

Eq.  t. 

= 

+ 

4'i  29"'  46^7 
II     14.7 

log  sin  X  t. 

9.74442 

L.  m.  t. 

= 

4    4'        1-4 

Long. 

= 

4     36     12  .0 

G.  m.  t. 
Chro.  t. 

0      4    49-4 
0      4    21  .0 

* 

Chro.  slow, 

28.4 

Art.  364»    By  a  star's  altitmit'. — First  find  the  hour  angle  of  the  star  by  either  the  formula  involving  the 
altitude  itself  or  that  involving  the  zenith  distance,  and  then  in  Fig.  66  there  are  given — 
QS,  or  QPS,  the  hour  angle  of  the  star. 

\'S,  the  right  ascension  of  the  star.  ^ 

VM,  the  right  ascension  of  the  mean  sun.  ^ 

To  find  VQ,  the  right  ascension  of  the  meridian; 
And  thence  QM,  the  local  mean  time. 

QS  +  VS  =:  VQ,  or  H.  A.  +  R.  A.  of  star  =  R.  A.  of  meridian. 
VQ  —  VM  :=  QM,  the  local  mean  time. 

Then,  by  comparing  the  chronometer  time  with  the  time  deduced  from  the 
observation,  the  error  of  the  chronometer  will  be  found. 

Hence  the 

Rule.  Find  the  Greenwich  time  and  take  from  the  Nautical  Almanac  the 
R.  A.  of  the  mean  sun  for  Gr.  o''  and  reduce  it  for  the  hours  and  parts  of  an 
hour  of  Gieenwich  time. 

Take  out  the  right  ascension  and  declination  of  the  star  from  the  Nauti- 
cal Almanac  or  from  the  Star  Catalogue  for  the  given  day. 

Find  the  star's  hour  angle  and  to  it  add  the  star's  right  ascension.     From 
the  sum  (increased,  if  necessary,  by  24'')  subtract  the  R.  A.  of  the  mean  sun ; 
the  remainder  will  be   the  local   mean   time  at   the  instant    of  observation. 
Compare  with  this  time  the  time  noted  by  chronometer  to  find  the  error  on  local  mean  time;  if  regulated  to  Green^ 
wich  mean  time  apply  the  longitude  to  find  the  error  on  Greenwich  mean  time. 

Example.  At  a  place  in  Lat.  30°  25'  22"  N.,  Long.  5''  25"^  42^  W.,  at  about  8  p.  m..  May  18,  1879,  observed 
the  following  double  altitude  of  Arcturus,  117°  36'  30";  the  time  noted  by  chronometer  regulated  to  Gr.  mean 
time  being  May  18,  13''  42'"  51^  Approximate  error  of  the  chronometer  —  2""  55^  Index  error  —  2'  o".  Bar. 
29'"-95-     Ther.  att.  71^.     Ther.  ext.  67°. 

Find  the  chronometer  error. 


Chro.  time, 
Chro.  corr.. 


13"  42"'  51^ 
2     55 


Approx.  Gr.  I.,  .May  18,       13    39     56 


R.  A.  Arcturus,  14''  lo""  118.7 

Dec.  x\rcturus,     -f     19'^  48'    33". 5 

P.  D.,  70    II     26 


R.  .\.  mean  sun,  Gr.  o'',  3I'  43»'  ii'*.69 

Corr.  (Table  9)  13'' 39"' 56s,     +  2     14.69 

R.  A.  mean  sun,  3    45     26.  38 

2  :4J       =         1 1 7^  36'  30" 
I.  C.     =  —  20 


h  = 

L  = 

P.  D.    = 


S  = 

S—  /4  = 


2)117 

34  30 

58 

47    15 
35 

58 

30 
70 

46  40 
25   22 
II   26 

159 

23  28 

79    41   44 
20    55     4 


log  sec 
log  cosec 


log  cos 
log  sin 


0.06434 
0.02649 


9.25257 
955270 

18.89610 


Column  p.  m.  =     2''  10'"  21S.3 


log  sin  yi,  t.,  9.44805 


106 


FINDING    THE    TIME. 


Column  p.  m. 

= 

2b 

IO"> 

2I^3 

H.  A.  :^ 
R.A.  * 

= 

21 
14 

49 
10 

38.7 
II  .7 

R.  A.  nierid. 

II 

SO 

50.4 

R.  A.  m.  sun 

= 

3 

45 

26 .4 

L.  m.  t. 
Long. 

8 

+  5 

14 

25 

24 .0 
42 

Gr.  m.  t. 
Chro.  t.  _ 

= 

13 
13 

40 
42 

6 
51 

Chro.  fast, 

2 

45 

Example.    April  16,  1879,  in  Lat.  48"^  57'  N.,  Long.  67°  25'  W.,  observed  an  altitude  of  Aldebaran  west  oi 
the  meridian  23*^  13'  20"  ;   the  time  noted  by  a  chronometer  regulated  to  Greenwich  mean  time  being  12''  13"'  3^ 
index  corr.  —  3'  o" ;  dip  of  sea  horizon  4'  o". 

Find  the  chronometer  error. 


Approx.  Gr.  m.  t.,  April  16,     12''  13'"  3" 


R.  A.  :%:         4''  29'"  o*^ 
Dec.  H<    +  16-'  15'  59 


Obs. 
I.  C. 
Dip. 

alt.  -^            2f> 

y 
» 

13' 
3 
4 
2 

20" 
0" 
0" 

16" 

R.  A. 

Red  ( 

R.  A. 

230    4'    4" 
48    57     0 
73    44     I 

m. 
Tal 

m. 

sun,  Gr.  0'', 
le  91  12''  13"' 

sun, 

log  sec 
log  cosec 

log  cos 
log  sin 

log  sin  Yz  t 

3%     +         204 
I    39    2.3 

h  = 

23    4 

A           = 
L          = 
P.  D.   -^ 

S          = 

S~  /i  = 

t                         = 
R.  A.  *             = 

R.  A.  merid.       = 
R.  A.  m.  sun      = 

L.  m.  t.                = 
Long.                   = 

Gr.  m.  t.             = 
Chro.  t.               = 

Chro.  slow         := 

4 
+ 

0.18262 
0.01774 

145    45 

72    52 
49    48 

4"  53" 
4    29 

5 

32 
28 

26^ 
0 

9.46902 
9.88303 

19- 55241 
,    9.77621 

9   22 
I    39 

26 

2 

* 

7   43 
4    29 

24 
40 

12    13 
12    13 

04 
03 

I 

BY  EQUAL  ALTITUDES. 
chauvenet's  method. 

Art.  365.  To  regulate  a  chronometer  to  Greenwich  time,  its  error  and  rate  must  be  determined  at  a  place 
whose  longitude  is  well  known.  The  most  accurate  method  of  doing  this  is  by  observing  the  transit  of  the  sun  or 
a  star  over  the  meridian.  For  the  Navigator  the  most  simple  and  accurate  substitute  for  the  meridian  observation 
is  that  of  equal  altitudes  of  the  same  object  on  each  side  of  the  meridian. 

In  the  case  of  a  star,  the  mean  of  the  two  chronometer  times  corresponding  to  the  equal  altitudes  is  the  chro- 
nometer time  of  transit;  but,  in  the  case  of  the  sun,  the  mean  of  these  times  differs  somewhat  from  the  time  of 
transit,  since,  in  consequence  of  the  change  of  the  sun's  declination  between  the  observations,  the  equal  altitudes 
do  not  occur  at  equal  intervals  before  and  after  the  transit. 

The  small  correction  necessary  when  the  sun  is  observed  to  reduce  the  mean  of  the  times  to  the  time  of  transit, 
is  called  the  equation  of  equal  altitudes. 

1.— EQUAL  ALTITUDES  OF  THE  SUN,  MORNING  AND  EVENING. 

Art.  266.  The  Observation. — On  shore,  at  a  place  whose  longitude  is  aeeumtely  known,  and  whose 
latitude  is  approximately  known,  observe,  with  an  artificial  horizon,  the  same  altitude  both  in  the  morning  and  in 
the  afternoon,  as  near  the  prime  vertical  as  convenient  after  the  altitude  is  more  than  10°,  noting  the  times  by  a 
chronometer.  In  low  latitudes,  however,  the  method  of  equal  altitudes  will  often  give  very  accurate  results,  even 
when  the  observations  are  quite  near  the  meridian.  In  general,  a  sufficiently  accurate  result  may  be  obtained  if 
the  observations  are  taken  when  the  sun's  change  of  altitude  is  not  less  than  10"  in  0^5,  or  when  the  change  in  the 
double  altitude  taken  with  the  artificial  horizon  is  not  less  than  20"  in  0^.$. 


\ 


FINDING    THE    TIME. 


107 


It  is  most  convenient,  as  well  as  conducive  to  accuracy,  to  take  the  observation  in  the  following  manner.  In 
he  morning,  liring  the  lower  limb  of  the  sun,  reflected  from  the  sextant  mirrors,  and  the  upper  limb  of  that 
eflected  from  the  mercury,  into  approximate  contact;  move  the  o  of  the  vernier  forward  (say  from  lo'  to  20'), 
,nd  set  it  on  a  division  of  the  limb;  the  images  will  be  cn\-rlappi'd  and  will  be  scparatiiii^ ;  wait  for  the  instant  of 
lontact,  note  it  by  chronometer,  and  immediately  set  the  vernier  on  the  next  division  of  the  limb,  that  is,  10'  in 
.dvance;  notice  the  instant  of  contact  again,  and  proceed  in  the  same  manner  for  as  many  observations  as  are 
hought  necessary.  If  the  sun  rises  too  rapidly,  let  the  intervals  on  the  limb  be  20'.  Find  (roughly)  the  time 
vhen  the  sun  will  be  at  the  same  altitude  in  the  afternoon,  and  just  before  that  time  set  the  vernier  on  the  last  alti- 
ude  noteil  in  the  morring  (of  course  using  the  same  sextant);  the  images  of  the  sun  will  be  separated,  but  will  be 
•pprotu/iing ;  wait  for  the  instant  of  contact;  note  it  by  chronometer;  set  the  vernier  ku/c  to  the  next  division  of 
he  limb  (10'  or  20'  as  the  ca5e  may  be);  note  the  contact  again,  and  so  proceed  until  all  the  A.  M.  altitudes  hav^e 
)een  again  noted  as  P.  M.  altitudes. 

Art.  267.  The  Comi'UTATION. — Take  the  mean  of  the  A.  M.  times  and  call  it  the .-/.  M.  Chronometer  Time. 
The  mean  of  the  P.  M.  times  call  the  P.  M.  Chivnometer  Time.  If,  instead  of  noting  the  times  by  the  chronometer, 
\\.  watch  is  used  (compared  with  the  chronometer  both  before  and  after  each  observation),  it  will  generally  be  found 
lecessary  to  make  an  allowance  for  its  gain  or  loss  on  the  chronometer,  so  as  to  obtain  the  exact  difference  between 
he  watch  and  chronometer  at  the  instant  of  observation.  This  difference  being  applied  to  the  mean  of  the  watch 
imes,  we  have  the  mean  chronometer  time  the  same  as  would  have  been  found  by  employing  the  chronometer 
Urectly. 

The  half  sum  of  the  k.  M.  and  P.  M.  Chronometer  Times  is  the  Middle  Chronometer  lime,  their  difference  is  the 
Elapsed  Time ;  observing  that  when  the  A.  M.  time  is  before  12''  by  chronometer,  while  the  P.  M.  time  is  after 
.2^,  the  latter  must  be  supposed  to  be  increased  by  12''  in  finding  this  half  sum  and  difference. 

Take  from  the  Nautical  Almanac  the  sun's  declination,  the  hourly  difference  of  declination,  and  the  equation 
)f  time,  reducing  each  to  the  instant  of  local  apparent  noon  by  applying  the  changes  for  the  longitude. 
Mark  north  latitude  and  north  declination  +• 
Mark  south  latitude  and  south  declination  — . 
Mark  hourly  diff.  of  decl.  when  toward  north  -\-. 
Mark  hourly  diff.  of  decl.  when  toward  south  — . 

Enter  Table  2,7  with  the  elapsed  time,  and  take  out  log  A  and  log  B,  prefixing  to  each  its  proper  sign  given 
n  the  table  at  the  head  of  the  page. 

To  log  .V  add  the  log  of  the  hourly  diff..  Table  42,  and  the  log  tangent  of  the  latitude  (Table  44).  Prefix 
o  each  log.  the  sign  of  the  quantity  it  represents,  and  to  their  sum  the  sign  which  results  from  the  algebraic  com- 
)ination  of  the  three  signs.  This  sum  is  the  log  (Table  42)  of  the  number  of  seconds  of  time  in  the.  Jirst  part  oi 
equation  of  equal  altitudes,  to  be  marked  -|-  or  —  like  its  log. 

To  log  B  add  the  log  of  the  hourly  diff.  and  the  log  tangent  of  the  declination,  marking  the  signs  as  before. 
The  sum  is  the  log.  of  the  seeond  part  of  the  equation  of  equal  altitudes,  to  be  marked  +  or  —  like  its  log. 

Apply  the  two  parts  of  the  equation,  according  to  their  signs,  to  the  Middle  Chronometer  Time;  the  result  is 
.he  Chronometer  Time  of  Apparent  Noon. 

To  this  apply  the  equation  of  time  (adding,  when  the  equation  of  time  is  additive  to  mean  time,  otherwise 
subtracting) ;  the  result  is  the  Chronometer  Time  op' Mean  A'oon,  which,  if  the  chronometer  is  regulated  to  local  time, 
ivill  be  12*^  o"'  o"  when  the  chronometer  is  right;  more  than  12''  when  fast,  less  than  12'^  when  slow. 

If  the  chronometer  is  regulated  to  Greenwich  time,  apply  the  longitude  (in  time)  lo  the  chronometer  time  of 
mean  noon  (subtracting  in  west,  adding  in  east);  the  result  will  be  more  or  less  than  I2'\  according  as  the  chro- 
[lometer  is  fast  or  slow. 

Repeat  this  process  on  a  subsequent  day.  The  difference  between  the  chronometer  errors  on  the  two  days, 
divided  by  the  number  of  days  in  the  interval,  will  give  the  daily  rate  of  the  chronometer,  gaining  ox  losing  as  the 
:hronometer  goes  too  fast  or  too  slow. 

Example.  April  13,  1879,  at  a  place  in  Lat.  30'^'  25'  N.,  Long.  51'  25™  42^5  W.,  observed  the  follo\ying  equal 
altitudes  of  the  sun  with  a  sextant  and  an  artificial  horizon,  noting  the  times  by  a  watch  compared  with  a  chro 
nometer  regulated  to  Greenwich  mean  time.     What  is  the  error  of  the  chronometer? 


A.   M.  COMPARISONS. 

Chro.  No.  729,  Negus,    2''  22"'  30*^ 
Watch,  8    52       2 


A.  M.,  watch  gains,  loses  o  in  34° 
Intervals  to  obs. 


p.  M.  COMPARISONS. 

Chro.  No.  729,         S^    4™  306 
Watch,  2   34      I 


Diff., 


5    30    28 


Chro.  No.  729,  Negus,   2    56    30         P.  M.,  watch  gains,  loses  o  in  29" 


Watch, 
Diff., 

9    26       2 

Interval  to  c 

,bs. 

5    30    28 

Watch,  A.  M. 

2£!Art 

.  Hor. 

gh  12m  ^qs 

910 

0' 

12    55 

10 

13       20 

20 

13    45 

30 

Mean, 

14     10 

40 

9    13     20 

Comparison, 

5    30    28 

A.  M.  Chro.  T., 
P.  M.  Chro.  T., 


2    43    48 
8    15     24 

2)10    59     12 


(Eq.  T.),  +  o"^  35'. 02        —  0^649 
-         3  -52        +  5  -43 


Diff., 

5    30 

29 

Chro.  No.  7: 
Watch, 

29, 

8    33 
3      3 

30 

I 

Diff, 

5    30 

29 

Watch,  P. 

.  M. 

2h  45" 

45 
44 
44 
44 

'45' 
20 

55 

30 

5 

Mean, 
Comparison, 

2   44 
5    30 

55 
29 

P.  M.  Chro. 
A.  M.  Chro. 

T. 

T., 

,       8    15 

,        2   43 

24 

48 

Elapsed  Time, 


Middle  Chro.  T.,  5    29     36         Eq.  T.,    +0     31    50 


3-524 


108 


FINDING    THE    TIME. 


A.  M.  COMPARISONS. 

Middle  Chro.  T.,  5^  ag-"  36^o 

Equat.  of  Eq.  Alts.,  -  7-i  (D-), +9°  o' 54".!    (H.  D.), 

+      4  55  -o 

Chro.  T.  App.  Noon,    5    29     28  .9 
Equat.  ofT.,  —  31  .5  D., 

Chro.  T.,M.Noon,     5    28     57.4 
Longitude,  5    25     42  .0 


P.  M.  COMPARISONS. 


9    5  49         H.  D., 


4-  54". 40  Decrease  in  24'' 
—      o  .08  Decrease  in  5.43 

+  54  -32 
+      5  -43 


+  294  -96 


o".37 
o  .08 


Chro.,  fast, 


3     15-4 


H.  D.,       54".32 


Lat.,+ 30-25' 
istPt.  Eq.,— 8.88   log 


log  A.Tnb.  37,  —  9.4445  log  B,  Tab.  37,  +9  3193 

logTal).  42,      +17350  +1-735^ 

log  tan  -f  9. 7687  D.,-|-9°6' log  tan  -(-9.2045 


o  94^52  2dPt.  Eq. +  I.81        log     +0.2588 


2.— EQUAL  ALTITUDES  OF  THE  SUN,  EVENING  AND  MORNING. 

Art.  26S.  The  Observation. — Take  a  set  of  altitudes,  in  the  nionner  already  explained,  in  the  afternoon 
of  one  day,  and  the  same  altitudes  in  leverse  order  on  the  morning  of  the  next,  noting  the  times  by  the  chronom- 
eter, or  by  a  watch  compared  with  it. 

Art.  269.  The  Computation. — The  half  sum  of  the  P.  M.  and  A.  M.  Chronometer  Times  is  the  Middle 
Chronometer  Tune;  their  difference  is  the  Elapsed  Time:  oljserving  that  when  the  P.  M.  time  is  before  12''  by  chro- 
nometer, while  the  A.  M.  time  is  after  12'',  the  latter  must  be  supposed  to  be  increased  by  12''  in  finding  this  half 
sum  and  this  difference. 

Take  from  the  Nautical  Almanac  the  sun's  decHnation,  the  hourly  difference  of  declination,  and  the  equation 
of  time,  reducing  them  each  to  the  instant  of  local  apparent  midnight. 

Mark  the  sign  of  each  quantity  as  before,  and  compute  the  two  parts  of  the  equation  of  equal  altitudes  pre- 
cisely as  in  the  preceding  case,  observing  to  mark  the  signs  of  log  A  and  log  B,  as  given  in  the  table  for  mid- 
night. 

Apply  the  two  parts  of  the  equation  to  the  middle  chronometer  time,  according  to  their  signs ;  the  result  is 
the  Chronometer  Time  0/  Apparent  Midnight. 

To  this  apply  the  equation  of  time  (adding,  when  the  equation  of  time  is  additive  to  mean  time,  otherwise 
subtracting);  the  result  is  the  Chronometer  Time  of  Mean  Midnight,  which,  if  the  chronometer  is  regulated  to  local 
time,  will  be  12''  o'"  o^  when  the  chronometer  is  right  ;•  more  than  12''  when  fast ;  less  than  12''  when  slow. 

If  the  chronometer  is  regulated  to  Greenwich  time,  apply  the  longitude,  in  time,  to  the  chronometer  time  oi 
mean  midnight  (subtracting  in  west,  adding  in  east);  the  result  will  be  more  or  less  than  I2i>  (or  24''),  according 
as  the  chronometer  is  fast  or  slow. 

A  repetition  of  this  process  at  a  subsequent  day  will  give  another  error,  whence  the  rate  will  be  found  as 
before.  Or  the  rate  may  be  found  by  comparing  the  results  of  an  A.  M.  —  P.  M.,  and  a  P.  M.  —  A.  M.  observa- 
tion, remembering  that  the  interval  elapsed  betwee.i  two  such  observations  is  equal  to  the  difference  between  the 
two  dates ////J  or  minus  half  a  day. 

Example.  April  20,  1879,  ^^  ^^e  same  place  as  in  the  preceding  example,  the  following  P.  M.  —  A.  M.  obser- 
vations of  equal  altitudes  of  the  sun  were  taken,  and  the  times  noted  by  a  watch  compare9  with  the  same  chro- 
nometer ;   to  find  the  error  and-  daily  rate  of  the  chronometer. 


P.  M.  COMPARISONS. 


A.  M.  COMPARISONS. 


Chro.  No.  729, 
Watch, 

Diff., 

Chro.  No.  729, 
Watch, 

Diff., 


P.  M.  watch  gains,  loses  0  in  24"'  30^. 
2    35        1.5     Interval  to  obs. 

5    31     58-  5 


8    34    30         A.  M.  watch  gains,  loses  o  in  20'"  30'' 
3      2     31.5     Interval  to  obs. 


5   31     58.5 


k'atch,  P.  M. 

2  £2  Art.  Hor, 

2^  51™  31s 

900  0' 

51  55 

89  50 

52  35 

40 

53   3 

30 

53  26 

20 

Mean,  2  52  30 .0 

Comparison,  5  31  58 .5 

P.  M.  Chro.  T.,  8  24  28  .5 

A.  M.  Chro.  T.+i2h,  26  30  11  .0 


2)34   54    39-5 


(Eq.  T.),-i™    4«.93 
9-34 


0^536 
1743 


Chro.  No.  729, 
Watch, 

Diff., 

Chro.  No.  729, 
Watch, 

Difif., 


Mean, 
Comparison, 


2'i  l6'»     0= 

8   43     59 


5  32 

I 

2  36 
9   4 

30 
29 

5  32 

I 

Watch,  a.  m. 

S"!  59'"    o'^ 
58     34-5 
58      9-5 
57    46.0 
57    20.0 

8   58    10 
5   32      I 


A.  M.  Chro.  T., +12^  =  26    30     11  .0 
P.  M.  Chro.  T.,  8    24    28.5 


Elapsed  Time, 


18     5    42-5 


Middle  Chro.  T., 


17   27     19.75      Eq-  T., 


14.27 


9-34 


FINDING    THE    TIME. 


109 


A.   M.»COMPARISON'S. 


P.  M.  COMPARISONS. 


Vfiddle  Chro.  T.,  1 7    27     19.75 

luat.  of  Eq.  Alls.,  +  19  .35  (1).),  +  ii*^  29' 17".!     (H.D.),  +  5i".45  Decrease  in  24", 

14  50  .7  o  .35  Decrease  in  1 7''. 43, 

"hro.  t.  App.  Midn.,    17    27     39. 1 
t^quat.  of  Time,        +  i      14.3     D., 


o".48 
o  -35 


Thro.  t.  Mean  Midn.,   17    28     53.4 
(.ongitude,  5    25     42.0 


II    44     7  .8    H.  D.,        51   .10 

17  -43 


+  890  .7 


'liro.  fast, 

hro.  fast  April  13, 

Loss  in  7^  days, 

I  »aily  rate  losing,  0^53!^. 


3  II  -4  log.  A,  Tab.  37, +9.9364 
3  15.4  H.  D.,  5i".io  log  Tab.  42,  +1.7084 
Lat.,      30^  25'     log  tan, 


4'^.o 


1st  rt.  Eq.  +25.91    log 


log  B,  Tab.  37,-9.7912 

.      .      .  +  1-7084 

+  9.76870.11-^44'     logtau  +9-3175 

+  I.4135    2d  I't.  Eq.,  —  6.56      log      — O.8171 


3.— EQUAL  ALTITUDES  OF  A  FIXED  STAR. 


Art.  270.  The  Observation. — In  selecting  stars  for  this  observation,  it  is  to  be  observed  that  the  nearer 
to  the  zenith  the  star  passes  the  less  may  the  elapsed  time  be;  and  when  a  star  passes  exactly  through  the  zenith 
the  two  altitudes  may  be  taken  within  a  few  minutes  of  each  other.  But,  with  the  ordinary  sextants,  altitudes  near 
;90'^  cannot  be  taken  with  the  artificial  horizon,  as  the  double  altitude  is  then  nearly  180^^.  The  prismatic  sextants, 
or  still  better  the  prismatic  circles  of  Pistor  and  Martin,  are  adapted  for  measuring  angles  of  all  magnitudes  up  to 
180^,  and  are  therefore  especially  sui  able  for  this  observation. 

Set  the  sextant  and  wait  for  the  coincidences  of  the  two  images  of  the  star,  as  in  the  case  of  the  sun's  limb, 
noting  the  times  by  chronometer  or  watch. 

Art.  271.  The  Computation. — Take  the  mean  of  the  times  before  the  meridian  passage  as  the  A.  M. 
I  ':iViiomtin   Time,  and  the  mean  of  those  after  the  meridian  passage  as  the  P.  M.  Chrononwtc'r  Time. 

The  mean  of  the  A.  M.  and  P.  M.  chronometer  times  is  the  Chronometer  Time  of  Star's  Transit.  This  time, 
if  the  chronometer  is  right,  will  agree  with  the  true  mean  time  of  star's  transit,  which  is  to  be  computed  according 
to  the  directions  given  already  (Art.  240,  Chap.  Ill,  Par.  II),  or  as  follows: 

To  the  right  ascension  of  the  star  apply  the  longi  ude  of  the  place  of  observation  (adding  in  west,  subtracting 

in  east);   the  result  is  Greenwnh  Sidereal  Time  of  Star\<:  Transit ;  from  this  subtract  the  sidereal  time  at  the  />/-e- 

[ceding  mean  noon  Greenwich  (Nautical  Almanac,  page  II  of  the  month);   the  remainder  is  the  Sidereal  Iiiten'al 

'since  mean  noon.     From  Table  8,  with  the  argument  Sidereal Intenial,  take  out  the  correction,  which  subtract  from 

jthe  sidereal  interval;   the  remainder  is  the  Grecnivieh  Mean  Time  of  the  Star's  Transit. 

The  chronometer  time  will  be  more  or  less  than  this,  according  as  the  chronometer  is  fast  or  slow. 

If  the  chronometer  is  regulated  to  local  time,  apply  the  longitude  to  the  Greenwich  mean  time  of  star's  transit 
.  (sul)tracting  in  west,  adding  in  east);   the  result  is  the  Loeal Mean  Time  of  Star's  Transit,  and  the  chronometer  is 


fast  or  slow  according  as  it  shoMS  more  or  less  than  this  time 
I         ExAMPiE.    July  15,  1S56,  at  the  Cape  of  Good  Hope,  Lat.  33"  56'  S.,  Long,  i''  13" 
•  altitudes  of  Antares  as  follows : 


56^  E.,  observed  equsJ 


A.  M.  Chro.  T. 
P.  M.  Chro.  T. 


Chronom.  A.  M. 

t,''  32™  io^5 

'5    32     35  -o 
5    32     59-3 

5    32     34-9 
9    33     56-1 

2)15      6-  31  .0 


2  Alt.  Antares. 


125^ 


40 

50 


P.  M.  Chro.  T., 


Chro.  T.  ^  Tran>it,       7    33     15  .5 
Or.  T.  ^  Transit,  7    31     22.1 


Chro.  fast, 


53-4 


Antares  R.  A., 
Longitude, 

Gr.  Sid.  T., 

July  15,  Gr.  Sid.  T.  Mean  Noon, 

Sid.  Interval, 
Correction,  Table  IV, 

Gr.  M.  T.  ;+;  Transit, 


Chronom.  P.  M. 

gh  34m  2o^3 

9   33     56.0 
9   33     32.0 

9    33     56.1 

16''  20™  37^58 
I    13    56  .00  E. 

15     6    41  .58 
7   34      5-25 

7   32    36.33 
I     14.15 

7   31     22 .18 


Art.  272.    To  correct  for  small  inequalities  in  the  altitudes. 

Although  the  sextant  readings  are  the  same  at  the  A.  M.  and  P.  M.  observations,  it  may  happen  that  neithei 
the  true  nor  even  the  apparent  altitudes  are  the  same.  1st.  Supposing  the  sextant  to  remain  unchanged,  the  atmos- 
pheric refraction  n-ay  be  different  at  the  two  observations  in  consequence  of  changes  in  the  density  and  temperature 
of  the  air  as  shown  by  the  barometer  and  thermometer.  In  this  case  the  apparent  altitudes  are  equal,  but  the  true 
altitudes  are  not  so.  2d.  The  sextant  may  be  affected  by  changes  of  temperature,  particularly  in  day  observations 
in  the  sun,  so  as  to  make  the  sextant  readings  the  same  for  apparent  altitudes  slightly  different.  These  changes 
in  the  sextant  caannot  always  be  elin  inated  by  determining  the  index  error  at  each  observation,  since  it  is  quite 
possible  that  the  expansion  and  contraction  of  the  various  parts  might  leave  the  index  correction  unchanged  while 
it  affected  the  readings  of  the  altitudes,  or  the  reverse.  The  only  course  appears  to  be  to  guard  the  instrument  as 
much  as  possible  from  changes  of  temperature,  exposing  it  to  the  sun's  rays  only  during  the  few  minutes  required 
for  each  observation. 

But  the  correction  for  changes  of  refraction  may  be  satisfactorily  made  as  follows:  Note  the  barometer  and 
thermometer  both  A.  M.  and  P.  M. ;  take  out  the  corresponding  refractions  for  each  observation  from  Tables  20,  21, 
22,  and  find  the  difference  of  these  refractions;  also  take  the  difference  between  any  t.vo  sextant  readings  and  the 
difference  between  the  two  corresponding  chronometer  times.     Then  the  correction  of  either  noon  or  midnight  will 


no 


FINDING    THE    TIME. 


be  found  by  the  following  proportion:  The  difference  o    the  sextant  readings  is  to  the  difference  of  the  refraction 
as  the  difference  of  the  chronometer  times  is  to  the  required  correction.  I 

Apply  this  correction  to  the  Chronometer  Time  of  Noon  or  Midnight  (obtained  by  the  preceding  rules)  as  foil 
lows  :  add  it  when  the  A.  M.  refraction  is  the  greater ;  subtract  it  when  the  P.  M.  refraction  is  the  greater.  Thi^ 
result  is  the  true  Chronometer  Time  of  Noon  or  Midnight.  ' 

Example.  Suppose  in  an  A.-M.— P.-M.  example,  we  have  in  the  morning,  Barometer  join.  Thermometer  55°  ; 
in  the  afternoon,  Barometer  agiu.s,  Thermometer  85°.  The  apparent  altitude  of  sun's  lower  limb  t,i°  o^;  th(' 
apparent  altitude  of  sun's  centre  '^T)°  16^.     We  have 


A.  M. 

Mean  refraction,  i'  29" 

Barom.  30  in.,  o 

Therm.  55^"",  —         i 

True  refraction,  i    28 


P.  M. 

Mean  refraction,  i    29 

Barom.  29.5  in.,  —         i 

Therm.  85^^,  —         6 


True  refraction. 


I    22 


Then  the  difference  of  the  sextant  readings  is  10'  (=600"),  and  the  corresponding  difference  of  chronometei 
times  is  about  26'';  whence 

600"  :  6''  =  26^  :  08.26 


The  (approximate)  Chronometer  Time  of  Mean  Noon  was  found  to  be 
Correction  for  change  of  refraction,  jl. 

True  Chronometer  Time  of  Mean  Noon, 


59^-5 
0-3 


5    6    59.8 

Note.— This  correction  may  be  found  by  the  following  rule,  which  we  should  have  to  resort  to  when  but  one 
altitude  was  taken  at  each  observation.  Add  together  the  log  of  the  diff.  of  refractions  (Table  42),  log  cosine  oi 
the  altitude,  log  secant  of  the  latitude,  log  secant  of  the  decHnation,  log  cosecant  of  half  elapsed  time  (or,  if  the 
elapsed  time  is  greater  than  12I',  half  its  supplement  to  24I'),  and  the  constant  log  8.523;  the  sum  is  the  log'(Table 
42)  of  the  required  correction.     Thus  in  the  preceding  example  we  have 


Diff.  refr.,                 6" 

log 

0.778 

Alt.  ©              330  16' 
Lat.,                 38°  59' 
Dec,                150  53' 
EL  T.,             7h  49m 

log  cos 
log  sec 
log.  sec 
log  cosec* 
const,  log 

9.922 
0.109 
0.017 
0.069 
8.523 

Correction,           0^.26 

log 

9.418 

Art.  273.    Deg7 

ee  of  Dependei 

ice. 

An  error  of  5'  in  the  latitude  would  not  affect  the  corresponding  part  of  the  equation  of  equal  altitudes  by 
more  than  one-hundredth  of  its  amount  in  the  most  unfavorable  case,  and  in  general  would  have  no  sensible  effect. 
It  IS  one  of  the  advantages  of  the  equal  altitude  method,  therefore,  that  it  does  not  require  an  accurate  knowledge 
of  the  latitude.  It  is  also  plain  that  errors  in  the  longitude  affecting  the  declination  and  its  hourly  difference  iiro- 
diice  but  small  proportionate  effects  upon  the  computed  equation.  The  absolute  error  of  the  chronometer  on  Green- 
wich will  be  affected  by  the  whole  error  iu  the  longitude,  but  the  rate  will  still  be  correct.  Hence,  we  conclude 
that  by  this  method  the  chronometer  may  be  accurately  rated  at  a  place  whose  latitude  and  loncduide  are  both 
imperfectly  known.  ^ 

The  chief  source  of  error  is  in  the  observation  itself     The  most  practised  observers  with  the  sextant  cannot 


depend  on  the  noted  time  of  a  j/;/ 
ete     " 


^le  contact  within  0^5,  and  hence  the  intervals  between  the  successive  chronom- 


ter  times  (which,  if  observations  could  be  perfectly  taken,  would  be  sensiblv  equal)  may  differ  2** 
robable  error  of  the  chronometer  time  of  sun's  or  star's  transit,  from  the'mean  of  six  such  ot 

of  the  meridian,  is  found  to  be  not  more  than  0^.2,  provided  the  rate  of  the  chronometer  between  the  obs 

5  is  uniform. 

Errors  resulting  from  changes  in  the  refraction  may  be  almost  wholly  removed  by  computation  as  above. 


*  Enter  Table  44,  column  P.  M.,  with  the  zvhole  elapsed  time  and  take  out  the  corresponding  cosecaiit. 


I 


LATITUDE. 


in 


CHAPTER   VII 


LATITUDE. 


1.— BY  MERIDIAN  ALTITUDE. 

Art.  274.    The  latitude  of  a  place  on  the  surface  of  the  earth,  being  its  distance  from  the  equator,  is 
:  measured  by  an  arc  of  the  meridian  between  the  zenith  and  the  equator ;  hence,  if  the  distance  of  any  lieavenly 
•  body  from  the  zenith,  when  on  the  meridian,  be  known,  and  tlie  declina- 
tion of  the  body,  the  latitude  can  thence  be  found. 

Let  Fig.  67  represent  a  projection  of  the  celestial  sphere  on  the  plane 
of  tlie  meridian  NZS;  C,  the  centre  of  the  sphere;  NS,  the  horizon;  P 
and  P',  the  poles  of  the  axis  of  tlie  sphere ;  QCQ',  the  projection  of  the 
equator;  Z,  the  zenith  of  the  observer's  position.  Then,  by  the  above 
definitioii,  ZQ  will  be  the  latitude  of  the  observer's  position  ;  NP,  the  alti- 
tude of  the  pole,  also  equal  to  the  latitude. 

Let  A  be  the  position  of  the  heavenly  Ijody  north  of  the  equator  but 
south  of  the  zenith ;  QA  =  r/,  its  declination,  and  ZA  =  z,  =:  90°  —  /i  (AS), 
its  zenith  distance. 

From  the  figure, 

OZ  =  QA  +  AZ,     or 

L  =  d-\-  z. 

By  atteni'ing  to  the  signs  of  s  and  d,  the  above  equation  may  be  con- 
sidered true  for  all  positions  of  the  body ;  marking  the  zenith  distance 
negative  when  the  body  is  north  of  the  zenith,  as  at  A". 

In  case  the  body  is  so  far  north  of  the  zenith  as  to  be  below  the  pole,  as  at  A'",  or  at  its  lower  culmiiiation, 
the  same  formula  may  be  used  by  substituting  iSo"  —  li  in  place  of  the  declination  itself. 

But  in  this  case  also 


NP 
L 


PA" 
P.D. 


+  NA'", 
+  /,. 


or 


In  this  formula,  for  south  latitude  P.  D.  must  be  the  body's  south  polar  distance,  and  the  value  of  P.  1  >.  -j-  //  is 
the  only  numerical  value  of  the  latitude. 

NVhcn  the  heavenly  body  is  on  the  equator,  or  its  declination  is  equal  to  o,  the  zenith  distance  will  be  equal  to 
the  latitude  of  the  place  of  the  same  name  as  the  zenith  distance.  When  tlie  body  is  in  the  zenith,  the  declina- 
tion will  be  equal  to  the  latitude,  which  will  be  of  the  same  name  as  ihe  declination. 

Art.  275.  TiiK  Oi!SEK\'A'riox. — The  usual  practice  at  sea  is  to  commence  observing  the  aiti.ud':  of  the 
sun's  lower  limb  above  the  sea  horizon,  20  to  30  minutes  before  noon,  and  then  by  the  tangent-screw  to  follow  the 
sun  as  long  as  it  rises;  as  soon  as  the  highest  altitude  is  reached,  tlic  sun  begins  to  fall  and  the  lower  limb  will 
appear  to  <■///.     When  the. sun  dips  the  observation  is  complete,  and  the  reading  of  the  limb  is  taken. 

But  in  case  of  a  heavy  sea  the  de]>ression  of  the  sea  horizon  is  constantly  changing,  and  it  is  therefore  imjws 
sible  to  keep  the  sun's  image  in  constant  contact  with  the  horizon.  Having,  the»i,  the  watch  set  to  the  time  o( 
apparent  noon  from  the  a.  m.  observation  for  time  and  the  run  of  the  ship  in  the  interval,  observe  and  read  off 
separate  altitudes  in  quick  succession  until  they  begin  to  decrease.  The  greatest  is  then  taken  as  the  meridian 
altitude,  or,  niore  accurately,  the  mean  of  the  greatest  and  the  mean  of  the  two  immediately  adjacent,  if  the  inter- 
vals are  ecpial. 

Ill  observing  the  meridian  altituile  of  the  moon  or  a_  star,  the  watch  should  be  set  beforeliand  to  the  lime  of 
its  culmination. 

Art.  276.  Till''.  Cu-Mi'fi  ai  lox. —  I-'r.nn  the  observed  altitude  deduce  the  true  altitude,  and  thence  the  true 
zenith  distance.  Mark  the  zenith  distance  -j-  or  X.  if  the  body  is  south  of  the  zenith  when  on  the  ineri<lian,  —  or  S. 
if  the  body  is  north  of  zenith  when  on  the  meridian. 

Take  out  the  declination  of  the  body  from  the  Nautical  Almanac  for  the  7'/Wl-  of  Mci-iduui  Passage,  having 
regard  for  its  proper  sign  or  name. 

The  algebraic  sum  of  the  declination  and  zenith  distance  will  be  the  latitude;  or,  in  other  words,  add  together 
the  zenith  distance  and  tire  declination  if  they  are  of  the  same  name,  but,  if  they  are  of  different  names,  take  their 
difference;   this  sum  or  difference  will  be  the  latitude,  which  will  be  of  the  same  name  as  the  greater. 

E-XAMI'LE.  At  sea,  June  21,  1S79,  in  Long.  60°  ^^^,  the  observed  meridian  altitude  of  the  sun's  lower  limb 
was  40°  4';   sun  bearing  south;   index  corr.  -\-  3'  o"  ;  height  of  the  eye,  20  feet;   reipiired  the  latitude. 


Obs.  alt., 
Corr., 


2 
d 


40^    4'    o'' 
+  13   21 

40      t7    21 

+  49    42  39 
+  23    27  22 


I.  c.. 

Dip, 

+ 

+ 
+ 

3'    0" 
4  23 
'     9 
7 

15  46 

Dec, 
Corr. 

d, 

+ 
+ 

+ 

23     27'  20".5 
I   -3 

23    27  21  .8 

11.  1). 
1.0., 

Corr., 

+     o.'32 
+     4 

par., 

S.  D., 

+     I  .28 

Corr.,    -|-      13   21 


L      ^ 


+  73    10 


112  LATITUDE. 

Example.  At  sea,  April  14,  1879,  ^^  Long.  140°  E.,  the  observed  meridian  altitude  of  the  sun's  lower  limb 
"was  60°  IS''3C;  sun  bearing  south;  L  C,  —  2' 30''';  height  of  the  eye,  20  feet. 

Obs.  alt,  60°  15'  3c/^  I.  C,     —       2'  30''         Dec,  +     9°  22'  35^^.4  H.  D.,  +  54^^03 

Corr.,  +  8    37  Dip,      —       4    23  Corr.,  —  8   24    .1  Lo.,       —     g^,  33 

*->  —       o    33  

/i     z=  60    24      7  par.,      -f       04.  d         -j-     9    14    n  Corr.,    —    504.1 

S.D.,    +     15    59 


-1-29    35    53 

+    9    14    II  Corn,    +       8    37 


L    =     N.      38    50     4 

Example.  At  sea.  May  15,   1879,  Long.  0°,  the  observed  meridian  altitude  of  the  sun's  lower  limb  was 
30°  13''  10^^;  sun  bearing  north;  I.  C.,  -f-  \'  2P''\  height  of  the  eye,  15  feet. 

Dec.  Or.  o'',     -f      iS°  50' 48'''.5 


Obs.  alt., 
Corr., 

30°  13'  lO^^ 

-f-          122 

I.e.,   + 

Dip,     — 
Ref.,     — 
par.,      + 
S.D.,   + 

Corr.,   -)- 

I'  30' 
3    48 

I    39 

8 

15    51 

k     = 

30    25    12 

—  59    34   48 

—  1 8    50   49 

d     = 

12      2 

L    = 

—  40    43    59 

ExAMi'LE.  January  i,  1879,  the  observed  meridian  altitude  of  Sirius  was  53°  23''  40''',  bearing  south;  I.  C. 
-j-  5'  o^';  height  of  the  eye,  17  feet. 

Dec*,  i6°33M^^3S. 


Obs.  alt., 
Corr., 

23/ 

40'' 
15 

I.e., 

r. 
Dip, 

Cor., 

+ 
+ 

5/    0'^ 

43 

4      2 

/i     = 

53 

23 

55 

15 

d      = 

-i-36 
—  16 

36 
33 

5 

4 

L    = 

-r  20 

I 

E.XAMi'i.K.  June  13,  1879,  '"  Long.  65°  W.,  and  in  a  high  northern  latitude,  the  meridian  altitude  of  the  sun's 
lower  limb  was  8°  16'  lo'^,  below  the  pole;  height  of  the  eye,  20  feet.  . 
Cheenwich  time  of  lower  culmination,  June  13,  16'^  20"'. 

;.,    +     2-,°  1 V    V^.S       H.  D.,     +       S'-'.sS 

+     16    .33 


Obs.  alt., 
Corr., 

S°  16' 

-f-          5 

12 

S.  D., 
Dip, 

par., 

Corr., 

+ 

+ 

+ 

IS' AT' 

4    23 

6    21 

9 

Dec, 
Corr., 

P.  D., 

+ 
+ 

+ 

23°  13'    3'^8 
2    20    .5 

/i          = 

8    21 

66    44 

22 
36 

23    15    24 

r.D.,z= 

5    12 

66   44    36 

L              rrr 

+  75      5 

5S 

Corr.,      +  140    .5 


E.KA.Mi'i.K.  June  26,  1879,   •"  Long.  80°  ^V.,  the  ol«er\cd   meridian  allitiidc  of  the   union's  upper  liuib  was 
59°  6'  40'^,  Ijcaring  soiUli ;   I.  C,  -j-  2'  o''';   height  of  the  eye,  19  feci. 

Long.,                                                5''  20"'.o                                                 S.  1).  —  16^    3^^ 

Moon's  Merld.  Pass.,  June  26,     5    27    .0        II.  1).,              r".98       Aug.,  —  14        II.  P.,       58' 46'^. 3 

Red.  for  Long.  +  5i'.3"3,  10    .6        Lo.,  5I' .33  

• I.  C,  -f-  20        Table  24,  29    53 

(.1.  lu.  I.,                                         10    57    .6                                 10.55        "'P'  —  4    16        2d  corr. 


1st  corr.,  —  iS  23 
Dec.  at  11'',  —  4°  51' 36^.5  M.  IJ.,  __  i5'/.o69  Olis.  .all.,  59°  6  40 
("orr.,  for     -  2'". 4,  +  36    .2  —      2"'.4  

.•\pii.  alt.,      58    48    07 


—      4    5'    00    .3  4-36^^2  2d  corr.,  -t  29    53 


-|-  30  42  GO  /i  =     59  18  00 

+  25  51  z  =   4-30  42  00 


LATITUDE.  113 

Example.  At  sea,  September  i6,  1879,  in  Long.  75°  E.,  the  observed  meridian  altitude  of  Jupiter  was  51° 
'J  24'',  bearing  north;  I.  C,  -\-  2/  o" ;  height  of  the  eye,  16  feet. 

Loqg.,  —     ^'^    o"\o 

Gn  Merid.  Pass.,         10  49    .8 
Corr.  for  Long.,     —  o   .9 


Gr.m.t.,Sept.  16,         5   48   .9 


L  a,    . 

+  3'    0" 

H.  P.,                2". 2 

Dip, 

—  3    55 

par.  Table  17,    V' 

r,      , 

—        47 

\ 

par.,    , 

+          I 

Corr.,  —  I    41 


Obs.  ah.,  51°  25' 24''  Dec,     —  10°  44' 2c/'.5  H.  D.,    —    6'^58 

Corr.,  ~ —  I    41  Corr.,    —  38    .2  —     5    .81 


h.  =  51    23    43  </    =    —   10    44    58    .7  —  38    .23 


Z  =  —    38    36    17 

d  =  —    10    44    59 


L  -=  S.  49    21    16 

Art.  STY.  In  all  that  has  gone  before,  tlie  greatest  altitude  has  been  regarded  as  the  meridian  altitude, 
I'hich  is  not  true  e.xcept  in  the  case  of  a  fixed  star,  owing  to  the  change  of  declination  of  the  heavenly  body  and  tlic 
ihange  of  position  of  the  observer  if  the  ship  is  in  motion. 

I'he  amount  of  the  correction  to  be  applied  may  be  estimated  in  the  following  manner: 

Find  the  number  of  miles  and  tenths  of  a  mile  north'nig  ox  soiUhing  made  by  the  ship  in  one  hour,  and  also 
he  variation  of  the  sun's  declination  in  an  hour,  expressed  also  in  miles  and  tenths.  Add  these  together,  if  they 
iQlh  conspire  to  elevate  or  depress  the  sun  ;  otherwise,  take  their  difference,  which  call  the  arc  A.  Find  in  Table 
6  the  arc  B,  expressed  in  seconds,  corresponding  to  the  latitude  and  declination  ;  then  the  arc  A,  di\ided  by 
:i'.i<' the  arc  B,  \\ill  express  the  time  in  miiiittcs  from  noon,  when  the  greatest  (or  least)  altitude  is  observed. 
Joreover,  the  square  of  the  arc  A,  divided  by  four  times  the  arc  B,  will  be  the  number  of  seconds  to  be  applied  to 
he  observed  altitude  to  obtain  tlie  true  ahitude,  which  would  have  been  observed  if  tiie  ship  had  been  at  rest. 

Thus,  if  the  ship  sail  toward  the  sun  south  11  miles  per  hour,  and  the  declination  increases  norllieily  i'  i>er 
our,  we  shall  have  A  =^  11  -|-  1  =  12.  If  the  latitude  is  42"  N.,  and  the  declination  2^  S.,  we  shall  liave,  by 
"alile  26,  B  =;  2".  In  this  case,  tlie  time  from  noun  is  -'4--  =^  3  minutes,  and  the  correction  of  altitude  -J^  =  18 
cconds  only. 

This  correction  is  of  iiille  practical  importance  at  sea,  where  the  altitudes  are  so  uncertain  and  the  latitude 
equired  to  the  nearest  minute  only. 

2.— BY  REDUCTION  TO  THE  MERIDIAN. 

Art.  ti'J'S.  ]Vhcn  tlic  local  time  of  ohscn'ation  is  kiioivn. — Should  the  meridian  observation  be  lost,  owing  to 
louds  or  other  causes,  altitudes  may  be  taken  near  noon  and  the  times  noted  by  a  watch  regulated  to  local  time 
rem  the  .A..  M.  observations  for  time,  carried  forward  to  noon  by  a  correction  due  to  the  difference  of  longitude  in 
he  interval. 

If  the  observations  are  within    13'"  from    the  meridian,  before  or  after,  the  correction  to  be  ajiplied  to  the 
•bserved  altitudes  to  reduce  them  to  the  meridian  altitude  may  l)e  found  by  inspection  of  Tables  26  and  27.     Table 
6  contains  the  variation  of  tlie  altitude  for  one  minute  from  the  meridian,  expressed  in  seconds  and  tenths  of  a 
econd.     Table  27  contains  the  square  of  the  minutes  and  seconds  contained  in  the  top  and  si<le  columns. 
Let  a  =  change  of  altitude  (in  seconds  of  arc)  in  one  minute  from  the  meridian. 
A  =  meridian  altitude. 
/t'  :=  observed  altitude. 
/    =  interval  from  apparent  noon. 
The  value  of  the  reduction  to  the  meridian  altitude  of  eacli  altitude  is  foimd  by  the  formula 

//  =:  /i'  4-  al' 

being  found  in  Table  26  an<l  /  being  found  in  Table  27;   hence  the  following 

Rule.  Take  from  Table  27  the  number  corresponding  to  each  time  from  noon  (the  minutes  being  found  at 
he  top  and  the  seconds  at  the  side,  the  correction  being  found  under  the  fornier  and  opposite  tlie  latter);  divide 
i3e  sum  of  these  tabular  numbe»s  by  the  number  of  observations;  the  quotient  being  multiplied  by  the  number 
.iken  from  Table  26,  corresponding  to  the  mean  of  the  altitiides,  will  be  the  correction  lo  be  applied  to  the  mean 
f  the  observed  altitudes  to  obtain  the  meridian  altitude. 

If  the  difference  of  the  altitudes  is  small,  the  refraction  will  be  sensibly  the  same  for  all ;  hence,  the  reductions 
lay  be  applied  to  the  meiidian  altitude  to  obtain  the  true  altitude  and  thence  the  zenith  distance. 

The  latitude  is  now  to  be  found  as  in  the  ordinary  method  by  meridian  altitude. 

EXAMTI.E.  At  sea,  July  12,  iS/U,  in  I. at.  50"  N.,  Long.  40-  \V.,  observed  the  following  circum-meridian 
llituues  of  the  sun's  lower  limfi,  noiing  the  times  by  a  chronometer  regulated  to  Greenwich  mean  time;  chro. 
orr.,  —  2'"  30^;   I.  C,  —  3'  o";   height  of  the  eye,  15  feet. 

Long.  40^'  W.  =  -f-  -'■  40'" 

)cc.  Cr.  o'',        +22      o    23".2  ILL..  20.71         (i:(!.  i.),  5'"  17^99         H.  D.,    +  o^32I 

'orr.  lor  2'' 40'",  —  55   .3  Lo.,         -f     2''. 07         Corr.,  -f  o  .86         Lo.,         -f- ^''.o? 


8    B 


+  21     59    28  Corr,      —  55".30         Lq.  t.  (+ to  app.  t.),  5      1S.85         Corr.,      +0^857 

L.  m.  t.  of  app.  noon,  o''     5'"  19^ 

Chro.  corr.  on  1.  m.  t.,   —  2    42     30 


114 


Chro.  times. 

43  34 

44  47 

45  39 


LAT 

ITUDE. 

- 

L.  m.  t. 

/ 

/2    (Table  27). 

11  *>  59™  98 
014 
0      2  17 
039 

—  6'"  108 

4     15 
3      2 
2     10 

38.0 

18. 1 

9.2 

4-7 

■  • 

Mean 
a     = 

17.5 
2.5  (Table  26). 

(•i 

"  + 
.+ 

61°  48'  30" 
49    30 

49  30 

50  30 

h!     = 

61    49    30 

44 

Corr., 

61     50    14 
»    31 

at"  =  43"-.  75 

I     Q       -,'      o" 

Dip,'  —     3    48  z      =  +  28°    1'  IS" 

r,  —     o    31  fl'     =  -f  21     59    28 

par.,     4- 


S.  D.,+  15    46  L     =         50      o    43  N. 

Ccrr.,  +     S    31 


h  -^    61     58    45 

Example.  The  approximate  latitude  being  40'^  N.,  the  sun's  declination  at  noon,  20°  S.  ;  sun  s  S.  D.,K  the 
height  of  the  eye,  16  feet;  ten  altitudes  of  the  sun's  lower  limb  were  measured  with  a  circle  of  reflection  WdOse 
surn  was  298°  20',  and  the  times  noted  by  a  watch  which  was  IC"  7.^  slow  of  local  apparent  time. 

Watch  time  of  apparent  noon,  ll''  49'"  5S\ 

298°  20'    o" 


Watch  times. 

t 

/•2 

Ill'  ^5,. 

'  4:v 

— 

4'" 

•S'' 

iS.I 

lOQ, 

46 

5S 

3 

0 

9.0 

47 

52 

2 

() 

44 

//' 

48 

50 

I 

8 

'•3 

<7/2 

49 

28 

0 

30 

0.2 

50 

48 

+ 

0 

50 

0.7 

5' 

10 

I 

12 

1.4 

Corr., 

52 

'3 

n 

'5 

5-< 

53 

8 

3 

10 

!0.0 

// 

54 

23 

4 

^5 
can 

•9  5 

6.97 

,/ 

il 

z:^ 

1.0 

=        29 
=  + 

50 

0 
11 

29 

+ 

50 
10 

II 

32 

=        30- 

'0 

43 

=  +  59 
=  —  20 

59 
0 

17 
0 

Dip, 

-    3' 55" 

r. 

—    I   41 

par. 

+    08 

S.  D., 

+  16     0 

Corr.,       -f-  10  32 


at^    -—  1I".I5  L  =        39    59   17  Is'. 

Example.  May  31,  1S79,  in  Lat.  30*^  25'  N.,  Long.  5I'  25'"  42^  W.,  observed  with  a  sextant  and  an  artificial 
horizon  '.he  folhnving  double  altitudes  of  Spica,  noting  the  times  by  a  watch  compared  with  a  Greenwich  mean 
time  chronometer,  whose  error  was  —  2'"  33''.3,  I.  C.  — 3. 

Chro.,       2''  28'"  30-'  !.o.,  5I' 25'"  4*^2MV.  >]<'  K.  .X..  13''  iS"' 52».2 

W  ,  <S    58     50  Chro.  error,  2     33    fast.  K.  .V.  m.  sun,       —     4    34     26   9 


W.,   5    29     40  Chro.  corr.  on  1..  m.  t.,    5    28     15 


Red.  for  Long.,     —  53  .5 


Sid.  int.  from  o''.  8    43  31  .8 

Red.  to  m.  t.,         •■              ^  25  .8 

L.  m.  t.  or  transit.             AZ  6 

Chro.  corr.,            -  •  '5 


Chro.  t.  of  transit,       -..  21 


Watch  times  +(C— W)  =  Chro.  times.  Mean  time.  Sid.  t. 


3'"' 

'  18-^ 

.0 

-■),i 

19 

■5 

SO 

7 

.0 

3« 

50 

.0 

41 

7 

-5 

43 

45 

•5 

45 

46 

.0 

47 

.0 

51 

12 

•5 

0'" 

'  58^0 

2 

59-5 

5 

47 -o 

8 

30  .0 

10 

47-5 

13 

25   5 

15 

2O  .0 

'7 

13.0 

20 

52-5 

Mean 

time. 

—  9111 

2'?^.0 

7 

2.  .5 

4 

34 -o 

I 

51  .0 

+  0 

26  .5 

3 

4-5 

5 

5-0 

6 

52  .0 

10 

3'  -5 

—    9"! 

'  24" 

&    ; 

7 

23 

54 

4 

35 

21.- 

I 

51 

3-'' 

+  0 

27 

0.2 

0 

5 

9-5 

5 

(. 

26.0 

0 

53 

47-4 

10 

Mean 

111-3 

40.2 

<t           = 

=      2.5 

c/s      =  Joo"5 


LATITUDE. 

2  att,  ifc                     980   2' 

0"  A-end 

6 

30 

'  .                             -7 

40 

.  10 

20 

10 

30    B-ead. 

9 

20 

6 

50 

5 

30 

0 

30 

115 


98 

6 

3 

34 
0 

.2)98 

3 

34 

49 

I 

47 
50 

=          49 

0 
I 

57 
41 

=          49 

0 

38 

=z    +     40 
=  —     10 

57 
32 

22 
4 

Mean, 
I.  C, 


r 

k' 

at''' 

h 

2 

L  =  30  25     18  N. 

Art.  279.    Table  26  extends  only  to  Declination  =  24° ;  and  if  a  star  is  used  whose  declination  exceeds 
that  limit,  the  correction  for  reduction  lo  the  meridian  may  be  found  by  the  formula: 

i".96^t;  cos  L  cos  d 

ked.  = "^^-Tf 7\ 

sm  (L  —  a) 

Tor  instance,  if  the  latitude  =  50-  N.,  and  the  declination  =  30°  S., 


I. 

L          =    + 
d          =    — 

h-d=    + 

"9f'35 

50^' 
300 

80 

i".ii 

log 

log  COS 
log  COS 

log  cosec, 
log 

0.2930 
9. 80S I 
9-9375 

0.0066 

Red.     = 

0.0452 

Art.  280.    Since  Table  27  for  tlie  value  of  /-  extends  only  to  /  =  13"',  the  following  formula  for  reduction 

to  the  meridian  may  be  used  for  a  single  altitude,  if  the  interval  of  time  from  apparent  noon  should  be  greater 

than  13"': 

...        ,  .        cos  L  COS  d  sin-  !^/ 

sin  "4  {/i  —  h' )  =  —.—r-. — ,    ,,, 

^  COS  j4  (Ai  +  h') 

in  which  (/z  —  h'')  is  the  quantity  necessary  to  reduce  //,  the  observed  altitude,  to  /;,  the  meridian  althude. 

In  order  to  hnd  an  ajiproximate  value  of  /•,  there  are  given  the  value  of  L  by  account,  and  the  value  of  d ;  hence, 

//I  =9oO-(L-y); 
or,  Jix  =;  90°  —  {d —  L)  if  the  zenith  is  south  of  the  star. 

Rule.    Add  together  the  log  cosine  of  tlic  latitude  by  account,  the  log  cosine  of  the  declination,  twice  the  log 
sine  corresponding  to  tiic  value  of  /  in  the  column  p.  m.  Tal)le  44,  and  the  log  secant  of  the  sum  of  the  observed 
:  altitude  and  the  approximate  meridian  altitude:   the  sum  will  be  the  log  sine  of  one-half  the  correction  to  l)e  applied 
I  to  the  observed  altitude  to  obtain  the  meridian  altitude.     Having  found  this  the  latitude  may  be  found. 

Should  the  latitude  differ  much  from  the  latitude  by  account,  or  assumed  latitude,  the  operation  should  be 
repeated,  using  tlie  new  value  of  L. 

This  method  of  finding  the  latitude  may  l)e  applied  to  any  other  celestial  object  than  the  sun,  ]irovi<led  that  in 
case  the  declination  changes  the  value  of  the  declination  used  in  the  formula  must  be  taken  out  for //■<■  i hue  of 
o/'sen    tioii. 

E.'A.Mi'i.i;.  At  sea,  near  the  end  of  the  ast.  day  January  20,  1879,  '"  ^^^'^-  49^  5°'  ■^•'  '')'  account,  Long.  15° 
^V.,  ob:  erved  the  altitude  of  the  sun's  lower  limb,  19"  32';  chro.  time,  12''  50"';  chro.  corr  ,  —  10'"  28*';  height 
of  the  eye,  16  feet.     Required  the  latitude. 

II.  1).  II.  D. 

Chro.  I.  1 2'' 50'"    o^    Dec,  —  19^55'  I5".6     +33"  42  (Kq.  t  ),  1 1'"  3i'.9i -f  o^7o6 

Ciiro.  coir,      —         10     28     Corr.  f  11- (h.  m.  t., -|-  22  . 1      -(-  o    .66  Corr,  -|-  0.47-J-0.66 


Gr.  m.  t.  Jan.  21,    o    39     32     ./,  —  19    54  53  .5     -(-    22.06  Eq.t.(-|-to  apjit.),  u     32.4    +0.47 

Long.,  -\-   \      <:,       i)     L.  by  ace, 


/ 


32 


— 19 

54 

53 

•5 

+  49 

SO 

0 

69 

44  53 

90 

0 

0 

20 

15 

07 

19 

41 

47 

L.  in.t.  J.U1.20,    23    39     32      \.  —  d  =        69    4453  Obs.  alt.,  19^32'     o" 

Eq.  t.,  —        1 1     32  90      o     o  Dip,  —  3     55 

Par,  +  8 


L.  app.  t.,     23  28   o  //,  =   20  1507  r,  —  2  43 
//          —   19  41  47         S.  D.,    -f     16  17 


//!  +  //       =   39  5654         A'  —.         19  41  47 

;^  (/., -f //')   =   19  5S  27 


1 


116 


LATITUDE. 

/              •              =           32" 

L                    =        49^ 
d                   =19 
>^  (/.,  +  /.')  ==         19 

50'     0" 

54    53. 
58    27 

log  sin^  yit, 
log  cos 
log  cos  ■ 
log  sec 

7.68716 
9.80957 
9.97322 
0.02694 

10    48 
21     36 

log  sin 

7.49689 

//                     =         19 

41     47 

^                      =         20 

3    23 

z                      =  +  69 
//                      =  —  19 

56    37 
54    47 

L  =        50       I     50  N. 

3.— BY  TWO  ALTITUDES  ISTEAR  THE  MERIDIAN  WHEN  THE  TIME  IS  NOT  KNOWN.* 

Art.  281.  Should  the  local  time  be  uncertain,  the  following  simple  method  of  finding  the  latitude  from 
circum-meridian  altitudes  may  be  used.  It  may  also  be  employed  to  find  the  approximate  time,  as  will  be  explained 
in  An.  299,  Chap.  YIII.  . 

The  chronometer  time  of  each  altitude  of  the  sun's  limb  is  noted,  in  order  that  the  chronometer  iiiUii'ais  may 
be  known.  Select  any  two  altitudes  that  are  not  more  than  26'"  apart  by  the  chronometer.  Correct  these  ahitudcs 
for  refraction  and  find  their  mean  and  their  dilTerence.  Find  the  difference  of  the  corresponding  chronometer 
tniies,  or  the  chnnwineter  in/ei-val. 

With  the  sun's  declination  at  noon  and  tlie  approximate  latitude  find  the  value  of «  from  Table  26. 

Let  t  =  one-half  \\\c.  chronometer  interval  and  find  the  value  of  t^  from  Table  27. 

Multiply  /"  by  a  and  call  the  product  \\i^  first  reduction. 

Divide  the  square  oi  one  fourth  the  difference  of  the  altitudes  (reduced  to  seconds)  by  the  first  reduction;  the 
quotient  is  the  second  reduction. 

Add  the  two  reductions  to  tlie  mean  of  the  altitudes  and  the  result  will  be  the  meridian  altitude  of  the  sun's 
limb. 

Let  h'  and  h"  represent  the  two  observed  altitudes  of  the  sim's  limb  corrected  for  refraction,  and 

//[,  the  meridian  altitude  of  the  limb; 

Then  the  following  formula  expresses  the  above  rule: 

h,  =  %  (//'  +  h")  +  <;/•  +  ^vi(^h'-h")Y 

at- 

The  meridian  altitude  thus  deduced  must  be  further  corrected  for  dip,  parallax,  and  semi-diameter,  and  then 
tlie  latitude  found  as  in  case  <.)f  meridian  altitude  directly  ol)scrvetl. 

Wlien  the  difference  of  the  altitiules  is  small  and  the  refraction  therefore  the  same  for  both,  the  correction  for 
refraction  may  be  ajiplied  to  the  deduced  meridian  altitude.  All  the  reductions  (including  the  index  correction) 
will  then  be  applied  to  the  reduced  meridian  altitude  of  the  limb. 

Example.  The  approximate  latitude  being  50^  N. ;  the  sun's  declination  at  noon  22°  o'  23"  N. ;  the  height 
of  the  eye,  16  feet ;    L  C.  —  3'  o"  ;   suppose  the  following  observations  taken  : 

//'  =  61-^  45'  30" 

h"  =:  61      A7     ^O 


Chronometer. 

2''4i"'39« 
2    45     39 

2) 

4       0 

i       = 
a      = 

2 

4 
2-5 

at^    =         10 


h'  —  h" 

— 

. 

2 

0 

(X  (/^'  - 

-  !^"))' 

= 

900 

%  {h'  + 

h") 

= 

61 

46 

30 

at- 

— 

10 

HV 

— 

I 

30 

h. 

61 

48 

10 

I.e. 

= 

— 

3 

0 

Dip 

= 

— 

3 

48 

r 

= 

— 

31 

par. 

= 

+ 

4 

S.  D.    . 

= 

+ 
+ 

15 

46 

h 

61 

56 

41 

z 

28 

19 

d 

= 

+ 

0  -> 

0 

-J 

L  =  50      3  42  N. 

Art.  28*2.  Degree  01^  accuracy. — The  accuracy  of  the  result  depends  in  a  great  degree  upon  the  accuracy 
with  which  ;he  difference  of  altitude  is  olitained.  Since  the  same  causes  of  eiror,  such  as  displacement  of  the  sea 
horizon  bv  extraordinary  refraction,  unknown  instrumentnl  errors,  &c.,   affect  both  altitudes  alike,  the  difference 


*  Chauvenct. 


LATITUDE.  117 

will  usmlly-^c  obtained,  even  at  sea,  within  less  than  i'.  The  most  favorable  case  is  that  in  which  the  altitudes 
arc  C(]ual,  and  the  second  reduction,  consequently,  /.ero.      It  will  be  well,  therefore,  always  to  endeavor  to  obtain 

i  altitudes  on  opposite  sides  of  the  meridian. 

I  When  several  circum-meridian  altitudes  have  been  observed,  they  may  l)e  reduced  in   pairs,  and  the  mean  of 

all  the  resulting  meridian  altitudes  will  be  taken. 

4.-  BY  A  SINGLE  ALTITUDE  AT  A  GIVEN  TIME. 

Ai't.  283.  This  observation  should  be  limited  to  altitudes  taken  within  an  hour  of  the  meridian,  for 
unavoidable  errors  occur  in  the  time  as  determined  at  sea,  and  the  error  in  the  latitude  produced  by  an  error  in  the 
time  increases  very  rapidly  as  the  celestial  object  leaves  the  meridian  and  ajiproaches  the  prime  vertical.  On  the 
prime  vertical  the  solution  by  this  method  is  impracticable. 

Note  the  time  by  chronometer  at  the  instant  of  observation,  from  which  find  the  true  local  time,  and  hence  the 
hour-angle  of  the  celestial  object. 

If  the  sun  is  observed  the  hour- angle  is  simply  the  local  apparent  time.     If  a  star  or  the  moon 

/  =  sid.  time  —  R.  A. 
Then  the  latitude  may  be  determined  from  the  following  formulae  : 


I 


Tan  X  =  tan  d  sec  t 

( 'os  Y  =  sin  Ji  sin  X  cosec  d 

L  =  X  ±Y 

Since  /  should  always  be  less  than  90°  or  6'^,  X  will  have  the  same  sign  as  d,  the  declination. 

The  sign  of  Y  may  be  either  -f-  or  — ;  hence  two  values  of  the  latitude  will  be  found  from  the  third  equation — 

L  =  X  ±  Y 


Should  one  of  these  values  be  greater  than  90°  it  is,  of  course,  not  admissible.  When  both  values  are  within 
90'-'  that  value  is  to  be  chosen  which  agrees  best  with  the  approximate  latitude,  or  the  latitude  by  account. 

Example.  June  7,  1879,  in  Lat.  30^  25'  X^.,  Long.  81^  25'  24"  \V.,  by  account;  chro.  time,  6''  22"'  52--'; 
obs.  Q  75"^  13' ;   I.  C.  —  3'  00" ;  height  of  the  eye,  25  feet;  chro.  corr.  —  2'"  36^  Gr.  m.  t. 

Chro.  t.,  6'^  22"' 52^         Dec,  +22^45'     9". 9         H.  D.,  +  14"- 64 

Chro.  corr.,  2     36  Corr.  for  Gr.  m.  t.,     -\-  i    32   .8  -(-  6     34 

Gr.  m.  t.,  6     20     16         </  =  -j-  22    46    42   .7  92   .82 

Long.  W., 


6    20 

5     25 

16 
42 

0    54 

I 

26 

L.  m.  t.,  o     54  34  (Eq.  t.) 

Eq.  t.,  +           I  26  Corr.  Gr.  m.  t., 

/  =  56  o  Eq.  t.  (+  to  m.  t.,) 

t  ^  56'"  log  sec  O.01310 

(/  =  +  22"^  46'  43"  log  tan  9.62318 

//  =  75    20  41 

X  =  +  23    24  9  log  tan  9.63628 

Y  =  7      2  30 


I™  28s. 85 

—                  2  8S 

H.  D., 

-           o^-4S5 
+           6.34 

I     26 

—           2 .885 

Obs.  alt., 

75°  13     0" 

log  cosec   0.41209 

log  sill       9-98563 
lug  sin        9-59899 

I.  C, 

Dip, 
S.  1)., 
par.  andref. 

-  30 

-  4   54 
+        '5   48 

.-              13 

//         = 

75    20   41 

L  =  30    26   39   X. 


Example.    May  28,  1879;  in  Lat.  30^  20'  N.,  by  account;   Long.  81-  25'  24"  W. ;  chro.  time,  7!'  36'"  8''.5 ; 
observed   altitude   of  moon's  i  pjier  limb,  30"-    44'   50";   I.   C.  —  3'  o"  ;   height  of  the  eye,   26  feet;  chro.   corr 
•       2'"  36",  Gr.  m.  t. 

Chro.  t.,  7''   36"'    S-.5  (("sR.  A.,  lo''   21'"     7^78         M.  D  ,      -f       2^0592 

Chro.  corr.,  —  2     30  .0         v  orr.  for  G.  m    l.,+  i       9  •"7  +     33"'-54 


•5 

/ 

jj 

J- 

4 

12 

0/ 

•J 

I 

14 

0 

II 

57 

24 

•3 

5 

25 

42 

.0 

6 

31 

42 

10 

22 

17 

Gr.  m.  t.  7  2,0  32 -5  K.  A.,                               ID     22  16 .85  -j-  69.066 

R.  A.  111.  sun,  4  12  37  .3 

Red.  Gr.  m.  t.,  -4-  i  ^4 .5  ({ 's  Dec,  +     6^    49'  52". 4  M.  D.,       —  14". 459 

Gr.  sid.  t.,  II  57  24.3  Gor^  for  33'"  33%  —             8  5  +  33     54 


Long.  W'.,  —     5     25     42 .0        d  =         -f     6    41     47 

L.  sid.  t., 
R.  A.  moon, 


—  484  -95 


20 

3 

57~ 

9 

50 
38' 

25 
35 

45" 

Obs.  ([ , 
L  C, 
S.  D., 
Dip 

h' 
Corr.'  Ta 

h 

Lie  24, 

+ 


(['sH.  P., 

58'   03" 

d'sS.  D., 

15'   51 

30'-'  44' 

50" 

0 

15 

51 

5 

0 

30    20 

59 

48 

29 

31      9 

28 

118 


LATITUDE. 

d 

= 

57° 
-f     6 

38' 
41 

45" 
47 

log  sec   0.27152 
log  tan   9.06973 

log  cosec  0.93324 

h 
X 

= 

31 

+    12 

i8 

9 

22 

2 

28 
30 

0 

log  tan  9.34124 

log  sin      9.71383 
log  sin      9.33104 

Y 

log  cos      9.9781 1 

L 

.^o 

24 

^0  N. 

5.— BY  CHANGE  OF  ALTITUDE  NEAR  THE  PRIME  VERTICAL. 

Art.  284.  The  last  method  becomes  indeterminate  when  the  body  is  on  the  prime  vertical,  and  it  may 
liecome  very  important  to  determine  the  latitude  approximately  when  the  sun  is  nearly  east  or  west,  which  may  be 
done  by  the  following  rule  : 

In  the  morning,  when  the  sun  is  near  the  prime  vertical,  bring  the  image  of  the  sun's  upper  limb  into  contact 
with  the  sea  horizon  and  note  the  time  by  the  chronometer  or  a  good  watch ;  let  the  sextant-reading  remain  the 
same,  and  note  the  time  when  the  lower  limb  makes  contact  with  the  horizon.  In  the  afternoon,  commence  with 
the  lower  limb. 

Take  the  sun's  semi-diameter  from  the  Nautical  Almanac  and  reduce  it  to  seconds. 

Find  the  chronometer  interval  between  the  contacts  in  seconds. 

To  the  constant  logarithm  9. 1 2494  add  the  log  of  the  sun's  semi-diameter  and  the  arithmetical  complement 
of  the  log  of  the  chronometer  interval.     The  sum  is  the  log  cosine  of  the  latitude. 

If  the  sun  is  not  very  near  the  prime  vertical,  observe  its  bearing  as  nearly  as  possible  with  the  compass, 
allowing  for  the  variation ;  and  to  the  above  logs  add  the  log  secant  of  the  sun's  amplitude ;  the  sum  will  be  the 
log  cosine  of  the  latitude. 

Example.  Suppose  that  on  June  10,  1865,  in  Lat.  42*^  N.,  Long.  126'^  W.,  by  account,  about  8''  20'"  a.  m., 
the  sextant  being  set  at  41^  o'  o",  the  two  contacts  of  the  upper  and  lower  limbs  of  the  sun  with  the  horizon  are 
observed  as  follows : 

Chronometer. 

Upper  limb,  4''  40'"  32" 

Lower  limb,  43     23 

the  amplitude  of  the  sun  at  the  middle  time  being  about  5'^  S. 


1 


Constant  log 

9.12494 

Sun's 

S.  D.  = 

=  15' 

47" 

-947" 

log 

2-97('35 

Chro. 

int.  = 

2"'  5 

(^  = 

171% 

ar-co 

log 

7.70700 

Am  pi 

tude  = 

5S 

log  sec 

0.00166 

Latitude  :=  42*^  10',  log  cos        9.86995 

Art.  285.  This  is  simply  an  approximate  method,  being  most  accurate  in  high  latitudes,  but,  taken  in  con- 
nection with  Sumner's  method,  it  wll  restrict  the  probable  position  of  the  ship  to  a  very  limited  portion  of  the 
Sumner  line,  provided  the  observations  be  taken  near  the  prime  vertical. 

It  wdl  be  noticed  that  in  finding  the  latitude  by  this  method  the  sun's  declination  is  not  used,  and  the  only 
quantity  taken  from  the  Nautical  Almanac  is  the  semi-diameter.  Should  there  be  no  copy  of  the  Almanac  avail- 
able the  sextant  may  be  set  successively  at  two  readings  30'  apart,  and  noting  the  times  when  the  same  limb  of  the 
sun  makes  contact  with  the  horizon;  then  in  the  computation,  in  place  of  the  sun's  semi-diameter,  use  15'. 

6.— BY  THE  POLE  STAR. 

Art.  2§6.  This  method,  though  confined  to  northern  latitudes,  may  always  be  resorted  to  at  sea  when  the 
star  is  visible  and  the  horizon  distinctly  visible,  provided  the  apparent  time  of  the  observation  is  noted  as  accu- 
rately as  it  is  usually  known  on  board  ship. 

Two  methods  are  given,  one  of  which  is  rigorous  and  embodies  Table  28.  The  second  irethod  is  sufficiently 
precise  for  nautical  purposes,  involving  the  computation  of  the  formula — 

V,  ■=  h  —  /  cos  t 
in  which 

h  =  true  altitude,  deduced  from  the  observed  altitude ; 

p  =  polar  distance  =  90^^  —  d,  the  apparent  declination  to  be  taken  from  the  Nautical  Almanac  for  the  date; 

i  =  sidereal  time  —  star's  R.  A. 

Rule.  Find  the  sidereal  time  of  the  observation  and  from  it  subtract  the  right  ascer  sion  of  Polaris  taken 
from  the  Nautical  Almanac ;   the  result  will  be  the  hour-angle. 

To  the  log  cosine  of  the  hour-angle  add  the  log  of  the  polar  distance  in  minutes;  llio  number  corresponding 
to  the  resulting  logarithm  will  Ije  a  correction  in  minutes  lO  be  subtracted  froui  the  sLir\  true  .■altitude  (o  find  the 
latitude. 

Attention  must  be  paid  to  the  sign  of  the  correction/  cos  /.  If /is  more  than  6''  and  le-s  than  iS'',  the  s.gn 
of  cos  /is  — ;  hence  the  formula  becomes  numerically 

L  =  //  -|-  /  cos  /. 


LATITUDE.  119 

ExAJfTLE.    June  II,  1879,  from  an  observed  altitude  of  Polaris  the  true  altitude  was  found  to  be  29°  5'  55". 
The  time  noted  by  a  Greenwich  chronometer  was  13''  41'"  26'';  chro.  corr.  —  2'"  22*;   Long.  5''  25'"  42*  W. 


k 


Chro.  time, 
Chro.  corr., 

+ 

i3h 

41"' 
2 

26s 
22 

*'s  R.  A 
He's  Dec, 

/     - 

log/ 
log  COS  / 

log 

/  cos  / 

A 

p  cos 

88^^  39'  47" 

Gr.  m.  t.,  June  li. 
Long.  W., 

13 

5 

39 

25 

4 
42 

I    20    13    =    8o'.2 

L.  m.  t., 

Sid.  t   of  Gr.  o'', 

Corr.  for  13''  39'", 

L.  sid.  time, 
*'s  R.  A., 

8 
5 

13 

I 

13 
17 

2 

14 

22 

49 
15 

26 
4 

I.904I7 

«9.99S45 
w  1. 90262 
=     —     79'-9 

^    "^ 

12 

19 

22 

=     —  i^  19'  54" 
=        29      5   55 

t  =         30  25  49  N. 

Art.  2§'7.  Rigorous  Method.— Reduce  the  observed  altitude  of  the  star  to  the  true  altitude,  and  the 
noted  time  of  the  observation  to  the  sidereal  time  of  the  place. 

Find  from  the  Nautical  Almanac  the  apparent  right  ascension  and  declination  of  the  star  at  the  time  of  observa- 
tion. 

Subtracting  the  right  ascension  from  the  sidereal  time  will  give  the  star's  hour  angle  west  or  +  ;  subtracting 
the  sidereal  time  from  the  right  ascension  will  give  the  hour  angle  east  or  — .  If  it  is  more  than  12''  subtract  it 
from  24''  and  change  the  sign. 

With  the  hour  angle  take  out  theyfrj-^  correction.  A,  from  Table  28,  giving  to  it  the  sign  —  when  the  hour  angle 
is  numerically  less  than  6'>;  the  sign  +  when  the  hour  angle  is  greater  than  6''. 

With  the  hour-angle  and  altitude  take  out  the  second  correction,  B,  from  Table  28.  The  sign  of  this  correction 
is  always  -)-.* 

With  1]  and  the  declination  take  out  the  third  correction,  C,  from  Table  28,  giving  it  the  sign  -{-  when  the 
declination  is  less  than  88^^  40'  ;   —  when  the  declination  is  greater  than  88'-'  40'. 

With  A  and  the  declination  take  out  'Cao.  fourth  correction,  D,  from  Table  28,  giving  it  the  same  sign  as  that  of 
.\  when  the  declination  is  less  than  88^  40' ;   the  opposite  sign  when  the  declination  is  greater  than  88^  40'. 

Combine  these  corrections  with  the  true  altitude  according  to  their  signs ;  the  result  is  the  latitude  of  the 
place  of  observation. 

When  great  precision  is  required,  or  the  intervals  are  great,  it  will  be  necessary  to  take  out  theyirj/  and  second 
corrections  for  each  observation  separately;  in  other  cases  the  mean  of  the  times  may  be  used. 

The  means  of  these  two  corrections  may  always  be  used  for  finding  the  third  3.\\d  foitrth  corrections;  and 
these  four  quantities  may  be  combined  with  the  mean  of  the  altitudes. 

If  the  nearest  lb"  suffices  for  each  correction,  they  may  be  taken  out  with  the  nearest  arguments  without 
interpolation ;    and  all  but  the  Jirst  may  thus  be  taken  out  when  a  precision  of  3"  is  required. 

If  a  precision  of  i'  is  sufficient  for  each  correction,  as  is  ordinarily  the  case  at  sea,  an  hour  angle  within  3'" 
will  suffice  for  A;   C  and  D  may  be  neglected  and  B  used  only  when  the  altitude  exceeds  47"^. 

Example.    June  11,  1879,  fiom  an  observed  altitude  of  Polaris  the  true  altitude  was  found  to  be  29^  5'  55' 
The  time  noted  by  a  Greenwich  chronometer  was  13''  41'"  46**;   chro.  corr.,  —  2'"  22^;   Long.  5''  25™  42^ 

Chro.  time,  13''  41"'  26^  ^'s  app.  R.  A.,        i''  14'"    4^ 

Chro.  corr.,  —  2     22  Dec,  88^  39'  47" 

Gr.  m.  t.,  June  11,         13    39       4 
Long.  W.,  —     5    25     42 


.-/; 


L.  m.  1 

t-, 

8 

13 

22 

k   = 

290 

S' 

^S" 

Sid.  t.. 

Gr.  c 

'", 

S 

17 

49 

A, 

Table 

28, 

+ 

I 

19 

42 

.8 

Red.  for  13I' 

39"', 

+ 

2 

15 

B, 

Table 

28, 

+ 

0 

.2 

L.  sid. 

time. 

13 

r, 

26 

c. 

Table 

28, 

0 

.0 

*'sR. 

A., 

I 

14 

4 

D,  Table 
Latitude, 

28, 

+ 

30^ 

25' 

12 

50" 

•9 

/ 

12 

19 

22 

•9 

= 

— 

II 

40 

3« 

7.— BY  T^'O  ALTITUDES  "WITH  THE  ELAPSED  TIME.t 

Art>  288.  Altitudes  of  the  Sun. — When,  by  reason  of  clouds,  or  other  causes,  the  meridian  altitude  has 
been  lost,  the  latitude  may  be  found  with  sufficient  accuracy  by  two  altitudes  of  the  sun  taken  at  any  time  of  day, 
the  interval  or  elapsed  time  being  measured  by  a  good  watch  or  chronometer. 

The  observed  altitudes  must  he  reduced  as  usual  to  true  altitudes,  and  if  the  ship  has  changed  her  position 
between  the  two  observations,  a  correction  must  be  applied  to  the  first  altitude  to  reduce  it  to  what  it  would  have 
been  if  observed  at  the  second  position.  This  is  usually  called  the  correction  foi-  the  rim  of  the  ship,  and  is  found 
as  follows  : 

The  azimuth  of  the  sun  should  be  observed  at  the  time  of  each  observation.     Enter  the  Traverse  Table  with 


*  If  the  altitude  is  greater  than  60°,  this  correction  may  be  found  by  taking  that  for  45°  and  multiplying  it  by  the  tangent  of 
altitude  ;  adding,  ifdesirable,  the  second  term  in  the  expression  for  B,  viz  :  -f  o".oo76  sin*  t  tan*  h. 
t Commonly  called  "Double  Altitudes." 


the  altitude 


120 


LATITUDE. 


the  angle  between  the  azimuth  at  the  first  observation  and  the  ship's  course  made  good,  as  a  course,  and  the  dis 
tance  run  in  the  interval  as  a  distance;  the  corresponding  difference  of  latitude  will  be  the  correction  to  be  added 
to  the  first  altitude  when  the  above  angle  is  less  than  eight  points ;  to  be  subtracted  when  it  is  greater. 

The  declination  to  be  used  is  that  at  the  middle  time  between  the  observations,  and  the  latitude  is  found  by  the 
following  formulae : 

Cosec  A  =  sec  r/ cosec  ^  To.  (To.  =  elapsed  time.) 
Cosec  B  =  cosec  d  cos  A 

Sin  C  =  cos  y^  {/t  -\-  hi)  sin  ^  (/^  —  hi)  cosec  A 
Sec  Z  =  cosec  ^  {h  +  hi)  sec  ^  {h  ■ —  hi)  cos  A  cos  C. 
Sin  Lat  =  cos  C  sin  (B  +  Z) 

If  the  declination  varies  sufficiently  the  latitude  found  by  these  formulae  should  be  corrected  for  the  change. 
This  correction  is  found  by  the  formula;, 

Corr.  L  =  A  '^  sin  C  sec  L  sin  J4  To. 

in  which  A  '/  =  one-half  the  increase  of  the  sun's  declination  between  the  observations :  positive  when  the  sun  is 
moving  northward. 

When  the  second  altittcde  is  the  greater,  apply  this  correction  to  the  computed  latitude  as  a  itortking -wh^n  the 
sun  is  moving  towards  the  north;   as  a  southing  when  the  sun  is  moving  towards  the  south. 

When  \he.  first  altitude  is  the  greater,  apply  the  correction  as  n.  southing  when  the  sun  is  moving  towards  the 
north,  as  a  northing  when  the  sun  is  moving  towards  the  south 

In  case  the  Navigator  chooses  to  neglect  this  correction,  the  mean  declination  should  be  Ksed  only  when  the 
middle  time  is  nearer  to  noon  than  the  time  of  the  greater  altitude.  In  all  otheV  cases  the  declination  for  the  time 
of  the  greater  altitude  should  be  used. 

The  following  is  a  convenient  logarithmic  form  for  computing  the  latitude  by  these  formulae : 


Col. 
*}2  elapsed  time, 
Declination, 

1. 

cosec 
sec 

A, 

cosec 

Half  sum  alts.. 

cos 

Half  diff.  alts.. 

sin 

c. 

sin 

[Z  less  than  90°  north  or  south, 
like  the  bearing  of  zenith.] 


Col.  2. 


Col.  3. 


cos 

B 

Z 

B  +  Z 

Latitude 

cosec 
cos 

cosec 

cosec 

sec 
cos 

[B  less  than  90^,  like 
declination  N.  or  S.] 

cos 

sec 

sin 

sin 

Example.    At  sea,  October  28,  1879,  p.  m. ;  course,  N.  E.  |^  E.  ;   Lat.,  by  account  at  time  of  last  observa-  '' 
tion,  48°  N.  ;   Long.,  45°  W.  ;   observed  two  altitudes  of  the  sun   for  latilude,  noting  the  times  by  a  Greenwich 
chronometer;   corrected  times  and  altitudes  given  below.     Required,  the  latitude  at  the  time  of  last  observation. 


Gr.  m.  t., 

3" 

31"'  40S 

{h)       =    28-  9'  30" 

d 

= 

-   '.3^ 

9' 

0" 

Gr.  m.  t.. 

5 
2 

58    20 
26    40 

//,          =     15    8  40 
Az.        =     S.   130  W. 

di 
d. 

z 

-  13 

II 

3 

To.            = 

—   13 

10 

1-5 

y^  To.    == 

I 

13    20 

Az,         =     S.  49°  W. 

A 

d 

^ 

I 

1-5 

= 

18^ 

20'    0" 

Distance  run  =  22  miles. 

Course,      N.  4^  pts. 

E. 

Az.        —  S.     I       pts. 

W. 

Diff,    _  =  i2>^  pts.  :  —  16  —  i2>^  =  3>^. 
Corr.  in  Lat.  column,  =:  —  17' 

(A)  =  28--     9' 


d            =  — 

18°  20^    0^' 
13    10      I 

21    30    35 
6    21    55 

1.78888 

9-52735 
0.50232 

0.17487 

1-99342- 

cose 
sec 

cose 

cos 

sin 

sin 
-  Corr. 

>c  0.50232 
0.01157 

h 

cos      9.97861 
cosec  0.43573 
sec      0.00269 

cos      9.97386 

B 

Z 

B  +  Z 

L 

Corr  L 

Latitude 

27     52    30 

=  —  13°  50'  V^" 

=  -|-  66      0   42 

:=             52      10         2 

=    +    48        2     42 
=    +                  I      38 

cosec  0.64247 

A 

y^{h^hi).= 

c  0.51389 
9.96865 
9.04481 

cos      9.97861 
cosec  0.62108 

c 

9-52735 
L  =  98^' 

cos      9.97386 

log  Art' 

sec      0.39089 

sin       9.89752 

cosec  )4  To. 
sec  L 

sin       9.87138 

iui; 

48°      4'  20'-' 

Or  enter  column  j).  in.  Tiil)le  44  willi  the  whole  elapsed  time. 


LATITUDE. 


121 


Art.  CSO.    Longitude. — Having  found  the  latitude,  the  middle  hour-angle  between  the  observations  may 
be  fount!  by  llic  formula 

sin  C 


sni  to  = f" 

cos  L 


and  thence  tlic  longitude. 

In  tl  e  preceding  example 


log  sin  C  9.5273s 
log  cos  L  9.82490 


to                            = 
Eq.  t.  (N.  A.),  - 

2I1         I'll        AS 

16       6  .4 

log  sin 

9.70245 

L.  m.  t.. 

Mid.  (Jr.  m.  t., 

I    44     58 
4    45       0 

Long., 


+ 


45°  o''  3°''''  approximate. 


Since  the  sun  was  near  the  prime  vertical  at  the  time  of  the  last  observation,  the  longitude  could  be  more 
accurately  determined  from  the  hour-angle  found  by  the  method  explained  in  Art.  263,  Chap.  VI. 

Ex.AMPLE.  At  sea,  December  22,  1879;  course,  N.  E.  by  E.  3^^  E.  ;  9  knots  per  hour;  Lat.,  by  account, 
49^'  17'  N.  ;  Long.,  60^^  \V.  at  time  of  last  observation  ;  observed  two  altitudes  of  the  sun  for  latitude,  noting  the 
times  by  a  Cireenwich  chronometer ;   corrected  times  and  altitudes  given  below : 


I 


( ir.  m.  t., 
Gr.  m.  t.. 
To. 
]4  To. 


2'' 

0" 

1    qS 

(/O 

5 

40 

0 

/h 

3 

40 

0 

Az. 

I 

50 

0 

Az, 

=  27°  30'    o' 


13"  24'        d  =        —       23^-  27'   15" 

14     12  Dist.  run  =  36  miles 

S.  28°  E.         Course  =  N.  134,'  points  E. 

S.  24^  E.         Az.  =  S.   2'/  points  E. 

Diff.  =  1 1 34:  pts.  :  16  —  1 1 34:  =  4X 


Corr.  in  Lat.  column,  = 

h 


y^To. 

270  30' 

d            =±  — 

23   27 

A 

K(/'+/^i)  = 

13  36 

'A  {h  -  //,)  =     - 

0    36 

c 

cosec  0.33559 
sec      0.03745 

cosec  0.37304  cos  9.95705 

CCS      9.98765  cosec  0.62867 

sin       8.02002  sec  0.00002 

sin       8.38071  cos  9.99987 

sec  0.58561 

log  sin  C    8.38071 
log  cos  L  9.81810 


—  24' 

I30  24' 
,30 

cosec  0.40009 
cos   9-95705 


B 


=  —  26^ 


=  +  74    57 


B  +  Z   =  -  48     53 

L  =48     52  N. 


cosec   0.35714 
COS       9.99987 

sin        9.S7701 


sin        9.S7688 


to 
Eq.  t. 


I,,  m.  t.,  Dec.  21, 
(ir.  m.  t.,  Dec.  22, 
Long.  =     + 


oil 

8"' 

22*^ 

•4 

I 

II 

8 

0 

9 

34 

.2 

23 

50 

25 

.8 

3 

5« 

0 

59' 

59 
53' 

34 

2 

1  ' 

Alt.  290 

1. 

log  sin       8.56261 


W. 

Douwe's  method,  using  Chativcnefs  formula  as  a  siibstitutc. 

This  short  method  of  obtaining  the  latitude  from  two  altitudes  of  the  sun  may  be  employed  when  the  interval 
between  the  observations  is  not  more  than  i'',  and  when  one  observation  is  taken  within  i''  from  the  meridian. 

An  assumed  latitude  being  employed,  this  method  involves  the  great  objection  that  the  computation  must  be 
repeated  when  the  assvimed  latitude  is  much  in  error,  and  the  operation  repeated  until  the  resulting  latitude 
approximates  closely  to  the  latitude  employed. 

Lr  case  the  observations  are  not  taken  within  the  limils  mentioned,  the  resulting  latitut 
in  error  than  the  assumed  latitude,  and  the  result  by  recomputation  differ  still  more  widely 


e  may  be  more  widely 
This  method  consists  in  finding  to,  the  middle  hour-angle,  by  using  an  approximate  latitude,  and  then  tlie 


latitude  from  the  greater  altitude  and  its  computed  hour-angle 

Let  h  and  //]  be  the  true  altitudes  ; 

d,  the  declination  at  the  middle  time ; 

T  and  Tj,  the  chronometer  times; 

^  and  /),  the  hour-angles. 

By  reducing  T  and  Ti  to  apparent  time,  there  can  be  found 
near  enough. 

To 
then,  t\ 

Let  L' 

to 
or  to 


the  value  of  To.,  the  elapsed  a])parent  time,  ox 


=  T,  -  T 

=  t    +  To. 

=  assumed  latitude, 

=  niiildle  time ; 

=  t  -^  ]A  To. 


Thence  there  may  be  derived  the  following  formula;: 

cos  %  {h  +  /^i)  sin 
cos  L'  cos  </  sin 


sin  to 


{h- 
To. 


/'O 


/=  to 


To., 


122  LATITUDE. 

and  the  reduction  of  h  to  the  meridian  altitude  hm,  by 

.     ,/  /  r            J-.       cos  L'  cos  d sin*  54  / 
sin  y,  {Jim  —  h)  = ^?_ 

cos  )4  V""  -r  ") 

Then,  having  the  value  of  (Am  —  /i),  by  adding  it  to  the  value  of  A  the  meridian  altitude  is  obtained  from 
which  the  latitude  is  found  in  the  usual  manner. 

Example.  At  sea,  1879,  September  10,  a.  m.,  in  Lat.  25°  10'  N.,  Long.  20°  30'  W.,  by  account,  observed 
two  altitudes  of  the  sun  for  latitude,  the  corrected  times  and  altitudes  being  as  follows : 


Gr.  m.  t., 
Gr.  m.  t., 

September 
September 

9. 
10, 

2  711  22'"  25^ 
0     27       ID 

/i 
L' 

A.) 

=z 

+ 
+ 

55^ 
66 

61 

5 
4 

25 

37'  48" 
26  48 

To.        = 
>^To.  = 

I      4    45 
32    22.5 

80    5'    38" 

2   18 
24  30 
59  26 

ID       0 

z 

— 

20 
90 

10  34 
0     0 

yU-A^) 

— ' 

61° 

2f 

18'' 

log  cos 

9.68505 

= 



5 

24 

30 

log  sin 

8.97429  « 

U 

r= 

+ 

25 

10 

0 

log  sec 

0.04332 

d 



+ 

4 

59 

26 

log  .sec 

0.00165 

/zTo. 

= 

8 

5 

38 

log  cosec 

0.85143 

to 

= 



21 

4 

18 

log  sin 

9-55574'' 

t' 

12 

58 

40 

y^' 

=^ 



6 

29 

20 

Yz  {Am^-h,) 

=: 

68 

8 

7 

Yz  {Am -A,) 

= 

I 

46 

19 

Am  —  A\ 

^^ 

-7 

32 

38 

A, 

= 

+ 

66 

26 

48 

1st  approx.  Am 

69 

59 

26 

z 

20 

0 

34 

d 



+ 

4 

59 

26 

vVpprox.  L  =  25      o   00  N. 

Second  appyoximatiou  : 


K(^'- 

A 

0 

■z=. 

61° 

2^ 

18^' 

%[l'- 

A 

) 

=zz 

— 

5 

24 

30 

w 

=IZ 

+ 

25 

0 

00 

d 

= 

+ 

4 

59 

26 

Y2  To. 

— 

8 

5 

38 

to 

—- 

— 

21 

2 

28 

t' 

12 

56 

SO 

Vzl' 

== 

— 

6 

28 

25 

y.  {All, 

+ 

/'O 



68 

13 

7 

y,  {Am 



/'.) 

I 

46 

21 

Am  —  // 

■= 

3 

32 

42 

A, 

I 

» 

+ 

66 

26 

48 

(2d)  //;/ 

69 

59 

30 

2 

20 

0 

30 

d 

+ 

4 

59 

26 

L 

24 

59 

56  N. 

Am 

:z^ 

69 

^  59'  26'' 

h, 

:, 

66 

26   48 

Am  +  A, 

36 

26    14 

Yz  {hmAr 

/<,)  = 

68 

13     7 

log  cos 

9.68505 

log  sin 

8.97429  n 

log  sec 

0.04272 

log  sec 

0.00165 

log  cosec 

0.85143 

log  .sin         9.55514  « 


69    49  26 


log  cos    9.95668 
log  cos    9.99835 


log  sin^  8.10624 
log  sec    0.42897 


log  sin     8.49024 


log  cos      9.95728 
log  cos      9.99835 


log  sin2      8.10420 
log  sec      0.43055 


log  sin       8.49038 


LATITUDE. 


123 


Example.  Same  as  preceding  one,  solved  by  the  first  method. 


^To 


8°    5^  38^^ 
+  4    59    26 


cosec  0.85143 
sec      0.00165 


A, 


(//-//,)    = 


61      2    i{ 
5    24   3^ 


C, 


cosec  0.85308  cos      9.99568 

cos     9.68505  cosec  0.05802 

sin      8.97429  sec      0.00194 

sin      9.5124I  cos      9.97569 


cosec     1.06052 
cos        9-99568 


B 


-|-    5°    2'  26''''       cosec     1.05620 


cos        9-97569 


l\d\\\  I ''.08 
sin  C, 

cosec  ^  To, 
sec  L, 


30^^73  log     1.4876 

9-5124 
0.8514 
0.0427 


sec      0.03133 


Z 

B  +  Z 


=  +  21    30    15 


-|-  26    32    41  sin         9.65024 


CorrL=;  —  78''''.4,  log         1.8941 


to                                           = 
Eq.  t                          ■       = 

—  ih  24m    8^8 

—  31-3 

H.A. 

L.  m.  t.,  .September  9, 
Gr.  m.  t.,  September  9, 

—       I    27     10. 1 

22  32     50 

23  54    47 

L  =       24    59   45  N. 

Corr.  L^  —  118 

Lat.       =        24    58    27 

log  sin  C      9.51242 
log  cos  L     9.95736 


sin         9.62589 


Long., 


I     21     57 


log  sin  to      9.55506 


20°  29'  15^^  W. 


Art.  29 1.  By  two  Altitudes  of  a  Fixed  Star. — In  this  case  the  angle  To  is  the  elapsed  sidereal  time;  the 
declination  is  the  same  at  both  observations.  The  elapsed  mean  time  must  be  reduced  to  the  equivalent  sidereal 
time  interval,  and  the  solution  accomplished  by  using  the  formulie  of  the  first  method. 

Example.  At  sea.  May  31,  1879,  p.  m.,  Lat.  30''  10'  N.,  Long.  60^'  W.,  by  account,  observed  two  altitudes 
of  Spica  for  latitude ;  the  corrected  times  and  altitudes  being  as  follows  : 


Cr.  ni.  t.,  M: 

Interval, 
Red.  to  sid. 

.y3i,                     12" 
14 

30'"    o« 
0       0 

//    =            48'^  47' 30" 
Ih  =            44    58  30 

,/    =     —     10    32     4 

I 
lime,               + 

30      0 
15 

To 
>^To 

=              22° 
=              II 

30     15 

33'   45' 
16    52 

1 

>^To 
d 

— 

11°  16'  52^^        cosec  0.70859 
—  10    32      4            sec     0.00738 

cosec  0.73796 

A, 

.) 

= 

46    53      0 
I    54   30 

cosec  0.71597 
cos     9.83473 
sin      8.52244 

cos      9.99182 
cosec  0.13^70 
sec     0.00024 
cos      9.99693 

B         =  _  10°  44^  13'^ 

cos      9.99182 

y^{h^h 

cosec  0.72978 

yz{h~h 

c, 

sin      9.07314 

cos     9.99693 

sec 

0.12569 

2          =  +  41    31    15 

E  +  Z  =  +  30   47      2 

L         =       30   32    38 

sin      9.70910 

sin      9.70603 

Art.  993.    By  two  altitudes  of  the  same  object,  or  of  different  objects,  the  declinations  being  different. 

As  has  been  already  shown,  the  value  of  To,  the  elapsed  time,  in  case  of  the  sun,  is  the  elapsed  apparent  time ; 
in  case  of  a  star,  the  elapsed  sidereal  time. 

In  the  case  of  the  moon,  or  a  planet,  it  is  equal  to  the  elapsed  sidereal  time  diminished  by  the  increase  of  the 
right  ascension  in  the  inten<al. 

When  two  bodies  are  observed  at  different  times,  add  to  the  sidereal  interval  the  right  ascension  of  the  body 
first  observed,  and  subtract  from  the  sum  the  right  ascension  of  the  other  body  to  find  the  value  of  To. 

When  two  bodies  are  observed  at  the  same  time,  To  is  equal  to  the  difference  of  their  right  ascensions. 

The  observed  altitudes  should  be  reduced  to  true  altitudes ;  watch  times  to  chronometer  times,  and  the  differ- 
ence of  the  chronometer  times  corrected  for  the  rate  in  the  interval,  and  reduced  to  a  sidereal  interval  when  the 
altitudes  of  two  different  bodies  have  been  observed. 

When  the  latitude  only  is  to  be  found,  the  (Ireenwich  mean  times  of  the  ol)servations  are  wanted  only  with 
sufficient  exactness  for  finding  the  right  ascensions  and  declinations  of  the  V^odies.  If  the  longitude  is  also  to  be 
found,  the  Greenwich  times  should  be  noted  accurately.     The  azimutli  should  also  be  noted  for  each  observation. 

This  method,  like  W\<i  first,  requires  only  tl.e  use  of  Fable  44;  and  the  words  sine,  eosiin',  &.C.,  are  written  for 


124 


LATITUDE. 


log  sine,  log  cosine,  &c.     The  logarithms  are  arranged  in  these  columns  as  in  the  first  method,  according  to  the  fol- 
lowing formula,  which  ought  to  lie  written  down  before  the  calculation  is  commenced ;   this  will  simplify  the  opera- 
tion, and  may  prevent  mistakes.     In  this  formula  it  is  said  that  C  is  of  the  same  aff'cction  as  B;   the  meaning  of 
which  is,  that  if  B  is  less  than  90^^,  C  also  is  less  than  90'^  ;   and  if  B  is  greate}-  than  90°,  C  also  is  greater  than  90^ 
Likewise  A  is  of  the  same  affection  as  the  hour  angle  To.,  meaning  that  if  the  hour  angle  is  less  than  6  hours  or  90° 
A  will  be  less  than  90'^ ;  and  if  the  hour  angle  exceed  6  hours,  the  angle  A  will  exceed  90°. 


Col.  I. 

Hour  angle  H  [     p.  M.], 
Dec.  <^/[at  gr.  alt.]. 


A  [diff.  name  from  d], 
Dec.  di  [at  least  alt.], 
B, 
C, 


sec 
tan 

tan 


Col.  2. 


Col. 


sin 


A[sameaff.  asH],    cosec 


cosec 


Least  altitude, 

Greatest  altitude, 

Sum,  3  last  num., 

yi  sum, 

^  s.  —  g.  alt.  =^  rem., 

.Sum  of  4  logs, 

%7., 


sec 


cos 
sin 


sin 


2) 


cos 


C  [same  aff.  as  B],  cosine 


G, 

I, 

Dec.  r/i, 
K, 


sm 

cotan 
tan 


tan 


cos 


cosec 


cotan 


Z, 
G, 


[F  less  than  900,  diff. 
name  from  B.] 


sin 


[at  least  alt.] 


[I  less  than  90^],    sec 
[I  named  as  G], 

sin 


sin 


Latitude. 


[Z  named  N.  or  S.,  like  the  bearing  of  the  zenith.] 


RULE. 


1.  Find  the  hour  angle  To.,    and  take  out  the  corresponding  secant,  which  put  in  Col.  i ,  and  its  tangent  in  Col.  3. 

2.  Take  the  declination  d,  corresponding  to  the  greatest  altitude  h,  place  its  tangent  in  Col.  i,  its  sine  in  Col.  2. 

3.  The  sum  of  the  two  logarithms  in  Col.  i  (rejecting  10  in  the  index)  is  the  tangent  of  the  angle  A,  which  is 
less  than  90^  if  the  hour  angle  is  less  than  6  hours  (or  90^)  but  greater  than  90°  if  the  hour  angle  is  greater  than 
6  hours.  This  angle  is  to  be  marked  }iorth  or  south,  with  a  different  name  from  the  declination  (/,  at  the  greatest 
altitude.     The  cosecant  of  A  is  to  be  placed  in  Col.  2,  its  cosine  in  Col.  3. 

4.  Place  the  declination  (/],  corresponding  to  the  least  altitude  h,  below  the  angle  A,  and  if  they  are  of  the  same 
name,  take  their  su;n,  but  if  of  different  names,  take  their  difference,  and  call  this  sum,  or  difference,  the  angle  B, 
making  it  north  or  south,  like  the  greatest  of  the  two  quantities  A,  D.  The  cosine  of  B  is  to  be  placed  in  Col.  2, 
its  cosecant  in  Col.  3. 

5.  The  sum  of  the  three  logarithms  in  Col.  3  (rejecting  20  in  the  index)  is  the  cotangent  of  an  angle  F  (less 
than  90"^),  which  is  to  be  taken  out  and  marked  north  or  south^  with  a  different  name  from  B. 

6.  The  sum  of  the  three  logarithms  in  Col.  2  (^rejecting  20  in  the  index)  is  the  cosine  of  the  angle  C,  which  is 
to  be  taken  less  than  90°  if  B  is  less  than  90^,  but  greater  than  90°  if  B  is  greater  than  90^.  The  angle  C,  and  its 
cosecant,  are  to  be  placed  in  Col.  i. 

7.  Place  the  altitudes  below  C,  take  the  half  sum  of  these  three  quantities,  subtract  the  greatest  altitude  from 
the  half-sum,  and  note  the  remainder.  Place  the  secant  of  the  least  altitude  in  Col.  I,  its  cotangent  in  Col.  2,  its 
sine  in  Col.  3;  the  cosine  of  the  half-sum  in  Col.  i,  and  the  sine  of  the  remainder  m  Col.  i.  The  sum  of  the  four 
last  logarithms  of  Col.  i  (rejecting  20  in  the  index)  being  divided  by  2,  gives  the  sine  of  an  acute  angle,  which, 
being  found  and  doubled,  gives  the  zenith  angle  Z,  which  is  to  be  nained  north  if  the  zenith  and  north  pole  are  on 
the  same  side  of  the  arc  or  great  circle,  passing  through  the  two  objects  (or  the  two  observed  places  of  the  same 
object),  but  south  if  the  zenith  and  south  pole  are  on  the  same  side  of  that  great  circle.* 

8.  Take  the  siitn  of  the  angles  Z  and  F,  if  they  are  of  the  same  name,  but  their  difference  if  o{ different  names  ; 
this  sum  or  difference  is  ihe  angle  G,  to  be  marked  7iorth  or  south,  like  the  greatest  of  the  angles  Z,  Ft  The  sine 
of  G  is  to  be  placed  in  Col.  2. 

9.  The  sum  of  the  two  lower  logarithms  of  Col.  2  (rejecting  10  in  the  index)  is  the  tangent  of  an  angle  I,  which 
is  to  be  taken  out  (less  than  90*^)  and  marked  north  or  sotith  like  G.     The  secant  of  I  is  to  be  placed  in  Col.  3. 

10.  Write  the  declination  di,  corresponding  to  the  least  altitude  below  I,  take  their  su!>t  if  of  the  same  names, 
their  difference  if  oi  dffe rent  na.mes.  This  sum  or  difference  is  the  angle  K,  of  the  same  name  as  the  greater  of 
these  two  quantities.     The  sine  of  K  is  to  be  placed  in  Col.  3. 

*  This  case  occurs  also  in  the  first  and  second  methods  of  solution,  and  it  must  be  determined  on  the  spot  by  the  situation  of 
the  objects.  In  double  altitudes  of  the  sun,  moon,  or  planets,  when  the  elapsed  time  is  not  very  great,  the  angle  Z  is  generally 
to  be  marked  with  the  bearing  of  the  zenith  from  the  observed  object,  when  at  its  greatest  altitude  on  the  meridian,  which,  in 
north  latitudes,  without  the  tropics,  is  in  general  iiortli :  in  south  latitudes,  without  the  tropics,  south.  Sometimes,  when  the  sun 
passes  the  meridian  near  the  zenith,  it  may  be  doubtful  whether  the  zenith  be  >iorth  or  soutli  ;  in  which  case  the  problem  may  be 
solved  for  (^(jM  cases  (which  increases  the  labor  but  little),  and  that  one  of  the  two  computed  latitudes  selected  which  agrees 
best  with  the  ship's  reckoning;  but  it  is  generally  safest  not  to  use  observations  of  this  kind,  which  are  generally  liable  to  great 
errors  from  small  mistakes  in  the  altitudes. 

+  If  the  sum  be  taken  to  find  G,  and  it  exceed  180°,  subtract  it  from  360°,  and  call  the  remainder  G,  with  a  different  nam» 
from  Z  or  F". 


LATITUDE. 


125 


II.  The  sum  of  the  three  last  logarithms  in  Col.  3,  rejecting  20  in  the  index,  is  the  sine  of  the  required  latitude, 
of  the  sanio  name  as  K. 

EXA.Mri.K.  tiiven  the  sun's  correct  central  altitutle  41^-'  ;^^',  and  his  declination  14"  N.  After  an  interval  of 
jh  ^o'",  by  watch,  his  correct  central  altitude  was  50"^  and  his  declination  13  58'  N.  Required  the  latitude,  the 
sun  being  south  of  the  observer  when  on  the  meridian. 


To 


Col.  I. 

22°  30'       sec      10.03438 
13    58  N.   tan       9-39569 


A[difT.name  froma?],  15    04  S.    tan       9.43007 

c'l  =  14    00  N. 

B, 


I    04  S. 


21    49        cosec  10.42988 


/i  = 

Sum  = 

l4  sum      = 


Col.  2, 

sin        9.38266 
A  [same  aff.  as  To],  cosec  10.58512 


cos 


9.99992 


C  [same  aff.  as  B],  cos        9.96770 
G, 


COL.  3. 

tan  9.61722 

cos  9.98481 

cosec  1 1. 73012 


F,     2°4o'N.  cotan    11.33215 


Z,   57    18  N.  [Flessthnngo'^ 
diff  name  from 


//  :=  rem. 


41  33 

50  00 

113  22 

56  41 

6  41 


sec      10.12588 

'l, 
'A, 
cos       9-73978    J^. 

1 

sin        9.06589  , 


sin         9-93738    C,  59    58  N.     B.] 

cotan  10.05243  sin     9.82169 


44^  20'  N. 


tan        9.98981    [I  less  than  90'-'.]  sec  10.14552 
L  I  named  as  CI.] 


14    00  N.  [at  least  alt.] 

Latitude, 


58    20  N. 


sni     9.92999 


52    7  N. 


sin    9  89720 


Sum  4  logs. 


2)19.56143 


28    39        sin        9.68071 


57     18  N.   [named  like  bearing  of  zenith.] 


P  If  the  latitude  had  been  south,  Z,  instead  of  being  57-  18'  nori/i,  would  be  57*^  18'  south;  G  =  54°  38'  S., 

"  T  =:  42'^  37'  S.,  K  =  28-  37'  S.,  and  the  latitude  25°  34'  S.  The  labor  of  making  this  extra  calculation  is  but 
little,  and  where  any  doubt  exists  of  the  iiaiiic  of  Z,  it  is  best  to  make  the  computation  both  ways  ;  this,  however, 
will  rarely  happen.  The  calculations  of  this  example,  and  most  of  the  following  ones,  are  made  to  the  nearest 
minute ;  where  great  accuracy  is  required  it  will  be  proper  to  take  the  logarithms  and  angles  corresponding  to 
seconds. 

Example.  Given  the  moon's  correct  central  altitude,  47"^  37';  the  moon's  declination,  17"^  29'  S.  ;  the  sun's 
correct  central  altitude  at  the  same  time,  27^^  22' ;  the  sun's  declination  8"^  28'  S.  ;  the  hour- angle,  or  difference  of 
right  ascensions  of  the  sun  and  moon,  5'^  40™  28^,  or  85^  7' ;  required  the  latitude,  supposing  it  to  be  north. 


To 


COL.    I. 

85^ 


sec 


17    29  S.  tan 
A  [diff  name  from  d'\,     74    53 N.  tan 


11.06993 
9.49828 

10.56821 


d, 
B, 
C, 


8    28  S. 


66    25  N. 


I 


82    51      cosec  10.00339 


\ 


hx 

27 

22 

sec 

k               = 

47 

37 

Sum            =r 

157 

50 

}4  Sum    = 

78 

55 

cos 

'2  s.  —  gr.  alt.  = 

=  rem. 

>  31 

18 

sin 

Sum  of  4  logs, 

K  z.. 

>9 

40 

sin 

z., 

39 

20  N.  [n 

10.05155 


9.28384 

9.71560 


2)19-05438 


9.52719 


COL.  2. 

sin       9.47774 
A[sameaff.asTo.],  cosec  10.01529  ; 

cos       9.60215  I 


CUL.   3. 

tan  11.06835 

cos  9.41628 

cosec  10.03788 


C  [same aff.  as  B],     cos       9.0951S    F,   16*^43' S.  cotan   10.52251 
G, 


Z,  39   20  N.  [F    less    tha  > 
90°,  diff.  name 


sin        9.58497    G,  22   37  iN.    from  B.  ] 
cotan  10.28599 


sin      9.66246 


I. 

K, 


36^^  37' N.  tan       9.87096    [I  less  than  90°]  sec  10.09548 
8    28  S.  [at  least  alt.]       [I  named  as  G.] 
28    09  N.  j  sin     9.67374 


Latitude,   15°  41' N.         sin     9.43168 


39    20  N.  [named  like  the  bearing  of  zenith]. 


126 


LATITUDE. 


If  the  zenith  had  been  south  of  the  great  circle  passing  through  the  objects,  we  should  have  Z  =  39°  20'  S , 
G  =  56°  3'  S.,  I  =  58°  2'  S.,  K  =  66°  30'  S.,  and  the  latitude  52^  46'  S. 

Example.  Given  the  moon's  correct  central  altitude,  47°  37' ;  the  declination,  17^29'  S. ;  the  right  ascen-j 
sion,  13''  56'"  39^6,  and,  at  an  interval  of  58'"  54^  of  mean  time,  the  moon's  correct  central  altitude,  37°  38'  22";] 
the  declination,  17°  40'  52"  S. ;   the  right  ascension,  13''  58'"  59^6;  required  the  latitude.  ' 


Elapsed  mean  time, 
Red.  to  sid.  time, 

Elapsed  sid.  time. 
Increase  in  R.  .V., 

To.  = 


58"'  54B 

+          9-7 

1st  R.  A., 
2d  R.  A., 

Increase, 

I3h  56'"  39^6 
13     58     59-6 

59      4 
2    20 

2     20.0 

56    44 
140  11' 

To. 

=        .40 
=  —  17 

II'    0" 
29     0 

sec 
tan 

tan 
cose 

0.01344 
9.49828 

A 

■=  +17 
=  —  17 

59  52 
40  52 

9-51172 

^1 

B 

=   4- 

ig     0 

C 

=          13 

31     0 

:  0.6^129 

h 
S. 

K  S.-  //  : 


z. 


37^  38' 22"  sec     0.10135 
47    37    o 


98    46  22 

49     23    II      cos       r. 81355 
I     46   1 1      sin       S. 48971 


2)19-03590 


+  19    14  36     sin      0.5-795 
38    29   12 


sm      9-47774 
cosec  0.51007 

cos   9.99999 


tan   9.40266 
cos   9.97821 

cosec  2.25752 


C, 


G, 


cos      9.98780 


sin      9.781 16 
cot      0.1 1 283 


I    =  +  38°    4'  32"  tan      9.89399 
./i  =  —  17    40    52 


K  =  +  20    23   40 


F 


i^'  19'    2"  cot       1.63839 


Z    =  +  38    29   12 
G 


+  37    10  10 


I, 


sin      9.78582 
sec      0.1 039 1 

sin      9.54218 


I 


Lat.     =   1 5°  41'  4"  N. 


sm      94319' 


The  latitude  may  be  found  from  two  altitudes  of  the  moon  by  the  first  method  when  the  elapsed  time  does  not 
;.xc  ed  i'',  provided  the  correction  due  to  tlie  change  of  declination  in  the  interval  is  applied  to  the  resulting  latitude. 
EXAMPLp;.     Same  as  the  preceding,  in  which  the  elapsed  time  or  To.  =  56'"  44*^. 


><To  =  7      3., 

'^  =  —  1 7    34    56 


5'  v," 


cosec  0.90851 
.Ncc      0.02078 


I 
I 


A 

^  (//  +  //,)  = 


y^{^h-h{)= 


A  d 


Corr.  I^        = 


42       T,l      41 

4    59    19 


356 


cosec  0.92929 
cos  9.86674 
sin       8.93931 


s^i"       9-73534 


log 

log  sin  C 

log  cosec  y^  To. 

log  sec  L 


cos  9.99697 
cosec  0.16926 
>-ec      0.00165 

cos      9.92392 


B 


;cc       0.09180  Z 


1625"  log 


2.55145 
9-73534 
0.90851 
0.01554 

3.21084 


1;  +  Z  = 


cosec 

0.51989 

cos 

9.99697 

^  -  ^r 

42' 

cosec 

0.51686 

CCS 

9.92392 

=  +35 

57 

20 

=        18 

14 

47 

sin 
sin 

9.49569 

=        15 

14 

9 

9.41961 

=  + 

27 

5 

Lat.        =        15    41    14  N. 


The  latitude  may  be  found  from  two  altitudes  by  Sumner's  method,  which  will  be  described  hereafter. 


LONGITUDE.  127 

CHAPTER   VIII. 

LONGITUDE. 

Art*  293.  The  longitude  of  a  position  on  the  earth's  surface  is  the  arc  of  the  equator  intercepted  between  the 
priiitc  vuridian  anil  the  meridian  passing  througli  the  place,  or  the  angle  at  the  pole  between  those  two  meridians. 

Meridians  are  great  circles  of  the  sphere  passing  through  the  poles,  and  consequently  are  secondaries  of  the 
equator. 

The  prime  meridian  is  that  one  assumed  as  the  origin,  passing  through  the  location  of  some  principal  observ- 
atory, such  as  Greenwich,  Paris,  or  Washington.  That  of  Greenwich  is  the  prime  meridian  for  English  and 
American  Navigators. 

Secondary  meridians  are  those  connected  with  the  primary  meridian,  directly  or  indirectly,  by  exchange  of 
telegraphic  time  signals. 

Tertiary  meridians  are  those  connected  with  secondaries  by  carrying  time  in  the  most  careful  manner  with  all 
the  corrections  which  can  be  devised. 

Longitudes  at  sea  are  determined  by  computing  the  hour  angle  from  the  altitude  of  a  celestial  object  measured 
with  the  sextant,  and  comparing  the  resulting  local  time  with  the  Greenwich  time  given  by  the  chronometer. 

TELEGRAPHIC  DETERMINATION  OF  SECONDARY  MERIDIANS. 

Art*  294.  In  order  to  locate  with  any  degree  of  accuracy  the  positions  of  prominent  points  on  the  coasts, 
it  is  necessary  to  refer  them,  by  chronometric  measurements,  to  secondary  meridians  of  longitude  which  have  been 
determined  with  the  utmost  degree  of  care  and  accuracy. 

Before  the  establishment  of  telegraphic  cables  this  was  attempted  principally  through  the  observation  of  moon 
culminations,  which  seemed  always  to  carry  witia  them  unavoidable  errors,  or  by  transporting  to  and  fro  a  large 
number  of  chronometers  between  the  principal  observatory  and  the  position  to  be  located;  and  in  tiiis  method  it 
can  readily  be  conceived  that  errors  would  naturally  be  involved,  no  matter  how  great  the  skill  or  how  thorough 
the  theoretical  compensation  for  error  of  the  instruments. 

But  by  the  aid  of  the  electric  telegraph  differences  of  longitude  have  been  determined  to  the  utmost  degree  of 
accuracy,  and  gradually  secondary  meridional  positions  are  l^eing  established  over  the  world,  to  afford  the  necessary 
bases  in  carrying  on  the  Surveys  to  map  correctly  the  various  coast  lines,  and  to  give  publication  to  reliable  and 
accurate  Navigators'  charts. 

Al"!.  295.  The  method  of  determining  telegraphically  the  difference  of  longitude  between  two  points  as 
generally  practiced  is  as  follows : 

A  small  observatory  containing  a  transit  instrument,  chronograph,  break-circuit  chronometer,  and  a  set  of 
telegraph  instruments,  is  established  at  each  of  the  two  points,  and,  being  connected  by  a  temporary  wire  with  the 
cable  or  land  line  at  each  place,  the  two  observatories  are  placed  in  telegraphic  communication  with  each  other. 

By  means  of  transit  observations  of  stars  the  error  of  the  chronometer  at  each  place  on  local  time  is  well 
determined,  and  on  the  same  night  the  faces  of  the  chronometers  and  their  difference  precisely  ascertained  by 
signals  sent  first  one  way  and  then  the  other,  the  times  of  sending  and  receiving  being  very  exactly  noted  at  the 
respective  stations.  The  errors  of  the  chronometers  on  local  time  at  each  place  being  applied  to  their  difference, 
as  shown  by  the  time  signals,  gives  the  difference  between  the  local  times  of  the  two  places,  and  consequently  their 
difference  of  longitude.  The  time  of  transmission  over  the  telegraph  line  is  eliminated  by  sending  signals  both 
ways. 

ESTABLISHMENT  OF  TERTIARY  MERIDIANS. 

Art.  296.  Let  it  be  supposed  that  the  meridional  distance  between  A  and  B  is  to  be  measured,  of  which  A 
is  a  seeondaiy  meridional  position  accurately  determined,  and  B  a  tertiary  meridional  position  to  be  determined. 

At  least  two  sets  of  equal  aliitudes  should  be  taken  at  A  to  ascertain  the  errors  and  rates  of  the  chronometers. 
The  run  is  then  made  to  B,  and  equal  altitudes  taken  to  determine  local  time  and  hence  the  difference  of  longitude; 
and  on  the  same  spot  circum-meridional  altitudes  of  the  sun,  or  of  a  number  of  pairs  of  stars,  or  both,  should  be 
taken  to  determine  the  latitude. 

Now,  if  chronometer  rates  could  be  relied  on  to  be  uniform,  this  measurement  would  suffice,  but  since,  owing 
to  vibration,  changes  of  temperature,  &c  ,  variations  arise,  the  run  back  to  A  should  be  made  or  to  another 
secondary  meridional  position  C,  and  there  new  rates  obtained.  The  errors  of  the  chronometers  on  the  day  when 
the  observations  were  made  at  the  tertiary  position  should  be  corrected  for  the  loss  or  gain  in  rate  and  for  the  dif- 
ference of  the  errors  (on  the  return  to  the  secondary  position  A,  or  on  the  arrival  at  the  other  secondary  position 
C)  as  carried  down  through  the  rates  so  corrected  and  as  actually  observed. 

Art.  297.    Alethod  of  correcting  errors  carried  daivn  by  unifor?n  rates  for  change  of  rate* 

At  a  station,  A,  a  chronometer  was  rated  by  equal  altitudes  on — 

May  27,  with  an  error  slow,      i''    7'"  18^.98 
Jure  3,  with  an  error  slow,        i      7     12    75 

Difference,  6  .23 

Daily  rate,  gaining,  o  .89 

The  ship  left  A  on  June  3  and  made  a  run  to  station  B  for  astronomical  observations ;  thence  back  t>)  A  on 
July  3  to  re-rate  the  chronometer. 

July  3,  with  an  error  slow,  i''     7'"    0^^.75 

July  10,  with  an  error  slow,  i      6     59  .84 


\ 


Difference,  o  .91 

Daily  rate,  gaining,  0.13 


*H.  O.  Pamphlet,  No.  36. 


128 


LONGITUDE. 


The  rate  obtained  by  the  first  set  of  observations  is  the  average  rate  for  the  week  ending  June  3,  and  may  beJ 
assumed  as  the  rate  on  May  30''  12''.  | 

The  rate  obtained  by  the  second  set  of  observations  is  the  average  rate  for  tlie  week  ending  July  10,  and  may 
be  assumed  as  the  rate  on  July  6''  12''. 

The  chronometer  has  been  steadily  losing  on  its  rate;   the  true  rate  is  represented  by  the  arithmetical  pro- 
gression : 

—  0.89 —0.13, 

for  the  39  daily  rates  between  May  30*^  12'^  and  July  6'*  la^^. 
Designating  by — 

a,  the  least  term  of  the  progression ; 

z,  the  greatest  term ; 

n,  the  number  of  terms ; 

d,  the  common  difference  (daily  loss  on  the  rate); 

s,  the  sum  of  the  terms. 


The  daily  loss  is  then — 


d  := and  j  =  («  4-  z)  — 

0.89  —  0.13  0.76 


39 


38 


0^02 


and  the  errors  of  the  chronometer  would  consequently  be  those  in  Col.  3  of  the  Table  below ;   in  which  Col.  2] 
gives  the  errors  by  the  initial  rate. 

The  rate  on  May  30'*  12''  being  —  o'^.Zq,  that  on  June  3,  allowing  for  the  accumulated  rate,  will  be 

0^.89  —  (o^02  X  3X)  =  0^.82. 


Date. 

Error  by  initial 
rate  at  A. 

Correction  for  accumulated  rate. 

Final  correction  for  diff.  of 
error  as  brought  back  to 
A  and  observed  sea-rate. 

—   0.89 

—  0 .  82 

June    3,  slow. 

I'l  7'"  i2\  75 

jh  yni    ,2^.  75 

—  (0.  82  —  0.  02)  =  —  0  .  80 

i''   7'"  i2-\  75 

4 

II  .86 

II  .95 

—    0.78 

+  o^  1 1 

12  .  06 

5 

10.97 

11  .17 

—    0.  76 

0.  22 

11.39 

6 

10.08 

10  .41 
—   0.74 

0.33 

10.74 

7 

9.19 

9.67 
—    0  .  72 

0.44 

10  .  II 

8 

8.30 

8.95 
—    0.  70 

0.55 

9.50 

9 

7.41 

8   25 
—  0.68 

0.66 

8.91 

10 

6.52 

7-57 
—  0.66 

0.77 

8.34 

II 

5.63 

6.91 
—  0.64 

0.88 

7-79 

12 

4-74 

6  .27 
—  0 .  62 

0.99 

7.26 

13 

3.85 

—  0 .  60 

I  .  10 

6.75 

14 

2  .96 

5 .  05 
—  0.58 

I  .21 

6.26 

IS 

2  .07 

4.47 
—  0.56 

1.32 

5-79 

16 

I.  18 

3-91 

—  0.54 

1.43 

5.34 

17 

0 .  29 

3-37 
—  0.52 

1-54 

4.91 

18 

I     6    59  .  40 

2.85 
—  0 .  50 

^.65 

4.50 

19 

58.51 

2.35 
—  0.48 

1.76 

4. II 

20 

57.62 

1.87 
—  0.46 

1.87 

3-74 

21 

56.73 

1. 41 
—  0.44 

1  .98 

3-39 

22 

55-84 

0.97 
—  0.42 

2  .09 

3.06 

23 

1 

54.95 

0-55 

2  .20 

2.75 

I.ONGITUDE. 

Table  of  Corrections — Continued. 


129 


f 

Error  by  initial 
rate  at  A. 

Final  correction  for  diflf.  of 

Date. 

Correction  for  accumulated  rate. 

error  as  hiouglit  hack  to 
A  and  observed  sea-rate. 

—  0  .40 

June  24 

54^  06 

0.15 
—  0.38 

2«.3I 

2^46 

25 

53-17 

6">  59 .  77 
—  0.36 

2.42 

2.19 

26 

52.28 

59-41 
—  0.34 

2-53 

1-94 

27 

51-39 

59-07 
—  0.32 

2  .64 

I.  71 

28 

50.50 

58.75 
—  0.30 

2.75 

1.50 

29 

49.61 

58.45 
—  0  .28 

2.86 

I-31 

30 

48.72 

58.17 
—  0.26 

2-97 

I.  14 

July      I 

47-83 

57-91 
—  0 .  24 

3.08 

0.99 

2 

46-94 

57-67 
—  0.22 

3-19 

0.86 

3 

46.05 
—    0.89 

57-45 
—  0 .  20 

3-30 

0.75 

The  formula  {a  -f-  2)  '  will  serve  to  test  the  correctness  of  the  figures.     The  daily  rates  between  June  3  and 

July  3  are 

—  0.80 —  0.22 ;  30  in  number. 

Their  sum  S,  —  (0.80  -4-  0.22)  ^  =  —  1.02  x  15  =  —  15.30- 


Error  June  3, 


jh   ym   12S.75 
15-30 

I    6    57.45 


Upon  returning  to  A,  the  error  as  deduced  from  the  error  at  starting  and  the  accumulated  rates 

should  have  been i''  6"'  57^-45 

But  it  i)r()ved  by  observation  to  be i     7       0.75 


A  difference  of 


+ 


J  -J*- 


Which  resulted  from  such  disturbing  influences  as  vibrations  from  the  motion  of  the  ship  at  sea  and  from  changes 
of  leniperature,  &c.  This  difference  may  properly,  therefore,  be  calied  the  sea-error,  and  its  daily  proportion  the 
sca-ralc.     This  difference  should  Ije  equally  distributed  through  all  the  days  of  the  run,  as  shown  in  Cols.  4  and  5. 

Had  the  vessel  arrived  at  the  tertiary  meridional  piosition  B,  on  June  20,  for  astronomical  observa- 
tions, I  he  error  on  that  date  by  correction  for  initial  rate i''  6"'  57^.62 

And  by  correction  for  accumulateii  rate i     7       i  .87 

And  finally  by  correction  due  to  sea  rate i     7       3-74 

In  case  the  vessel  had  started  from  A  without  a  rate,  and  not  rated  after  returning,  using  the  errors  by 
observations  on  June  3  and  July  3  for  rating,  the  rate  would  have  been — 

Error  by  observation  on  June  3,  slow,     i'^  7""  12^.75 
Error  by  observation  on  July  3,  slow,      i    7      0.75 


Daily  rate, 


o  .40 


This  would  have  given  for  June  20  an  error  of  i""  7'"  12^.75  —  (17  +  0^4)  ^ i*' 

While,  by  ihe  better  method  of  rating  before  and  after  the  run,  and  correcting  for  accumulated  rate 
.  nd  difference  of  errors,  it  proved  to  be i 


Differing 


5'-95 
3.21 

2  .21 


LONGITUDE  AT  SEA. 

Art.  29S*  By  Chronometer. — The  process  of  determining  the  longitude  at  sea  consists  in  comparing  the 
local  mean  time  with  the  Creenwich  time  at  the  same  instant.  The  Greenwich  time  is  found  from  the  chronom- 
eter, which  has  previously  been  regulated  and  its  error  and  rate  tabulated.  The  daily  ra-e  being  properly 
applied  according  to  its  sign  or  name,  the  Greenwich  time  can  be  known  at  any  instant. 

9  ^ 


130 


LONGITUDE. 


The  local  time  is  found  by  measuring  the  altitude  of  a  celestial  body  above  the  sea  horizon  with  the  sextant> 
finding  the  hour-angle  of  the  body  by  the  method  described  in  Chap.  VI,  Arts.  260-264,  and  thence  lie  local  time, 
which  is  compared  with  the  Greenwich  chronometer  time  of  the  instant  of  observation.  The  difference  of  these 
limes  is  the  longitude,  which  is  Ttt-j-/ when  the  G;eenwich  time  is  the  greater  and  east  when  it  is  the  lesser. 

As  has  been  already  stated,  the  most  favorable  position  of  the  celestial  body  for  finding  the  hour-angle  from 
its  altitude  is  when  nearest  the  prime  vertical,  provided  the  altitude  is  not  so  small  as  to  be  seriously  affected  by 
refraction. 

In  determining  the  longitude  at  sea  from  a.  m.  or  p.  m.  observations  of  the  sun,  it  is  necessary  to  employ  the 
latitude  by  account,  carried  back  from  the  meridian  observation  for  latitude  for  an  a.  m.  observation  or  forward  for 
a  p.  m.  observation,  making  due  allowance  for  current  if  sailing  in  one  that  is  sufficiently  well  known  to  estimate 
its  rate.     The  longitude  thus  determined  is  reduced  ior  the  run  to  noon. 

In  determining  the  longitude  from  night  observations  the  latitude  employed  is  that  by  account  from  the  pre- 
ceding noon  and  recorded  for  the  time  of  observation.  ■^« 

h'-XAMi'LE.    At  sea,  May  18,  1879,  a.  m.  ;   Lat.  41"^  25'  N.;   Long.  33^30'  W  ,  l)y  1).  R.  from  preceding  noon^j 
the  following  altitudes  of  the  sun's  lower  limb  were  observed ;   the  times  noted  by  a  watch  compared  with  the 


Greenwich  chronometer. 
17  feet.  ;  C  — W.,  2''  17" 

Watch  times. 


Mean, 
C  —  W, 

Chro.  t., 
Chro.  corr. 


Chro.  corr., +4'"  59^2;   I.  C,  —  i'  10";   Bar.,  30'". 32  ;  Thei.  ,59°;  height  of  the  eye, 


+ 


7h 

20"'  15= 

20  47 

21  14 

Mean, 
Corr., 

/i 
d 

+ 
=  + 

290 

> 

35 
46 

30" 

20 

10 

I.e., 

Dip, 
S.  D., 
r, 
par., 

Corr., 

A.) 

+ 
+ 
+ 

I' 

4 

15 

I 

9 

10' 
2 

51 

42 
8 

5 

7 
2 

20    45-3 
17      6 

29 

29 
19 

41 
9 

50 
30 

0 

5 

5 

46  (N 

9 

37    51 -3 

4    59-2 

Or.  m.  t.,  May  17,      21     42     50.5         Eq.  t. 


3"'  47^.9  ( —  from  app.  t.) 


At  noon,  May  18,  the  latitude  by  meridian  altitude  was  found  to  be  41"  40'  N.  ;  the  run  of  the  ship  from 
'/'  30"^  a.  m.,  E.  N.  E.  (true),  18  miles. 

Traverse  Table,  for  course  E.  N.  E.,  dist.  18;  D.  L.  =  6'.9  N.  ;  Dep.  =  i6'.6  E. ;  D.  Lo.=  22'.i4E 
Hence,  the  Lat.  by  ace.  at  7'^  30'"  was  41^^  33'. 


h 
L 
A 

=  29 
=^   41 

=   70 

50' 

33 

29 

5" 
0 

14 

log  sec 
log  cosec 

log  cos 
log  sin 

0.12588 
0.02569 

141 

52 

19 

s 
s—h 

=   70 
=  41 

1 

9 

5 

9.51406 
9.81782 

2)19.48345 


L.  app.  time  =       i^  32"!  7^2         log  sin  y^,  t.  9.74172 


L.  app.  t. 
Eq.  t. 


7'i  32'"    7*'.  2 
3    47-9 


L.  m.  t..  May  17,  19     28     19.3 

Or.  m.  t.,  21     42     50.5 


Long. 

D.  Lo. 

Long,  at  noon, 


-}-     2     14    31  .2 

33°  37'   48"  W. 
—  22     14 


33     15     34  W. 


Art.  399.  By  Ciraim-mcridian  Altitudes. \ — When  solving  the  problem  to  determine  the  "Latitude  from 
two  altitudes  near  noon  when  the  time  is  not  known".  Chap  VII,  Art.  2S1,  the  longitude  may  be  approximately 
found  by  the  following 

Rule.  Employing  the  same  altitudes  that  have  been  used  to  find  the  latitude,  divide  one- fourth  the  difference 
of  the  altitudes  (in  seconds)  Dy  the  product  of  the  change  of  altitude  in  one  minute  (Table  26)  and  one-half  the 
chronometer  interval  (in  minutes);  the  quotient  is  the  number  of  minutes  from  noon  of  the  mean  instant  between 
the  two  observations,  and  it  will  represent  a  time  before  or  after  noon,  according  as  the  second  altitude  is  greater  or 
le  s  than  the  first  altitude. 

Applying  the  equation  of  time  to  this  interval  will  give  the  local  mean  time,  to  be  compared  with  the  Green- 
wich chronometer  time  to  find  the  longitude. 

FORMULA. 

For  latitude,  ,^^  ^  %  {h' ^  h")  +  ar^  +  i-Y.  U^' -h'')-? 


at''' 


For  longitude. 


to  ■ 


y^{h'-h") 


at 


*  Instead  of  taking  the  hour-angle  from  Tal)le  44  corresponding  to  the  log  sin  J^  t.,  the  local  app.  time  is  taken  directly  from 
the  column  a.  m.,  and  so  for  all  a.  m.  observations  of  the  sun. 
t  ( '.hauvcuet. 


LONGITUDE. 


131 


Exam{*le.    The  approximate  latitude  being  38  ■  N. ;  tiie  declination  at  noon,  1°  J.8'  9".S. ;  ih*.  ci|.  ol  lime,  8" 
55'  -f  to  app.  time;  ciiro.  corr  ,  +  27'"  zi"*;  heiglit  of  the  eye,  19  feet.     To  find  the  latitude  and  longitude. 


T' 
T' 


—  8''    o"'  22^5 

=  8    10     13.5 

9     51 

=  4    55-5 


To.  =  S     5     18 

Chro.  corr.    ^      +  2721 


Table  27,  /"- 

Table  26,  a 

at- 


=  24.2 

=  2.4 

58" 


Gr    m.  t. 


L.  ni.  t.  = 


8    32     39 
o      6    49 


{'A  ill'- 1'")  Y  = 


at 


625 


Long,  =      +     8    25     50  Eq.  t. 

=  126*-^  27'  30"  W.    L.  m.  t. 


h' 
h' 


=        50*^^  10'    o" 
=        50    II   40 


h'  —  h"         =  - 

A{h'-h")  =  - 

I  40 

25 

^  (/,'  +  /,")  ^     50  10  50 

rt/«  =  58 


625 

58 


II 


—  2'"   6*5 

hi 

=    50 

II  59 

+  8  55 

Dip 
S.D. 

=  + 

4  16 
16  6 

6  49 

h 
z 

d 

Lat. 

par. 

=^  — 

42 

> 

=    50 

23  7 

=  +  39 

36  53 
48  9 

=    37 

48  44  N, 

Art.  300a  Littrcni<'s  method  bv  cimtni-iiicridian  altitudes. — Two  altitudes  of  the  sun's  limb  are  taken  near 
the  meridian  with  a  chronometer  interval  which  may  vary  from  5"'  to  30"'  or  40'",  according  to  the  latitude,  the 
interval  being  made  longer  in  high  latitudes.  Deduce  the  true  altitudes  of  the  sun's  centre  and  find  the  half-sum 
and  the  half-difference;  also  fncl  the  half-sum  and  the  half-difference  of  the  chronometer  times  of  the  two  obser- 
vations. Take  the  sun's  declination  for  the  Greenwich  time  corresponding  to  the  half-sum  of  the  chronometer 
limes,  /.  <•.,  for  the  middle  instant  between  the  two  observations,  and  bring  up  the  latitude  by  account  to  the  same 
instant. 

The  apparent  time  from  noon  at  the  mean  of  the  chronometer  times  is  then  found  by  the  following  formula: 


Sin>^(T  +  T.)  = 


sin  ><  {h  —  h{)  cos  %,  {h -\- h{) 
sin  Yz  (T —  Ti)  cos  L  cos  d 


This  time  ^  (T-j-Tj)  is  biforc  or  after  noon,  according  as  the  second  altitude  '\'^  greater  ox  less  than  the  first. 

Ri'i.E.  Add  togetlicr  the  log  cosecant  of  the  half  chronometer  interval,  the  log  sine  of  the  hall-difl'erence  of 
the  altitudes,  the  log  c  sine  of  the  half-sum  of  the  altitudes,  the  log  secant  of  the  latitude  and  the  log  secant  of 
ihe  declinition. 

In  using  Table  44  enter  the  column  p.  m.  with  the  whole  chronometer  interval  to  find  the  log  cosec  y^  (T  —  Ti), 
and  by  entering  the  column  sine  with  the  sum  of  the  logarithms  take  out  from  the  p.  m.  column  the  number  of 
hours,  minutes,  and  seconds,  one-half  of  which  is  the  required  apparent  time  from  noon. 


Example. 
taken : 


May  II,    1879,   Lat.   15'^  30'  N.,   Long.  71^  W.,  by  account,  the  following  observations  were 


Chronometer. 
4^  41™  30^ 


\ 


Mid.  chro.  t., 
Chro.  ccrr., 

Gr.  m.  t..  May  11, 


K  (h  -  /', ) 

L 

d 

>^(T  +  TO 
Eq.t. 

L.  m.  t. 
Gr.  m.  t. 


5  " 

ID 

4  56 
3 

20 
40 

h 

h  +  /^, 

d 
Eq.  t. 


True  altitudes     0 
:=     870  16'    o" 
=     81     18   30 


=  168    34   30 
=       5    57   30 

=  I70  54'45"N. 

=  3"'  48'*  ( —  from  app.  time). 


14" 

2'^ 
84 
15 
17 


+ 


58'  45" 

17    15 
30     o 

54  45 

2o"i      18 

3    48 


log  cosec 
log  sin 
log  cos 
log  sec 
log  sec 


I. 18925 
8.71577 
8.99797 
0.01609 
0.02158 


log  sin       8.94066 


16™  13S 
o      o 


Long. 


=  +    4   43     47 
=        70''^  56'  45  w. 


132 


LONGITUDE. 


taken 


Example.  November  13,  1879,  Lai.  150  30'  N.,  Long.  60°  45'  E.  by  account,  the  following  observations  were 


November  12, 


Mid.  chro.  time, 
Chro.  C(  rr., 

Gr.  m.  t.,  November  12, 


;^(T-T,)  = 

L  = 

d  =* 

Eq.  t.  = 


+ 


L.  m.  t. 
Gr.  m.  t. 

Long. 


Chron6meter. 

True  altitudes     © 

19b  33, 

"  20^ 

h 

= 

56°  33'  45" 

20 

13 

40 

h 

+  /n 

55    30     0 

19 

53 

30 

112     3  45 

2 

36 

h 
d 

-Ih 

I      3  45 

19 

56 

6 

17'' 54' 45" 

V. 

1-t. 

= 

15"'  38"  (— frt 

20'" 

10^ 

lo^r 

cjsec 

;    1.05611 

0'^ 

31' 

52" 

log 

sin 

796703 

56 

I 

52 

log 

cos 

9.7  720 

1.5 

30 

0 

log 

sec 

0.01609 

17 

54 

45 

log 

sec 

0.02158 

14"' 

44f  p.  m. 

log 

sin 

8.80801 

IS 

38 

=        23  •>  59">  06s 
19   56      6 


4     3    00 
600  45'         E. 


Art.  301.    Navigators  should  be  exceedingly  cautious  in  the  use  of  this  method.     It  should  not  be  relied' 

on  when  the  altitude  of  the  sun  is  less  than  80'-"',  ^\hich  restricts  it  to  tropical  navigation  when  the  sun  passes  near 
the  zenith.  The  interval  between  the  observations  should  be  at  least  as  great  as  half  an  hour.  The  limits  of  its 
use  can  be  easily  inferred  from  the  following  table,  in  which  the  error  of  time  corresponding  to  an  error  of  one 
minute  in  each  of  the  observed  altitudes*  for  all  zenith  distances  from  4-  to  50'^',  and  for  the  interval  of  30"'  (  f 
time  between  the  observations  is  given.  For  other  intervals  of  time  between  the  observations  the  error  is  inversely 
proportional  to  the  interval,  so  that  for  25"'  it  is  20  per  cent,  more  than  that  of  the  t-able,  for  20™  it  is  50  per  cent, 
more,  and  for  15'"  it  is  twice  as  great  as  that  of  the  table;  whereas,  on  the  contrary,  for  35'"  it  is  14  per  cent,  less 
than  the  tr.ble,  for  40'"  it  is  25  per  cent,  less,  for  50"'  it  is  40  per  cent,  less,  for  55'"  it  is  45  per  cent,  less  than  the 
table,  and  for  60'"  it  is  one-h.alf  that  of  the  table  Hence,  each  observer  can  ascertain  in  each  case  the  degree  of 
approximation  of  his  time  obtained  by  this  method;  and  the  trustworthy  navigator  will  allow  a  wide  margin  of 
possible  error.  Thus,  in  the  second  example  the  number  given  by  the  table  is  36^^,  which  is  to  be  diminished  25 
per  cent.,  because  the  interval  is  40'",  which  leaves  27^  as  the  error,  which  correspoucs  to  an  error  of  2'  in  the 
difference  of  the  observed  altitudes. 

In  order  to  facilitate  the  comparison  of  this  method  with  the  usual  method  of  finding  the  time  by  observations 
near  the  prime  verticsl,  the  following  table  has  been  computed  of  the  errors  in  that  method,  which  correspond  to 
an  error  of  one  mile  in  the  assumed  latitude,  and  to  the  observed  bearing  of  the  sun  during  the  observation  from 
the  east  cr  west  point  of  the  horizon.     This  bearing  needs  only  to  be  roughly  observed  to  the  nearest  half  point. 

Table  shmviiig  the  error  0/  iinte  in  Liiirtnv''s  method,  lohieh  iiuiy  correspond  to  an  error  of  one  ininnte  in  each  of  thi 
obse>~L'ed  altitudes  lolien  the  interval  of  time  l>etween  the  ohsei~i'alio)is  is  thirty  minutes. 


N    o 

s 


4 

5 
6 

7 
8 

9 

10 

II 
12 

13 

14 

15 
16 


When  the  latitude 
between  the  sun' 
zenith  distance. 


is  the  difference 
s  declination  and 


When  the  latitude  is  the  sum  of  the  sun's 
declination  and  zeni.h  distance. 


25 

20^ 

s. 

s. 

5-0 
6.3 

4-7 
5-9 

7-4 
8.6 

7.0 

8.1 

9.8 

9-3 

II.  0 

10.4 

12.  I 

"•5 

13-3 

12.6 

14.4 

13-7 

\n 

14.7 
15.8 

17.7 
18.8 

16. 9 
18.0 

15°      10 


s. 

4.5 
5-6 
6.7 
7.8 
8.9 
9-9 

II. o 

12.  I 

13.  2 
14.2 

15-3 
16.4 

17.4 


Declination  of  the  sun. 


s. 

4.4 

5-4 

6.5 
7.6 

8.6 

9-7 
10.8 
II. 8 
12.9 
14.0 
15.0 

16.  I 

17.  2 


50 

0° 

50 

s. 

s. 

s. 

4.2 

4.2 

4-3 

n 

u 

6.5 

u 

u 

7.6 
8.8 

9.7 

9-7 

9-9 

10. 7 

10.8 

II. 0 

II. 8 

II. 9 

12.2 

12.8 

13.0 

13-3 

13-9 

14. 1 

14-5 

15.0 
16.  I 
17.2 

15-2 

16.4 
17.6 

16.9 
18.  I 

10^ 


s. 
4-5 

6.7 

7-9 

9-1 

10.3 

"•5 
12.  7 

13-9 
15-2 
16.4 
17.7 
19.  o 


I 


15° 

20° 

s. 

s. 

4.7 

5-0 

5-9 

6.3 

7-1 

7.6 

«.3 

8.9 

9.6 

10.2 

10.8 

II. 6 

12.  I 

13.0 

13-4 

14-5 

14.8 

15-9 

16.  I 

17.4 

17-5 

19.0 

18.9 

20.  5 

20.3 

22. 2 

25'^ 


s. 

5-4 
6.8 

8.2 

9-7 
II. 2 
12.  7 

14-3 
15-9 
17.6 

19-3 
21.0 
22.8 
24.  6 


*The  errors  of  altitude  are  assumed  to  be  in  opposite  directions,  so  as  to  make  an  error  of  one  miniite  in  the  half-difference 
of  the  altitudes. 


LONGITUDE. 

Table  shmuing  the  error  of  time  in  Littnnu^s  method,  ^'e. — Continued. 


138 


1 

n— 1 

When 

the  latitude  is  the  difference        ^^.,        ,     ,    •     ,    .    ,. 

mm  of  tl 

le  sun's 

The  sun's  zenith  ( 
tance. 

between  tne  suns 
zeniih  distance. 

ciecnnaiion  ana                 ,     ,-      • 

and  zeni 

th  distance. 

Declination  of  the  sun. 

25^ 

20° 

15^ 

J. 

5° 

0° 

50 

10° 

15° 

20° 

s. 

25° 

J". 

s. 

J. 

s.  • 

s. 

s. 

'  J. 

s. 

S  , 

17 

19.9 

19.0 

1S.5 

IS.  3 

18.3 

18.7 

19.3     20.3 

21.8 

23.8 

26.5 

i8 

20.9 

20. 1 

19.6 

19.4 

19.4 

19.9 

20.6  i  21.  7 

23-3 

25-5 

28,  5 

19 

22.  I 

21.  2 

20.  7 

20.  5 

20.6 

21.0 

21.8     23.1 

24.  8 

27.  2 

3«-5 

20 

23-  I 

22.  2 

21.7 

21.5 

21.  7 

22.2 

23. 1     24.  5 

26.4 

29.0 

32.6 

21 

24.2 

23-3 

22.8 

22.6 

.  22.9 

23-4 

24.4     25.9 

28.0 

30-9 

34-8 

22 

25-3 

24.4 

23-9 

23.8 

24.0 

24.7 

25.8     27.4 

29.7 

32.8 

37- 0 

23 

26.4 

25-4 

25.0 

24.9 

25.2 

26.0 

27. 1     28.9 

31-4 

^\'l 

39-4  1 

24 

27.4 

26.  5 

2O.  0 

26.0 

26.4 

T.'J.I 

28.  5     30. 4 

33-1 

36.8 

41.8  j 

25 

28.  5 

27.6 

27.1 

27.1 

27.6 

28.5 

29.9     32.0 

34-9 

38.9 

44-3 

26     29. 6 

28.7 

28.2 

28.3 

28.8 

29.8 

31-4    Zl-^ 

^'%-\ 

41.0 

47.0 

27     30. 6 

29.7 

29.4 

29,4 

30.0 

31- I 

32.8     35-3 

38.6 

43-3 

49.7  1 

28 

31-7 

30.8 

30-5 

30.6 

31-3 

32-5 

34-3     37.0 

40.6 

45.6 

52.6  \ 

29 

32.8 

31-9 

31.6 

31.8 

32.6 

33-9 

35-9     38.7 

42.7 

48.  I 

51-^ 

30 

33-9 

33-  0 

32.8 

33- 0 

33-8 

35-3 

37-4  i  40.5 

44-7 

50.6 

58.8 

31 

34-9 

34-1 

33-9 

34-2 

35-1 

36-7 

39- 0  ,  42.3 

46.9 

53-2 

62. 1 

32 

36.0 

35-2     35- 0 

35-5 

36.5 

38.2 

40.  7  '  44.  2 

49.1 

56.0 

65.6 

33 

37-1 

36. 3     36-  2 

Z^'l 

37-8 

39-7 

42. 4  i  46.  2 

51-5 

58.8 

69-3 

34 

38.2 

37-5     37-4 

38.0 

39-2 

41.2 

44.  I  ,  48.  2 

53-9 

61.9 

73-2 

!     35 

39-3 

38.6 

38.6 

39-3 

40,6 

42.8 

45-  9     50.  3 

56.5 

65.0 

77.3 

1     36 

40.4 

39-^ 

39- S 

40.6 

42.1 

44.4 

47.  8     52.  5 

59-1 

68.3 

81.7 

:    37 

41-5 

40.9     41.  I 

41.9 

43-5 

46.0 

49-  7  '  54-  7 

61.9 

71.9 

86.4 

38 

42.6 

42.1 

42.3 

43-3 

45- 0 

47.7 

51-7     57-1 

64.7 

75-7 

91.4 

39 

43-7 

43-3 

43-6 

44.6 

46.6 

49-5 

53-  7     59-  5 

67.7 

79.6 

96.6 

40 

44.9 

44-5 

44.9 

46.0 

48.  I 

51-3 

55.8  ,  62.  0 

70.9 

83.6 

102.  5 

41 

46.0 

45-7 

46.  2 

47-5 

49-7 

53-1 

57-9     64-7 

74-3 

88.0 

108.7 

42 

47.2 

46.9 

47.5 

49.0 

51-4 

55- 0 

60.  2     67. 4 

77-7 

92.7 

II5-4 

43 

48.3 

^8.2 

48.9 

50-5 

53-1 

57- 0 

62.  5     70. 3 

81.4 

97-7 

122.  7 

44 

49-5 

49-5 

50-3 

52.  0 

54.8 

59- 0 

65-0  ,   73-3 

85.4 

103.0 

130.7 

45 

50-7 

50.7 

51-7 

53-6 

56.6 

61.  I 

67.5      76.5 

89.5 

108.  7 

139.4 

46 

51-9 

';2.o 

53-1 

55-2 

58.5 

63-3 

70.  I      79-  8 

93-9 

115. 0 

148.9 

47 

53-2 

53-4 

54-7 

56.8 

60.4 

65-5 

72.  9     83. 3 

98.6 

121.  7 

159-5 

48 

54-4 

54-7 

56.1 

58.5 

62.3 

67.9 

75.7     87.0 

i"3-5 

129.  0 

171. 4 

49 

55-7 

56.1 

57-6 

60.3 

64.4 

70.3 

78.  8     90.  9 

108. 9 

137.0 

184.6 

50 

57- • 

57-5     59-2 

62.0 

66.5 

72.8 

81.9 

95- 0 

114.  7 

145.6 

199-5 

In  this  case  and  in  the  preceding  one,  if  the  ship  has  changed  her  latitude  between  the  two  ol:)servations,  the 
first  altitude  should  be  corrected  by  adaiug  to  it  the  ship's  change  of  latitude  in  the  inerval  if  the  ship  has  sailed 
tenoard  the  sun,  or  subtracting  it  if  the  ship  has  sailed y'nw/  the  sun. 

LUNAR  DISTANCES. 

Art.  302.  In  order  to  facilitate  the  method  of  determining  the  longitude  from  lunar  distances,  there  is 
published  in  the  Nautical  Almanac,  for  every  third  hour  of  Greenwich  mean  lime,  the  angular  distances  of  the 
centre  of  the  moon  from  the  centre  of  the  sun,  from  the  brightest  planets,  Saturn,  Jupiter,  Mars,  and  Venus,  and 
from  nine  bright  fixed  stars  selected  in  the  path  of  the  moon,  viz:  a  Arietis,  a  Tauri  {A/debaraii),  i3  CJeminorum 
{/W/iix),  a  Leonis  {/\egu/iis),  a  Virginis  {S/iea),  u  Scorpii  (At/tares),  a  Aquilre  {.4 /fair),  u  Piscis  Auslralis(/''(W/(// 
haiit).  and  u  Tcgasi  {Markab). 

All  the  distances  that  can  be  ob-  erved  on  the  same  day  are  grouped  together  under  that  date,  and  the  columns 
are  read  from  left-to  right,  across  both  pages  of  the  same  opening.  The  letter  W.  or  E.  is  affixed  to  the  name  of 
the  sun,  planet,  or  star,  to  indicate  that  it  is  on  the  west  or  east  side  of  the  moon. 

An  observer  on  tlie  surface  of  the  earth  having  measured  a  Lunar  Distance,  corrected  it  for  instrumental 
errors  and  for  the  semidianietcrs  of  the  ol)jects,  and  cleared  it  from  tlie  effects  of  refraction  and  parallax,  finds  tlie 
//v/e?  or  _^(Y)r(';//;7c  distance.  With  this  distance  and  the  distances  in  the  Nautical  Almanac  of  the  same  bodies  on 
the  same  day,  the  Greenwich  mean  time  of  the  observation  can  be  found,  as  will  be  hereafter  described. 

Art.  303.  Could  the  chronometer  he  relied  upon  implicitly  as  a  perfect  piece  of  mechlnism,  no  other 
means  of  determining  the  longitude  at  sea  would  be  necessary.  Since  the  local  time  can  be  determined  with  suffi- 
cient accuracy  by  day  or  by  night,  a  comparison  with  the  (Jreenwich  time  as  given  l)y  a  /nv/ir/ time-keeper  would 
suffice,  l)ut  tlie  chances  of  error  and  accident,  or  ihrou^h  carelessness,  during  a  protracted  voyage,  renders  the 
longitude  by  chronometer  unreliable  at  times.  Through  the  method  of  lunar  distances  the  Greenwich  time  is 
given  with  almost  certainty,  provided  the  Navigator  possesses  average  skill  in  observation  and  in  computing  the 
results. 


134 


LONGITUDE. 


Hence  it  may  be  seen  that  lunars  may  be  used  not  alone  for  findlr.g  the  longitude,  but  as  checks  upon  the    i 
chronometer,  and  should  frequen  ly  be  taken  on  a  long  voyage  for  the  latter  purpose ;  and  l)y  taking  the  mean  of  I 
all  the  results  a  very  reliable  correction  to  the  chronometer  is  ascertained  when  approaching  the  land ;  and  a  toler- 
able raie  may  be  found  by  comparing  the  mean  of  a  number  of  observations  in  the  begini  ing  of  a  voyage  with  a 
similar  mean  in  the  latter  part  of  it. 

The  obscrva/ion  of  the  lunar  distance  is  subject  to  unavoidable  errors  which  are  diminished  by  making  a  num- 
ber of  measurements. 

Errors  of  the  instrument  may  be  diminished  by  measuring  distances  on  opposite  sides  of  the  moon,  when 
possible,  and  combining  the  results. 

Art.  30<]:«  Before  taking  the  observation,  the  Nautical  Almanac  must  be  examined  to  see  from  what 
objects  the  distances  are  computed. 

There  are  only  nine  fixed  stars  and  four  planets  from  which  I  he  angular  distances  are  computed  in  the  Nautical 
Almanac;  and  as  it  is  of  the  greatest  importance  to  be  able  to  discover  them  easily,  we  shall  here  add  a  number  of 
remarks  which  will  be  found  useful  for  that  purpose. 

The  best  way  of  discovering  any  star  or  p'anet  is  by  means  of  a  celestial  globe;  observing  that,  when  a 
planet  is  used,  we  must  estimate  roughly,  by  inspecting  the  Nautical  Almanac,  the  right  ascension  and  declination 
of  the  planet,  and  make  a  mark  on  the  corresponding  point  of  the  globe  with  a  pencil,  or  by  attaching  a  small 
piece  of  moist  paper,  and  this  must  be  considered  as  the  place  of  the  planet.  If  a  globe  cannot  be  obtained,  the 
time  of  passing  the  meridian,  and  the  meridian  altitude  of  the  object,  may  be  calculated;  and  by  observing  at  that 
time,  the  object  may  be  easily  discovered.  The  distances  marked  in  the  Nautical  Almanac  afford  also  to  the 
observer  an  easy  method  of  knowing  the  star  or  planet  f.om  which  the  moon's  distance  is  to  be  observed;  for  he 
has  nothing  to  do  but  to  set  the  sextant  or  circle  to  the  distance  computed  roughly  for  the  apparent  time,  esti- 
mated nearly  for  the  meridian  of  Greenwich,  and  direct  his  sight  to  the  east  or  west  of  the  moon,  according  as  the 
object  is  marked  E.  or  W.  in  the  Nautical  Almanac;  and,  having  found  the  reflected  image  of  the  moon  upon  the 
horizon  glass,  sweep  the  instrument  to  the  right  or  left,  and  the  image  will  pass  over  the  sought  star  or  planet,  if 
above  the  horizon,  and  the  weather  clear :  the  star  or  planet  is  always  one  of  the  brightest,  and  is  situated  nearly 
in  the  arc  passing  through  the  moon's  centre,  perpendicular  to  the  line  connecting  the  two  horns. 

The  computed  distance  made  use  of  in  sweeping  for  the  star  may  be  found  in  this  manner :  Reckon  the  appa- 
rent time  at  the  ship,  and  to  this  time  apply  the  longitude  turned  into  time,  by  adding  in  west,  or  subtracting  in 
east  longitude;  the  sum  or  difference  will  be  the  apparent  time  at  Greenwich  nearly,  'lake  the  distances  from  the 
Nautical  Almanac  for  the  time  immediately  preceding  and  following  this  estimated  time,  and  note  the  difference  of 
these  distances;  then  say.  As  3'^  or  180'",  is  to  the  difference  of  the  distances,  so  is  the  difference  between  the 
apparent  time  at  Greenwich  and  the  next  preceding  time,  set  down  in  the  Nautical  Almanac,  to  a  proportional  part 
to  be  added  to  the  next  preceding  distance  taken  from  the  Nautical  Almanac,  if  the  distance  be  increasing,  but 
subtracted  if  decreasing;   the  sum  or  difference  will  be  the  distance  at  which  the  quadrant  or  sextant  is  to  be  fixed. 

In  sweeping  for  the  stars  by  this  method,  it  will  often  happen  that  two  or  more  are  swept  upon  at  once;  this 
might  cause  some  difficulty  to  an  inexperienced  observer,  who  would  be  at  a  loss  to  know  which  to  make  use  of. 
To  remove  this,  the  following  description  of  these  stars  is  added : 

a  ARIETIS. 

^1^  This  star  bears  about  west,  distant  23°  from  the  Pleiades,  or  the  Seven  Stars ;  it  is 

^  of  the  second  magnitude,  and  may  be  known  by  means  of  the  star  n,  of  the  third  mag- 

nitude, situated  S.  W.  from  a  Arietis,  at  the  distance  of  3^  degrees.  South  from  the 
star  7r,  at  the  distance  of  1%"-',  is  the  star  v,  of  the  fourth  magnitude.  The  northern- 
most of  these  stars  is  a  Arietis. 


ifTT 


*v 


ALDEBARAN. 


^ 


X 


POLiaJX. 


REGULUS. 
+         ^ 

^  BPgulus, 


^  SPICA. 


About  35^^  E.  S.  E.  from  a  Arietis,  and  14°  S.  E.  from  the  Pleiades,  or  Seven  Stars, 
is  the  bright  star  Aldebaran.  Near  this  star,  to  the  westward,  are  six  or  seven  stars  of 
the  third  or  fourth  magnitude,  forming,  with  Aldebaran,  a  figure  resembling  the  letter 
V,  as  is  represented  in  the  adjoined  figure,  where  Alc'.ebaran  is  marked  a.  At  the  dis- 
tance of  23^  from  this  star,  in  a  S.  E.  direction,  are  three  very  bright  stars,  situated  in 
a  straight  line,  near  to  each  other,  forming  the  belt  of  Orion. 

At  the  distance  of  45°  from  Aldebaran,  in  the  direction  of  E.  N.  E.,  is  the  star 
Pollux,  which  is  a  bright  star,  though  not  of  the  first  magnitude.  N.  W.  from  it,  dis- 
tant 5°,  is  the  star  Castor,  of  nearly  the  same  magnitude;  and  you  will  almost  sweep 
both  at  once:  the  southernmost  is  the  one  used. 


E.  by  S.  }4  S.  from  Pollux,  at  the  distance  of  37j^°,  is  the  star  Regulus,  of  the  first 
magnitude;  to  the  northward  of  this  star  (at  the  distance  of  8°)  is  a  star  of  the  second 
magnitude;  near  to  these  are  five  stars  of  the  third  magnitude,  the  whole  forming  a 
cluster  resembling  a  sickle,  represented  in  the  adjoined  figure,  Regulus  being  in  the 
extremity  of  the  handle.  A  line  drawn  from  the  northern  polar  star,  through  its 
pointers,  passes  about  12*^  to  the  eastward  of  Regulus. 


E.  S.  E.  from  Regulus,  at  the  distance  of  54°,  is  the  star  Spica,  of  the  first  magni- 

m  tude,  with  no  very  brtght  star  near  it;   S.  W.  from  this  star,  at  the  distance  of  about 

<  16*^,  are  five  stars  of  the  third  or  fourth  magnitude,  situated  as  in  the  adjoined  figure; 

+  the  two  northernmost  cf  these  stars,  r/,  v,  form  a  straight  line  with  Spic  i,  and  by  this 

mark  it  n  ay  be  easily  discovered.     A  line  drawn  from  the  'northern  polar  star,  through 

the  middle  star  of  the  tail  of  the  Great  Bear,  will  pass  near  to  Spica. 

■V 


ANTAEES. 


^ 


LONGITUDE.  135 

E.  S.  E.  from  Spica,  at  the  distance  of  46*^,  is  the  star  Antares,  in  26°  of  south 
%  (lechnation ;   it  is  a  remarkable  star,  of  a  reddish  color;  on  each  side  of  it-  to  the  W.  N. 

W.  aad  S.  S.  E.,  about  2    distant,  is  a  star  of  the  third  or  fourtli  magnitude,  no  very 


hni^lit  star  being  near 


aAQVILjE. 

+  N.  E.  from  Antares,  at  the  distance  of  60°,  is  the  very  bright  star  a  Aquilse ;  N.  N. 

W.  from  which,  at  2^  distance,  is  a  star  of  the  third  magnitude,  an<l  S.  S.  E.,  at  3° 
aistance,  another  star  of  a  less  magnitude.  Tlicse  three  stars  appenr  nearly  in  a  straight 
line.     The  star  n  Acjuila-  is  nearly  of  the  same  color  as  Antares. 


* 


rOMALIIAUT. 


S.  E.  from  a  Aquila:,  at  the  distance  of  60'  ,  is  the  star  Fomalhaut.  which  is  a  bright 
star  of  high  southern  declination,  its  altitude  in  northern  latitudes  1  eing  small,  never 
exceeding  20*^  in  the  latitude  of  40^  N.  This  star  bears  nearly  south  f  om  the  star  a 
Pegasi,  distant  45'^.  A  line  drawn  from  the  pointers,  through  the  noillurn  jiolar  star, 
and  continued  to  the  opposite  meridian,  will  pass  very  near  to  a  Pegasi  and  Eomalhaut. 


a  PEGASI. 


^¥: 


a% 


^  E.  by  N.  from  a  Aquilas,  at  the  distance  of  48°,  and  westward  from  a  Arietis,  at 

the  distance  of  44P,  is  the  star  a  Pegasi,  which  may  be  known  by  means  of  four  stars  of 

different  magnitudes,  situated  as  in  the  adjoined  figure;   in  which  a  represents  a.  Pegasi, 

./'Ar  /j  a  star  of  the  second  magnitude,  bearing  north  of  it,  distant  13*-^;   the  others  are  of  less 

nH*  magnitudes,  and  two  of  them,  rj,  n,  form  a  straight  line  with  the  star  a  Pegasi ;   and  by 

this  mark  it  may  easily  be  discovered. 


GENERAL   REMARKS   ON   THE  TAKING  OF  A  LUNAR   OBSERVATION. 


Art.  305.  The  accuracy  of  a  lunar  observation  depends  chiefly  on  the  regulation  of  the  chronometer, 
and  on  the  exact  measurement  of  the  angular  distance  of  the  moon  from  the  sun  or  star;  a  small  error  in  the 
observed  altitudes  of  those  objects  will  not,  in  general,  much  affect  the  result  of  the  calculation. 

The  best  method  cf  regulating  a  chronometer  at  sea  is  by  taking  an  altitude  of  the  sun  when  rising  or  falling 
quickly,  or  when  bearing  nearly  east  or  west,  the  altitude  being  sufficiently  great  to  avoid  the  irregular  refraction 
near  the  horizon,  and  noting  the  time  by  the  chronometer.  With  this  altitude,  the  latitude  of  the  place,  and  the 
sun's  declination,  find  the  mean  time  of  observation  by  either  of  the  preceding  methods ;  the  difference  l)etween 
this  time  and  that  shown  by  the  chronometer  will  show  how  much  it  is  too  fast  or  slow.  A  single  observation, 
taken  with  care,  will  generally  be  exact  enough,  but  if  greater  accuracy  is  required,  the  mean  of  a  number  of 
observations  may  be  taken.  If  the  distance  of  the  sun  and  moon  be  observed  when  the  sun  is  three  or  four  points 
distant  from  the  meridian,  the  mean  time  of  observation  may  be  deduced  from  the  altitude  of  the  sun  taken  at  the 
precise  time  of  measuring  the  distance;  this  will  render  the  use  of  a  chronometer  unnecessary,  and  will  prevent 
any  irregulariry*  in  its  g'ingfrom  affecting  the  result  of  the  observation.  If  a  night  observation  is  to  be  taken, 
the  chronometer  sb.ould  be  regulated  by  an  altitude  of  the  sun  taken  the  preceding  evening,  and  its  going  examined 
by  means  of  another  observation  taken  the  next  morning ;  for  the  time  found  by  an  altitude  of  a  star  cannot  be  so 
well  depended  up.  n,  except  in  the  morning  and  evening  twilight,  as  the  horizon  is  generally  ill  defined ;  but  the 
altitude  may  be  sufficiently  exact  for  finding  the  correction  used  in  determining  the  angular  distance. 

.Mthough  all  the  instruments  used  in  these  observations  ought  to  be  well  adjusted,  yet  particular  care  should 
be  tal.cn  of  the  sextant  or  circle  used  in  measuring  the  angular  distance  of  the  moon  from  the  sun  or  star,  since  an 
error  of  i'  in  this  distance  ■will  cause  an  error  of  nearly  30'  in  the  longitude  deduced  therefrom.  When  a  great  angu- 
lar distance  is  to  1  e  measured,  it  is  absolutely  necessary  to  use  a  telescope,  and  the  parallelism  of  it,  with  respect  to 
the  plane  of  the  instrument,  must  loe  carefully  examined ;  but  in  measuring  small  distances  the  use  of  the  telescope 
is  not  of  such  great  importance,  and  a  sight-tube  may  then  be  used,  taking  care,  however,  that  the  eye  and  point 
of  contact  of  the  objects  on  the  horizon-glass  be  equally  distant  from  the  plane  of  the  instrument.  But  it  ought  to 
be  observed  that  it  is  always  conducive  to  accuracy  to  use  a  telescope,  and,  after  a  little  practice,  it  is  easily  done. 

While  one  person  is  observing  the  distance  of  the  objects,  two  others  ought  to  be  observing  the  altitudes. 
The  chronometer  should  be  placed  near  one  of  the  observers,  or  put  into  the  hands  of  a  fourth  person  appointed  to 
note  the  time  ;  the  observer  who  takes  the  angular  distance  giving  previous  notice  to  the  others  to  be  ready  with 
their  altitudes  by  the  time  he  has  finished  his  observation ;  which  being  done,  the  time,  altitudes,  and  distance! 
should  be  carefully  noted,  and'other  sets  of  observations  taken,  which  must  be  done  within  the  space  of  15  minutes, 
and  the  mean  of  all  these  observations  must  be  taken  and  worked  as  a  single  one.  f 

When  a  ship  is  close-hauled  to  the  wind,  with  a  large  sea,  or  when  sailing  before  the  wind,  and  rolling  con- 
siderably, it  is  difficult  to  measure  the  distance  of  the  objects;  but  when  the  wind  is  enough  upon  the  quarter  to 
keep  the  ship  steady,  there  is  no  difficulty,  especially  in  small  distances,  which  are  much  more  easily  measured 
than  large  ones,  and  are  not  so  liable  to  error  from  an  ill  adjustment  of  the  telescope  ;  an  observer  would  there- 
fore do  well  to  choose  those  times  for  observation  when  the  distance  of  the  objects  is  less  than  70^'  or  80^.  An 
observation  of  the  sun  and  moon  is  generally  much  easier  to  take  when  the  altitude  of  the  moon  is  less  than  that 
of  the  sun,  because  the  instrument  will  be  held  in  a  more  natural  and  easy  manner.  When  the  moon  is  near  the 
zenith,  the  observation  is  generally  difficult  to  take,  and  liable  to  be  erroneous,  because  the  observer  is  forced  to 
place  himself  in  a  disagreeable  posture.  For  the  same  reason  an  observation  of  the  moon  and  a  star  or  planet  is 
generally  much  easier  to  take  when  the  star  or  planet  is  lower  than  the  moon.     This  situation  of  the  objects  may 

*  Jt  is  not  uncommon  to  find  a  difference  in  ttie  regulation  of  a  chronometer  in  the  forenoon  and  afternoon  ;  tliis  difference 
generally  arises  from  the  uncertainty  in  the  estimated  latitude,  or  some  slight  error  in  the  observation,  and  perhaps  partly  from 
the  irregularity  in  the  going  of  the  chronometer. 

t  It  the  distances  are  measured  by  a  circular  instrument,  it  will  not  be  necessary  to  note  the  several  distances  measured,  but 
only  the  times  and  altitudes,  as  the  sum  of  all  the  distances  measured  by  the  circle  will  be  given  by  the  instrument  at  the  end  of 
the  observations ;  and  if  the  altitudes  of  the  objects  are  also  measured  by  circular  instruments,  it  will  not  be  necessary  to  note 
the  several  altitudes,  but  only  the  times  of  observation. 


136  LONGITUDE. 


i 


in  most  cases  be  obtained  by  taking  the  observation  at  a  proper  time  of  the  clay.  But  it  must  be  observed  that 
neither  of  the  olijects,  if  possible,  ought  to  be  at  a  less  altitude  than  lo^,  upon  account  of  the  uncertainty  of  the 
refraction  near  the  horizon,  for  the  horizontal  refraction  varies  from  33'  to  36'  40''  only  by  an  alteration  of  40°  in 
the  thermometer.  This  alteration  might  cause  an  error  of  2^'  in  the  longitude  with  an  observer  who  uses  the  mean 
refraction. 

In  measuring  the  distance  of  the  moon  from  the  sun  we  must  bring  the  moon's  round  limb  in  contact  with  the 
nearest  limb  of  the  sun.  In  measuring  the  distance  of  the  moon  from  a  planet  or  fixed  star  her  round  limb  must 
be  brought  in  contact  with  the  centre  of  the  star  or  planet ;  observing  that,  the  semi-diameter  of  the  planet  being 
only  a  few  seconds,  the  centre  of  it  can  be  estimated  sufficiently  njar  for  all  the  purposes  of  this  observation. 

In  taking  the  altitude  of  the  moon,  the  round  limb,  whether  it  be  the  upper  or  lower,  must  be  brought  to  the 
horizon.     In  damp  weather  it  is  rather  difficult  to  observe  the  altitude  of  the  stars  on  account  of  their  dimness,  par- 
ticularly a  Pegasi  and  a  Arietis.     Sometimes  they  are  so  dim  that  they  cannot  be  seen  through  the  telescope  of  a . 
sextant,  particularly  if  the  mirrors  are  not  well  silvered;    in  this  case  the  telescope  must  be  laid  aside,  and  the 
altitude  must  be  taken  with  a  sight-tube. 

We  have  here  supposed  that  there  were  observers  enough  to  measure  the  altitudes  when  the  distance  was 
observed;  but  if  that  is  not  the  case,  the  a'.titudes  may  be  estimated  by  either  of  the  methods  which  will  he  here- 
after given. 

Art.  306.  To  correct  the  Lunar  Distance. — The  method  here  given  is  that  of  Professor  Chauvenet, 
and  involves  the  use  of  Tables  29  to  36,  inclusive. 

The  object  of  these  tables  is  to  give  the  i?7w  correction  of  a  lunar  distance  in  all  cases  when,  with  the  apparent 
distance  of  the  moon  from  the  sun,  a  planet,  or  star,  the  apparent  altitures  of  the  two  objects  have  also  been 
obtained  by  observation.  They  enable  us  readily  to  take  into  account:  1st,  the  parallax  of  the  moon  in  the  lati- 
tude of  the  observer,  allowing  for  the  spheroidal  figure  of  the  earth;  2d,  the  parallax  of  the  sun  or  a  planet ;  3d, 
the  true  atmospheric  refraction,  allowing  for  the  actual  state  of  the  air  as  shown  by  the  barometer  and  thermometer; 
and  4th,  that  effect  of  refraction  which  gives  the  apparent  discs  of  the  moon  and  sun  an  oval  or  elliptical  figure. 

The  longitude  deduced  from  a  lunar  observation,  when  no  attention  is  paid  to  the  spheroidal  figure  of  the 
earth,  to  the  barometer  and  thermometer,  and  the  elliptical  figure  of  the  discs,  may  in  certain  cases  be  in  error  a 
7vhole  degree.  It  is  true  these  extreme  cases  are  rare  in  practice;  but  cases  are  common  in  which  from  such  neglect 
the  error  in  the  longitude  is  10',  15',  or  20'.  Smce  lunars  are  now  chiefly  valuable  as  checks  upon  the  chronometer, 
it  is  absolutely  necessary  to  get  rid  of  such  errors,  and  to  leave  no  other  inaccuracy  in  the  result  than  that  which 
unavoidably  follows  from  the  observations.  This  is  accomplished  by  means  of  these  tables,  with  an  amount  of 
labor  very  little  greater  than  that  which  is  required  by  the  inaccurate  methods  in  common  use. 

The  observation. 

Al't.  30'7.   The  record  of  a  complete  observation  embraces — 

1.  The  latitude  and  approximate  longitude  of  the  place  of  observation. 

2.  The  approximate  local  time. 

3.  The  time  of  observation  as  shown  by  a  chronometer,  and  the  error  of  the  chronometer,  or  its  difference 
from  mean  Greenwich  time. 

4.  The  apparent  distance  of  the  moon's  bright  limb  from  a  star  or  planet,  or  from  the  nearest  limb  of  the  sun. 

5.  The  apparent  altitude  of  the  moon's  upper  or  lower  limb  above  the  sea  horizon. 

6.  The  apparent  altitude  of  the  star,  planet,  or  lower  limb  of  the  sun  above  the  sea  horizon. 

7.  The  height  of  the  baroineter  and  thermometer. 

8.  The  height  of  the  eye  above  the  level  of  the  sea. 

9.  The  index  correction  of  the  sextant,  if  a  sextant  is  used. 

The  index  correction  of  the  sextant  may  be  supposed  to  be  previously  determined;  but,  since  even  in  the  best 
instruments  it  is  not  constant,  its  determination  should  be  considered  a  necessary  part  of  the  observation  ;  and 
when  the  greatest  precision  is  sought,  it  should  be  found  both  before  and  after  the  measurement  of  the  distance, 
and  its  mean  value  taken. 

The  error  of  the  chronometer  above  alluded  to  is  that  which  is  obtained  by  applying  the  daily  rate  (multiplied 
by  the  proper  number  of  days)  to  the  error  found  before  leaving  port.  The  agreement  or  disagreement  of  the 
error  thus  found  with  that  found  by  the  lunar  observation  will  be  the  test  of  the  good  or  bad  going  of  the 
chronometer. 

Preparation  ok  the  data. 

Art.  308o  Greenwich  Date. — Correct  the  chronometer  time  for  its  eiror  from  Greenwich  time  and  deduce 
the  Greenwich  date,  i.  e.,  the  Greenwich  day  and  hour  (mean  time),  reckoning  the  hours  in  succession  from  o  to 
24,  beginning  at  noon. 

A'aiitical  Alnia)iac. — With  the  Greenwich  date  enter  the  Almanac  and  take  out  the  moon's  semi-diameter  and 
horizontal  parallax;  and  if  the  sun  is  olserved,  its  semi-diameter  and  horizontal^ parallax;*  but  if  a  planet  is 
observed,  its  horizontal  parallax  only. 

Apparent  Altitude  of  the  Moon. — To  the  altitude  given  by  the  sextant  apply  the  index  correction  of  the  instru- 
ment and  subtract  the  dip  of  the  horizon.  Table  14.  If  tne  lower  limb  is  observed,  add  the  semi-diameter  aug- 
mented by  Table  18;  if  the  upper  hmb  is  observed,  .subtract  the  augmented  semi-diame:er.  The  result  is  the 
njjparent  alti'.ude  of  the  moon's  centre,  denoted  "  ([  's  App.  Alt.^^ 

Apparcftt  Attitude  of  the  Sun.  Planet,  or  Star.— To  the  observed  altitude  apply  the  index  correction  of  the 
sextant,  and  subtract  the  dip.  Table  14;  an'  if  the  sun  is  used,  add  its  semi-diameter  when  the  l&wer  limb  is 
I  l)served,  or  subtract  it  when  the  upper  limb  is  observed.  The  result  is  ihe  apparent  altitude  required,  denoted  by 
'■"7)'s  or  :^'s  App.  Alt." 

Apparent  Distance.  —  1st,  when  the  sun  is  used,  to  the  observed  distance  (corrected  for  index  error  when 
necessary)  add  the  moon's  augmented  semi-diameter  and  the  sun's  semi  diameter ;  2  ',  when  a  planet  or  star  is 
used,  add  the  moon's  augmented  semi-diameter  if  its  nearest  limb  is  observed,  but  subtract  it  if  its  farthest  limb  is 
observed.     The  result  is  "App.  Dist." 

A/oon's  Reduced  Parallax  and  Refaction. — Enter  Table  19  with  the  latitude  of  the  place  of  ,  bservation  and 
the  moon's  horizontal  parallax,  and  take  out  the  correction,  wdiich  add  to  the  horizontal  parallax.  <  all  the  result 
the  moon's  reduced  parallax,  or  "  (J  's  Red.  P." 


7>   )J 


*  The  sun's  horizontal  parJ'ax  may  be  assumed  as  8"  5. 


LONGITUDE.  137 

Enter  Table  29  with  the  moon's  apparent  altitude,  and  talvc  out  the  mean  reduced  refraction,  and  apply  to  this 
mean  refraction  the  corrections  given  in  Tables  21  and  22,  adiUng  or  subtracting  these  corrections  according  lo  the 
directions  in  the  Tables.     The  result  is  the  moon's  reduced  refraction,  or  '■  ([  's  /u'(/.  A'." 

Sul)tract  the  "  ([  's  Red.  R."  from  the  "  <l  's  Red.  P."  and  mark  the  result  as  "  (J  's  AW.  P.  and  A'." 
A'riiiiiiti  Paraildx  and  Refraction  of  Sun,  Planet,  or  Star.* — With  the  apparent  altitude  of  the  sun,  planet,  or 
>tar,  take  from  Table  29  the  mean  reduced  refraction,  which  correct  by  Tables  21  and  22.  If  the  sun  is  observed, 
subtract  its  horizontal  parallax  (which  may  alw<  ys  be  taken  at  8. "5)  from  its  reduced  refraction,  and  mark  the 
result  as  "©"s  Red.  P.  and  R."  If  a  planet  is  observed  subtract  its  horizontal  jiarallax,  and  mark  the  result  as 
">jc's  Red.  P.  and  R"     If  a  star  is  observed,  its  reduced  refraction  is  at  once  the  reiiuired  "  ^'s  Red.  P.  and  R." 

Art.  300.    Coiupittatio)t  of  llic  Pnir  Distance. 

Take  from  Table  30  the  four  logarithms  A,  B,  C,  Dt,  and  place  these  logarithms  each  at  the  head  of  a  col 
unm,  marking  the  colunms  .'\,  B,  C,  and  D,  respectively;   then  put  the — 
log  of  (J  's  Red.  P.  and  R.  (Table  34)  in  columns  A  and  B. 
log  of  ©'s  Red.  P.  and  R.  (Table  34)  in  columns  C  and  D. 
log  sine  (J  's  App.  Alt.  (Talile  44)  in  columns  A  and  1). 
log  sine  0's  App.  Alt.  (Table  44)  in  columns  B  and  C. 
log  cot  App.  Dist.  (Table  44)  in  columns  A  and  C. 
log  cosec  App.  Dist.  (Table  44)  in  columns  B  and  D. 

The  sum  of  the  four  logs  in  Col.  A  is  the  log  (Table  34)  of  the  First  Part  of  (I's  Correction,  which  is  to  be 
marked  -{-  when  the  app.  dist.  is  less  than  90'-',  but  —  when  the  app.  dist  is  greater  than  90^. 

The  sum  of  the  four  logs  in  Col.  B  is  the  log  (Table  34)  of  the  .Second  Part  of  (J  's  Correction,  which  is  always 
to  be  marked  — , 

Th-e  sum  of  the  four  logs  in  Col.  C  is  the  log  (Table  34)  of  the  First  Part  of  the  (y's  or  -^^s  Correction,  which 
is  to  be  marked  —  when  the  app.  dist.  is  less  than  90^,  but  -f-  when  the  app.  dist.  is  greater  than  90°. 

The  sum  of  the  four  logs  in  Col.  D  is  the  log  (Table  34)  of  the  Second  Part  of  the  ©'j  or  jjc'j-  Correction,  whicl: 
is  .always  to  be  marked  +. 

Combine  the  first  and  second  parts  of  the  ([ 's  correction  according  to  the  signs  prefixed;  that  is,  take  tlieir 
Slim  if  they  have  the  sai/ie  sign,  but  their  difference  if  they  have  different  signs,  and  prefix  the  sign  of  the  greater 
to  the  result,  which  call  "  ([  's  ivliole  cortectionP 

In  the  same  manner  form  the  "  0's  or  ^c's  iv/iole  correction." 

First  Correction  of  Distance. — Combine  the  (J  'j-  whole  corr  and  the  Q'j  or  :^'j  whole  corr.,  according  to  their 
signs ;  the  result  is  the  First  Correction  of  Distance,  which  is  to  be  added  to  or  subtracted  from  the  apparent  dis- 
tance, according  as  its  sign  is  -J-  or  — . 

Second  Correction  of  Distance. — Enter  Table  31  with  the  Apparent  Distance  and  the  First  Correction  of  Distance, 
and  take  out  the  .Second  Correction  of  Distance,  which  is  to  be  applied  to  the  distance  according  to  the  directions  in 
the  side  columns  of  the  Table. 

Correction  for  the  Flliptical  Figure  of  the  Mooit's  Disk,  or  Contraction  of  the  J/oon^s  Seiiii-diaineter  (Table  32). — 
Enter  Table  32,  A,  with  the  ([  's  App.  Alt.  and  ([  's  Red.  P.  and  R.,  and  take  out  the  number.  With  this  numlicr 
and  the  ([  's  whole  correction  enter  Table  32,  B,  and  take  out  the  required  contraction,  wliich  is  to  be  added  lo 
the  app.  dist.  when  iYve  farthest  limb  is  observed,  but  subtracted  when  the  nearest  limb  is  observed. 

Correction  for  the  Flliptical  Figure  of  the  Stints  Disk,  or  Contraction  of  the  Slat's  Semi-diameter  (Table  T^Tf). — 
Enter  T.able  33,  A,  with  the  Q's  App.  Alt.  andQ's  Red.  P.  and  R.,  and  take  out  the  number.  With  this  number 
and  ihe  Q's  whole  corr.  enter  Table  t^t,,  B,  and  take  out  the  required  contraction,  which  is  always  to  be  subtracted 
from  the  distance  (the  nearestXwah  of  the  sun  being  always  observed). 

Correction  for  Compression,  or  for  the  Spheroidal  Figure  of  the  Earth. — Take  from  the  Nautical  Almanac  for 
the  Greenwich  date  the  declinations  of  the  bodies  to  the  nearest  whole  degree.  With  the  moon's  declination  and 
apparent  distance  take  from  Table  36,  A,  \\\q  first  part  of  N,  and  mark  it  with  the  sign  in  the  table  if  ihe  declina- 
tion is  N'orth;  but  if  the  declination  is  South,  change  the  sign  from  -f-  to  —  or  from  —  to  -{-.  With  the  sun's  or 
star's  declination  and  tlie  apparent  distance  take  from  Table  36,  B,  the  second  part  of  N^,  giving  it  the  same  sign  as 
the  declination.  T.ake  the  sum,  or  difference,  of  the  two  parts,  accordiiig  as  their  signs  are  the  same  or  different, 
and  to  the  resulting  number  prefix  the  sign  of  the  greater.  The  logarithm  of  this  number  of  seconds,  taken  from 
Table  34,  with  its  sign  prefixed,  is  the  required  log  N.  To  log  N  add  the  log  sine  of  the  latitude  of  tiie  place  uf 
observation;  the  sum  is  the  log  (Table  34)  of  the  required  correction  for  covipression.  In  north  latitude  add  this 
correction  if  log  N  is  -}-,  or  subtract  it  if  log  N  is  — ;  in  south  latitude  subtract  the  correction  when  log  N  is  -|-, 
and  add  it  when  log  N  is  — . 

All  these  corrections  being  applied  to  the  Apparent  Distance,  the  result  is  the  True  Distance. 

Art.  310.    To  find  the  Greemvich  Time. 

Find  in  the  Nautical  Almanac  the  two  distances  between  which  the  true  distance  falls.  Take  (  ut  the  first  r  f 
these,  together  with  the  Prop.  Log  following  it,  and  the  hours  of  Greenwich  time  over  it.  Find  the  difference 
between  the  distance  taken  from  the  Almanac  and  the  true  distance,  and  to  the  log  of  this  difference  (Table  34) 
add  the  Prop.  Log  from  the  Almanac;  the  sum  is  the  log  (Table  34)  of  an  interval  of  time  to  be  added  to  llie 
hours  of  Greenwich  time  taken  from  the  Almanac.     The  result  is  the  approximate  Cjreenwich  time. 

To  correct  this  Greenwich  time,  take  the  difference  between  the  two  Prop.  Logs  in  the  Almanac  which  stand 
against  the  two  distances  between  which  the  true  distance  falls.  With  this  difference  and  the  interval  of  time  just 
found,  enter  Table  35  and  take  out  the  seconds,  which  are  to  be  added  to  the  approximate  Greenwich  time  when 
tile  Prop.  Logs  are  decreasing,  but  subtracted  when  the  Prop.  Logs  are  increasing.  The  result  is  the  true  Greenwich 
time. 

By  comparing  with  this  the  local  mean  time  the  longitude  will  be  found ;  or,  if  testing  the  time  shown  by 
chronometer,  the  difference  between  the  true  Greenwich  time  and  the  time  shown  by  the  chronometer  is  the  error 
of  the  chronometer  as  determined  by  the  lunar  observation. 


*  The  parallax  of  a  star  being  zero,  its  "reduced  parallax  and  refraction"  become,  of  course,  merely'  its  "reduced  refrac- 
tion" ;  but  as  no  mistake  can  arise  from  marking  it  as  "  -jt's  Red.  P.  and  R.,"  this  designation  has  been  retained  in  order  to  give 
simplicity  and  uniformity  at  once  to  the  rules  and  the  tables. 

tN'o  interpolation  is  necessary  in  taking  out  tlicse  logarithms. 


138 


LONGITUDE. 


Degree  of  Dependence. 

Al't«  31 1»  If  the  erroi'  ihus  determined  agrees  with  that  deduced  by  means  of  the  rate  and  original  error,  the 
chronometer  has  run  well,  and  its  rate  is  confirmed;  if  otherwise,  more  or  less  doubt  is  thrown  upon  the  chronome- 
ter, according  to  the  degree  of  accuracy  of  the  lunar  observation  itself.  An  error  of  lo"  in  the  measurement  of  the 
distance  produces  about  20"*  error  in  the  Greenwich  time  ;  and  since,  even  with  the  best  observers,  a  single  set  of  dis- 
tances is  subject  to  a  possible  error  of  10",  it  may  be  well  to  consider  the  chronometer  as  still  to  be  trusted  so  long 
as  it  does  not  differ  from  the  lunar  by  more  than  20^.  Since,  however,  so  much  depends  upon  skill  in  measuring 
the  distance,  the  observer  can  only  form  a  correct  judgment  of  the  degree  of  dependence  to  be  placed  upon  his 
own  observations  by  repeated  trials  and  a  careful  comparison  of  his  several  results. 

Example.  In  Lat.  35°  30'  N.,  Long.  30^^'  W.,  by  account,  at  the  local  mean  time,  1855,  September  6,  18^ 
8'",  the  observed  distance  of  0's  and  ^  's  nearest  limbs  was  43^  52'  10" ;  observed  alt.  (i_,  49^'  32'  50"  ;  observed 
alt.  0,  5°  27' 10"  ;  barometer,  29'".! ;  thermometer,  75'^ ;  height  of  the  eye  above  the  sea,  20'';  I.  (J.  o. ;  required 
the  longitude. 

Preparation  of  the  Data. 


L.  m.  t.,  Sept.  6, 
Long.,  D.  R., 


18"  8"V  d's  S.  D., 
-f-  2     o      Aug.,  Table  18, 


14'  5o".oj  (['s  Par.,  N.  A., 
+  II    .2  !  Aug.,  Table  19, 


+ 


54'  i9"-4 
3  -6 


Gr.  m.  t.,  approx., 

Obs.  Alt.  1,                 49^ 
Dip,  Table  14,         — 
(I  's  Aug.  S.  1).,      + 

20 

32' 

4 

15 

43 
I' 

8 

50" 

23 
I 

28 

16" 

3 

4 

([  's  Aug.  S.  D, 

Obs.  Alt.  0,                  5' 

1  )ip, 

O's  S.  D.,                  + 

O'.s  App.  Alt  ,               5 

O's  Red.  R.,  Table  29, 
Bar.,  Table  21,          — 
Thcr.,  Table  22,       — 

0's  Red    R., 
O's  Par., 

O's  Red.  P.  and  R., 

CoinpiUatioii  of  the  Tri 

C. 

log  C,  Table  30, 
log  O's  Ked    P.  and  R., 
log  sin  O's  ^"^PP-  Alt., 
log  cot  A]'p.  1  'ist.. 

5 

27' 

4 

15 

38 

8' 

I    .2 

10" 

23 

55 

42 

57" 
16 

28 

({  's  Red.  P., 

Obs.  Dist.  0       d  , 
d's  Aug,  S.J)., 
O's  S.  D., 

App.  Dist  , 
e. 

54    23   .0 

430  52'  10" 

+         15      I 

+        15    55 

([  's  App.  Alt  ,            49 

(J's  Red.  R  ,  Table  29, 
Bar.  29'". I,  Table  2J,     - 
Ther.  75",  Table  22,      — 

44    23     6 

^  's  Red.  R  , 
^'s  Red.  P., 

I 
54 

9 
23 

8 

13 
8 

d  's  Red.  P.  and  R., 

A. 

log  A,  Table  30, 
log  (['s  Red.  P.  and  i^., 
log  sin  ([  's  Ajip.  Alt., 
log  cot  Apj).  1  )ist., 

53    '4 

0.0021 

3-  5043 
9.8825 
0.0093 

8     5 
le  Distanc 

9.9949 
2.6857 
8.9929 
0.0093 

\  Ir-g,  Table  34, 

\  1st  Part  (J  's  corr. 

B. 

logB, 

log  ({  's  Red.  P.  and  R. 
log  sin  0's  App.  Alt., 
^og  ".osec  App.  Dist., 


3-3982 

+  41'  42'' 


S  log,  Taljle  34, 
\  1st  Part  O's  corr. 

D. 


99951  logD, 

3.5043  logo's  Red.  P.  and  R., 

8.9929  log  sin  (J  's  App.  Alt., 

0.1552  log  cosec  App.  Dist., 


1.6828 
o'  48" 


9.9992 
2.6857 
9.8825 
0.1552 


log.  Table  34, 
2d  Part  ((  's  corr., 
^  's  whole  corr.. 


log  N, 

log  sin  Lat.  +  35  '  30',     +  9.764 


2.6475 
-  7'  24" 
+  34'  18" 


—  0.764 


log,  Table  34, 

Corr.  forCoinpression, 


0.528 

3" 


log.  Table  34, 
2d  Part  O's  corr., 
O's  whole  corr., 


2.7226 
+  8'  48" 
+  8'    o" 


liue  Distance, 

Distance,  N.  A.,  at  XVIII'', 

Difference, 

Approximate  interval. 
Add 

Approx.  Gr.  time, 
Corr.,  Table  35, 

True  Gr   m.  time, 
Local  m.  time, 

Longitude, 


45^^ 
46 


4'  45' 
3    17 


P.  L., 


App.  Dist.,  44°  23'    6' 

1st  Corr.,  -j- 

2d  Corr.,  Table  31,  — 

Contraction  of  ([  's  \ 

S.  D.,Table  32,       \ 
Contract'on   of  Q's  X     

S.  1 ).,  'lable  33,     S 
Corr.  for  Compressiim,  — 

True  Distance, 
0.3433         Diff.  P.  logs 


42 

18 
16 

0 

20 

3 

45       4 

45 

+  5 

58 

3 

2 

2'- 
18 

9'" 

3^ 

20 

9 

3 

2 

20" 
18 

91" 
8 

IS 
0 

log,  Table  34,  3.5456 
log.  Table  34,  3.8889 


4-2     I     I   =  yp  15'   15"  W„ 


LONGITUDE. 


139 


Example.  In  Lat.  55^^  20'  S.,  Long.  I20<^  25'  W.,  by  account,  on  August  29,  1855,  at  9''  40"'  p.  ni.,  local 
mean  time,'*tlic  folldwing  ilistance  and  altitudes  were  found,  being  the  mean  of  six  observations  corrected  for 
index  error.  ( )l)servod  distance  of  Fonialhaut  and  moon's  farthest  limb,  46  '  30' 23"  ;  observed  alt.  C^,  6"^  26'  10"; 
observed  alt.  lomalhaut,  52^  34'  40";  barometer,  31'";  thermometer,  20-;  height  of  the  eye  above  the  sea,  iSf'. 


L.  m.  t.,  August  29, 
Long,  by  D.  R., 

Approx.  Gr.  m.  t., 

Obs.  all.  iL 

Dip, 

(['a  aug.  S.  i),, 

([  's  App.  Alt  , 


9i>  40"'    QS 
+     S      I     40 

17    41     40 


+ 


([  's  Red.  R.,  Table  29, 
Bar.,  Table  21,  -|- 

Ther.,  Table  22,  -j- 

([  's  Red.  R., 
d's  Red.  P., 

(I 's  Red.  P.  and  R., 


6°  26'  10" 

4     9 
16   28 

6    38   29 

7'  48" 
16 


8  36 
60   20 

51    44 


Preparation  of  the  data. 

(['s  S.  D.,  Naut.  Al.,  16' 26".3 

Aug.,  Table  18,  +  2  .0 


d'sPar.  N.  A.,  60'  11". 8 

Aug.,  Table  19,     +  8  .3 


([  's  aug.  S.  D.,  16  28 

Obs.  Alt.  -X-, 
Dip, 

^'s  App.  Alt., 


d's  Red    P., 


60  20   .1 


52    34'  40'' ,  Obs.  Dist.  ^  d  ,  46^  30'  23" 

4     9       d's  aug.,  S.  D.,    —  16  28 


52    30  31     I  App.  Dist. 


.)(. 's  Red.  R.,  Table  29, 
Bar.,  Table  21,  + 

Ther.,  Table  22,  + 

■)f' s  Red.  R., 
>i;'s  Red.  P., 

>}c's  Red.  P.  and  R.,  i    20 


I'  13" 

2 

5 

d  's  Dec, 
>tc's  Dec, 

I  20 

0 

46    13  55 


4°N. 

30°  s. 


Coviputation  of  t lie  True  Distance. 
C. 


log  A,  Table  30, 
log  d  's  Red.  P.  and  R., 
log  sin  d  's  App.  Alt., 
log  cot  Ap^^.  Dist., 

^  log,  Table  34, 

\  1st  Part  d  's  corr.,  + 

B. 

log  B  , 

log  d'sRcd.  P  and  R., 
log  sin  -X-'s  App.  Alt., 
log  cosec  App.  Dist., 

k  log.  Table  34, 

\  2d  Part  d  's  corr.,  — 

d  's  whole  corr.,  — 

log  X,  Table  36      =  — 

log  sin  Lat.  55^  S,  — 

^  log  Table  34,  + 

\  Co  r.  for  Comp.,  -\- 

True  Distance, 
Di.st.,  N.  A.,  at  XVI', 

Difference, 

Approx.  interval. 
Add., 

Approx.  Gr.  t., 
Corr.,  'i'able  35, 

True  Gr.  time, 
Local  m.  time. 

Long,, 


0.0274 

log  C,  Table  30, 

9.9999 

3-4919 

log>!<'s  Red.  P.  and  R., 

1. 9031 

9.0632 

log  sin  >ic's  App.  Alt., 

9.8995 

9-9813 

log  cot  App.  Dist., 

9-9813 

2.563S    ^  log,  Table  34, 
6'    6"     \  1st  Part  -)f' s  corr., 

i  1^- 

log  D, 

log  >fc's  Red.  P.  and  R., 
log  sind  's  App.  Alt., 
log  cosec  App.  Dist., 

S  log'  Table  34, 

\  2d  Part  -)f's  corn, 

•^'s  whole  corr., 


0.000 1 

3-4919 
98^95 
o.  1414 


3.C32Q 
56'  51" 

50  45 

1.230 
9-913 

I -143 

14" 

45^ 


43 


22'  32' 
51  59 


P.  L., 


1.7838 

i'  I" 


0.0267 
1. 903 1 
9,0632 
o.  1414 


+ 


1-1344 

o'  14" 
o  47 


App.  Dist.,  46°  13'  55'' 

1st  corr.,  —        51   32 

2d  corr..  Table  31,    —  22 

Contraction  of  d  's  \  _. 

S.  D,  Table  32,    ^  +  ^' 

Corr.  for  Comp.,        -\-  14 


0.2527 


True  Distance, 
Diff.  P.  Iocs 


45    22  32 
6 


I 

30  To 

2" 
15 

42"'  i^ 

17 

+ 

42     I 

I 

17 

9 

42     2 
40     0 

log.  Table  34,     3.735° 
log.  Table  34,     3.9877 


2     2 


120*^  30'  30"  W. 


Method  of  taking  a  Lunar  Obsei-oation  l>y  one  Observer. 

Art.  312.  Three  observers  are  required  to  make  the  necessary  observations  for  determining  the  longitude ; 
one  to  measure  the  distance  of  the  bodies,  and  the  others  ttj  take  the  altitudes.  In  case  of  not  having  a  sufficient 
number  of  instruments  or  observers  to  take  the  altitudes,  it  has  been  customary  to  calculate  them;  there  being  given 
the  latitude  of  the  place,  the  apparent  time,  the  right  ascensions,  and  the  declinations  of  the  objects.    These  calcula. 


140 


LOKGITUDE. 


tions  are  long,  when  an  altitude  of  a  star  is  to  be  computed,  and  much  more  so  when  that  of  the  moon  is  required; 
and  a  considerable  degree  of  accuracy  is  required  in  finding,  from  the  Nautical  Almanac,  the  moon's  right 
ascension  and  declination,  which  must  be  liable  to  some  error  on  account  of  the  uncertainty  of  the  ship's  longi- 
tude. The  following  method  of  obtaining  those  altitudes  is  far  more  simple,  and  sufficiently  accurate.  This 
method  depends  on  the  supposition  that  the  altitudes  increase  or  decrease  uniformly. 

Bef  HC  measuring  the  distance  of  the  bodies,  take  their  altitudes,  and  note  the  times  by  a  chronometer ;  then 
measure  the  distance,  and  note  the  time  (or  measure  a  number  of  distances,  and  note  the  corresponding  times,  and 
take  the  mean  of  all  the  times  and  distances  for  the  time  and  distance  respectively) ;  after  having  measured  the 
distances,  again  measure  the  altitudes,  and  note  the  times ;  then,  from  the  two  observed  altitudes  of  either  of  the 
vjbjects,  the  sought  altitude  of  that  object  may  be  found  in  the  following  manner : 

^\dd  together  the  proportional  logarithm  (Table  45)  of  the  variation  of  altitude*  of  the  object  between  the  two 
times  of  observing  the  altitudes,  a^d  the  prop,  log  of  the  time  elapsed  between  taking  the  first  altitude  and  measur- 
ing the  distance ;  from  the  sum  subtract  the  prop,  logt  of  the  time  elapsed  between  observing  the  two  altitudes  of 
that  object;  the  remainder  will  be  the  prrp.  log  of  the  correction,  to  be  applied  to  the  first  altitude,  additive  or 
subtractive,  according  as  the  altitude  was  increasing  or  decreasing;  to  the  altitude  thus  corrected  apply  the  correc- 
tion for  dip  of  the  horizon  and  semi-diameter  as  usual. 

ExAMiM.E.  Suppose  the  distances  and  altitudes  of  the  sun  and  moon  were  observed,  as  in  the  following  table; 
it  is  required  to  find  the  altitudes  at  the  time  of  measuring  the  mean  distance. 


I 


Mean, 


Ohscn>ations. 

Times  by  chro- 
notneie7\ 

Dist.  ©  and    ' 

i  N.L. 

Times  by  chro- 
7iomctcr. 

Ohs.  alt. 
C'sL.  L. 

Times  hy  c/ir}~ 

nomcter. 

Obs.  alt. 
%'s  L.L. 

2''  3'"  20>* 
2      4     20 

2    5    50 

40'-^  0'  00" 
40     0    30 
40     I    30 

Uiffe 

■ence 

2''  2'"     0^ 
26      10 

20  '   46' 

21  20 

Difl 

erence, 

2''  2"'   Tf>^ 
2     7      00 

40°  20' 
39    J2 

4       10 

34 

4     30 

I      8 

2     4    30 

40     0   40 

Variation  ^  's  altitude,  34' 

Time  1st  observation  ^     2''  2'"    o"* 
Mean  time()fol).-.er\in!7  \ 

distance,  ^        -+     J 


Difference, 


Prop. log      7238 


50        Prop,  log  1.S57J 


Elapsed  lime  between   \         „,       j, 
the  '  wo  obsei  vations,  \       ^ 

Correction  of  altitude,  o^' 20' 

First  altitude  of  moon,  20    46  ad 

Alt.  ([  's  L.  L.  at  time  of  ? 


2.5S11 
Prop. log   1.6355 


Prop,  log      9455 


the  mean  rit)s.  of  (list.,  \ 


21 


Variation  ©'s  altiuide.  1°   8' 

Time  1st  observation  ©,    2''  2'"  30** 
Time  mean  ol)servatioii,    2    4     30 

Difference, 

Elapsed   time    between   \ 
the  two  obser  'ations,  ^ 

Correction  of  altitude. 

Sub.  from  ©'s  i;t  altitude,  40     20 


Prop. log       422S 


2    00 

Prop,  log 

Sum, 
Prop,  log 

Prop,  log 

1.9542 

4     30 

2-3770 
1. 6021 

QP    30' 

7749 

Alt.  ©'s  L  L.  at  time  of  ) 

the  mean  observation  >     39     50 
of  the  distances,  \ 


Thus,  at  the  lime  2''  4"'  30'',  the  mean  observed  distance  of  the  sun  and  moon's  neaiest  limbs  was  40°  o'  40", 
the  altitude  of  die  moon's  lower  limb  21^'  6',  and  the  altitude  of  the  sun's  low  er  limb  39^  50' ;  these  altitudes  must 
be  corrected  for  dip  and  semi-diameter  as  usual. 

Art.  313.  In  order  to  calculate  strictly  the  apparent  altitudes,  the  following  rule  may  be  followed,  which 
is  derived  from  the  formula^ : 

Tan  A  =:  tan  d  sect  / 


Sin  h 


cos  (.'\  —  L)  sin  d 
sin  A 


in  which  d  is  the  declination,  /  the  hour  angle,  L  tlie  latitude,  h  the  true  altitude  of  the  centre  of  the  object,  A  an 
arc  whiih  lias  the  same  name  o?'  sign  as  the  deelijiattoii  and  is  lun/n  riea/tv  in  the  same  quadtaiit  as  t. 

Given  the  apparent  time,  the  latitude  and  hmgitiide,  to  fiad  the  apparent  altitude  of  a  heaiunly  I'ody. 


Rui.i:.  I  ind  the  declination  of  the  body  and  its  hour  angle  at  the  given  time.  Add  the  log  tangent  of  the 
declination  to  the  log  secant  of  the  hour  angle  to  obtain  the  log  tangent  of  an  arc,  A,  which  is  of  the  same  sign  as 
the  declin.Tl'o  1 

Subtract  the  latitude  from  the  arc,  A,  having  regard  to  their  signs,  and  to  the  log  cosine  of  the  difference  add 
the  log  sine  of  the  declination  and  the  log  cosecant  of  A;   the  sum  is  the  log  sine  of  llie  true  altitude. 

The  refraction  less  the  parallax  being  added  to  the  true  altitude  will  give  the  apparent  altitude. 


*  Table  45  is  only  calculated  as  far  as  3°,  and  if  the  variation  of  altitude  exceed  that  quantity,  enter  the  table  with  minutes 
and  seconds  instead  of  degrees  and  minutes;  and  the  correction  of  altitude  talcen  out  in  minutes  and  seconds  must  be  called 
degrees  and  minutes  respectively. 

t  Or  add  its  arithmetical  complement,  neglecting  10  in  the  index  of  the  sum. 


LONGITUDE.  141 

lv\AMrj«':.    l\c([aiiC(l  the  ;i[)paieiit  altiliuie  of  the  sun's  centre  on   I)eceml)or  22,  1879,  in   I. at.   48^^  23'   N., 
Long.  60^-^  W.,  at  10''  r"  14"  a.  m.,  app.  time. 

L.  app.  t.,  December  21,         22''    i'"  14^  t  =  —  i'' 58"' 46* 

Long.,  4-400  ©'s  Dec.       =        23°  27'  16"  S. 

Gr.  app.  t.,  December  22,  2      i     14 

t  =         29'-"' 41' 30"         log  sec       0.061 13 

d  —  —  23    27    16  log  tan       9.63735         log  sin       9-59991 


A  =  —  26    32  20  log  tan       9.69848         log  cosec   0.34989 

L  =  +  48    23     o 


A  — L       :^  —  74    55    2o  log  cos       9.4-1520 

h  =         13    23    58  log  sin       9.36500 

r— par.     =  +  3    50 


App.  alt.    =         13    27   48 

Example.    Required  the  ajiparcnt  altitude  of  the  moon  on  S.\>x\\  29,  1879,  at  7^  55™  52^  p.  m.  (L.  m.  t.)  in 
Lat.  42°  34'  S.,  Long.  65^'  7'  30"  W.  ^  4''  20'"  30^. 

L.  m.  t.,  April  29,                         7''  55'"  52*^        L.  m.  t.,  7''  55'"  52= 

.Sid.  t.,  oh,                                      2    28     1 7. 1      Long.,  4    20     30 

Red.  for  Long.  (Table  9)  +  42  .8  

Red.  for  L.  m.  t.,                 -j-             i      18.2     Gr.  m.  t.,  12    16     22 


Local  sid.  time,                          10    26     10         ([ 's  R.  A.  (N.  A  )  9''    5'"    4^49  M.  D.,        2M369 

d 's  R.  A.,                                    9      5     39         CVn-r.  for  16'"  22^  34-98  ^''-37 

/■             ■                             =            I    20     31          (['sR.  A.,  9      5     39.47  Corr.,            34^<,8 

=  19      7     45 

({ 's  Dec.  (X.A.)  +  15     14'  32. '7  M.  1).,   —12". 227 

Corr.  for  16'"  22*^ —  3    20  . 1  -\-       16.37 


(J'sDec,  +    15     II    32  .6        for.,       -   20o".i 


t 
d 


A 

L  =  —  42    34     o 


-=      19 

=  +  '5 

7 
II 

45'' 
33 

log  sec 
log  tan 

0.02467 
9-433''<5 

log  sill         9.41S40 

=  +  16 

2 

9 

log  tan 

9.45852 

log  cosec    0.55872 

A  — L  =  -|-  58    36      9  log  cos       9.71682 


h        ■  =         29    37    10  log  sin        9-69394 

Table  24  (r  and  ]wr.)    :=  —  48    20 


App.  alt.  =         28    48    50 

Example.    Re(|uired  the  apparent  altitude  of  Antares  on  May  31,  1879,  at  8''  30'"  p.  m.  (L.  m.  t.),  in  Lat. 
30-^  25'  N.,  Long.  60    \V. 

L.  m.  t..  May  31,  8'' 30"'    o^        -L  4I' :=  Gr.  m.  t.,        12^  30"^    cfi 

Sid.  time  o''  Gr.,  4    34    26  .94 

Red.  for  Long.,  -f  39-43        R.  A.  Antares,  16    22       3 

Red.  for  L.  m.  t.,  -)-  i     23  .78        Dec.  Antares,  —  26       9     55 

L.  Sid.  time, 
*'s  R.  A., 

t  =  —   3    15    33 

log  sec      0.18208 

log  tan      9.69135        log  sin       9.64440 


I 

23 

.78 

13 

6 

30 

•15 

16 

22 

3 

/ 

^ 

48° 

5.3' 

15' 

d 

^z: 



26 

9 

55 

A 

rr: 

— 

36 

46 

0 

L 

-L 



+ 

30 

25 

0 

A- 

67 

II 

0 

A 

= 

16 

35 

59 

r 

= 

^- 

3 

12 

log  tan      9.87343        log  cosec  0.22289 
log  cos      9.58859 


log  sin      9.45588 


App.  alt.  =         16    39    II 


142  Sumner's  method. 


CHAPTER    IX. 

SUMNER'S  METHOD 

OF  FINDING  A  SHIP'S  POSITION  AT  SEA. 

Art.  314.    By  the  various  methoils  whicli  liave  heretofore  been  described,  in  which  single  observations  arc 

alone  concerned,  the  latitude  has  Ijeen  found  which  places  the  ship  upon  a  certain  cast  and  -west  line ;  by  others 
the  longitude  has  been  found  which  places  the  ship  upon  a  certain  norlh  and  south  line  ;  but  in  neither  case  can  the 
ship  be  located  upon  any  particular  point  of  the  line.  For  instance:  by  the  A.  M.  observation  when  the  sun  is 
near  the  prime  vertical,  the  hour  angle  is  determined  with  a  certain  degree  of  accuracy,  depending  upon  the  lati- 
tude by  account,  from  which  the  longitude  is  ascertained;  hence  the  position  of  the  ship  is  approximately  known 
upon  a  certain  meridian.  Again,  by  the  meridian  observation,  when  possible  to  obtain  it,  the  position  of  the  ship 
is  known  upon  a  certain  parallel  of  latitude;  and  by  a  combination  of  the  two  observations  the  ship's  position  may 
be  located  upon  the  chart,  but  there  has  been  involved  a  lapse  of  tinre  which,  under  some  circumstances,  may  be 
\  ital  for  the  safety  of  the  ship. 

But,  by  the  Sumner  method,  the  ship  is  at  once  located  upon  a  line,  generally  oblique  to  both  parallels  and 
meridians;  and  in  approaching  a  dangerous  coast  the  imijortance  of  this  line  is  obvious,  since  it  exhibits  on  the 
chart  the  bearing  of  the  land. 

The  title  given  to  this  method  is  retained  here,  for  it  was  by  Capt.  Thomas  H.  Sumner,  an  American  ship- 
master, first  reduced  to  a  system ;  and  as  the  strongest  proof  of  the  value  of  the  method,  the  incident  which  led  to 
its  discovery  may  well  be  related : 

"Having  sailed  from  Charleston,  S.  C,  25th  November,  1837,  bound  for  Greenock,  a  series  of  heavy  gales 
from  the  westward  promised  a  quick  passage ;  after  passing  the  Azores  the  wind  prevailed  from  the  southward,  with 
thick  weather;  after  passing  longitude  21^  W.  no  observation  was  had  until  near  the  land,  but  soundings  were  had 
not  far,  as  was  supposed,  from  the  bank.  The  weather  was  now  more  boisterous,  and  very  thick,  and  the  wind 
still  southerly;  arriving  about  midnight,  17th  December,  within  40  miles,  by  dead  reckoning,  of  Tuskar  light,  the 
wind  hauled  S.  E.  true,  making  the  Irish  coast  a  lee  shore;  the  ship  was  then  kept  close  to  the  wind  and  several 
tacks  made  to  preserve  her  position  as  nearly  as  possible  until  daylight,  when,  nothing  being  in  sight,  she  was  kept 
on  E.  N.  E.  under  short  sail,  with  heavy  gales.  At  about  10  a.  m.  an  altitude  of  the  sun  was  observed,  and  the 
chronometer  time  noted;  but,  having  run  so  far  without  observation,  it  was  plain  the  latitude  by  dead  reckoning 
was  liable  to  error,  and  could  not  be  entirely  relied  upon." 

The  longitude  by  chronometer  vi'as  determined,  using  this  uncertain  latitude,  and  it  was  found  to  be  15'  E  of 
the  position  by  dead  reckoning;  a  second  latitude  was  then  assumed  10'  nortla  of  that  by  dead  reckoning,  and 
towards  the  danger,  giving  a  position  27  miles  E.  N.  E.  of  the  former  position;  a  third  latitude  was  assumed  10' 
farther  north,  and  still  towards  the  danger,  giving  a  third  position  E.  N.  E.  of  the  second  27  miles.  Upon  plotting 
these  three  ])ositions  on  the  chart  they  were  seen  to  be  in  a  straight  line,  and  that  this  line  passed  through  Small's 
Light. 

^^ It  then  at  once  appeared  that  the  obsen'ed  altitude  must  have  happened  at  all  the  three  points  and  at  StiiaWs 
Light  and  at  the  ship  at  the  same  instant.'''' 

Then  followed  the  conclusion  that,  although  the  absolute  position  of  the  ship  was  uncertain,  she  must  be 
somewhere  on  that  line.  The  ship  was  kept  on  the  course  E.  N.  E.,  and  in  less  than  an  hour  Small's  Light  was 
made,  bearing  E.  N.  E.  J^  E.  and  close  aboard. 

The  latitude  by  dead  reckoning  was  found  to  be  8'  in  error,  and  if  the  position  gi\eu  by  that  latitude  had  been 
assumed  correct  the  error  would  have  been  8  miles  too  far  S.  and  31'  30"  of  longitude  too  far  W.,  and  the  result  to 
the  ship  might  have  been  disastrous  had  this  wrong  position  been  adopted.  This  represents  one  of  the  practical 
applications  of  Sumner's  Method. 

Art.  315.  Various  new  terms  are  introduced  in  this  method,  and  to  render  their  meaning  clear  it  must  be 
understood  that  the  basis  is  a  primitive  great  circle  with  a  dependent  system  of  parallels,  entirely  distinct  from 
those  systems  of  co-ordinates  already  treated  of.  Thus  far  the  most  important  great  circles  have  been  the  Equator 
and  the  Horizon.     Now  we  are  to  regard  the  earth's  surface  with  reference  to  its  illumination  Isy  the  sun. 

The  same  system  obviously  applies  to  any  other  heavenly  body  than  the  sun,  but  the  case  of  the  latter  being 
n:ore  conspicuous  is  assumed  as  the  basis  of  explanation ;  practically  speaking,  the  application  of  the  method  is 
more  important  when  applied  to  the  stars. during  that  period  of  twilight  when  the  atmosphere  is  so  clear  and  the 
sea-horizon  so  well  defined. 

At  any  particular  instant  of  time  the  surface  of  the  earth  is  divided  into  two  equal  parts  by  the  sun's  illumi- 
nating power  after  applying  the  corrections  due  to  parallax,  refraction,  and  semidiameter — one  hemisphere  in  the 
shade  and  one  enlightened  The  great  circle  dividing  these  hemispheres  is  the  primitive  of  this  system  and  may 
be  called  the  Circle  of  Illumination. 

In  Fig.  68  let  S  represent  the  centre  of  the  sun,  C  the  centre  of  the  earth,  and  SC  a  line  joining  them  A, 
the  point  in  which  ihis  line  intersects  the  earth's  surface,  will  be  the  pole  of  the  circle  of  illumination  II II.  At  A 
the  altitude  of  the  sun  will  obviously  be  90^",  and  at  any  point  in  the  circle  of  illumination  the  sun  will  be  in  the 
horizon. 

Consider  a  system  of  small  circles  parallel  to  the  primitive,  having  the  common  ]iole  A,  of  which  i)o  is  one. 
Now,  at  the  same  instant  of  time,  the  altitude  of  the  sun  will  evidently  be  the  same  at  all  points  of  each  of  the 
small  circles  (considering  the  rays  to  be  sensibly  parallel  as  they  reach  the  earth).  These  small  circles  may  there- 
fore be  called  Parallels  of  Position. 

The  sun  being  vertical  to  the  pole  of  the  circle  of  illumination,  the  latitude  0/  this  pole  must  always  be  equal  to 
the  sun'' s  declinat'ion. 

This  pole  moves  daily  along  its  parallel  of  latitude  with  its  attendant  system  of  parallels  of  position^  so  that 
at  any  instant  i.f  time  there  may  be  projected  upon  the  earth's  surface  this  system,  or  any  parallel  of  position,  cor- 
resjjonding  to  a  given  altitude  of  the  sun. 

It  will  also  be  seen  that,  if  the  declination  of  a  heavenly  body  is  e(jual  to  the  latitude  of  a  place  on  the  earth's 
sui  face  (and  of  the  same  name),  the  body  will  be  in  the  zenith  of  the  place  when  the  hour  angle  of  the  body  is 
o''    or  when  on  the  meridian. 


SUMNER  S    MP:TH0D. 


143 


In  Fi^.  65  c  represents  a  place  on  the  earth's  surface,  z  its  zenith,  and  hk'  its  horizon.     Soh  is  the  altitude  of 
(he  heavenly  body  at  S,  and  ?>oz  its  zenith  distance. 

Knowing  the  Grcenwicli  time  when  tlie  body  is  vertical  at  A  antl  the  altitude  observed  at  o,  describe  about  A 
on  the  i;U>be  a  small  circle,  00,  with  a  jiolar  distance,  A(',  equal  to  the  zenith  distance,  S('c  (Fig.  69).     It  will  lie 
evident  that  to  an  observer  within  this  small  circle  the  zenith  distance  would  be  smaller,  and  to  an  observer  w  ith 
out  the  small  circle  the  zenith  distance  would  be  greater  than  that  observed;  hence  00  is  a  circle  of  position,  on 
some  point  of  wliose  circumference  the  observation  was  made. 

"If,  then,  the  Navigator  can  project  ihis  small  circle  upon  an  artificial  globe  or  a  chart,  ///(•  kii(nvledt^e  that  he 
is  upon  this  circle  will  be  just  as  7'aluablc  to  him  in  enabling  him  to  avoid  dangers  as  the  kitcnoledge  of  his  latitude 


Fig.  68. 

alone  or  his  longitude  alone :  since  one  of  the  latter  elements  only  determines  a  point  to  be  in  a  certain  circle,  with- 
out fixing  upon  any  particular  point  of  that  circle." — Chauvenet. 

Now,  suppose  at  t  e  same  instant  of  time  (Fig.  68)  another  body  was  cLserved  r.t  s'  vertical  to  A',  ilic  pole 
of  the  circle  of  illumination  ll'H'.  Its  altitude  measured  gives  the  zenith  distance  s'oz ;  with  this  as  a  polar  dis- 
tance, about  the  pole  A'  on  the  globe  (Fig.  69)  describe  the  circle  of  position  </«',  on  some  point  of  which  ihe 
observer  must  be;  ilurefDre,  he  must  lie  at  one  of  the  two  points  of  intersection  of  the  two  circles  <if  ])osiiiiiH, 
and  the  proper  one  can  lie  determined  liy  the  known  approximate  position  by  account 

The  method  of  projecting  lliis  system  on  a  large  scale  may  be  seen  in  Captain  Sumner's  work;  but  for  the 
purposes  of  the  Navigator  it  will  be  sufficient  to  project  a  limited  portion  of  a  circle  of  position,  corresponding  to 


144 


SUMNER  S    METHOD. 


a  given  altitude,  upon  llie  Navigator's  chart,  with  an  e.xplanation  of  its  practical  application  to  the  necessities  of 
Navigation. 

One  other  jioint  should  be  noticed  in  connection  with  this  system,  in  order  to  avoid  confusion  in  nomenclature. 

The  heavenly  body,  or  the  pole  of  illumination,  will 
always  be  90^  from  the  direction  of  the  parallel  of  posi- 
tion. Hence,  in  projecting  any  part  of  the  parallel  on  a 
chart,  it  should  be  called  a  Li.\E  of  Positiox,  and  the 
line  representing  the  direction  of  the  body  a  Line  of 
Bearing. 

Art.  316«  To  project  a  parallel  of  position,  hav- 
ing observed  an  altitude  of  a  heavenly  body  and  knowing 
its  declination.  On  a  meridian,  whose  longitude  is  equal 
to  the  Greenwich  hour  angle  of  the  body  (since  the  body 
is  in  the  zenith  of  the  pole  of  illumination),  project  the 
pole  of  illumination,  whose  latitude  will  be  equal  to  the 
dec'ination.  The  north  and  south  points  of  the  parallel 
of  position  will  be  distant  from  the  pole  of  illumination 
by  a  quantity  equal  to  the  complement  of  the  correct  alti- 
tutle.  Assume  latitudes  at  equal  intervals  between  the 
norlh  and  south  limits,  and  compute  the  corresponding 
hour  angles,  there  being  one  on  each  side  of  the  meridian 
for  the  same  latitude.  By  plotting  the  various  points 
and  by  drawing  tlir.nigh  them  a  curve  line  the  parallel 
of  ).osition  will  be  shown.  On  the  Mercator  chart,  owing  to  the  distortion,  the  curve  shewn  will  not  be  7 
circle. 

After  the  body  has  advanced  during  a  certain  interval  of  time,  if  a  second  altitude  is  observed  and  the  corre- 
sponding parallel  of  position  plotted,  the  two  curves  will  intersect  in  two  points,  at  one  of  which  the  observer  is 
situated.     That  one  can  be  determined  by  the  bearings  of  the  body  at  the  limes  of  observation. 

Ihe  position  of  the  observer  may  also  be  found  by  taking  the  altitudes  of  two  different  objects  at  the  same 
time  and  plotting  the  corresponding  parallels  of  position. 

Since  the  Navigator  knows  approximately  the  ship's  latitude  and  longitude,  it  is  necessary  to  project  but  a 
limited  j)ortion  of  the  line  of  position ;  hence,  it  may  generally  be  regarded  as  a  straight  line,  and  two  points  will 
suffice,  except  in  case  of  high  altitudes,  when  three  or  four  points  are  needed. 

To  find  the  latitude  and  longitude  by  lines  0/  position  projected  on  a  Mercator  chart. 


Fig.  69. 


Art.  317.  Case  L  By  the  altitudes  of  two  objects  taken  at  the  same  time. — Since  the  position  of  a  shij)  is 
determined  by  the  intersection  of  two  lines  of  position,  it  can  be  most  accurately  determined  when  the  lines  inter- 
sect at  right  angles  ;  hence,  two  objects  should  be  chosen  whose  azimuths  differ  about  90". 

Observe  the  altitude-;  and  reduce  them  to  true  altitudes;  note  the  times  of  observation  by  chronometer. 
.\ssume  two  latitudes  which  will  embrace  the  jirobabe  position  of  the  ship,  differing  5',  10'.  or  20',  as  con\enient. 
It  is  better  to  use  the  s  me  latitudes  for  both  cl)servations,  to  save  logarithms. 

Compute  the  local  times,  and  thence  the  longitudes  for  each  observation,  which  will  give  two  points  for  each 
line  of  position.  Plot  the  lines  of  position  upon  the  chart,  and  the  point  of  their  intersection  will  be  the  position 
of  the  ship. 

ExAMi'LK.  At  sea,  June  26,  1S79,  p.  m.,  in  Lat.  49°  50''  N.,  Long.  7°  W .,  by  account,  the  true  altitude  of 
the  Sim  was  55°  b'  20^^;  the  true  altitude  of  the  moon,  22°  20^;  Gr.  m.  t.,  2''  27'"  40s. 


O's  Dec,     23°  22^  38'^  N.  R.  A.  M.  Sim, 

5  's  Dec,       2    36    14     S.  (I 's  R.  A., 

Eq.  t.  (  +  to  app.  t.), 
Assumed  latitudes,  49°  40''  and  50°  o'.  . 

Line  of  Position  by  Sun's  Altitude. 


6b  ijra  21S.7 


II 


39 


//          = 

L               = 

1'.  1).         = 

2) 

+ 

+ 

55°  6' 
50    0 

66   37 

20" 

0            log  sec 
22            log  cosec 

0.19193 
0.03720 

8.85806 
9.70878 

h 
L 
P.D 

s  —  h 

t 
Eq.  t. 

L.  m.  t. 
Gr.  m.  t 

Long., 

^ 

55°    6'  20''' 
49    40     0 
66    37    20 

log  sec 
log  cosec 

log  cos 
log  sin 

log  sin  % 
(A2) 

0.18894 
0.03720 

s  -h        = 

171    43 

85   51 
30  45 

i"55" 
2 

42 

5 1             log  cos 
31             log  sin 

50*^          log  sin  yi 
30 

2)171    23   40 

85    41    50 
3c    35   30 

i''  57">29s 
+            2    30 

8.87520 
9.70665 

18.79597 

18.80799 

L.  app.  t.  = 

Eq.  t.           = 

f  9-39799 

t   9.40399 

L.  m.  t.     ^= 
Gr.  m.  t.  = 

1  58 

2  27 

20 
40 

1  59    59 

2  27    40 

Long.        = 

29 
7°  20^ 

20 
o'f  W.  (Ai) 

+       27    41 
6°  55'  15^'  W 

U4 

a  given  altitude, 
Navigation. 

One  other  i 


Sumner's  method. 


t 


will 


upon  the  Navigator's  chart,  with  an  explanation  of  its  practical  application  to  the  necessities  of 

loint  should  be  noticed  in  connection  with  this  system,  in  order  to  avoid  confusion  in  nomenclature. 

The  heavenly  body,  or  the  pole  of  illumination,  will 
always  be  90*^  from  the  direction  of  the  parallel  of  posi- 
tion. Hence,  in  projecting  any  part  of  the  parallel  on  a 
chart,  it  should  be  called  a  Line  of  Position,  and  the 
line  representing  the  direction  of  the  body  a  Line  of 
Bearing. 

Art.  316.  To  project  a  parallel  of  position,  hav- 
ing observed  an  altitude  of  a  heavenly  body  and  knowing 
its  declination.  On  a  meridian,  whose  longitude  is  equal 
to  the  Greenwich  hour  angle  of  the  body  (since  the  body 
is  in  the  zenith  of  the  pole  of  illumination),  project  the 
pole  of  illumination,  whose  latitude  will  be  equal  to  the 
dec'ination.  The  north  and  south  points  of  the  parallel 
of  position  will  be  distant  from  the  pole  of  illumination 
l)y  a  quantity  equal  to  the  complement  of  the  correct  alti- 
tude. Assume  latitudes  at  equal  intervals  between  the 
north  and  south  limits,  and  compute  the  corresponding 
hour  angles,  there  being  one  on  each  side  of  the  meridian 
for  the  same  latitude.  By  plotting  the  various  points 
and  by  drawing  through  them  a  curve  line  the  parallel 
owing  to  the  distortion,  the  curve  shewn   will  not   be  p 


Fig.  69. 
be  shown.      On  the   Mercator  chart. 


of   position 
circle. 

After  the  body  has  advanced  during  a  certain  interval  of  time,  if  a  second  altitude  is  observed  and  the  corre- 
sponding parallel  of  position  plotted,  the  two  curves  will  intersect  in  two  points,  at  one  of  which  the  observer  is 
situated.     That  one  can  be  determined  by  the  bearings  of  the  body  at  the  times  of  observation. 

Ihe  position  of  the  observer  may  also  be  found  by  taking  the  altitudes  of  two  different  objects  at  the  same 
time  and  plotting  the  corresponding  parallels  of  position. 

Since  the  Navigator  knows  approximately  the  ship's  latitude  and  longitude,  it  is  necessary  to  project  but  a 
limited  portion  of  the  line  of  position ;  hence,  it  may  generally  be  regarded  as  a  straight  line,  and  two  points  will 
suflice,  except  in  case  of  high  altitudes,  when  three  or  four  points  are  needed. 

To  find  the  latitude  and  longitude  by  lines  of  position  projected  on  a  Mercator  chart. 

Ai't.  SIYo  Case  L  By  the  altitudes  of  two  objects  taken  at  the  same  ti)iie. — Since  the  position  of  a  ship  is 
determined  by  the  intersection  of  two  lines  of  position,  it  can  be  most  accurately  determined  when  the  lines  inter- 
sect at  right  angles  ;  hence,  two  objects  should  be  chosen  whose  azimuths  differ  about  90^'. 

Observe  the  altitudes  and  re(iace  them  to  true  altitudes;  note  the  times  of  oliservation  by  chronometer. 
.\ssume  two  latitudes  which  will  embrace  the  prolmb'e  position  of  the  ship,  differing  5',  10'.  or  20',  as  con\enient. 
It  is  better  to  use  the  s:me  latitudes  for  both  observations,  to  save  logarithms. 

Compute  the  local  times,  and  thence  the  longitudes  for  each  observation,  which  will  give  two  points  for  each 
line  of  position.  Plot  the  lines  of  position  upon  the  chart,  and  the  point  of  their  intersection  will  be  the  position 
of  the  ship. 

sea,    lune  26,    1879,  p.  m.,  in   Lat.  49°  50^  N.,  Long.  7°  W.,  by  account,  the  true  altitude  of 


I 


th. 


EXAMI'I.K. 

sun  was  55 


,  At 

O    (^/ 


10" ;  the  true  altitude  of  the  moon,  22°  20^;  Gr.  m.  t.,  2''  27'^ 


O's  Dec, 
(J 's  Dec, 


22' 
36 


38^^  N.  R.  A.  M.  Sun,  6'' 

14     S.  ([ 's  R.  A.,  II 

Eq.  t.  (+to  app.  t.). 


40s, 
17.1 
38 


Assumed  latitudes,  49°  40^  and  50°  o' 
Line  of  Position  by  Sun's  Altitude. 


21S.7 

39 

30 


h              = 
L              = 
P.D.        = 

55°    6'    20^' 

50     0       0            log  sec 

66    37'    22            log  cosec 

0.19193 
0.03720 

8.85806 
9.70878 

h 
L 
P.D 

s 

s  —  h 

i 
Eq.  t. 

L.  m.  t. 
Gr.  m.  t 

Long., 

= 

55°    6'  20^' 
49    40     0 

66    37    20 

log  sec 
log  cosec 

log  cos 
log  sin 

log  sin  y^  t 
(A.) 

0.18894 
0.03720 

s  -  h        = 

2)171    43     42 

85    51     51             log  cos 
30   45     31            log  sin 

ih  jyi.  5o«          log  sin  y2,t 
+            2    30 

2)171    23   40 

85    41    50 
30    35   30 

I'l  57i"29'5 
+             2    30 

8.87520 
y. 70665 

18.79597 

18.80799 

L.  app.  t.  = 

Eq.  t.          = 

9-39799 

9.40399 

L.  m.  t.     = 
Gr.  m.  t.  = 

1  58     20 

2  27     40 

1  59    59 

2  27    40 

Long.        = 

-(-          29     20 

7°  20^     o''W.(Ai) 

+       27    41 
6°  55^  15^^  W. 

■^ 


57 

rot 


57 
lot 


54 


78 


77 


5^ 


55 


61 


«t 


i7 


69 


57 
sb. 


60. 


B 


L 


SI 


SS 


62 


SI 


52 


SO 


41 


V9 


54  / 


_W_ 


g*_ 


i\ 


I 


sumnek's  method. 


145 


Line  of  Posit  ion  I'v  Moon's  Altitude. 


h 

!l 
P  0. 

t, 

R.  A., 

.Sid.  t., 
R.  A.  M. 

L.  m.  t., 
G.  m.  t., 

Long., 

s., 

+ 

22°  20'      O'^ 

50      O      O 

92  42    35 

log  sec 
log  cosec 

log  cos 
log  sin 

log.  sin  yi  t 
(B.) 

0.19193 
0.00049 

9.11447 
9-93835 

19.24524 

// 
L 
P.D. 

s 
s  —  h 

t, 

R.  A., 

Sid.  t. 
R.  A.  M. 

L.  m.  t., 
G.  m.  t., 

Long. 

S., 

22°  20^    0" 
49   40      0 
92  42    35 

log  sec 
log  cosec 

log  cos 
log  sin 

log  .sin  y, 
(B.) 

0.18894 
0.00049 

1)165   02    35 

82   31     17 
60   1 1    17 

3h  l8ni228 

II    38    39 

2)164  42    35 

82   21    17 
60     I    17 

—        3''  1 9'"  47'' 
II    38    39 

9.12398 
9.93762 

19.25103 

9.62262 

t  9.62551 

8   20    17 
6    17    22 

8    18    52 

6    17    22 

2     2    55 
2   27    40  .0 

2      I    30 

2    27    40 

24    45 
6°  11^  is^MV. 

-(-            26    10 
6°  32^  30''^  W. 

Then  by  plotting  the  lines  Ai  A.2  and  Bi  Bj,  the  point  of  intersection,  or  ship's  place,  will  be  found  to  be  in 
Lat.  49  '  30'  N.,  Long.  6^  43' W.     (See  Chart,  Case  L)  r        •• 

Art.  318.  C.A.SE  n.  By  altitudes  of  the  same  olfrt  obsemed  at  different  times.— ¥\\\d.  the  lines  of  position 
corresponding  to  each  altitude,  and  project  them;  the  point  of  their  intersection  will  be  the  true  place  of  the  ship 
if  she  has  not  changed  her  position.  ,       j  1       1  1    j 

If  tlie  ship  has  changed  her  position  between  the  observations  the  first  altitude  must  be  reduced  by  the  method 
given  in  Art.  288,  Chap.  VH,  to  the  place  of  the  second,  or, 

Plot  the  two  lines,  and  move  one  of  them  parallel  to  itself  by  a  quantity  equal  to  the  distance  run  m  the  inter- 
val on  the  course  made  good.  .  .    , 

EXAMI'I.E.  At  sea,  June  27,  1879,  a.  m.,  observed  the  following  altitudes  of  the  sun  to  determine  the  ships 
place  by  the  intersection  of  the  lines  of  position  ;   the  ship  having  run  in  the  interval  25  miles  on  a  course  East  (true). 

Ship's  place  by  account  at  first  observation,  Lat.  49-^  40'  N. ;   Long.  S*-"  53'  30"  W. 

Ship's  place  by  account  at  second  observation,  Lat.  49-  40'  N. ;   Long.  5-  15'  W. 

Chro.  t.,         8h  24"'  \i?  O's  true  alt.,     36'^  24'  20"  Az.,  N.  8>^  points  E. 

Chro.  t.,        1051     40  O's  true  alt.,     58      920  -Az  ,  N.  12  points  E. 

Eq.t.,     +  2     40(ist)     Eq.t.,  +      2'»4I^3(2d)    O's  Dec,  23^^  20' 55"  N. 

Assumed  Latitudes,  49°  50'  and  49^  30. 


h 
L 
P.  D. 


s—h 


=         36°  24'  20" 
=        49     50     o 
=        <-0    39     5 

2)152    53    -5 


;=^        76    26   42 

=:  40  2      22 


log  sec 
log  cosec 


log  cos 
log  sin 


o.  19043 

0037II 


9.3699; 

9.80842 

19.40587 


L 
P.  D. 


=  36"  24'  20" 

49    3"     o 
60     ;q      S 


L.  app.  t.,  7''   57'"  34'         log  'in  >2  /•  9  70293 

Kq.  t.,  -I-  2    40 


L.  ni.  '., 
(i.  m.  t., 

Long., 

// 
I, 

r.  I). 


8       o     14 
8     24     14 


+  24      o 

=     6^^     o'  00"  W.  (Ai) 


=  58  9'  20' 
=  49  50  o 
=-  66      M       1; 


^) 

174    7,^    25 

s 

87     19    12 

log  cos 

s-h 



29      9    52 

log  sin 

L.  app.  t. 

J 

10''  29'"  30^.2 

log  sin 

Eq.  t., 

+ 

2    41  .3 

L.  m.  t.. 

10   32     II .5 

G.  m.  t., 

10   51     40.0 

log  sec  0.19043 

log  cosec        0.0371 1 


8.66985 
9.68781 


18.58520 


L.  app.  t., 
Eip  t., 

L.  ni.  t., 
G.  in.  t.. 

Long., 


h 
1, 
P.  1). 


s 

s  —  h 


L.  app.  t., 
Eq.  t., 

L.  m.  t., 
G.  m.  t.. 


2)152    33    25 

76     16   42 

39     52    22 


-j-  2       40  .0 

8007 
8    24     14 .0 


log  sec 
log  cosec 


log  cos 
log  sin 


0.18746 
0.03711 


9-37512 
9. 80692 

19.40661 


log  sin  >^  t.    9.70330 


+         24     13 .3 

=      6"    3'  20"  W.  (A.,) 


log  cos 
log  sin 


Long.,  +        19    28.5 

=       4^  52'  7"  W.  (BO 

10    B 


Long., 


58^-'     9'  20' 

49     30      o 
66     39      5 

2)174     18    25 

87      9    12 
28    59   52 


io'>  27'"  15^8 

+  2    41.3 

10  29    57.1 

10  51     40 


-r        21     43 

=  5°  25'    45"  W.  (B,) 


log  sec  0.18746 

log  cosec       0.0371 1 


8.69603 
9.68554 

18.60614 


log  sin  Yz  t.  9.30307 


146 


Sumner's  method. 


By  plotting  these  lines  on  the  chart  and  moving  the  first  line  A,A,  parallel  to  itself,  East  2?  miles    the  noir 

r/y  acSS'^sIe  ata^: ci"  HO  ''  '"'  ""•'  '^°"''  '^  "''  ^^  "'"'  ''  "  "''^^  '^  '^^  '>'  ^^  •  -"--"^ 'p «-" 
By  reducing  the  first  altitude  to  the  place  of  the  second  by  the  precept  in  Art.  2S8,  the  line  VA,  niiv  h 
determined  m  its  advanced  position  ;  but  when  approaching  a  coast  it  is  preferable  to  determine  and  plo  the  lin 
of  position  corresponding  to  the  first  altitude  at  once,  which,  particularly  in  case  of  its  being  parallel  lo  the  re,, 
eral  coast  line,  may  l)e  of  great  value.      See  next  case.  i=  F        '^i  lu  uie  i,en 

Art.  319.  Case  III-— At  sea,  October  16,  1879,  a.  m.,  in  Lat.  48^  30'  N.,  Long.  50  46'  W.,  by  account 
the  ship  approaching  the  land,  observed  an  altitude  of  the  sun  on  a  bearing  which  Avould  make  the  line  of  posi  io 
nearly  parallel  to  the  general  coast  line.     Determine  and  plot  the  line  of  position.  ^        1|. 


/i 

L, 

P. 


D, 


Chro.  time  (true 
G.  m.  t.,  Oct.  15, 

=        28°  13'  30" 
=       48    20     o 
=       98    50     o 

2)175  23  30 


iqIi 

22 


sec 
cosec 


22'"  20^         G's  true  Alt. 

20     20  0's  Dec.  S., 

Assumed  Latitudes,  48 


280  13'  30'' 
8    50     o 

20',  48'J  30',  48- 


Az.,  N.  13  pts.  E 

Eq.  t.  (—  from  App.  t.),   14'"  k/ 


40 


0.1 773 1 
0.00518 


L.  = 


28- 

48 

98 


13' 

30 
50 


30' 
o 
o 


sec 
cosec 


0.17874 
0.00518 


L,= 


280 

48 

98 


13' 

40 

50 


30' 
o 
o 


I 


sec         o.  i8oi; 
cosec      0.0051! 


2)175     33    30 


s  =        87    41   45      cos  8.60427 

s  —  h=z        59    28   15      sin  9-93519 


18.72195 


L.  app.  t.,  10''  I3">48^7  sin  ^ /.  9.36097 
Eq.  t.,  —   14  19 .0 


87  46  45  cos    8.58828 
59  Zl    15  sin    9-93556 

18.70776 

10'' 15"' 33'- 8  sin>^  A  9.35388 
—        14    19.0 


2)175     43    30 

87     51    45     cos         8.5716S 
59     3^    15     sin  9-9359: 

i8.6929( 

10''  17"'  21^4  sin  Yj,  t.  9.3464J 
—        14     19 .0 


L.  m.  t.,        9   59    29.7 
G.  m.  t,      IO   22    20  .0 


10      I     14.8 
10   22    20 .0 


10     3      2.4 
10   22     20 .0 


Long.,     -4-       22    50.3 


=     5°42'35"  W.  (Ai) 


+ 
=    5 


21 

^  16' 


5-2 

18"  W.  (A3) 


+       19    17-6 

=     4O   49'    24"W.  (A:3) 


By  plotting  this  line  A, A, A,  it  will  be  seen  by  the  chart  that  by  steering  a  course  parallel  to  it  the  sliin  will 
approach  the  land  at  the  nearest  point,  at  a  distance  of  three  miles,  whereas  on  tlie  same  course  from  the  posilioni 
hy  account  the  nearest  distance  would  be  thirteen  miles. 

Art.  320.  rience  it  can  be  seen  that,  although  the  absolute  position  of  the  ship  may  not  be  known,  how' 
valuable  a  guide  to  the  Navigator  in  approaching  the  land  in  thick  weather  the  line  of  position  may  be,  when  the 
sun  can  be  observed  on  a  bearing  nearly  at  right  angles  to  the  general  direction  of  the  coast  line. 

Again,  in  running  for  any  landmark  or  in  running  a  line  of  soundings,  frequent  observations  can  be  taken 
re  iir  d"^*^  ^^  "        ^"  ^°         ^^"^'  ^^^  *'^"^  '^'^  '^°"''^*^  °^  ^^^  ''^^^  '"'^^  '^^  constantly  verified  and  corrected  as 

If  the  objects  observed  should  be  near  the  prime  vertical,  longitudes  should 
be  determined  from  assumed  latitudes ;  if  near  the  meridian,  the  local  times, 
and  thence  the  hour  angles  should  be  found  from  the  Greenwich  time  and  as- 
sumed longitudes.  With  these  hour  angles  and  the  altitude  the  corresponding 
latitudes  are  to  be  found. 

The  practical  Navigator  knows  the  impossibility  of  locating  the  ship  upon 
a  definite  point  at  sea;  various  errors,  which  are  unavoidable,  conspire  against 
strictly  accurate  work,  such  as  errors  in  the  altitude  and  errors  in  the  Green- 
wich time.  But  it  remains  within  the  ability  of  the  Navigator  to  locate  the  ' 
ship  within  a  circumscribed  space  which  may  be  projected  on  the  chart,  the 
limicing  lines  of  which  are  those  obtained  by  the  estimated  errors  of  altitude  and 
errors  of  the  chronometer. 

The  error  of  altitude  must  be  estimated  at  the  time  of  oliservation  by  due 

consideration  of  the  atmosphere  as  affecting  the  refraction,  of  the  motion  of  the  ' 
ship  and  state  of  the  sea  as  affecting  the  dip  of  the  sea  horizon.     The  instrumental  errors  are  under  control  and 
may  be  checked;   the  personal  error  may,   or  may  not,  be  known;   but  the  accidental  errors  must  be  estimated 

^y  and  applied  in  this  manner :  Suppose  an  altitude  of  a  celestial  ob- 
ject to  be  measured,  the  Greenwich  time  and  the  body's  declination 
known,  two  latitudes  assumed;  then  the  line  of  position.  A;  A2, 
can  be  determined  and  plotted  upon  the  chart  as  Ai  Ao  in  the 
figure. 

Assuming  the  altitude  to  be  in  error  5',  either  too  great  or 
too  small,  and  remembering  that  if  the  altitude  is  too  small  the  I 
hour  angle  is  too  great,  and  if  too  great  the  hour*  angle  is  too 
small.  Hence,  project  two  lines  a^  a.i,  a' x  ,/•...,  one  on  either  si  !c 
of  Ai  A:;,  at  a  distance  equal  to  the  estimated  error.  It  is  now 
within  the  limit  of  safety  to  assume  the  ship's  position  within  the 
space  bounded  by  these  parallel  lines. 

Suppose  at  the  same  instant  anotlier  celestial  object  had  been 
observed  whose  azimuth  differed  60-  to  120  '  from  that  of  the  first 

.     I      T>   r.  ,    ,        ,".•"'' "I  "x,  using  the  same  assumed  latitudes  to  save  logarithms.      Plot  the  lines 

Ai  A2,  b,  Bj,  and  also  the  lines  a,  a.,  a\  d'o,  /;,  />.,,  b\  //.>. 

A     \^^tx   5]"P's  position  will  now  be  regarded  not  at  "the  positive   point  of  intei  section  of  the  lines  of  position    ' 
u't   d  '^''     "  quadrilateral  formed  by  the  intersection  of  the  lines  representing  the  estimated  error 


body. 


A  2       ai  h,     /?. 

Determine  the  line  of  position  B,  B.. 


i 


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SUMNER  S    METHOD. 


147 


Showld  there  be  any  uncertainty  in  the  Greenwich  time  parallels  may  be  drawn  on  both  sides  of  the  lines  of 
position  or  on  the  side  of  uncertainty ;  the  distance  in  longitude  being  measured  on  a  parallel  of  latitude  equal  to 
the  amount  of  uncertainty. 

Two  points  are  usually  sufficient  to  project  a  line  of  position,  but  the  determination  of  a  third  point  serves  to 
verify  the  work. 

Art.  321.    To  find  the  azimuth  of  the  body  front  the  Hue  of  position. 

Yxom.  the  latitudes  and  longitudes  of  the  two  points  Ai,  A^,  find  the  course,  or  the  direction  of  the  line, 
by  mitlille  latitude  sailing.  Since  the  bearing  of  the  body  is  90°  from  this  line  the  azimuth  may  be  found  by 
adding  or  subtracting  90^ 


Example.    Same  as  Case  III. 

Li 
L3 


48°  20' 
48    40 


Loi 
L03 


50  42' 
4    49 

53 
35-1 


Azimuth  N.    =:  150°  E.,  or  N.  13  pts.  E. 

Or  if  the  line  is  plotted  on  the  chart  the  azimuth  may  be  found  by  referring  the  direction  of  the  line  to  the 
nearest  compass-rose.  If  there  be  no  compass-rose,  measure  with  a  protractor  the  angle  which  a  perpendicular  to 
the  line  of  position,  or  a  line  of  l^earing,  makes  with  a  meridian. 


Mid.  L. 

=     48    30 

D.  Lo. 

D.  L. 

=            20 

Dep, 

Course  N. 

=     60"  E. 

Add 

90° 

Art.  3212.    To  find  the  Latitude  and  Longitude  by  a  Line  of  Position  and  the  change  of  the  Sun's  altitude  near  the 

prime  vertical. 

In  high  latitudes  the  ship's  position  may  be  approximately  determined  when  the  sun  can  be  observed  rear 
the  prune  vertical,  by  deducing  the  approximate  latitude  by  Prestel's  method,  Art.  284,  Chap.  \'II.  Then,  l)y 
assuming  that  the  error  in  this  latitude  is  about  20',  determine  the  line  of  position  by  finding  the  longitudes  from 
the  aliitude  measured,  and  two  assumed  latitudes  differing  20'  each  from  that  already  found.  This  is  but  a  rough 
approximation,  l)ut  it  confines  the  position  of  the  ship  to  a  limited  portion  of  the  line. 

Example.  Same  as  in  Case  II.  The  sextant  being  set  at  36-  24'  30"  the  two  contacts  of  the  upper  limb  and 
the  lower  limb  were  observed  as  follows  : 


Upper  limb 
Lower  limb 

Interval 


Chronometer, 
gii  22'"  36^ 
25     52 


=      8 


Semi-diameter 

Interval 

Amplitude 

Latitude 


=       6- 


15'    46"  =  946" 


16 

Constant  log  9.12494 

log  2.97589 

ar-co  log  7.70774 

log  sec  0.00239 


=     49-  40'    40"  N. 


log  cos 


9.81096 


By  using  assumed  latitudes,  differing  each  10'  or  20'  from  the  latitude  found  above,  and  the  same  altitude,  a 
line  of  position  will  be  found  which  will  coincide  with  Ai  A3  of  Case  II,  on  the  chart. 


148  VARIATION    OF    THK    COMPASS. 

CHAPTER    X. 
VARIATION   OF  THE   COMPASS. 

Al't«  333.  It  was  many  years  after  the  discovery  of  the  compass  before  it  was  suspected  that  the  magneti;: 
needle  did  not  point  accurately  to  the  north  pole  of  the  world;  hut  about  the  middle  of  the  sixteenth  century 
observations  weie  made  in  England  and  France  which  fully  proved  that  the  needle  pointed  to  the  eastward  of  the 
true  north. 

The  angle  which  measures  this  difference  of  direction  is  called  the  Variation  of  the  Compass,  and  is  named 
easterly  when  the  north  point  of  the  compass  needle  is  drawn  to  the  eashvard  o{  true  north,  and  ivesterly  -when 
drawn  to  the  -iveshsjard  of  true  north.  HI 

Although  charts  are  now  constructed  on  which  are  drawn  lines  of  equal  variation,  for  the  assistance  of  the  ™* 
Navigator,  still  it  is  absolutely  necessary  to  be  able  to  find  the  variation  at  anytime  in  order  to  correct  the  courses 
steered  by  compass. 

The  amount  of  the  variation  is  determined  by  comparing  the  True  Azimuth  of  some  celestial  or  terrestrial 
object  with  the  observed  Compass  Azimuth  of  the  same  object;  then  the  variation  is  found  by  taking  the  diflercnce 
between  the  compass  azimuth  and  the  true  azimuth,  and  is  marked  E.  or  W.,  according  as  the  comimss  azimuth 
falls  to  the  left  or  right  of  the  true  azimuth. 

There  are  several  methods  of  finding  the  true  azimuth,  and  hence  the  variation ;  those  useful  to  the  Navigator 
are — 

1.  By  Amplitudes. 

2.  By  Time  Azimuths. 

3.  By  Altitude  Azimuths. 

4.  By  the  True  Bearing. 

1.— BY  AN  AMPLITUDE. 

Art.  3t24.  The  method  by  am])litudes  consists  in  observing  the  compass-bearing  of  the  sun  or  other  celes- 
tial body  when  its  centre  is  in  the  true  horizon;  or,  in  other  words,  at  its  true  rising  or  setting.  Since  the  objtct 
can  only  be  referred  to  ihe  visible  horizon,  and  being  subject  to  vertical  displacement  from  rcfr.clion,  parallax,  and 
dip,  it  is  necessary  to  observe  its  centre  in  the  visible  horizon  and  to  apply  a  correction. 

Art.  335.  The  Observation. — With  cbjects  having  ap])reciable  discs,  like  the  sun  and  the  moon,  no  prepara 
tion  is  needed  except  being  ready  at  the  compass  a  few  minutes  in  advance,  and  keeping  the  sight-vanes  pointed  in 
the  right  tlirection. 

If  the  Sun  is  to  be  observed  at  the  rising,  when  the  upper  limb  appears  in  the  sea  hori/on,  take  the  bearing 
by  compass;  and  continue  to  taVe  bearings  of  the  centre  l)isecting  the  disc,  noting  each  bearing  until  the  lower 
limb  appears.  At  the  setting,  commencing  when  the  lower  limb  touches  the  horizon,  proceed  in  tlie  s-ame  manner 
until  the  upper  limb  disappears.  The  mean  of  the  bearings,  reckoning  from  the  E.  or  W'.  jioinl,  will  be  tlie  observed 
amplitude. 

The  Moon. — Proceed  in  the  same  manner  as  in  observing  the  sun  if  the  luminous  jiorlion  of  the  disc  is  bright 
enough  for  the  rising  to  be  anticipated  in  time  to  get  the  bearing  of  the  upper  limb  as  it  comes  upon  tie  horizon. 
Otherwise  it  would  be  better  to  wait  until  a  sufticient  altitude  has  been  reached  to  observe  an  azimuth. 

There  should  also  be  noted  with  this  observation,  as  well  as  with  a  1  others  for  delei  mining  the  variation,  the 
ship's  head  by  the  standard  compass,  the  angle  of  heel  if  an  iron  vessel,  and  if  to  starboard  or  to  port. 

Art.  336.   The  Computation. 

To  correct  the  observed  amplitude. — Enter  Table  40  with  the  latitude  and  declination  to  the  nearest  degree,  and 
apply  the  correction  there  found  to  the  observed  amplitude. 

For  the  sun,  a  planet,  or  a  fixed  star,  at  the  rising  in  N.  Lat.  and  at  the  setting  in  S.  Lat.,  to  the  right ;  or, 
at  the  setting  in  N.  Lat.  and  rising  in  S.  Lat.,  to  the  left. 

For  the  moon  apply  half  the  correction  in  the  contrary  manner. 

The  result  will  be  the  corrected  compass  amplitude,  which,  by  comparison  with  the  true  amplitude,  will  give 
the  variation. 

To  find  the  true  amplitude. — To  the  log  secant  of  the  latitude  add  the  log  sine  of  the  declination ;  the  sum 
(rejecting  10  in  the  index)  is  the  log  sine  of  the  true  amplitude;  or  the  angular  distance  from  the  east  or  west 
point  towa.d  the  north  in  north  declination,  but  toward  the  south  in  south  declination. 

By  Inspection. — Enter  Table  39  with  the  declination  at  the  top  and  the  latitvde  in  he  side  column;  under  the 
former  and  opposite  the  latter  will  be  the  true  amplitude.  When  great  accuracy  is  required  interpolate  for  minutes 
of  latitude  and  declination. 

To  find  the  variation.  —  If  the  corrected  compass  amplitude  and  the  true  anqilitutle  be  of  the  same  name,  their 
difference  will  lie  the  variation;  if  of  different  names,  their  sum  will  be  the  variation.  The  variation  will  be  E.  or 
W.  according  as  the  compass  amplitude  falls  tq  the  left  or  right  of  the  true  amplitude. 

Example.  At  sea,  June  5,  1875,  in  Lat.  Ii'^  29'"  N.,  Long.  30^  \V.,  about  6''  10"'  a  m.,  the  observed  bearing 
of  the  sun  at  rising  was  E.  31^^  N. ;   Greenwich  date,  June  4,  20'',  Q's  l^ec,  22^'  32'  N. 

By  Table  39.  By  computation. 

Lat.  =     11^.5  N.>T,         ,  p,         „^o  ^„/ i\r       L  =     II'' 30'        log  sec       0.00881 

Dec.  :-     22  .5N.  JT'^^^'^P-^-'       22059'N.      J  _     2230         log  sin        9.58284 


Obs,  Amp.  E.  31*^'  N.  >  ^  .  ^        ^       ' 

Corr.  Table  40  (right),  JComp.  Amp.  E.,    30    54 


N. 


True  Amp.       =     22    59        log  sin       9-59'^S 
Comp.  Amp.    =     30    54 


Variation,  8     E.  Var.  =      8    E. 


VARIATION    OF    THE    COMPASS. 


149 


ExAAJiii.K.   At  sea,  May  30,  1S75,  in  Lat.  25°  3'  S.,  Long.  22°  W.,  about  6^  42'"  a.  ni.,  the  oliserved  bearing 
of  the  sun  at  rising  was  E.  18'-'  30'  N. ;   Greenwich  date,  May  29,  20'';  O's  Dec,  2l"  44'  N. 

By  computation. 
L  :=        25*-'       3'      log  sec       0.04290 

f/  =        21       44       log  sin        9.56854 


[.at. 
Dec. 


By  Table  39. 


Obs.  Amp.  =     18  .5 

Corn   Table  40  (left),        o  .3 


0.1  N. 
Comp.  Amp.,  E.  18  .8  N. 


True  Amp. 
Comp.  Amp. 


E.  24      8    N.  log  sin        9  61 144 
E.  18  48    N. 


Variation, 


\\'.       V.T.riation, 


5    20    W. 


Example.    At  sea,  November  27,  1875,  i"  Lat.  40^'  27'  N.,  Long.  20-'  7'  \V.,  about  4''  43'"  p.  m.,  the  observed 
bearing  of  the  sun  at  setting  was  \\ .  17"^  S. ;  Greenwich  date,  November  27,  6'';  Q's  Dec,  21*^.2  S. 


Lat. 
Dec 


By  Table  39. 


—        40°.5  N.  J-p^^^^  .      ^       W.  280.4S.       V 
=         21   .2  S.    )  '  ^  It 


By  computation. 

=        40^'  30'        log  sec 
=         21     12         log  sin 


Obs.  Amp.  =  W.  17        S.    ?Po„-,,     A,„,-     w    17    7S        True  Amp.       =   W.  28    24  S.    log  sin 

Corr.  Table  40  (left),       0.7         ^  ^omp.  Amp.,  w.  17  .7  .-5.       Comp.  Amp.,         W.  17    42  S. 


o.  1 1 S95 
9.55S26 

9.67721 


Variation, 


10". 7  W.     Variation, 


ID     42  W. 


Example.    At  sea,  December  18,  1S75,  in  Lat.  31*^  35'  S.,  Long.  60'"   13'  E.,  about  7''  ji.  m.,  the  observed 


earing  of  the  sun  at  setting  was  N.  83^^.4  \V. ;   (Jreenwich  date,  Decemlier  18,  3'';  Q\  Dec, 

By  computation, 
r 
True  Amp.,     W.  27' '.9  S. 


By  Table  39. 
Lat.,  '  3i'^'-6  S 

Dec,  23  .4  S 


L 


31^'  35' 


•3  .4S. 

log  sec 
log  sin 


0.06962 
9-59^95 


( )l)s.  Amp.,  W.    6  .6  N. 

Corr.  Table  40  (right),     o  .4 


■Comp. Amp.,  W.    7  .0  N 
Variation,  34  .9  \V.      Variation, 


True  Amp.,       \V.  27.  47  S. 
Comp.  Amp.,    W.     7      o  N. 


log  sin        9.66857 


34    47  W, 


Dt'giri'  of  Dependence. — In  low  latitudes  this  method  is  susceptible  of  great  precision,  the  observations  not 
being  affected  by  the  relative  temperatures  of  the  sea  and  air,  verticality  f>f  the  sight  vane,  horizontality  of  the 
compass  bowl.     In  high  latitudes  refraction  renders  it  less  trustworthy. 

2.— BY  TIME  AZIMUTHS. 

Art.  327.  In  this  method  there  are  given  in  the  triangle  of  posHion  PZX,  Fig.  70,  tlie  hour  angle  ZPX, 
deduced  from  the  local  time  of  oliservation  ;  the  co-declination  PX,  and  the  co-latitude  PZ,  to  find  PZX,  the 
azimuth  of  the  body  at  X. 

Hence  it  will  be  seen  that  the  data  rerpiired  are: 

The  Iiour  angle  deduced  from  the  local  time  of  the  observation ; 

The  declination  taken  from  the  Nautical  Almanac;   and 

The  latitude  as  brought  up  by  the  reckoning,  or  as  known  by  obser- 
vation. 

In  finding  the  variation  for  a  single  heading  of  the  ship,  any  celestial 
object  sufficiently  bright  to  be  seen  through  the  sight-vanes  of  the  compass 
may  be  employed  in  time  azimutiis  with  more  or  less  convenience. 

During  the  day  the  sun  is  to  be  observed,  or  the  moon  by  day  or 
night,  the  planets  Venus,  Mars,  Jupiter,  and  Saturn,  or  the  brightest  fixed 
stars,  according  to  circumstances.  As  a  general  rule,  an  object  should  be 
selected  which  is  relatively  low  in  altitude,  not  oi.ly  that,  in  being  seen 
through  the  sight  vanes  directly  rather  than  by  reflection,  the  compass 
azimuth  is  more  reliable,  but  because  the  condition  is  more  favorable  for 
a  reliable  true  azimuth,  when  the  data  are  somewhat  reliable. 

Art.  33S.  The  Observation. — Take  a  set  of  bearings  of  the  object 
with  the  standard  compass  as  quickly  as  possible,  bisecting  it  each  time  -^ 

if  it  has  a  sensible  disc,  and  noiing  the  times  with  a  watch  whose  error  in  r  IG.  70- 

local  time  is  known.     Note  tlie  heading  of  the  ship  with  the  same  compass,  and  tlie  corresponding  headings  with 
the  other  compasses;  also  the  angle  of  heel  if  the  ship  is  iron-built. 

The  mean  of  ihe  bearings  is  the  compass  azimuth ;  the  mean  of  the  times  is  the  corresponding  watcli  time  of 
the  observation. 

Art.  3ti9.  Finding  the  True  Azimiilh. — This  method  of  finding  the  true  azimuth  consists  of  two  paits: 
1st,  the  preparation  of  the  data  ;  and  2d,  the  solution  of  the  triangle  of  position. 

The  second  part  may  be  accomplished  by  logarithmic  computation,  by  Time  .Izimuth  Tables,  of  which  there 
are  several  reliable  ones,  or  by  the  Graphic  IMethod,  such  as  Godlray's.  The  method  by  computation  alone  is  here 
given : 

Preparation  of  the  Data. 

1.  Find  the  Green  vich  date  corresponding  to  the  local  time  of  ol)servation. 

2.  Take  out  tlie  declination  of  the  body  from  the  Nautical  Almanac,  and  note  the  polar  distance  and  the 
co-latitude. 

3.  Find  the  hour  angle  of  the  body  by  rules  heretofore  given. 


150 


VARIATION    OF    THE    COMPASS. 


Let 


Then 


Solution  by  Computation. 

S  =  }4  sum  of  polar  distance  and  the  co-Lat. 

D  ^  ^  difference  of  polar  distance  and  the  co-Lat. 
y^  t  ^=  Yz  hour-angle. 
Az.  =  True  Azimuth. 

Tan  X  =  sin  D  cosec  S  cot  ^  t. 
Tan  Y  =  cos  D  sec  S  cot  y^,  t. 

Az.  =  X  -t  Y. 


First  Case. — If  the  half-sum  of  the  polar  distance  and  co-Lat.  is  less  than  90°. 

Take  the  sum  of  the  angles  X  and  Y  if  the  polar  distance  is  greater  than  the  co-Lat. ;  take  the  difference  if 
the  polar  distance  is  less  than  the  co-Lat. 

Second  Case. — If  the  half-sum  of  the  polar  distance  and  co-Lat,  is  greater  than  90°. 

Always  take  the  difference  of  X  and  Y,  which  subtract  from  180°,  and  the  result  will  be  the  True  Azimuth. 

In  either  case,  mark  the  True  Azimuth  N.  or  S.  according  to  the  latitude,  and  E.  or  \V.  according  to  the  hour 
angle. 

It  may  sometimes  be  convenient  to  use  the  supplement  of  the  True  Azimuth,  by  sulitracting  it  from  180" 
and  reversing  the  prefix  N.  or  S.,  in  order  to  make  it  correspond  to  the  Compass  Azimuth  less  than  90'-'. 

Example.  December  3,  1879,  a.  m.,  in  Lat.  30°  25'  N.,  Long,  s'"  25'"  42"  W.,  the  observed  bearing  of  sun's 
centre  was  N.  135°  30'  E.,  and  the  Greenwich  mean  time  was,  December  3,  2''  36'"  ii^. 


Gr.  m.  t.,  Dec.  3,        2'^  36'"  11^ 
Long.  W.,  — 

L.  m.  t.,  Dec.  2, 
Eq.  t.,  + 


5 

25 

42 

21 

10 

29 

10 

3 

L.  app.  t., 
H.  A., 


21     20     32 

—  2     39     28 

—  I     19    44 


S  = 

D  = 

X  = 

Y  = 

X-fY  = 


19° 

26 

56' 

51 
16 

50 

88 

44 
19 

log  cot  0.44051 
log  cosec  o. 001 14 
log  sin       9.64596 

log  tan      0.08761 


N.  139'-^     3'E.,TrueAz. 
N.  135     30   E.,  Comp.  Az, 
3     33    E.,  Variation, 


log  cot  0.44051 
log  sec  1. 14045 
log  cos  9.95267 


log  tan  1.53363 


O's  Dec, 
Eq.  t., 
co-Lat., 
P,  D., 


22^  7'  S. 
—        10'"  3« 

=       59°  35' 
^     112"     7' 


Example.    December  8,  1879,  a.  m.,  in  Lat.  30'^  25'  N.,  Long.  5''  25'"  42^  W.,  the  observed  bearing  of  the 
moon's  centre  was  N.  133°  30'  W.,  and  the  Greenwich  mean  time  of  observation  3''  24'"  54^. 


Gr.  m.  t.,Dec.8, 
Long.  \V., 


3"  34"  54^ 
5    25     42 


L.  m.  t.,  Dec.  7,  21  59  12 
R.  A.  M.  Sun  qI',  17  7  29 
Red.  forGr.  m.  t.,  2>1> 


R.  A.  Merid., 
R.  A.  Moon, 

Moon's  H.  A., 
lAt  = 


15  7  14 

12  26  17 

2  40  57  W. 

I  20  29 


s 

D 

X 

Y 

X-fY 


20°  7' 

^S" 

79  2 
19  27 

21 

21 

42  48 
85  46 

0 
0 

log  cot  0.43609 
log  cosec  0.00799 
log  sin       9-52254 


log  cot  0.43609 
log  sec  0.72087 
log  cos  9.97446 


log  tan       9.96662 


log  tan  1. 1 3 142 


N.  128°  34^  W.,  True  Az. 
N.  133    30  W.,Comp.  Az. 


4    56    E.,  Variation. 


([  's  Dec,  8°  29'  42'^  S. 

P.  D.,  98   29    42 

co-Lat.,  59   35      o 

S  =  79     2    21 

D  =  19   27    21 

Example.   April  9,  1879,  in  Lat.  42°  16'  S.,  the  observed  bearing  of  the  sun's  centre  was  S.  105°  30'  E.; 

Sun's  H.  A.,  3''  44'"  l6^   true  altitude,  iS"^  40';   Dec,  7°  38'  N. 


y^t  = 

s  = 

D  = 

X  = 

Y  -= 


28°    2' 
72    41 
24    57 

39    41 
80      5 


log  cot  0.27372 

log  cosec  0.02014 

log  sin  9-62513 

log  tan  9.91899 


X  +  Y  =  S    119    46  E.,  True  Az. 
S    105    30  E  ,  Comp.  Az. 


14     16  W.,  Xariatiiin. 


log  cot  0.27372 
log  sec  0.52629 
log  cos    9.95745 


log  tan    0.75746 


VARIATION    OF    THE    COMPASS. 


151 


the  observed  be 

arir 

ig  of  Jupiter 

was 

s.  49^  J 

E.     Rt 

■quired  the 

date,  »bruary 

23. 

oil  7m  _ 

*'sH.  A., 

_ 

_     2''  29™ 

Yzt 

= 

18^  37' 

*'s  Dec, 

10°  42'  S. 

s 

= 

64   55 

P.  D., 

100    42 

D 

= 

35    48 

co-Lat., 

29      7 

X 



62    27 

. 

Y 

— 

80     I 

'  5'"  a.  m.,  local  app.  time  ; 
the  Deviation.     Greenwich 


log  cot  0.47255 
log  cosec  0.04302 
log  sin       9.76712 


log  cot 
log  sec 
log  cos 


0.47255 
0.37270 
9.90906 


log  tan      0.28269 


log  tan     0.75431 


X  +  Y  =  N.  142°  28'  E.,  True  Az. 


N.  131 


o  E.,  Comp.  Az. 


II 
19 


28   E.,  App.  Variation. 


18   E.,  True. 


7    50  W.,  Deviation. 

Art.  330.  Swinging  Ship  at  Sea. — The  method  of  Time  Azimuths  affords  a  convenient  and  reliable 
manner  of  ascertaining  the  Deviation  of  the  Compass  at  Sea  for  different  headings  of  the  Ship.  Since  the  oppor- 
tunity can  be  chosen,  the  sun  should  be  the  body  selected  for  the  observations ;  it  should  be  low  in  altitude,  and,  if 
possible,  when  the  hour  angle  is  greater  than  4''. 

Having  a  fine  day  and  a  smooth  sea,  either  steam  or  sail  the  ship  around,  steadying  her  a  minute  or  two  on 
each  heading  in  order  to  allow  the  compass-card  to  come  to  rest.  Take  the  bearing  of  the  sun's  centre  on  each 
heading,  noting  the  time,  also  noting  the  corresponding  headings  with  the  steering  compasses  and  the  angle  of  heel. 
This  mav  be  done  for  every  point  of  the  compass,  every  other  point,  or  every  fourth  point,  as  deemed  desirable. 

The  same  may  be  done  when  in  sight  of  any  prominent  point  of  land  whose  true  bearing  can  be  established. 

Art.  331.    Rule.     To  get  the  serial  True  Azimutks  by  Computation. 

1.  Find  the  Greenwich  date  for  the  middle  local  time  of  the  set  of  observations. 

2.  With  this  date  take  out  the  sun's  declination  and  the  equation  of  time. 

3.  Deduce  the  co-Lat.  and  middle  polar  distance  to  the  nearest  minute. 

4.  Prepare  the  sun's  hour  angles,  marking  them  E.  if  A.  M.,  W.  if  P.  M. 

5.  Find  the  value  of  S  and  D,  or  the  half-sum  and  half-difference  of  the  Mid.  P.  I^.  and  the  co-Lat.  ;   then  to 

the  log  sine  of  D  add  the  log  cosecant  of  S;  the  result  will  l)e  the  Log  A.  To  the  log  cosine  of  D  add 
the  log  secant  of  S;  the  result  will  be  the  Log  B. 

6.  Now  proceed  in  tabular  form  by  ruling  several  vertical  columns,  and,  dividing  each  hour  angle  by  2,  place 

the  series  of  !^/  in  proper  order  in  C"ol.  I.  Place  the  log  cotangent  of  each  y^t  in  Col.  2.  Add  Log  A  to 
each  log  cot  ji/and  place  the  resulting  log  tangents  X  in  Col.  3;  also,  do  the  same  with  Log  B  and 
place  the  resulting  log  tangents  Y  in  Col.  4.  Then  take  out  for  each  log  tan  X  the  corresponding  angle 
X  and  place  them  in  Col.  5 ;  also,  for  each  log  tan  Y  the  corresponding  angle  Y  and  place  them  in  ("ol.  6. 

7.  Then,  remembering  the  precejits  with  regard  to   X  and  Y,  place  the  resulting  True  Azimuths  in  Col.  7, 

marking  them  N.  or  S.  according  to  the  latitude,  and  E.  or  \V.  according  to  the  hour  angle. 

8.  Place  in  proper  order  the  several  Compass  Azimuths  in  Col.  8 ;  the  total  compass  errors  in  Col.  9,  and 
then,  knowing  the  magnetic  variation,  the  series  of  Deviations  in  Col.  10. 

Example.    May  13,  1875,  in  New  York  Bay,  Lat.  40*^  41'  N.,  Long.  74"^  2'  \V.,  about  5I'  45'"  p. 


the  following  observations  of  the  sun,  on  a  careful  swinging  of  the  ship  for  Compass  Deviations, 
local  mean  time,  47**  fast.     Magnetic  Variation,  7^.9  W. 


made 
Watch  error  on 


Standard  Compass. 

Standard  Compass. 

Watch  1 

"ime. 

Watch  Time. 

Ship's  Head. 

O's  Centre. 

Ship's  Head. 

Q"s  Centre. 

h.    m. 

s. 

0     ' 

h.    in. 

s. 

0       / 

5     18 

10 

N. 

N.  72      0  W. 

5    37 

50 

S. 

N.  70    30  W. 

20 

30 

N.  N.  E. 

64    30 

41 

0 

8.  S.  W. 

79    30 

22 

0 

N.  E. 

57      0 

46 

30 

S.  W. 

86      0 

25 

10 

E.  N.  E. 

51     30 

48 

30 

W.  S.  W. 

89    30 

27 

50 

E. 

49      0 

55 

0 

W. 

88    30 

30 

20 

E.  S.  E. 

48    30 

57 

20 

W.  N.  W. 

85     30 

32 

30 

S.  E. 

52    30 

6      0 

30 

N.  W. 

80      0 

34 

40 

S.  S.  E. 

60    30 

3 

10 

N.  N.  W. 

73      0 

Mid.  date,  May  13,     5''. 7 
Long.  W.,  4.9 


Gr.  m.  t.,  May  13,     10  .6 


Q's  Dec,  1 8°  28'  N. 

P.  D.,  71    32 

co-Lat.,  49    19 

S  =  60    25 

D  =:  II  7 


S    =  60°  25' 
D  =  II       7 


log  cosec  0.06066 
log  sin      9.28512 


Eq.  t.  (-f  to  m.  t.), 
Watch  error  on  L.  m.  t.. 

Watch  error  on  L.  app.  t., 


log  sec  0.30655 
log  cos  9.99177 


3m  518 

-      47 


Log  A      9.345  78        Log  B  0.29832 


152 

VARIATION 

OF    THE    COMPASS. 

Tabular  Foi 

■mfor  Computation. 

Log  A, 

LogB, 

Tabl 

e  44. 

Sun's* 
Hour  An- 

Log  cot 

9-34578. 

0.29832. 

Sun's  True 
Azimuth. 

Sun's  Com- 
pass Azimuth. 

Total 
Error. 

Compass 
Deviations. 

gle. 

Tan  X. 

TanY. 

Angle  X. 

Angle  Y. 

h.  III.    s. 

0     / 

0     ' 

0     ' 

0       / 

0     ' 

0     / 

5  21   14 

0.  07382 

9.41960 

0.  37214 

14  43 

67     0 

N.81  43  W. 

N.  72     0  W. 

9  43  W. 

I  49  W. 

23  34 

0.  06933 

9-415" 

0.  36765 

14  35 

66  47 

81  22 

64  30 

16  52 

8  58 

25     4 

0. 06646 

9.41224 

0. 36478 

14  29 

66  39 

81     8 

57    0 

24    8 

16  14 

28  14 

0. 06039 

9.40617 

0.35871 

14  18 

66  21 

80  39 

51  30 

29    9 

21   15 

30  54 

0. 05529 

9. 40107 

0. 35361 

14    8 

66    6 

80  14 

49    0 

31   14 

23  20 

Z2,  24 

0. 05052 

9.  39630 

0.  34884 

13  59 

65  52 

79  51 

48  30 

31  21 

23  27 

35  34 

0.  04638 

9.39216 

0. 34470 

13  51 

65  40 

79  31 

52  30 

27     I 

19     7 

27  44 

0. 04226 

9-  38804 

0. 34058 

13  44 

65  28 

79  12 

60  30 

18  42 

10  48 

40  54 

0. 03623 

9.  38201 

0.  33455 

13  33 

65  10 

7843 

70  30 

8  13  W. 

0  19  W. 

44    4 

0.03021 

9-  37599 

0.32853 

13  22 

64  52 

78  14 

79  30 

I   16  E. 

9  10  E. 

49  34 

0.01977 

9- 36555 

0.31809 

13    4 

64  20 

77  24 

86    0 

8  36 

16  30 

51  34 

0.01598 

9.36176 

0.  31430 

12  57 

64    8 

77    5 

89  30 

12  25 

20  19 

58    4 

0. 00366 

9- 34944 

0.  30198 

12  36 

63  29 

76    5 

88  30 

12  25 

20  19 

6    0  24 

9.  99924 

9- 34502 

0.  29756 

12  29 

^3  '1 

75  44 

85  30 

9  46 

17  40 

3  34 

9- 99324 
9. 98818 

9-  33902 

0.29(56 

12  19 

62  56 

75  15 

80    0 

4  45  K. 

12  39 

6  14 

9-  33396 

0. 2S650 

12  11 

62  40 

74  51 

n  0 

I  51  W. 

6     3E. 

*  Enter  Col.  P.  M.,  Table  44,  with  whole  H.  A. 


3.— BY  ALTITUDE  AZIMUTHS. 


Art.  332.    In  this  method  there  are  given  in  the  triangle  of  position,  Fig.  69 — 


to  find  the  angle 


ZX,  the  zenith  distance, 
PX,  the  polar  distance,  and 
PZ-,  the  co-latitude, 

PZX,  the  azimuth  of  tlie  body  X. 


Art.  333.  T/ic  Obserz'ation. — Take  several  l^earings  of  the  celestial  body  with  the  Standard  Compass 
bisecting  it  each  time  if  it  have  a  sensible  disc,  taking  its  altitude  simultaneously,  notin  j  the  times  with  a  watch. 
Note  the  heading  cf  the  ship  by  the  Standard  Compass  and  the  correspon  ing  headings  by  the  Steering  Com- 
passes, also  the  angle  of  heel,  if  an  iron  ship,  and  wdieiher  to  starboard  or  to  port. 

The  mean  of  the  bearings  is  the  Compass  Azimuth;   the  mean  of  the  altitudes  is  the  oljserved  altitude. 

Art.  334.  To  find  the  True  Aziiiniih. — With  the  Greenwich  date  corresponding  to  the  mean  of  the  times, 
take  out  the  declination  of  the  body,  and,  if  the  moon,  its  Semi-diameter  and  Horizontal  Parallax. 

Get  the  true  altitude  by  applying  the  proper  corrections  to  the  observed  altitude. 

Then  compute  the  True  Azimuth  from  the  following  formula : 


Cos 


Az.= 


V( 


cos  S  cos  (S  —  PD)\ 
cos  L  cos  h         I 


in  which  S  ^  half-sum  of  the  polar  distance  latitude  and  true  altitude. 

Or,  in  words  : 

Add  together  the  polar  distance,  the  latitude,  and  the  true  altitude;  take  the  difference  between  the  half-sum 
and  the  polar  distance,  and  note  the  remainder.  Then  add  together  the  log  secant  of  the  latitude,  the  log  secant 
of  the  altitude  (rejecting  10  in  each  index),  the  log  cosine  cf  the  half-sum,  and  the  log  cosine  of  the  remiinder; 
half  the  sum  of  these  four  logarithms  will  be  the  log  cosine  of  ha  f  the  true  azimuth,  which,  being  doubled,  will 
give  the  true  azimuth,  reckoned  from  the  north  in  north  latiude,  but  from  the  south  in  south  latitude. 


Ex.vMi'LE.    December 


1879, 


bearintr  of  the  sun's  centre  was  N. 


m 

t  rO 

j5 


Lat.  30-'  25'  N.,  Long.   5I1  25"'  42^  W. 
30'  E.,  and  its  true  altitude  24"-  59'. 


at  9''  10"'  29^  a.  m.,  the  observeclJ 


L.  m.  t.,  December  2, 

Long.  W., 

Gr.  m.  t.,  December  3, 

P.  D.  = 

L  = 

h  = 


21''  10"'  29** 
+    5   25    42 
2   36    II 

1X2'^      7' 
30     25 

_24    59 
167    31 


O's  Dec, 
P.  D., 


22"- 
112 


7'S. 
7 


log  sec 
log  sec 


0.05431 
0.04267 


S 

S- 


P.  D.    = 


83    45 
28    22 


>^Az. 
True  Az., 

Comp.  Az.. 
Variation, 


69°  30' 
N.  139      o  E. 
N.  135    30  E. 

3    30  K. 


log  cos         9.03690 

log  cos         9.94445 

2)19.08833 

log  cos         9  54416 


VARIATION    OF    THE    COMPASS. 


153 


Kx.\\^rLF..  December  8,  1879,  '"  I-^t-   30°  25^  N.,  Long.  5''  25'"  42^  W.,  at  9''  59'"  I2«  a.  m.,  the  observed 
bearing  of  the  moon's  centre  was  N.  133°  30'  W. ;  its  true  altitmle  was  36°  30'. 


I.,  m.  t.,  1  )ecember  7, 
Long.  W., 

(Ir.  m.  t.,  December  8, 

P.  D. 

L 

A 


2l'i  59"'    12" 

5    25    42 

3    24     54 

98°  30^ 
30   25 
36   30 


165    25 


d  's  Dec, 
r.  D., 


8°  30^  S. 
98   30 


log  sec 
log  sec 


0.06431 
0.09482 


s 

S  — p.  D. 

N. 

82 
15 

65° 
130 

42 

48 

10' 
20  W. 
30  w. 

log  Cos 

log  COS 
log  COS 

9.10402 

9.9S327 

2)19.24642 

Y  Az. 
True  Az., 
Comp.  Az., 

9.62321 

Variation, 

3 

10  E. 

Art.  33'3.  By  Sumner's  Lines  of  Position. — Among  the  observations  for  ascertaining  the  variation  of 
the  compass,  there  is  no  more  simple  method  of  determining  the  'I'rne  Azimuth  than  the  graphic  method  by  lines 
of  position  plotted  on  the  chart,  and  tufficiently  accurate  for  the  Navigator. 

Let  A1.V2  (Fig.  71)  be  a  line  of  position  plotted  on  the  chart.  At  any 
point,  C,  of  the  line,  draw  CM  perpendicular  to  AiA.^,  and  let  NCS  be  the 
meridian  passing  through  C;  then  SCiVI  is  evidently  the  body's  azimuth. 
The  line  CM  is  of  course  drawn  on  that  side  of  the  meridian  upon  which 
the  body  was  known  to  be  at  the  time  of  observation. 

Comparing  with  this  the  Compass  Azimuth  observed  at  the  time  of 
measuring  the  altitude  from  which  the  line  AiA-:  was  derived,  will  give  the 
variation. 

4.— BY  THE  TRUE  BEARING. 

Art.  330.  Thus  far  sea  observations  for  combined  variation  and 
deviation  have  been  discussed,  but  if  it  becomes  necessary  to  ascertain  the 
Triw  Jnariiig  at  a  new  station,  or  to  find  the  variation  at  a  place  about  to 
be  surveyed,  more  accurate  methods  than  the  foregoing  must  be  resorted  to. 

The  most  reliable  method  is  that  by  rn  Astronomical  Bearing.  It  coi- 
sists  in  finding  the  true  bearing  of  some  well-defined  object  by  taking  the 
angle  between  't  and  the  sun  with  a  sextant  or  a  theodolite,  and  simul  ane- 
ously  noting  the  timj  by  chronometer,  or  by  measuring  the  altitude. 

Arl.  337.  The  Obsci-i'ation. — By  .SVx/<?;//.— Measure  the  angular 
distance  between  the  object  and  the  sun's  limb;  and  if  there  is  a  second 
observer,  measure  the  altitude  of  the  sun  at  the  same'moment  and  note  the 
time.  In  the  absence  of  an  assistant,  first  measure  the  altitude  of  the  sun; 
ne.xt,  the  angular  distance  between  the  sun  and  the  object;  then,  a  second 
altitude  of  the  sun,  noting  the  time  of  each  observation.  Also,  measure  the  altitude  of  the  defined  point  above  the 
sea  or  shore  horizon,  and  rote  whether  the  object  is  to  the  right  or  left  of  the  sun. 

By  the  Theodolilc. — This  instrument  is,  of  course,  far  more  convenient  than  the  sextant,  for,  being  leveled, 
the  horizontal  angle  between  the  sun  and  the  object  is  at  once  given,  no  mat  er  what  may  be  the  altitudes  of  the 
objec  s.  And  in  case  the  altitude  of  the  sun  is  needed  for  the  local  time,  i^  may  be  read  accurately  enough  from 
the  veitical  circle,  although  not  as  finely  graduated  as  the  limb  of  the  sextant,  'fhe  error  in  altitude  must,  how- 
ever, be  found  by  the  level  attached  to  the  telescope,  since  it  will  usually  l:e  found  to  differ  with  the  levels  of  the 
horizontal  circle. 

If  i  1  directing  the  telescope  to  the  sun  there  is  no  colored  eye-piece,  an  image  of  the  sun  may  be  cast  on  a 
jiiece  of  white  ]iaper  held  at  a  little  distance  from  the  eye-piece,  and  by  adjusting  the  focus  the  shadow  of  the  cross- 
wires  will  be  seen, 

Art.  338.  The  Computation.  (Sextant  used). — First,  find  the  True  Azimu  h  of  the  celestial  body,  either 
by  the  Time  method  or  the  Altitude  method,  as  may  suit  best  the  circumstances  of  the  case. 

Secondly,  find  the  Azimuth  difference  as  follows:  change  the  observed  altitudes  of  the  bodes  \n\.o  appaj-ent 
altitudes,  by  correcting  them  for  index-error  of  the  sextant,  dip,  and  semi-diameter;  change  the  observetl  angular 
dista  ce  into  apparent  angular  distance,  by  correcting  for  index  error  and  semi-diameter  whenever  necessary. 

Add  together  the  apparent  distance  and  the  two  apparent  altitudes;  take  the  difference  between  their  half-sum 
and  the  apparent  distance;  t  en  add  together  the  log  secants  of  the  two  apparent  altitudes,  the  log  cosine  of  the 
half-sum  and  the  log  cosine  of  the  difference.  The  half-sum  of  these  four  logs  (rejecting  10  in  the  index)  will  lie 
the  log  cosine  of  half  the  Az.  difference,  which  take  out  and  double;  the  result  will  be  the  required  Azimuth 
Difference. 

There  will  now  be  two  cases  to  consider,  according  as  the  Az.-Diff ,  reckoned  from  the  celestial  body  is  in  the 
same  sense  as  the  True  Azimuth,  or  in  the  opposite  sense. 

First  Case. — The  Az.-Diff.  in  the  same  sense.  Take  the -w/w  of  the  True  Az.  and  the  Az.-Diff.,  and  the  result 
will  be  the  True  I^earing  of  the  object,  wdiich,  if  less  than  180"  will  have  the  same  name  as  that  of  the  True  Az. ; 
but  U  greater  \\\z.n  iSo"^,  subtraet  from  360°  and  change  the  meridional  reference. 

Second  Case. — The  Az.-Diff.  in  the  opposite  sense.  Take  the  diffei'ence  of  the  True  Az.  and  Az.-Dilf.,  and  the 
result  will  be  the  True  Bearing  of  the  object,  which  will  have  the  same  or  different  meridional  reference  according 
as  the  True  Az.  is  greater  or  less  than  the  Az.-D:ff. 


154 


VARIATION    OF    THE    COMPASS. 


Example.    December  lo,  1879,  a.m.,  in  Lat.  30°  25'  24"  N.,  Long.  81°  25'  24"  W.,  made  the  following 
observations  with  a  sextant  for  finding  the  True  Bearing  of  a  well-defined  station : 


Watch  time, 

C  — W, 

Chro.  corr.,  + 

Watch  t., 
C  — W, 

Chro.  t., 

Chro.  corr., 

G.  m.  t.,  Dec.  to, 

Eq.  t., 

G.  app.  t.. 
Long.  W., 

L.  app.  t., 

/  =     - 

S  = 

D  = 

X  = 

Y  = 


iih  22" 
5   21 


II    22 
5   21 


36^ 

16 


3^ 
18 


4 

43 

54 

+ 

2 

16 

4 

46 

10 

+ 

7 

0 

4 

53 

10 

-    5 

25 

42 

23  27    28 

32   32 

40  4' 

86  15 

26  41 

81  01 

89  42 


Obs.  Ang.  Dist.  |3, 

Obs.  2  Q, 

Obs.  alt.  Station, 

I.  C.  =  o  S.  D.  O     = 

O's  Dec,        22°  56'  27"  S. 
P.  D.        =112    56  27 
co-L.         =    59    34  36 


1170    7'  Left. 

71°  37'  20" 
20' 
16'   17" 


Eq.  t.  (—  from  app.  t.),    7™  o^ 


Simi  =172    31   03 

DifT.  =    53    21    51 


Obs.  Ang.  Dist.      =         117'-^    7'    o" 
Q's  S.  D  =  +  16   17 

App.  Ang.  Dist.      =  117    23    17 


log  cot  1.14815 
log  cosec  0.00093 
log  sin       9.65230 


log  tan       0.80138 


log  cot  1.14815 
log  sec  1. 1 8440 
log  cos  9.95 1 10 


log  tan  2.28365 


2   Q, 
Corr. 


+ 


71°  37'  20'' 

35    48  40 
16  17 


App.  Ale,  36      5     o 


X  -f  Y  =  N.  170    43  E.,  True  Az.  Q 


App.  Dist.  = 

App.  Alt.  O        = 
App.  alt.  object   = 


117°  23' 

36     5 
20 


log  sec  0.09250 
log  sec  o.ooooi 


s         ■          = 

S  —  App.  Dist.  = 

153 
76 
40 

62^^ 
125 

I/O 

48 

54 
29 

30' 
oL. 

43  E- 

log  cos  9.35536 
log  cos  9.881 15 

}i  Diff.  Az.         = 
Diff.  —  Az.         = 
True  Az.  0  ^•. 

2)19.32902 

log  cos  9.66451 

True  Bearing  N.,  45    43  E. 

Example.    Same  date  and  same  objects  as  in  the  preceding  example.     Measurements  made  with  a  theodolitej 
as  follows  : 

Ang.  Dist.,  1230  6'    (D 


Watch  time,  11''  16"'  34^5 

Error  in  App.  t.,   +  4     53  -5 


I.  C.  vertical  circle 


L.  app.  t. 
t 

= 

— 

TI      21      28 
38     32 

S 
D 

= 

4°  49 
86    15 
26    41 

X 

Y 

^= 

79    24 
89    39 

x  + 

Y 

= 

N. 

169      3E 
123      6  L. 

O's  Dec.     =     22° 

S6' 

S. 

P.  D.           =112 

56 

co-L.            =     59 

35 

log  cot       1.07435 

log  cot    1.07435 

log  cosec  0.00093 

log  sec    1. 18440 

log  sin       9.65230 

log  cos    9.95 1 10 

N. 


46^ 


log  tan      0.72758 


3  E.,  True  Az.  O 
'      "iff.  —  Az, 

E.,  True  Bearing. 


log  tan    2.20985 


In  the  above  examples  the  sun  has  been  the  celestial  object  observed,  but  it  must  be  understood  that  the  moon, 
or  stars,  may  be  observed  for  finding  the  True  Bearing,  and  with  fixed  instruments,  the  results,  by  observing' 
them,  are  even  more  exact ;  but  under  the  ordinary  circumstances  of  establishing  a  True  Bearing  the  sun  is  the 
most  convenient  body  to  observe. 


WINDS,  ]  55 


CHAPTER    XI. 

WINDS.* 

Art.  339.  Wind  is  air  in  motion.  The  direction  of  the  wind  is  designated  by  the  point  of  the  compass 
frtini  which  .t  'olows.  This  direction  is  commonly  indicated,  in  Navigation,  by  the  terms  North,  North-by-East, 
&c.  To  indicate  the  direction  with  greater  precision,  degrees  of  azimuth  may  be  employed  as  in  Astronomy ;  thus, 
■a  wind  designated  by  N.  13*^  E.  comes  from  a  point  13*^  to  the  eastward  of  north. 

CAUSE  OF  WIND. 

Art.  310.  AH  winds  are  caused,  directly  or  indirectly,  by  changes  of  temperature.  If  two  neighboring 
regions  become, very  unequal  in  temperature  from  any  cause,  the  air  of  the  warmer  region  bung  lighter  than  the 
other  will  ascend  and  be  poured  over  it  from  above,  while  the  heavier  air  of  the  colder  region  will  (low  in  below 
to  supply  lis  place.  Thus  a  difference  in  the  temperature  of  the  two  districts  gives  rise  to  two  currents  of  air — 
one  blowing  from  the  colder  to  the  warmer  along  the  surface  of  the  earth,  and  the  other  from  the  warmer  to  the 
colder  in  the  upper  regions  of  the  atmosphere;  and  these  currents  will  continue  to  flow  until  the  equilibrium  is 
restored. 

Changes  of  temperature,  although  the  prime  cause  of  all  winds,  bring  about  changes  of  barometric  pressure 
and  changes  of  the  specific  gravity  of  the  air,  both  of  which  are  commonly  considered  as  causes  of  wind  ;  they  are, 
however,  but  secondary  causes. 

The  rotation  of  the  earth  would  alone  pr(5duce  no  permanent  wind,  because  if  there  were  no  other  disturbing 

causes  the  atmosphere  would,  by  friction  upon  the  earth's  surface,  soon  acquire  the  same  velocity  of  rotation  as 

that  of  the  ])ortion  of  the  earth  upon  which  it  rested;  but  the  earth's  rotation  materially  modifies  the  operation  of 

other  disturbing  causes.     Since  the  earth  is  nearly  a  sphere,  rotating  upon  its  axis  once  in  twenty-four  hours,  the 

velocity  of  rotation  of  different  parallels  of  latitude  is  very  different. 

Miles  per  hour. 

In  latitude  0°  the  velocity  eastward  is 1036 

In  latitude  15"^  the  velocity  eastward  is 1000 

In  latitude  30"^  the  velocity  eastward  is 897 

In  latitude  45-  the  velocity  eastward  is 73^ 

In  latitude  60 "  the  velocity  eastward  is 5'^ 

In  latitude  75"^'  the  velocity  eastward  is 268 

If  a  mass  of  quiescent  air  from  the  parallel  of  30  could  be  suddenly  transported  to  the  parallel  of  15°,  it 
would  have  an  easterly  motion  of  103  miles  per  hour  less  than  that  of  the  parallel  arrived  at;  that  is,  it  would 
have  a  relative  motion  westward  of  103  miles  per  hour.     So,  also,  if  a  mass   of  a'r  from  the  parallel  of  15^  could 


ha 

relative  motion  westward. 

Winds  are  classified  as  Constant,  Periodical,  and  Variable  Winds. 

CONSTANT  WINDS. 

THE   TRADE-WINDS. 

Art.  341.  When  the  portion  of  the  earth's  surface  which  is  heated  is  a  whole  zone,  as  in  the  case  of  the 
tropics,  a  surface  wind  will  set  in  toward  the  equator  from  both  sides ;  these  having  united  will  ascend,  and  then 
separating  tlow  as  upper  currents  in  opposite  directions.  Hence,  a  surface  current  will  flow  from  the  higher  lati- 
tudes toward  the  equator,  and  an  upper  current  from  the  ecpiator  in  the  direction  of  the  poles.  If,  then,  the  earth 
was  at  rest,  a  north  wind  would  prevail  in  the  northern  half  of  the  torrid  zone,  and  a  south  wind  in  the  southern 
half  But  these  directions  are  modified  by  the  rotation  of  the  earth.  From  the  explanation  given  above,  it  will  be 
seen  that  a  wind  blowing  along  the  earth's  surface  in  the  direction  of  the  equator  is  constantly  arriving  at  places 
which  have  a  greater  velocity  than  itself.  The  wind  thus  lagging  behind,  these  places  will,  as  it  were,  come  up 
against  it ;  in  other  words,  an  east  wind  will  prevail  there.  Since,  then,  the  wind  north  of  the  equator  is  under  the 
influence  of  two  forces— one  drawing  it  south,  the  other  drawing  it  west — it  will,  by  the  law  of  the  composition 
of  forces,  take  an  intermediate  direction,  and  blow  from  the  northeast  to  the  southwest.  Similarly,  south  of  the 
equator,  the  wind  will  Idow  from  the  southeast  to  the  northwest.  All  observations  confirm  this  reasoning.  From 
the  great  service  these  winds  render  to  Navigation,  on  account  of  their  steadiness  and  constancy,  they  are  called 
the  Trade-  Winds. 

Speaking  generally,  the  polar  limits  of  the  trade  winds  are  30  north  and  30-  south,  with  a  belt  of  calms  and 
variables  between,  commonly  known  as  the  Doldrums.  This  belt  extends  across  the  Atlantic  and  Pacific,  its  gen- 
eral direction  being  parallel  to  the  equator.  It  marks  the  meeting-ground  of  the  north  and  south  trades,  where 
they  mutually  neutralize  each  other.  It  must  be  understood  that  both  the  polar  and  equatorial  limits  of  the  trades 
are  constantly  changing,  being  directly  influenced  by  the  sun — advancing  to  the  northward  and  retreating  to  the 
southward  with  that  luminary.  The  N.  E.  trades  extend  farther  north,  and  the  S.  E.  trades  farther  south,  in  the 
Atlantic  than  in  the  Pacific.  Instances  are  recorded  of  vessels  carrying  the  N.  E.  trades  in  the  Atlantic  as  high  as 
36-  or  37-,  while  the  same  trades  in  the  Pacific  are  rarely  experienced  above  30°.  The  S.  E.  trades  seldom  extend 
farther  south  than  30^  in  the  Atlantic  and  27;^^'  in  the  Pacific.  The  calm-belt  is  variable  in  position  and  width. 
In  the  spring  its  centre  is  only  i°  or  2°  north  of  the  equator,  while  in  summer  it  often  rises  to  latitude  9°  or  10". 
Its  width  is,  in  general,  about  5°,  but  it  sometimes  extends  to  15^.  On  the  other  hand,  vessels  very  frequently 
run  directly  from  one  trade  to  the  other,  experiencing  no  calms  or  variables. 

*  By  Lieut.  Charles  H.  Judd. 


156  WINDS. 

RETURN   OR   ANTI-TRADES. 

Art.  343.  It  is  clearly  established  by  numerous  observations  that,  while  the  surface  wind  within  the  tropics 
is  directed  toward  the  equator  or  region  of  calms,  there  exist,  in  the  upper  regions  of  the  atmosphere,  counter-currents 
flowing  from  the  equator  toward  the  poles.  These  upper  currents,  or  anti-trades,  in  their  passage  to  ihe  poles, 
descend  to  the  earth  and  become  surface  currents,  beyond  the  ridge  of  high  barometer,  which  lies  on  each  side  of  the 
tropics.  These  are  the  prevailing  S.  W.  or  W.  S.  W.  winds  of  the  north  temperate  and  the  N.  W.  or  W.  N.  W. 
winds  of  the  south  temperate  zone.  The  westing  of  these  two  great  equatorial  currents  is  brought  about  by  the 
same  cause  that  gives  casting  to  the  trade-winds,  viz,  the  rotation  of  the  earth  round  its  axis.  These  winds  do  not 
constantly  prevail  in  the  middle  and  higher  latitudes,  being  often  either  counteracted  by  the  polar  current  flowing 
southward  to  the  equator,  or  turned  out  of  their  course  to  restore  the  atmospheric  equilibrium  which  has  been 
destroyed  by  storms,  or  disturbed  by  the  different  temperatures  which  are  frequently  occasioned  by  the  unequal 
distribution  of  land  and  water. 

PERIODICAL   WINDS. 

LAND  AND  SEA  BREEZES. 

.  Art.  343.  Laiid  and  Sea  Breezes  are  the  most  general  as  well  as  the  most  readily  comprehended  of  the  peri- 
odical winds.  It  will  be  remembered  what  has  been  stated  above  in  reference  to  changes  of  temperature  being  the 
cause  of  all  winds ;  this  is  especially  perceptible  in  the  case  of  land  and  sea  breezes.  During  the* day  the  land  is 
heated  more  rapidly  than  the  sea,  and  during  the  night  it  is  more  rapidly  cooled.  In  the  morning,  the  air  in  imme- 
diate contact  with  the  land,  being  heated,  is  displaced  by  the  cooler  air  in  contact  with  the  sea,  and  thus  arises  a  breeze 
from  the  sea  to  the  lard.  In  summer  this  breeze  usually  springs  up  soon  after  8am.,  and  attains  its  greatest 
intensity  about  the  time  of  highest  temperature.  About  sunset  the  breeze  ceases  entirely.  During  the  night  the  land 
becomes  colder  than  the  sea,  and  a  breeze  springs  up  from  the  land  to  the  sea,  which  attains  its  greatest  force  about 
the  time  of  lowest  temperature.  This  breeze  extents  only  to  a  short  distance  from  the  coast.  If  no  other  cause 
operates  to  produce  a  wind,  the  direction  of  the  land  and  sea  breeze  will  be  perpendicular  to  the  coast ;  but,  if 
some  other  cause  operates  at  the  same  time,  the  actual  direction  of  the  wind  will  be  such  as  results  from  the  com- 
position of  the  two  forces.  The  land  and  sea  breezes  are  more  regular  and  especially  noticeable  in  tropical  regions; 
but,  in  the  temperate  zones,  the  diurnal  change  of  temperature  also  produces  a  sensible  effect  in  modifying  the 
direction  of  the  prevaiUng  wind  of  any  particular  locality,  and  sometimes  entirely  reverses  its  direction. 

MONSOONS. 

Art.  344.    The  term  monsoon,  derived  from  the  Arabic  word  tnausim,  a  set  time  or  season  of  the  year,  is 
ajiplied  to  the  prevailing  winds  in  the  Indian  Ocean  (which  are  periodical  in  their  nature),  which  blow  from  the  south- 
west from  April  to  October,  and  from  the  northeast,  or  opposite  direction,  from  October  to  April.     The  monsoons  are 
caused  by  the  inequality  of  heat  at  different  places,  and  the  earth's  rotation  on  its  axis ;  more  particularly  they  arise 
out  of  the  same  circumstances  which  produce  the  trade-winds  and  land  and  sea  breezes,  being  the  combined  effects 
of  these  two  sets  of  causes.     If  the  equatorial  regions  had  been  entirely  covered  with  water  the  trade-winds  would 
have  blown  from  the  northeast  all  the  year  round;   but  in  the  south  of  Asia  large  tracts  of  land  stretch  into  the 
tropics,  giving  rise  to  the  extensive  atmospheric  disturbances  for  which  those  parts  of  the  earth  are  so  remarkable.  ^ 
During  the  summer  half  of  the  year,  when  the  sun  is  north  of  the  equator,  the  south  of  Asia  and  the  north  of 
Africa  become  heated  to  a  much  greater  degree  than  the  Indian  Ocean,  which  in  its  turn  is  warmer  than  Australia 
and  South  Africa.     Hence,  as  the  heated  air  of  Southern  Asia  expands  and  rises,  and  colder  air  from  the  south  ^ 
flows  in  to  take  its  place,  a  general  movement  of  the  atmosphere  of  the  Indian  Ocean  sets  in  toward  the  north, 
thus  giving  a  southerly  direction  to  the  wind.     But  as  the  wind  comes  from  parts  of  the  globe  which  revolve  quicker 
to  those  which  revolve  more  slowly,  a  westerly  direction  is  communicated  to  it.     The  combination  of  these  two 
directions  results  in  the  southwest  monsoon,  which  accordingly  prevails  there  in  summer.     Since,  during  winter, 
w  hen  the  sun  is  south  of  the  equator.  South  Asia  is  colder  than  the  Indian  Ocean,  which  again  is  colder  than  South 
Africa,  a  general  movement  of  the  atmosphere  sets  in  toward  the  south  and  ivest.     As  this  is  the  same  direction  as  ,i 
the  ordinary  trade-wind,  the  result,  during  winter,  is  not  to  change  the  normal  direction  of  the  trade-wind,  but ; 
only  to  increase  its  velocity.     Thus,  while  south  of  the  equator,  owing  to  the  absence  of  sufficiently  large  tracts  of 
land,  the  southeast  trades  prevail  throughout  the  year,  on  the  north  of  the  equator,  in  the  east,  we  find  the  south- 
west monsoon  in  summer  and  the  northeast  in  winter,  it  being  only  in  summer,  and  north  of  the  equator,  that  '■ 
great  changes  are  effected  in  the  trade- winds. 

Similar,  though  less  strongly  marked  monsoons  prevail  off  the  coasts  of  Upper  Guinea  in  Africa,  and  Southern 
Mexico  in  America.  The  east  and  west  direction  of  the  shores  of  these  countries,  or  the  large  heated  surfaces  to 
the  north  of  the  sea»  which  wash  their  coasts,  produce,  precisely  as  in  the  case  of  South  Asia,  a  southwest  monsoon 
in  summer. 

As  might  have  been  expected,  the  trade-winds  off  the  coast  of  Mozambique  have  an  easterly  direction,  and  off 
the  coast  of  West  Australia  a  northwesterly  direction.  They  are  also  in  some  degree  turned  out  of  their  normal 
direction  on  the  coasts  of  Brazil,  Peru,  Lower  Guinea,  and  a  few  other  places.  Since  these  winds  veer  through 
only  a  few  points  of  the  compass,  they  are  not  true  monsoons,  the  term  being  strictly  applied  only  to  those  winds 
which  change  their  direction  so  as  to  blow  from  opposite  quarters  at  different  seasons. 

About  the  month  of  April  the  northeast  monsoon  changes  into  the  southwest,  and  about  October  the  south- 
west into  the  northeast.  These  times  depending  on  the  sun's  course,  and  consequently  varying  with  the  latitude, 
are  called  the  breaking-up  of  the  monsoons,  and  are  marked  by  variable  winds,  intervals  of  calm,  and  furious  tem- 
pests and  hurricanes.  Like  the  trade-winds,  monsoons  play  a  most  beneficial  and  important  part  in  the  economy  I 
of  the  globe,  Their  great  speed,  and  the  periodical  change  in  their  direction,  favor  increased  facility  of  commer- 
cial intercourse  between  different  countries. 

VARIABLE  WINDS. 

Art.  345.  Variable  winds  are  such  as  blow  without  any  regularity  as  to  time,  place,  or  direction.  The  direc-  '' 
lion  of  the  wind  is  influenced  by  a  great  many  local  causes,  such  as  the  nature  of  the  ground,  whether  covered  with  ; 
vegetation  or  barren;  the  physical  configuration  of  the  surface,  whether  level  or  mountainous;  and  the  vicinity  of  j 
the  sea  or  of  lakes.  Within  the  tropics  these  local  influences  are  generally  overpowered  by  the  great  atmospheric  i 
currents  which  prevail  there  in  all  their  force ;  but  in  temperate  regions,  owing  to  the  diminished  force  of  the  per-  i 
manent  winds,  there  is  almost  a  constant  warfare  waged  between  them  and  the  temporary  winds  arising  from  local  , 
causes. 


WINDS.  157 

The  teriti  Variable  has  been  defined  above  in  its  general  sense,  or  as  compared  to  the  terms  Constant  and 
Periodical.  But,  in  Navigation,  it  is  used  in  a  special  sense,  that  is,  in  designating  and  recording  certain  winds  in 
^the  columns  of  the  Log-Hook.  It  is  often  misapplied,  by  seamen,  to  denote  an  unsteady  wind,  which,  during  the 
period  of  observation,  may  have  veered  and  liauled  through  several  points.  In  such  cases  the  direction  of  the  wind 
should  be  averaged  to  the  nearest  whole  point.  The  term  I'ariable  should  only  h^  used  to  designate  very  ligli:  airs 
flying  all  round  the  compass. 

It  was  remarked  by  Lord  Bacon  and  other  writers,  l)oth  in  Europe  and  .\merica,  that  the  wind  more  frequently 

'veers  with  the  sun's  motion,  or  passes  round  the  compass  in  the  direction  of  N.,  N.  E.,  E.,  S.  E.,  S.,  S.  W.,  W., 

'and  X.  W,,  to  N.     This  follows  in  consequence  of  the  influence  of  the  earth's  rotation  in  changing  the  direction  of 

the  wind.      Hove  has  the  merit  of  having,  from   Iladley's  principle,  propoundefl  X\\t  law  of  rotation  of  the  wind, 

and  proved  tliat  the  whole  system  of  atmospheric  currents,  the  permanent,  periodical,  and  variable  winds,  obey 

the  influence  of  the  earth's  rotation. 

An  important  characteristic  of  winds  is  their  quality,  being  dry  or  humid,  warm  or  cold,  according  to  their 
direction,  and  the  nature  of  the  earth's  surface  over  which  they  have  passed.     Thus,  in  the  northern  hemisphere 
southerly  winds  are  warm  and  moist,  while  northerly  winds  are  cold  and  dry ;  and  in  the  southern  hemisphere 
vice  versa.      In  Europe  westerly  winds  are  moist  and  easterly  winds  are  dry,  while  in  North  America  north-  . 
easterly  are  cold  and  humid  and  northw'esterly  winds  cold  and  dry. 

MISCELLANEOUS, 

Art.  346*  Hot  winds  of  Deserts. — On  the  deserts  of  Africa  and  Arabia  there«  sometimes  prevails  a  wind 
.extremely  dry  and  intensely  hot,  which  raises  clouds  of  sand  and  transports  it  to  a  great  distance.  This  wind  is 
known  in  the  desert  of  Africa  and  Western  Asia  as  Simoon,  or  Siiuoiin  (from  the  Arabic  savuna,  signifying  liot, 
poisonous,  or  anything  disagreeable  or  dangerous),  while  in  Egypt  it  is  called  Khamsin  (Arabic  for  fifty),  because 
it  generally  blows  for  50  days,  from  the  end  of  April  to  the  time  of  the  inundation  of  the  Nile.  This  hot,  dusty  wind 
is  felt  in  neighljoring  regions  where  it  is  known  under  different  names.  In  Sicily,  South  Italy,  and  adjoining  dis- 
tricts it  is  called  the  Sirocco.  This  wind  is  the  plague  of  the  Two  Sicilies,  and  sometimes  extends  to  the  shores  of  the 
Black  and  Caspian  Seas  and  to  the  steppes  beyond  the  Volga.  It  is  called  the  Samicl  in  Turkey,  from  its  reputed 
poisonous  qualities.  The  Solano  of  Spain  is  a  southeast  wind,  which  prevails  at  certain  seasons  in  the  plains  of 
Mancha  and  Andalusia,  particularly  at  Seville  and  Cadiz.  This  wind  produces  dizziness  and  heats  the  blood  to  an 
I  unusual  degree.  The  Ilarmattan  of  (juinea  and  Senegambia  belongs  to  the  same  class  of  winds.  It  is  a  periodical 
wind,  blow'ing  from  the  dry  desert  of  Africa  to  the  Atlantic,  from  latitude  15°  north  to  latitude  i*-  south,  during 
December,  January,  and  February.  It  may  be  said  of  all  these  winds  that  their  destructive  effects  on  animal  and 
vegetable  life  are  due  rather  to  their  parching  dryness,  glowing  heat,  and  choking  dust  than  to  any  really  poison- 
ous qualities. 

Art.  347.  Peculiar ities  of  Winds  from  Mountains . — The  winds  proceeding  from  mountains  present  many 
interesting  phases,  a  few  of  which  will  be  described.  The  Pampero  is  a  wind  which  blows  chiefly  in  the  summer 
season  from  the  Andes,  across  the  pampas  of  Buenos  Ayres  to  the  sea  coast.  It  is  thus  a  northwest  wind,  or  part 
of  ihe  anti-trade  of  the  southern  hemisphere.  It  is  a  dry  wind,  frequently  darkening  the  sky  with  clouds  of  dust, 
drying  up  the  vegetation  of  the  pampas,  and  often  extending  10  a  considerable  distance  seaward.  Some  competent 
authorities  assert  that  the  dust  which  is  brought  to  the  shores  of  Southern  Europe  comes  not  from  Africa  but  from 
South  -America.  They  arrived  at  this  conclusion  by  making  microscopic  examinations  of  the  sand  or  dust,  in  which 
were  found  certain  organisms  and  dried  infusoria  which  are  known  to  exist  only  in  South  America.  This  theory 
further  slates  that  the  dust  was  elevated  into  the  upper  regions  of  the  atmosphere,  where  it  met  a  current  from  the 
southwest  and  was  transported  over  5,000  miles  before  it  again  fell  to  the  earth. 

Art.  34IS.  Puna  ]Vi>ids. — To  the  eastward  of  Arequipa,  in  Peru,  there  is  a  barren  table-land,  between  two 
great  chains  of  the  Andes,  called  the  Puna  or  the  Punos,  which,  for  four  months  of  the  year  is  swept  by  cold, 
dry  winds.  These  winds  are  part  of  the  south  trade-winds,  which,  after  having  crossed  the  lof  y  range  of  the 
Cordilleras,  are  cooled  and  parched  to  a  degree  that  has  perhaps  no  parallel  in  any  other  country  in  the  world. 
The  inhabitants,  in  traveling,  find  it  necessary  to  protect  their  faces  from  the  glare  and  heat  of  the  day  and 
from  the  intense  cold  of  the  night.  The  drying  qualities  of  the  Puna  wind  are  so  excessive  that  the  bodies  of  dead 
animals  exposed  to  it  are  very  soon  turned  into  mummies.  Prescott  states  that  it  was  in  this  district  that  the 
ancient  inhabitants  of  Peru  preserved  their  dead. 

In  the  south  of  Europe  north  winds  are  notorious  for  their  violence.  The  great  differences  of  the  temperature 
of  tlie  Alps,  the  Mediterranean,  and  .Vfrica,  explain  them  ;  and  w  hen  the  polar  current,  with  high  atmospheric  press- 
ure generally  accompanying  it,  is  descending  at  the  same  time  over  Europe,  the  effect  is  greatly  heightened. 

Art.  349.  Of  these  winds  the  most  noted  is  the  Bora.  This  word  seems  to  be  a  corruption  of  Boreas, 
though  said  to  be  derived  from  a  Sclavonic  term  for  "furious  tempest."  The  Bora  is  greatly  dreaded  in  the  upper 
part  of  the  Gulf  of  Venice,  where  it  rushes  down  from  the  whole  line  of  the  Julian  Alps  with  such  irresistible  fury 
that  not  only  numbers  of  vessels  are  sacrificed  but  it  ravages  the  shore  also,  being  feared  as  much  for  the  sudden- 
ness of  its  attack  as  for  its  violence.  Entire  districts  are  rendered  nearly  uninhabitable  by  the  destructive  effects 
of  this  wind  on  all  vegetation.  Its  general  direction  is  between  north  and  northeast,  and  its  most  usual  continu- 
ance about  fifteen  or  twenty  hours,  with  heavy  squalls  and  terrible  thunder,  lightning,  and  rain  at  intervals.  But 
the  Bora  most  feared,  and  with  justice,  is  that  which  blows  in  sudden  gusts  for  three  days,  subsides,  and  then 
resumes  its  former  force  for  three  days  more. 

Art.  350.  The  Mistral  {maestrat)  is  the  term  applied  by  the  country  people  to  the  northwest  wind  which 
sweeps  from  France  down  on  the  Gulf  of  Lyons.  This  wind  is  experienced  in  both  summer  and  winter,  though 
It  IS  more  violent  and  of  longer  duration  in  the  latter  season.  In  summer  the  mistral  usually  blows  during  clear 
weallier  and  seldom  lasts  more  than  twenty-four  hours,  while  in  winter  it  often  lasts  for  several  days  and  is  accom- 
panied l)y  heavy  rains.  As  a  rule  this  wind  blows  hardest  during  the  day,  decreasing  toward  sunset,  showing  the 
direct  effect  of  change  of  temperature  in  producing  wind ;  for,  during  the  day,  the  difference  of  temperature  between 
the  cold  air  of  the  mountains  and  the  warm  air  over  the  sea  is  much  greater  than  at  night.  These  same  winds 
prevail  in  the  Gulf  of  Genoa  and  with  equal  strength,  only  that  here,  from  the  trend  of  the  coast,  they  become 
N.  N.  E.  in  the  middle  of  the  Gulf. 

The  terrific  !.qualls  experienced  in  the  Straits  of  Magellan,  called  by  the  natives  IVilli^oazcs,  undoubtedly  owe 
their  suddenness  and  violence  to  the  great  height  of  the  mountains  in  that  region  (which  are  covered  with  ice  and 
snow  all  the  year)  and  to  the  corresponding  differences  of  temperature  of  the  air  at  such  great  elevations  and  tha; 
at  the  surface  of  the  water. 


158  REVOLVING    STORMS. 


CHAPTER   XII. 

PRACTICAL  NOTES  ON  REVOLVING  STORMS.* 

Art.  351.  It  is  now  generally  conceded  by  all  who  have  had  opportunity  for  personal  observation,  and  wh( 
have  given  sufficient  attention  to  the  subject  of  Ocean  Storms,  that  the  most  severe  gales  met  with  at  sea  are  wha 
is  commonly  known  as  Revolving  Storms,  variously  called  by  seamen  Hurricanes,  Typhoons,  Cyclones,  &c. 
according  to  the  locality  in  which  they  blow. 

The  distinctive  characteristics  of  these  storms  are  suflficiently  marked  to  distinguish  them  from  the  ordinary 
straightdine  gales  that  blow;  and  the  following  brief  practical  remarns  are  intended  to  assist  and  enable  thl 
Navigator  who  may  not  be  familiar  with  the  subject  of  revolving  storms,  to  not  only  judge  of  the  character  of  th( 
coming  gale,  but  also  to  take  timely  measures  to  avoid  the  dangerous  part  of  it,  either  by  heaving-to  on  the  prope: 
tack  or  by  running  away  from  it,  as  the  case  may  be;  and  also,  in  particiJar  cases  where  the  track  of  the  storm  liei 
in  the  same  direction  as  the  ship's  course,  to  take  advantage  of  it  and  lun  along  with  it. 

In  ih;  year  1831  Mr.  William  Redfield,  of  New  York,  after  long  and  careful  personal  investigation  and  stud} 
of  the  subject,  published  a  yaper,  in  which  he  demonstrated  that  the  gales  on  the  American  coast  were  whirlwind^ 
and  had  a  progressive  or  forward  movement,  traveling  on  curved  tracks  at  a  considerable  rate,  and  were  traceabh 
from  the  West  Indies  along  ihe  coast  of  the  United  States,  curving  off  to  the  eastward  at  some  point  between  thi 
Bermudas  and  the  banks  of  Newfoundland. 

Professor  1  )ove,  of  Berlin,  after  investigating  a  number  of  heavy  gales  that  had  attracted  the  attention  of  sci 
entitle  men  in  (Germany  about  the  same  time,  came  to  similar  conclusions  regarding  the  character  of  those  gales. 

In  1838  Lieutenant-Colonel  Reid,  of  the  Royal  Engineers,  published  a  valuable  work  on  the  law  of  storms, 
in  which  he  agreed  in  all  particulars  with  the  views  of  Mr.  Redfield,  having  verified  by  personal  observation  all  hi;; 
theory.  From  investigations  of  storms  in  the  South  Indian  Ocean,  Colonel  Reid  further  proved  that  the  storms  ir 
the  southern  hemisphere  revolve  in  the  opposite  direction  to  those  in  the  northern  hemisphere. 

T/u'ory  of  Storms. — Upon  the  above  standard  authorities,  and  upon  the  recorded  experience  of  a  great  man) 
seamen  whose  reports  are  confirmatory  of  the  Redfield  theory,  is  based  the  assumption  that  the  currents  of  aii 
wi  hiu  the  limits  of  the  storm  disc  move  in  concentric  circles  around  a  centre  of  low  pressure,  or,  in  other  words, 
that  the  direction  of  the  wind  at  any  point  within  the  storm  disc  is  tangent  to  a  circle  the  centre  of  which  is  thf 
storm  centre,  and  lies  90°  (eight  points)  to  the  right,  or  on  the  right  hand  in  the  northern  hemisphere,  and  go*-' 
(eight  points)  to  the  left,  or  on  the  left  hand  in  the  southern  hemisphere,  supposing  the  observer  to  be  facing  the 
wind,  as  will  appear  by  inspection  of  the  accompanying  storm  cards. 

Art.  35i2.  Exceptions  to  the  Theory. — It  is  not  pretended  here  to  assert  that  this  theory  is  absolutely  true, 
or  that  the  rule  has  no  exception.  To  the  contrary,  the  same  experience  that  proves  the  theory  also  goes  to  show 
that  the  winds  within  the  storm  disc  may,  from  various  causes,  be  diverted  from  the  circular  course  to  any  directior, 
between  the  t.ingent  and  the  radius  of  the  circle,  toward  the  centre. 

1st.  Proximity  of  Land. — The  proximity  of  land  may  generally  be  expected  to  affect  the  course  of  the  winds 
in  that  part  of  the  storm  disc  either"  in  contact  with  it  or  under  the  influence  of  it,  and  may  also,  if  the  course  ol 
the  storm  is  such  as  to  strike  a  high  coast  at  a  considerable  angle,  so  distort  the  entire  storm  disc  as  to  render  it 
difficult  to  determine  the  locality  of  the  centre  from  the  direction  of  the  wind;  but  if  it  be  remembered  tha:  the 
effect  of  land  upon  a  storm  will  always  be  to  flatten  it  in,  and  thus  bring  the  centre  nearer  to  the  shore  than  the 
direction  of  the  wind  according  to  the  circular  theory  would  indicate,  the  Navigator  may,  even  in  such  a  case,  by 
taking  into  account  the  character  of  the  land  and  its  distance  from  the  place  of  the  ship,  estimate  sufficiently  near: 
the  position  of  the  centre  to  take  proper  measures  for  avoiding  it. 

2d.  Local  Disturbances. — Temporarily,  from  local  disturbances  within  the  storm  disc,  for  a  full  discussion  ol' 
which  the  Navigator  is  referred  to  the  standard  works  on  storms,  viz  :  Piddington's  Sailors'  Hornbook,  Reid  on 
the  Law  of  Storms,  Dove's  Law  of  Storms,  &c. 

Art.  333.  Storm  Problem. — The  stonn  problem,  considered  only  in  its  relation  to  the  safe  navigation  of  a 
ship  at  sea,  is  very  simple,  and  may  be  briefly  summed  up  under  the  following  heads,  which  contain  all  that  is 
necessary  for  a  practical  solution  of  it : 

1st.  Ascertain  the  character  of  the  storm  and  locate  the  centre. 

2d.  Determine  the  position  of  the  ship  in  the  storm  disc,  or  the  semicircle  of  the  storm  in  which  the  ship  is 
situated. 

3d.  Ascertain  approximately  the  direction  in  which  the  storm  is  moving. 

4th.  Decide  what  to  do  with  the  ship  to  escape  the  centre,  or  take  advantage  of  the  fair  winds,  as  the  case 
may  be. 

To  ascertain  the  character  of  the  storm,  consult  the  barometer  and  the  general  appearance  of  the  weather. 

BAROMETER. 

First.  The  barometer  generally  indicates  the  approach  of  a  storm  by  a  restless  oscillating  motion  of  the  mer- 
cury, caused  by  a  disturbed  condition  of  the  atmosphere  in  the  vicinity  of  a  storm,  and  the  consequent  passage 
over  it  of  atmospheric  waves  of  different  heights.  These  oscillations  have  been  observed  to  vary  from  a  just  per- 
ceptible motion  to  0.02"'. 

Second.  The  barometer  often  rises  suddenly  just  on  the  border  in  front  of  a  storm,  by  reason  of  the  air  bankingi 
up  there,  and  therefore,  if  the  clouds  and  general  appearance  of  the  weather  indicate  the  approach  of  a  storm,  the 
rise  in  the  barometer,  if  any  occurs,  is  no  guarantee  that  it  will  not  come,  but  rather  a  sign  that  a  severe  storm  is! 
coming.     (The  barometer  will  probably  not  rise  much  in  front  of  a  slowly  moving  storm.)  } 

Third.  A  very  rapid  fall  of  the  barometer  after  fairly  entering  the  storm  disc  may  be  regarded  as  evidence  ofl 
a  very  violent  storm  of  small  diameter,  and  a  gradual  fall  would  indicate  the  contrary. 

Fourth.  The  following  table,  from  Piddington's  Sailors'  Hornbook,  page  252,  may  be  of  service  in  aiding  thCi 


*  By  Lieutenant-Commander  Thomas  Nelson. 


REVOLVING    STORMS.  159 

•to  decide  how  to  act  under  pe 
when  the  question  of  distance  fr< 
j)roblem : ' 


Navigator *to  decide  how  to  act  under  peculiarly  trymg  circumstances,  where  a  risk  has  to  be  taken  to  save  the 
ship,  and  when  the  question  of  distance  from  the  centre  becomes  the  most  important  factor  in  the  solution  of  the 


Table. 

Average  fall  of  barometer  per  hour :  Distance  in  miles  from  centre  : 

From  0.02'"  to  0.06'"  From  250  to  150 

From  0.06'"  to  0.08'"  From  150  to  100 

From  0.08'"  to  0.12'"  From  100  to    80 

From  0.1 2'"  to  0.1 5'»  From    Soto    50 

Art.  354.  Appearance  of  the  Weather. — The  indications  of  the  approach  of  a  cyclone  do  not  differ  materi- 
ally from  those  of  the  ordinary  gale;  but  a  few  such,  as  a  hard  steel-gray  sky,  or  having  a  greenish  tint,  a  ])lood 
red  or  bright  yellow  sunset,  a  heavy  swell  unaccounted  for  in  any  other  way,  and  a  thick  lurid  appearance  of  the 
sky,  may  be  regarded  in  connection  with  a  general  threatening  appearance  of  the  weather,  and  particularly  with  a 
restless  state  of  the  barometer,  as  significant  signs  of  a  more  than  ordinary  gale,  and,  whether  seen  separately  or 
together,  ought  not  to  be  disregarded. 

Art.  u55.  Bearing  of  Centre,  N'orth  Latitude. — Having  reason  to  suppose,  from  the  action  of  the  barom- 
eter and  from  the  general  appearance  of  the  weather,  that  a  revolving  storm  is  near  at  hand,  determine  at  once  the 
bearing  of  the  centre.     To  do  this,  look  in  the  wind's  eye. 

Then,  if  the  ship  is  in  the  north  latitude,  the  centre  bears  eight  points  to  the  right  of  the  wind  point,  or  on 
the  right  hand,  because  in  the  northern  hemisphere  the  currents  of  air  wii'hin  the  storm  disc  move  from  right  to 
left;  that  is,  from  north  to  west  to  south,  and  over  east  to  north,  &c  ,  left-handed  (in  nautical  parlance,  against 
the  sun),  or  in  the  opposite  direction  to  the  hands  of  a  watch,  looking  at  its  face ;  and  hence,  at  the  north  point  of 
the  storm  circle  the  wind  is  east  and  the  centre  bears  south  ;  at  the  west  point  of  the  storm  circle  the  wind  is  north 
and  the  centre  bears  east,  always  90^  or  eight  points  to  the  right  of  the  wind  point. t 

Art.  356.  Bearing  of  Centre,  South  Latitude. — But  if  in  south  latitude,  the  centre  bears  eight  points  to  the 
left  of  the  wind  point,  or  on  the  left  hand,  because  in  the  southern  hemisphere  the  currents  of  air  within  the  storm 
disc  move  from  left  to  right;  that  is,  from  north  to  east  to  south,  and  over  west  to  north,  &c.,  right-handed  (7otth 
the  sun),  or  in  the  same  direction  as  the  hands  of  a  watch,  locking  at  ils  face.  Hence,  at  the  north  point  of  the 
storm  circle  the  wind  is  west  and  the  centre  bears  south;  at  the  east  poirt  of  the  storm  circle  the  wind  is  north 
and  the  centre  bears  west,  &c.,  always  90^'  or  eight  points  to  the  left  of  the  wind  point. + 

Art.  357.  Semicircles  of  Storm  Disc. — The  storm  disc  is  divided  into  two  equal  parts  by  the  line  of  the  axis 
of  the  storm  track,  and  the  portion  lying  on  the  right  side  of  this  line  (looking  in  the  direction  of  the  storm  track) 
is  termed  the  right  semicircle,  while  the  other  half,  or  that  portion  lying  on  ihe  left  of  the  line,  is  called  the  lejl 
semicircle. 

In  the  right  semicircle  the  change  of  wind  will  be  to  the  right;  that  is,  from  north  toward  east,  from  easl 
toward  south,  from  south  toward  west,  &c.,  and  the  first  change  of  wind  will  therefore  indicate  that  the  ship  is  in 
the  right  semicircle.      Then  put  the  ship  on  the  starboard  tack. 

In  the  left  semicircle  the  change  of  wind  will  be  to  the  left ;  that  is,  from  north  toward  west,  from  west  toward 
south,  Occ,  which  will  in  like  manner  indicate  that  the  ship  is  in  the  left  semicircle.  Then  put  the  ship  on  the  par, 
tack. 

The  rule  for  the  determination  of  the  semicircle  and  thj  tack  to  heave-to  on  applies  equally  to  all  parts  of  the 

world;   and  if  it  be  remembered  that  the  name  of  the  semicircle,  the  direction  of  the  change  of  the  wind,  and  the 

tack  to  heave-to  on,  all  three  correspond  to  the  same  side  of  a  given  line,  we  may  reduce  all  that  is  necessary  to 

reme.iiber,  in  order  to  place  the  ship  in  a  safe  position  in  the  storm  disc,  to  six  words.     Doing  which,  we  should 

have: 

C  "Right" (Semicircle). 

J  «-■   -    - 


For  Right  Semicircle,/  "  Right" (Wind  changes  to  the  right). 

(  "  Starboard" (Tack  to  heave-to  on). 

("Left" (Semicircle) 

For  Left  Semicircle,  <  "  Left " (Wind  changes  to  the  left). 

{  "Port" (Tack  to  heave-to  on). 


On  the  Storm  Track  Ktut  before  the  Wind. — A  vessel  directly  on  the  track  of  the  storm,  or  near  it  on  either  side, 
would  not  experience  any  perceptible  change  of  wind,  but  would  have  a  falling  barometer  and  rapidly-increasing 
severity  of  the  weather,  if  in  front  of  the  storm ;  and  a  rising  barometer,  w  ith  a  gradual  moderation  of  the  weather, 
if  in  rear  of  the  storm  centre. 

If  the  ship  be  put  before  the  wind  and  steered  in  one  direction  for  a  few  hours,  she  will,  if  the  storm  be  a 
revolving  storm,  change  the  wind,  and  reveal  by  this  change  the  semicircle  of  the  storm  into  which  she  has  run. 

Art.  358.     To  ascertain  the  Direction  of  the  Storm  Track  by  Lnspection. 

In  Piddington's  Sailor's  Hornbook,  charts  are  found  upon  which  are  projected  the  tracks  of  a  number  of 
storms  in  the  Atlantic  and  Indian  Oceans  and  the  China  Seas,  including  the  Bay  of  Bengal  and  a  portion  of  the 
Pacific.  An  inspection  of  these  charts  will  show  that  storms  in  particular  localities  generally  travel  in  the  same 
direction,  and,  ordinarily,  the  probable  course  of  a  storm  may  be  found  by  inspection  from  one  of  these  charts, 
the  approximate  position  of  the  ship  being  known.  But,  as  there  is  no  absolute  certainty  that  every  storm  will 
pass  over  the  beaten  track,  no  (opportunity  to  verify  the  tracks  on  the  charts  or  to  ascertain  by  observation  the 
approximate  course  of  the  storm  should  be  neglected. 

Art.  359.     To  ascertain  the  Direction  of  the  Storm  Track  by  Observation. 

The  approximate  direction  of  the  storm  track  may  be  found  by  plotting  the  positions  of  the  ship  and  centre  on 
two  or  more  consecutive  bearings,  using  an  estimated  distance  on  the  first  bearing,  and  keeping  an  accurate  account 

*  A  case  in  point  is  cited  on  page  252,  Vol.  V,  Proceedings  of  the  United  States  Naval  Institute,  1879. 
t  See  Storm  Card,  Northern  Hemisphere. 
tSee  Storm  Card,  Southern  Hemisphere. 


160 


KEVOLVING    STORMS. 


of  the  ship's  way  during  the  interval  between  the  bearings.     It  follows  here,  as  a  matter  of  course,  that  the  greater 
the  angle  between  the  beanngs  used  the  better  the  results  obtained  by  this  method. 

To  obtain  satisfactory  results  from  any  of  the  foregoing  methods  of  observation  the  ship  should  be  hove-to 
Having  determmed  the  position  of  the  ship  in  the  storm  disc,  and  the  approximate  direction  of  the  storm's  for- 
ward movement  on  its  track,  the  Navigator  may  intelligently  so  dispose  his  vessel  as  to  incur  the  minimum  amount 
of  d.^.nger  or  reap  the  maximum  attainable  advantage,  as  the  case  may  be. 

Tf  it  Ijc  necessary  to  distance  the  centre  or  to  run  out  of  the  storm  disc,  the  following  rules  should  be  observedT 


Nd   =^  northu<ard. 

eh.    =  change. 

E'i   ^=E  eashveird. 

h.      =  heave-to. 

S'i    =  southward. 

Str.  =  starboard. 

IVd  =  westward. 

P.      —  port. 

REMA 

RKS. 

N^^^^S^^ 


WcstTvini  chioJi^-h^^ir.iack 


The  courses  here  given  are  for  the  wind  2  points  on  the  star- 
board quarter,  but  if  sea  and  wind  permit  bring  the  wind  broad 
on  the  quarter.  If  in  either  of  these  positions  there  be  danger  of 
broaching-to,  run  before  the  wind  until  more  moderate,  and  then 
bring  wind  on  starboard  quarter. 

A  ship  hove-lo  having  the  wind  s'.eady  is  on  the  storm-track. 

Run  before  the  wind  ;  note  the  course  and  keep  it. 


cJi.lo  S'' mil  F.^'iE. 
or  h  .1?  tuck. 


Northern  Hemisphere.* 

Art.  360.  Pight  Semicircle. — Haul  by  the  wind  on  the  starboard  tack  and  carry  sail  as  long  as  ijossible; 
If  obliged  to  heavc-to,  do  so  on  starboard  tack. 

Lejt  5.7;^ /V/;r/<'.— Bring  the  wind  on  the  starboard  quarter.  Note  the  direction  of  the  ship's  head  and  steer 
that  course.     If  obliged  to  heave-to,  do  so  on  port  tack. 

On  the  Storm  T>aek. 

In  front  of  the  <c«/;v.  —  Square  away  and  run  before  it.     Note  the  course  and  keep  it,  and  trim  the  yards  when 
the  wind  draws  on  the  starboard  quarter.      If,  however,  obliged  to  heave- to,  do  so  on  port  tack. 
1)1  rear  of  the  centre. — Run  out  with  wind  on  starboard  quarter,  or  lieave-to  on  starboard  ta 


tack. 


*  See  Storm  Card,  Northern  Hemisphere. 


REVOLVING    STORMS. 


161 


Southern  Hemisphere.* 

Art.  361.    Rig^'t  Sc»ticirclc.—Wmg  wind  on  the  port  quarter.     Note  the  course  and  keep  it.     If  obliged  tc 

^''"zi/;  l",?;j."if-S^^^^^^        wind  on  the  port  tack.     Carry  sail  as  long  as  possible,  and  if  obliged  to  heave- 
to,  do  so  onjjort  tack. 


"West  wind-ch.  to  S 


i 

k 

a 

A\ 

a\ 

f^ 

h  \  \ 

N4   =  northward. 

ch.    =  change. 

Ed    =  eastward. 

h.      =  heave- to. 

Sd    =  southward. 

Sir.  =  staiiward. 

Wd  =  westward. 

P.     =  port. 

REMA 

RkS. 

"2^ 


o 


courses   here  given  are   for  the  wind  2  points  on  port 
but  if  sea  and  wind  permit  bring  the  wind  broad  on  the 
If  in  either  of  these  positions  there  be  danger  of  broach- 
run  before  the  wind  until  more  moderate,  and  then  bring 
L  on  the  port  quarter. 

I  hove-to  having  the  wind  steady  is  on  the  storm-track. 
I  before  the  wind ;  note  the  course  and  keep  it. 


oH^h-rEtacL 


run  WSW 

-sir.  tack. 


On  the  Stonn  Track. 

In  front  of  the  centre. -V^yxr.  before  it.     Note  the  course  and  keep  it   and  trim  the  yards  as  the  Nvmd  gradually 

hauls  on  the  port  quarter.     If  obliged  t.J  hcave-to,  do  so  on  tlie  starboard  tick 

In  rm,  of  the  centre. -"^xxn  out  witli  the  wind  on  port  cpuuter,  or  lieave  to  on  port  ^ck_ 

A  rise  in  th.  barometer,  improvement  of  the  weather,  and  a  gradual  abatement  of  J'^  f"  ,'-':,  "/^^"/^"^^  ^'^ 

result  from  ilie  al.ove  maneuvers ;  and  the  ship  should  in  each  case  be  kept  on  her  cou.-se  until  b>  the.e  sign,  it  .s 

made^^ulemtlKit  she  ^^l^^^^-^^^,^^^  ^  ,^  „f  ,,,rse,  on  sea-room  and  the  ability  to  carry  sail  If  sail 
cann:^  I**c?.?if:i  Jr  land  inSSres  the  ship  sh^.uld' be  hovc-to  on  the  starboard  Uck  ur  the  R.ght  Semicircle,  and 
on  the  port  lack  in  the  Left  Semicircle,  and  never  otherwise. 


*  See  Storm  Card,  Southern  Hemisphere. 


II    B 


162 


REVOLVING   STORMS. 


A  vessel  lying-to  on  the  port  tack  in  the  left  semicircle  in  the  Northern  Hemisphere,  and  on  the  starboarc 
tack  in  the  right  semicircle  in  the  Southern  Hemisphere,  lies  with  her  head  toward  the  storm  centre,  but  there  i; 
no  danger  in  this ;  as  hove-  to  she  will  not  head-reach  to  any  great  extent,  and  will  therefore  not  approach  th( 
centre  so  as  to  endanger  the  safety  of  the  ship.  A  vessel  so  disposed  comes  up  to  the  sea  with  every  shift  of  wine 
and  will  ride  out  the  gale  safely,  whereas  if  she  is  on  the  opposite  tack  she  is  headed  off  by  every  shift  of  wine 
and  will  eventually  bring  ihe  sea  on  the  beam  and  quarter,  in  which  position,  even  if  she  does  not  founder,  she  is 
certainly  likely  to  receive  serious  damage  from  the  sea. 

A  vessel  finding  herself  in  a  favorable  place  in  the  storm  circle  may  safely  run  along  with  the  storm  in  tht 
following  positions : 

To  Profit  by  the  Storm,  i< 

V 

Northern  Hemisphere.*  ^. 


1st.  In  rear  of  centre  on  the  line  of  its  axis.     Wind  on  port  beam. 

2d.   Anywhere  in  the  right  rear  quadrant.     Wind  on  port  side  abaft  the  beam. 

3d.  Abreast  and  to  the  right  of  the  centre.     Wind  aft. 

Southern  HEMispHERE.t 

1st.   In  rear  of  centre  on  the  line  of  its  axis.     Wind  on  starboard  beam. 

2d.   Anywhere  in  the  left  rear  quadrant.     Wind  on  starboard  side  abaft  the  beam. 

^d.  Abreast  and  to  the  left  of  centre.     Wind  aft. 


*  See  Storm  Card,  Northern  Hemisphere. 
+  See  Storm  Card,  Southern  Hemisphere. 


TIDES. 


163 


CHAPTER    XIII. 

TIDES.* 

It  is  beyond  the  province  of  this  work  to  give  more  than  a  general  outline  of  the  theory  of  the  tides,  and  the 

student  desirous  of  a  more  thorough  investigation  may  refer  to  the  articles  by  Sir  John  Lubbock  and  Dr.  Whewcll 
in  the  Philosophical  Transactions  of  the  Royal  Society;  by  Mr.  Airy,  in  the  Encyclopaedia  Metropolitana;  by 
Professor  Hilgard,  in  Appleton's  New  Encyclopaedia;  to  the  numerous  valuable  articles  in  the  United  States  Coast 
Survey  Reports  of  i854-'55-'56-'57,  1861-62,  and  to  Navy  Scientific  I'apcr  No.  2,  1868,  liy  Henry  Mitchell, 
Assistant  United  Stales  Coast  Survey,  on  Tides  ami  Tidal  Plwiiomena. 

Art.  363.  Tidal  piu-nomcua  present  themselves  to  the  observer  under  two  aspects :  as  alternate  elevations 
and  depressions  of  the  sea,  and  as  recurrent  inflows  and  outflows  of  streams. 

The  word  tide,  in  common  usage,  is  applied  without  distinction  to  both  the  vertical  and  the  horizontal  motion 
of  the  sea,  and  much  confusion  has  arisen  among  navigators  from  this  double  application  of  the  term.  Careful 
writers  of  modern  times,  however,  use  the  word  tide  in  strict  reference  to  the  cluittgt-s  of  elevation,  while  they  dis- 
tinguish the  recurrent  sti  earns  as  tidal  eurrents  or  tidal  drifts.  The  words  rise  and  fall  should  be  used  in  referring 
to  the  tide,  and  the  words  flood  and  ebb  in  referring  to  the  tidal  current.  The  word  stand  should  be  used  specific- 
ally for  the  period  of  time,  at  high  or  low  water,  when  no  vertical  change  can  be  detected,  and  the  word  slack  for 
the  period  of  time  when  no  horizontal  motion  can  be  detected.  Set  and  drift  are  terms  applicable  only  to  the  tidal 
currents,  the  first  for  direction  and  the  second  for  velocity.  The  range  of  the  tide  is  the  height  from  low  water  to 
high  water.  This  term  is  usually  applied  to  the  average  height;  but  upon  the  Coast  Survey  Chart  the  expression 
mean  rise  and  fall  replaces  it. 

Art.  364.  The  canse  of  the  tides  is  the  unequal  attraction  of  the  sun  and  moon  upon  different  parts  of  the 
earth;  for  they  attract  the  parts  of  the  earth's  surface  nearer  to  them  with  a  greater  force  than  they  00  its  centre, 
and  attract  the  centre  more  than  they  do  the  opposite  surface.  To  restore  the  equilibrium  the  waters  take  a  sphe- 
roidal figure,  whose  longer  axis  is  directed  toward  the  attracting  body.  The  mean  force  of  the  sun  in  raising  the 
tide  is  to  that  of  the  moon  only  as  I  to  2j^ ;  for  though  the  mass  of  the  sun  is  vastly  greater  than  that  of  the 
moon,  its  distance  causes  it  to  attract  the  different  parts  of  the  earth  with  nearly  the  same  force.  A  small  inland 
sea,  such  as  the  Mediterranean  or  Baltic,  is  little  subject  to  tides,  because  the  action  of  the  sun  and  moon  is  always 
nearly  equal  at  the  extremities  of  said  seas.  The  mathematical  theory  of  the  tides  has  not  yet  reached  the  point 
where  the  tides  at  any  given  place,  or  even  the  changes  from  tide  to  tide  at  the  same  place,  can  be  calculated  by 
merely  knowing  the  position  of  the  sun  and  moon  without  resort  to  observation.  Nevertheless,  by  theory  com- 
bined with  observation,  we  are  enabled  to  predict  the  tides  within  moderate  limits. 

Art.  365.  High  water  occurs,  on  the  average  of  the  twenty-eight  days  comprising  a  lunar  month,  at  about 
the  same  interval  after  the  time  of  the  moon's  crossing  (transit  over)  the  meridian.  This  nearly  constant  interval, 
expressed  in  hours  and  minutes,  is  known  as  the  hinitidal  interval.  The  observed  interval  at  the  time  of  full  and 
change  at  any  port  is  called  the  establishment  of  the  port,  a  term  which  is  in  common  use  among  navigators. 
When  more  extended  observations  are  made,  taking  the  average  of  all  the  lunitidal  intervals  for  at  least  a  lunar 
month,  the  result  is  termed  the  corrected  establishment,  to  distinguish  it  from  the  other  number  which  is  termed  the 
vidgar  {or  common)  establishment.  The  corrected  establishments  which  are  given  on  the  United  States  Coast  Survey 
charts  are  the  results  of  long  and  careful  observations. 

The  following  extract  from  the  Coast  Survey  Chart  of  the  harbor  of  Key  West,  Florida,  will  show  the  manner 
in  which  this  important  information  is  laid  down  for  the  convenience  of  navigators : 

Tides, 


Corrected  establishment 

Rise  of  highest  tide  above  plane  of  reference , 

Fall  of  lowest  tide  below 

Rise  of  mean  low  water,  neap  tide,  above , 

Fall  of  mean  low  water,  spring  tide,  below , 

Mean  rise  and  fall  of  tides , 

Mean  rise  and  fall  of  spring  tides , 

Mean  rise  and  fall  of  neap  tides 

Mean  duration  of  rise,  )  From  middle  of  one  stand  to  the  middle  of 

Mean  duration  of  fall,    \        the  next. 

Mean  duration  of  stand 


Sand  Key. 


Vnih  XL'" 

2ft.  O 

o  .8 

O    .2 

0  -3 

1  -3 

2  .0 

o  .6 

6''  31"' 

5    55 
13 


Fort  Taylor. 


IX"  XXI I"> 
2ft.6 
I  .2 
o 
o 
I 

2 
0 

6''  59'" 

5    25 
12 


Northwest 
Channel. 


Xlbx™ 
3ft.  2 

■4 
■4 
•7 
•5 
•5 
•9 


I 
o 
o 
2 

3 
I 


N.  B.— The  result  for  Sand  Key  is  from  four  months  of  hourly  observation;  that  at  Fort  Taylor  from  twelve  months;  in  the 
Northwest  Channel  from  two  months  of  day-tides  only. 

Art.  366.  The  highest  tides  do  not  occur  at  the  precise  time  of  full  and  new  moon,  but  subsequent  to  full 
and  change.  Upon  our  Atlantic  coast  they  occur  one  day  after,  and  on  the  Atlantic  coast  of  Europe  two  daya 
after,  but  on  our  Pacific  coast  nearly  at  full  and  change.  The  highest  tides  are  called  spring  tides,  and  the  lowest, 
occurring  when  the  moon  is  near  the  first  and  third  quarters,  are  called  neap  tides.  At  the  periods  of  full  and 
change  the  attraction  of  the  sun  and  moon  conspire  to  raise  the  tide  at  a  given  place ;  at  the  first  and  third  quar- 
ters the  high  water  produced  by  the  moon  would  occur  at  the  time  of  the  low  water  caused  by  the  sun,  and  vice 
versa,  so  that  the  two  actions  oppose  each  other.     The  nearer  the  moon  is  to  the  earth  the  stronger  the  attraction, 

*  By  Lieut.  Charles  H.  Judd. 


164 


TIDES. 


I 


and  as  it  is  nearest  in  perigee,  the  tides  will  be  larger  then  on  that  account,  and  consequently  less  in  apogee.  For 
a  like  reason  the  tides  will  be  increased  by  the  sun's  action  when  the  earth  is  near  its  perihelion,  about  the  first  of 
January,  and  decreased  when  near  its  aphelion,  about  the  first  of  July. 

Art.  367.    Different  Types  of  Tides. 

The  observed  tide  is  not  a  simple  wave;  it  is  a  compound  of  several  elementary  undulations,  rising  and  falling 
from  the  same  common  plane,  two  of  which  can  be  distinguished  and  separated  by  a  simple  grouping  of  the  data| 
These  two  waves  are  known  as  the  semi-diurnal  TynA  the  diurnal  tides,  because  the  first  if  alone,  would  give  twc 
high  and  two  low  waters  in  a  day,  while  the  second  would  give  but  one  high  and  one  low  water  in  the  same  or  ar 
equivalent  period  of  time.  In  nearly  all  ports  these  two  tides  coexist,  but  the  proportion  between  them  varies 
remarkably  for  different  seas.  Along  our  Atlantic  coast  the  semi  diurnal  wave  predominates  and  the  diurnal  is  so 
small  that  its  presence  is  made  scarcely  sensible  in  the  small  differences  which  i  causes  between  the  morning  and 
afternoon  tides — diurnal  inequalities.  In  some  ports  of  the  Gulf  of  Mexico  it  is  the  diurnal  wave  which  usually 
prevails,  and  so  much  does  it  exceed  the  semi-diurnal  in  height  that,  upon  the  average,  but  one  high  and  one  low 
water  occur  in  twenty  four  hours.  Upon  our  Pacific  coast  the  two  elementary  wa>/es  have  nearly  the  same  range, 
so  that  although  there  are  usually  two  tides  per  day  they  are  very  unequal. 

In  undertaking  to  investigate  the  tides  of  a  port  it  is  important  to  ascertain  as  early  us  possible  the  form  of  ihe 
tide  ;  that  is,  whether  it  resembles  the  semi-diurnal,  the  diurnal,  or  the  mixed  type;  because  not  only  m.iy  this 
information  be  itself  of  scientific  value,  but  the  knowledge  thus  gained  at  the  outset  will  enable  the  observer  to  fix 
upon  the  best  method  of  keeping  his  record. 

The  type  forms  referred  to  are  illustrated  in  the  following  diagram,  where  the  figures  of  the  waves  are  ])l(>Ued 
in  curves,  using  the   times  as  abscisses  and  the  heights  as  ordinates.     In  this  diagram  the  curve  traced  in  tlie  full 

line  is  a  tide-wave  of  the  semi-diuinal  type; 
that  traced  by  the  dotted  line  one  of  the  diur- 
nal; while  the  broken  line  is  one  of  the  mixed 
type — in  this  case  the  compound  of  the  two 
others. 

Art.  368.  In  order  to  determine  the 
type  to  which  the  tide  of  any  port  belongs,  it 
is  usually  only  necessary  to  make  hourly  ob- 
servations for  a  day  or  two  at  the  date  of  the 
moon's  maximum  declination,  and  to  repeat 
the  series  about  a  week  later,  when  the  moon 
crosses  the  equator.  The  reported  irregu- 
larities of  the  rise  and  fall  at  any  place  should 
not  deter  persons  from  careful  investigation. 
We  could  mention  many  instances  where  the 
phenomena  are  apparently  so  complicated  that 
the  local  pilots  could  not  formerly  detect  any 
sort  of  order,  yet  when  subjected  to  careful 
tabulation  the  skein  has  been  so  completely 
unraveled  that  useful  predictions  can  be  made. 
It  is  natural  that  changes  following  the  phases 
of  the  moon  should  be  easily  recognized,  but 
those  followmg  the  moon's  declination  must 
everywhere  appear  accidental,  or  at  least  in- 
consistent, to  the  ignorant.  Upon  our  Atlantic 
coast  two  popular  rules  fur  the  time  of  the 
To  the  northward  of  Nantucket,  ^^  South  moon  makes  high 
hii^h  water.''''     These  two  rules  are  nearly  as  correct  as  they 


( 

)     12     3     4,    5     6     7     S     9    10  H  12   13  14   15  16   17  18  19  20  21  22  23  24 

Ft. 

3 
2 
1 
0 

1 
2 
3 
4 

1 

, — 

^ 

^ 

1    -N 

^r 

.'- 

.-«, 

-N 

' 

^ 

/ 

^' 

w 

/ 
^ 

/ 

^^ 

/ 

\ 

/ 

V 

\^A 

/ 

/ 

1  - 

-^ 

1 

/ 

/ 

\/ 

K 

/' 

/ 

■\ 

/ 

I' 

f 

•  \ 

\ 

y 

/ 

/ 

tv 

if 

— 

/ 

/ 

V 

\    ^ 

•-'" 

/ 

\;-r 

J 

/ 

\ 

/ 

^\  \ 

/ 

/ 

i 

\ 

1 

A 

\ 

\J  • 

■-.  / 

.' 

\ 

/ 

\  ^ 

' 

;>'- 

-/ 

^— 

^ 

\ 

/ 

\ 

/ 

\ 

1 

1 

Semi-diurnal. 


■  diurnal . 


mixed. 


tide  are  found  among  the  fishermen  and  coasters : 

zuater ;"  to  the  southward,  "  Southeast  tnoon  makes 

are  convenient,  for  between  Nantucket  and  the  Bay  of  Fundy  high  water  occurs  in  the  various  ports  shortly  before 

the  moon  reaches  the  meridian,  while  along  the  southern  coast,  between  Nantucket  and  Florida,  high  water  visits 

the  ports  four  or  five  hours  before  the  moon's  transit,  or  while  she  is  in  the  southeast.     Another  general  rule, 

which  applies  to  our  entire  Atlantic  coast,  is,  that  '^  the  greatest  tides  {springs)  follffia  soon  after  the  full  and  new 

moon,  tlie  least  {neaps)  soon  after  the  ijuarters." 

In  the  Gulf  of  Mexico  no  such  rules  as  those  we  have  mentioned  would  apply,  because  the  tides  belong  to  the 
diurnal  and  mixed  types.  If,  for  instance,  the  new  or  full  moon  occurs  at  her  zero  declination,  the  tides,  instead 
of  increasing  as  the  time  of  syzygy  draws  near,  undergo  a  decline  and  perhaps  vanish.  The  jjhenomena  of  spring 
and  neap  tides  are  not  recognized  in  some  parts  of  this  sea,  and  yet  the  tides  are  generally  obedient  to  the  influences 
of  the  sun  and  moon. 

To  collect  data  for  the  construction  of  prediction  tables  has  been  the  leading  object  of  tidal  observations,  and  a 
multitude  of  such  tables  have  been  constructed  for  different  ports  Those  for  the  North  Atlantic  and  those  for  the 
Pacific  coast  of  America  are  practically  complete. 

It  is  the  custom  of  the  United  States  Coast  .Survey  to  publish,  in  advance,  annual  Tide-Tables,  which  are 
indispensable  to  the  Navigator.  These  tables  give,  for  every  day  in  the  year,  the  predicted  times  and  height  of 
the  tides  at  all  the /;7««/«/ ports  on  both  the  Atlantic  and  Pacific  coasts  of  the  United  States,  and  then,  by  a  sys- 
tem of  "TiDAi,  Constants,"  the  times  and  heights  at  any  of  the  neighboring  ^pori?,  can  leadily  be  calculated. 

Tidal  Observations. 

The  following  remarks  on  Tidal  Observations,  in  connection  with  a  Hydrographic  Survey,  will  be  found  ol 
service : 

Art.  369.    d'lane  of  Referenee. 

The  plane  of  refnrnee  'k  the  datum-plane  to  which  the  soundings  upon  a  chart  are  reduced,  and  this  datum- 
plane  for  Coast  Survey  charts  has  been  fixed  at  mean  low  zvater. 

The  immediate  object  of  observing  tides  in  connection  with  a  hydrographic  survey  is  to  tletermine  \\\\f.  plant 
o/' /•(•/t'rtv/o' and  furnish  the  means  for  reducing  the  soundings  to  this  plane.     The  tides,  however,  are  observed 


TIDES.  165 

also  for  the  purpose  of  supjilying  the  <l:ita  necessary  to  construct  a  tide-table  for  the  chart.  Continuous  observa- 
tions of  tiMes  are  necessary  while  tlie  soundings  are  being  made,  and  in  order  that  the  plane  of  reference  may  be 
determined  closely  and  the  elements  of  a  tolerable  tide-table  procured,  the  observations  of  consecutive  high  and 
low  waters  should  Ite  carried  through  an  entire  lunar  month;  or,  if  it  be  impracticable  to  observe  tides  at  night, 
the  day  tides  of  uvo  lunar  months  may  be  substituted. 

The  tides  are  sul)ject  to  so  many  variations  dependent  upon  the  movements  of  the  sun  and  moon,  and  to  so 
many  irregularities  due  to  the  action  of  winds  and  river  outflows,  that  a  very  long  series  of  observations  would  be 
necessary \o  fi.\  any  natural  plane.  In  consideration  of  this,  and  keeping  in  view  the  possil)ilities  of  repetitions  of 
the  surveys  or  subsequent  discoveries  within  the  field  of  work,  it  is  necessary  to  ascertain  the  position  of  the  plane 
of  reference  which  a  short  series  has  given  by  leveling  up  from  the  tide-gauge  to  a  permanent  hciicJi,  precisely  as  if 
the  adoptetl  plane  were  arbitrary. 

Art.  370.     Bench  Mark. 

The  plinth  of  a  light-house,  the  wa'.er-table  of  a  substantial  building,  the  base  of  a  monument,  and  the  like, 
are  proper  benches ;  and  when  these  are  not  within  reach,  a  mark  in  a  rock,  not  likely  to  be  moved  or  started  by 
tlie  frost,  may  be  made,  or,  if  no  rock  naturally  exists  in  the  neighborhood,  a  block  of  stone  buried  below  the  reach 
of  frost  and  jilowshare  should  be  the  resort.  When  a  bench  is  made  on  shore,  it  should  be  marked  by  a  circle  of 
two  or  tln-ee  inches  diameter  with  a  cross  in  the  centre,  indicating  the  reference  ])oint.  The  levelings  between 
this  ]->oint  and  the  gauge  should  lie  run  over  twice  and  the  details  recorded.  A  bench  made  upon  a  wharf  or  other 
perishable  stiuciure  is  of  little  value,  l)ut  in  the  absence  of  permanent  objects  it  is  better  than  nothing.  In  all 
ca>.es  the  marks  should  be  ntt  in  as  deep  as  convenient,  if  on  stone;  and,  if  on  wood,  copper  nails  should  be  used. 
In  all  cases  the  bench  must  be  sketched  and  carefully  described  in  the  field-book,  and  its  location  marked  on  the 
liydrographic  sheet,  with  a  statement  of  the  position  of  \\\&  plane  of  reference  {mean  loiu  -water)  relative  to  it. 

By  the  term  mean  /o7c<  'U'atei;  upon  the  Atlantic  and  Gulf  coasts,  is  to  be  understood  the  mean  of  all  the  low 
waters  observed ;  but  upon  the  Pacific  coast,  where  there  is  a  great  difference  between  the  heights  of  the  two  low 
waters  of  each  day,  tlie  plane  of  reference  is  the  mean  of  all  the  loioer  Icnv  waters. 

The  leveling  from  the  bench  mark  to  the  tide-gauge  may  be  done,  when  a  leveling  instrument  is  not  available, 
bv  measuring  the  difference  of  height  of  a  number  of  intermediate  points  by  means  of  a  long  straight-edged  board, 
held  horizortal,  by  the  aid  of  a  carpenter's  spirit-level,  or  even  a  plummet-square,  taking  care  to  repeat  each  step 
with  the  level  inverted  end  for  end.  A  line  of  sight  to  the  sea  horizon,  when  it  can  be  seen  from  the  bench  across 
die  tide-staiT,  will  afford  a  level  line  of  very  sufficient  accuracy,  especially  when  observed  with  the  spy-glass.  It 
will  often  be  convenient  to  combine  the  two  latter  methods. 

TIDE-GAUGES. 

STAFF    GAUGE. 

Art.  S?*!.  In  perfectly  sheltered  localities  the  simplest  and  best  gauge  is  a  staff  graduated  upward  in  feet 
and  tenths,  and  so  placed  that  its  zero  shall  lie  below  the  lowest  tides.  The  same  gauge  may  also  be  used  where 
tiiere  is  considerable  chopple,  if  a  glass  tube  with  a  float  inside  is  secured  alongside  of  the  staff,  care  being  taken  to 
])ractically  close  the  lower  end  of  the  tube  so  as  to  exclude  undulations.  The  empty  bulb  of  the  thermometer, 
with  a  portion  of  the  stem,  to  give  it  more  weight,  makes  a  good  float,  and  in  lieu  of  this  a  little  colored  oil  has 
been  successfully  used  to  give  definition  to  the  water-line  within  the  tube. 

BOX   GAUGE. 

Art.  3'5'2.  Where  there  is  considerable  swell,  and  w  here,  from  the  situation  of  the  gauge,  or  the  great  range  of 
the  tide  (making  it  inconvenient  for  the  observer  to  see  the  figures  from  different  positions),  the  Staff  Gauge  cannot 
be  used,  recourse  must  be  had  to  the  Box  Gauge.  This  gauge  consists  of  a  vertical  box,  closed  at  the  bottom,  with 
a  sufficient  number  of  )s-hich  gimlet-holes  On  each  side  from  the  bottom  up  to  a  height  of  a  foot,  to  allow  free 
access  of  water,  but  to  prevent  the  admission  of  any  outer  undulations.  If  the  waves  cause  too  great  oscihation 
with  these  holes,  they  can  be  covered  by  a  thickness  of  coarse  blanket  or  sponge  tacked  over  them.  \\  ithin  the 
box  is  a  copper  float,  with  graduated  rod,  moved  up  and  down  with  the  tide.  The  observer  notes  in  this  case  the 
figures  of  the  rod  as  they  pass  a  certain  point  (the  top  of  the  box  or  an  opening  in  the  side  of  it),  which  is  tech- 
nically called  the  reading-point.  The  staff  of  a  box  gauge  is  graduated  downward,  and  the  box  must  extend  some 
distance  below  the  lowest  tide,  in  order  that  the  float  may  never  touch  bottom.  One  of  the  objections  to  the  use 
of  the  box  gauge  has  arisen  from  the  carelessness  of  hydrographers  in  properly  referring  its  zero  reading  to  the 
bench.  To  make  this  reference  properly,  a  line  of  levels  must  be  run  from  the  bench  to  the  reading-point,  and 
then  the  distance  measured  from  the  zero  (or  some  other  stated  division  of  the  staff)  to  the  water-line  of  the  float, 
so  that  the  elevation  of  the  bench  above  the  surface  of  the  sea  for  any  reading  of  the  gauge  can  be  calculated. 
The  water-line  is  well  marked  upon  the  copper  float  after  the  gauge  has  been  in  operation  for  a  few  days.  As  this 
float-line  is  apt  to  rise  upon  the  float  as  the  rod  is  made  heavier  by  dampness,  another  determination  of  its  position 
relative  to  the  zero  of  the  staff"  should  be  made  at  the  close  of  the  season  and  recorded.  The  chief  source  of  error 
in  tlie  results  from  this  gauge  is  found  in  the  want  of  sufficient  freedom  for  the  ingress  and  egress  of  the  water  at 
the  foot  of  the  box.  In  order  to  keep  out  the  swells  and  chopples,  and  at  the  same  time  to  avoid  the  trouble  or 
inconvenience  of  sinking  the  foot  of  the  gauge  box  below  their  influences,  the  holes  are  often  made  of  the  miniinum 
size  at  the  outset,  and  soon  btcome  more  or  less  choked  by  weeds  and  barnacles,  so  that  the  observer  unwittingly 
records  a  distorted  tide.  The  effect  of  inadequate  water-holes  is  to  increase  the  intemals,  reduce  the  ranges,  alter 
tlie  magnitudes  of  all  the  inequalities,  and  especially  to  displace  the  middle  portion  of  the  wave-figure. 

SF.LF-REGISTERING   GAUGE. 

Art.  373.  The  box  gauge  is  sometimes  provided  with  a  self-registering  apparatus,  so  arranged  that  the  rising 
or  falling  float  carries  a  pencil  with  which  it  describes  a  curve  upon  paper  wrapped  about  a  cylinder  revolving  by 
clock-work.  In  tlie  self-registering  gauge  the  graduated  rod  is  replaced  by  a  wire  kept  taut  by  a  counterpoise.  In 
the  form  of  apparatus  used  in  Great  Britain  the  paper  is  secured  to  a  vertical  cylinder  which  makes  one  revolution 
in  twenty- four  hours,  and  the  same  sheet  is  suffered  to  remain  for  about  a  fortnight,  or  until  some  tw-enty-eight 
tides  are  drawn  upon  it.  The  self-registering  instrument  used  by  our  government,  devised  for  the  United  States 
Coast-Survey  by  Joseph   Saxton,   esq.,    differs  from  the  Ihitish   instrument  in  some  essential   particulais.     Tb.** 


166  TIDES. 

vertical  motion  of  the  float  is  converted  into  horizontal  motion  for  the  pencil,  find  the  papet  unrolls  from  one  cylinder 
and  rolls  up  upon  another,  so  that  the  curves  do  not  repeat.  By  this  improvement  a  continuous  line  is  traced  for 
upwards  of  thirty  days  before  the  paper  is  exhausted.  The  receiving  cylinder  makes  two  revolutions  in  the  course 
of  a  day,  and  each  half  hour  is  pricked  through  the  paper,  as  it  rolls  up,  by  needle-points  projecting  from  either  end 
of  the  cylinder.  The  Saxton  self-registering  gauge  is  portable,  and  may  be  set  upon  an  ordinary  timber  wharf  or 
on  a  platform  supported  by  a  half  dozen  piles  well  tied  and  braced  together.  The  instrument  will  work  well  in 
any  situation  where  the  jar  is  not  too  great  for  the  proper  motion  of  the  pendulum  attached  to  the  clock. 

In  connection  with  the  self-registering  gauge,  occasional  observations  upon  a  staff-gauge  fixed  in  the  imme- 
diate neighborhood  are  lequisite,  in  order  to  give  the  absolute  heights  represented  by  the  curve  upon  the  sheet. 
These  staff  observations  should  be  made  on  very  quiet  days,  at  even  hours,  and  about  the  time  of  tidal  stand.  If 
at  these  even  hours  the  pencil  of  the  self-registering  gauge  is  drawn  back  for  an  instant,  so  as  to  make  a  vertical 
mark  upon  the  sheet,  and  the  record  of  the  true  time  and  height  by  staff  made  on  this  line,  a  check  upon  the  work- 
ing of  the  clock  and  gauge  will  be  given.  Such  checks  cannot  be  made  too  frequently  or  too  carefully.  The  curves 
on  the  sheet  of  this  gauge  are  read  off  and  converted  into  figures  Ijy  the  use  of  scales.  In  order  to  make  the  sheet 
convenient  for  future  reference,  it  is  well  to  write  out  the  dates  and  hours ;  also,  to  draw  vertical  lines  connecting 
the  corresponding  pricks  of  the  upper  and  lower  margins,  and  equidistant  horizontal  lines  parallel  to  the  lines  of 
pricks,  which  shall  divide  the  verticals  into  feet  and  tenths. 

The  freezing-up  of  the  box  in  winter  may  be  prevented  by  pouring  in  a  small  quantity  of  kerosene,  or  other 
oil  which  remains  fluid  at  low  temperatures.  To  insure  success  under  ordinary  circumstances,  it  has  not  been 
found  necessary  to  displace  the  water  to  a  great  depth  in  the  box,  but  simply  to  sink  its  surface  about  the  depth  of 
frost  in  still  sea  water — a  foot,  perhaps. 

For  stations  exposed  to  the  open  sea  peculiar  modes  of  securing  tide-gauges  have  been  resorted  to,  and  in 
some  cases  the  gauges  themselves  have  been  made  in  peculiar  forms.  In  most  cases  where  short  series  of  obser- 
vations are  required,  a  slender  iron  staff,  with  tube  attached,  may  be  held  in  place  by  securing  it  within  a  skeleton 
pyramid  of  iron  rods  anchored  to  the  bottom.  In  the  form  used  in  the  recent  survey  of  the  Cape  Cod  canal  sites, 
the  base  of  the  pyramid  was  a  triangle  of  one-and-a-half-inch  iron  rods,  to  each  angle  of  which  a  small  anchor  was 
lashed  by  its  shank.  The  staff  was  let  down  from  the  apex  of  the  pyramid  and  driven  into  the  bottom,  within  the 
base,  then  firmly  fixed  by  screw  at  top.  The  observer  occupied  a  boat  which  he  could  always  fasten  to  the  appa- 
ratus, without  disturbing  it. 

In  the  Coast  Survey  Report  of  1854  a  form  of  tide-gauge  is  described  which  was  successfully  used  at  many 
stations  on  the  open  coast  of  Massachusetts.  An  iron  tube  with  an  auger  at  foot  is  passed  through  the  ring  of  a 
heavy  anchor  and  screwed  into  the  bottom.  It  is  held  in  a  vertical  position  by  three  chain  guys  secured  by  screw 
band  to  the  middle  of  the  tul^e,  and  extending  to  three  other  anchors  well  buried  at  short  distances  from  the  foot. 
Within  the  tube  a  rod  and  float  are  placed  as  in  the  ordinary  box  gauge. 

Again,  in  the  Coast  Survey  Report  of  1857,  a  device  for  observing  tides  at  a  short  distance  from  the  coast  is 
described.  It  was  very  successfully  used  in  ten-fathom  water,  but  would  not  probably  answer  so  well  in  less 
depths,  where  the  waves  would  offer  too  great  disturbance.  A  long  pine  spar,  bolted  at  the  foot,  with  a  universal 
joint,  to  a  block  of  stone,  is  lowered  down  to  the  bottom  of  the  sea.  The  portion  above  the  surface  of  the  water 
is  slender,  so  as  to  be  less  affected  by  the  wind,  while  the  part  near  the  bottom  is  large,  in  order  to  be  as  buoyant 
as  possible.  To  the  top  of  this  spar,  which  projects  some  ten  or  fifteen  feet  above  the  water,  is  attached  the  rod  of 
a  heavy  pendulum,  which  slides  over  an  arc  five  to  eight  feet  below,  and  determines  the  inclination  of  the  spar. 
To  this  buoy,  thus  arranged,  is  fastened  the  gauge,  whicli  is  a  glass  tube  set  into  a  graduated  staff,  and  having  a 
red  glass  bubble  rising  and  falling  within.  By  a  small  hole  in  this  tube,  some  eight  to  ten  feet  below  the  surface 
of  the  sea,  the  water  enters,  upon  which  the  bubble  floats.  The  observer  records  at  once  the  height  of  the  bubble 
and  the  angle  of  inclination  of  the  gauge.  The  computer,  with  the  aid  of  a  table  of  natural  cosines,  readily 
reduces  these  observations  to  perpendicular  heights. 

Art.  3'S'4.  ^'■Off-shore  Tide  ami  Scioiding  Meier"  is  the  name  given  to  an  apparatus  in  which  the  heights  of 
the  water  are  determined  barometricaUy.  The  pressure  of  the  sea  upon  an  elastic  air  bag  lying  upon  the  bottom  is 
communicated,  through  a  flexible  tube,  to  a  manometer  above.  It  was  invented  by  Major  E.  B.  Hunt,  U.  S.  A., 
as  a  sounding  instrument,  in  1857,  and  as  such  is  described  in  the  Coast  Survey  Report  of  that  year.  Subse- 
quently this  instrument,  in  an  improved  form,  was  proposed  by  John  M.  Batchelder,  esq.,  as  a  tide-gauge,  and  was 
successfully  used  during  the  recent  war,  by  the  Coast  Survey,  off  Charleston  bar.  In  connect  on  with  hydrographic 
work  on  the  open  coast  and  in  the  neighborhood  of  exposed  shoals,  this  gauge  has  a  decided  advantage  over  many 
others  proposed,  because  a  continuous  record  can  be  made  from  the  deck  of  a  vessel,  the  observer  being  required 
simply  to  note  the  position  of  a  hand  upon  a  dial  plate. 

In  the  Arctic  expeditions  of  Dr.  Kane  and  Dr.  Hayes  the  ''pulley  tide-gauge'"  was  used.  The  observations 
were  made  by  the  party  of  Dr.  Hayes  on  a  graduated  vertical  line,  which  was  stretched  from  an  anchor  on  the 
bottom  over  a  pulley  at  the  apex  of  a  tripod  built  over  a  hole  in  the  ice.  A  counterpoise  kept  the  line  taut  as  the 
tripod  rose  and  fell  with  the  tide,  and  the  observer  read  off  the  heights  as  he  would  have  done  from  a  staff  gauge. 
For  further  descriptions  we  must  refer  the  reader  to  Dr.  Kane's  "Arctic  Expeditions,"  vol.  I,  chap,  xi,  and  to  the 
Arctic  tidal  articles  in  the  Smithsonian  Contributions  of  i860  and  1865. 

General  Observations. 

Art.  375.  Tn  classifying  tides  according  to  type,  no  very  exact  rule  can  be  followed.  We  should  call  those 
tides  semi-diurnal  in  which  the  maximum  difference  between  successive  high  waters  does  not  exceed  the  difference 
between  springs  and  neaps,  and  those  diurnal  \\\  which  the  existence  of  two  tides  in  the  same  day  cannot  ordinarily 
l)e  traced.  From  the  data  thus  far  collected,  it  would  appear  that  the  tides  of  our  globe  may,  for  the  most  part, 
lie  classed  with  the  mixed  type;  notwithstanding  that  those  of  the  Caribbean  Sea,  Gulf  of  Mexico,  and  China  Sea 
are  diurnal,  and  those  of  the  Atlantic  semi-diurnal. 

In  the  case  of  tides  of  the  semi-diurnal  type,  the  data  required  for  practical  use  are  the  times  and  heights  of 
high  and  low  water.  To  obtain  the  true  times  and  heights,  the  observations  for  each  tide  should  be  made  every 
two  minutes,  commencing  at  least  twenty  minutes  before  and  continuing  till  twenty  minutes  after  the  stand.  The 
middle  of  the  stand  is  the  true  time  of  the  high  or  low  water.  As  a  general  rule,  at  least  fifty-seven  eonsecutive 
high  waters  and  the  eorres ponding  loiu  waters  should  be  observed  before  a  suitable  tide- table  can  be  made  for  a  chart. 

For  the  proper  study  of  tides  of  the  w/.nv/ and  diurnal  types,  frequent  and  continuous  observations  are  neces- 
sary. It  will  not  suffice  to  observe  only  the  high  and  low  w'ate  s,  even  if  these  are  distinct  phases,  but  the  whole 
tidal  curve  for  each  day  should  be  developed  by  recording  ihe  heights  at  least  every  fifteen  (15)  minutes.     Series 


1 


{ 


TIDES. 


167 


of  observations  of  less  tlian  a  month  are  of  little  value  for  practical  use  in  drawing  up  tables  and  rules  for  Navi- 
gators, althbugh  they  may  serve,  as  we  have  before  said,  to  indicate  to  what  type  the  tides  of  a  place  belong. 

Art.  376.  As  the  tidal  observations  are  to  be  used  to  correct  the  soundings,  care  niust  be  taken  to  make 
sure  that  the  gauge  is  placed  in  a  situation  visited  by  the  same  form  of  tide  as  that  which  occurs  at  the  place  where 
soundings  are  to  be  made.  It  will  not  answer,  for  instance,  to  correct  the  soundings  upon  an  inlel-liar  by  tidal 
observations  made  within  the  lagoon  with  which  this  inlet  communicates,  because  the  range  of  the  tide  within  the 
lagoon  is  less  than  upon  the  outside  coast.  A  partial  ol)struction,  like  a  bridge,  or  a  natural  contraction  of  the 
channel- section,  while  it  may  not  reduce  the  total  range  of  the  tide  or  materially  affect  the  time  of  high  or  low 
tides,  will  alter  the  relative  heights  above  and  below  at  intermediate  stages,  so  that  the  hydrographer  must  be  care- 
ful to  see  that  no  such  obstruction  intervenes  between  iiis  field  of  work  and  the  gauge. 

Wherever  in  the  course  of  a  survey  it  becomes  necessary  to  make  new  tidal  stations  from  point  to  point,  the 
different  gauges  and  their  benches  should  be  referred  to  each  other,  if  it  is  deemed  necessary  to  reduce  all  the 
soundings  to  the  same  plane,  as  it  would  be  if  they  are  all  to  appear  upon  the  same  published  chart  of  a  harbor  or 
bay  not  of  the  lagoon  form. 

Art.  377.    There  are  frequently  remarkable  facts  in  reference  to  the  tides  known  to  persons  navigating  the 
waters  in  tlie  vicinity  of  the  work.     These  should  be  examined,  and,  if  the  alleged  facts  are  important,  with  pro 
portionate  care.     The  highest  or  lowest   tide  ever  known  in   the  vicinity,  its  date  and  circumstances,  should  be 
obtained. 

The  tide-observer  should  compare  his  watch  frequently  with  the  time  on  board  the  vessel,  and  if  several  gauges 
are  employed,  the  observers  should  compare  their  watches  daily,  at  some  specified  hour,  by  signal  or  otherwise. 

The  officer  in  charge  will  be  specially  careful  to  fill  in  the  opening  pages  of  the  tide-books  all  the  information 
required,  /.  <•.,  descriptions  of  tide-gauge,  locality,  Ijench-mark,  &c.  In  any  extended  tidal  observations  the  mete- 
orological record  should  be  kept  with  great  care,  and  the  instruments  in  use  frequently  compared  with  standards. 

Finding  the  Time  of  High  Water. 

Art.  378.  Rule.  Take  from  the  Nautical  Almanac  the  mean  time  of  the  moon's  meridian  passage  and 
correct  it  for  longitude  (Table  il). 

To  this  corrected  time  add  the  tide  hour,  or  establishment,  from  Tables  46,  47. 
The  result  would  be  the  time  of  high  water  on  that  day,  did  not  the  lunitidal  interval  vary. 
Example  i.  Required  the  time  of  high  water  at  Charleston,  S.  C,  November  19,  1880,  civil  account.  From 
the  Nautical  Almanac  the  moon's  meridian  passage  is  found  to  be  at  Cireenwich,  November  18,  13''  28'". 6;  Long, 
of  Charlestort,  about  80^  W. ;  corresponding  to  which,  by  Table  11,  the  correction  is  11'",  to  be  added.  The 
moon's  meridian  passage  at  Charleston  is,  therefore,  November  19,  i''  40'"  a.  m.  Adding  to  this  the  establishment 
from  Table  46,  7''  26'",  the  approximate  time  of  high  water  will  be  9''  6'"  a.  m. 

Example  2.  Required  the  time  of  high  water  at  Portland,  Me.,  December  13,  1880,  civil  account. 
The  Nautical  Almanac  gives  the  moon's  meridian  passage  at  Cireenwich  December  12,  8''  56"'.     The  longi- 
tude of  Portland  is  70^  12'  W. ;   the  corresponding  correction  9"',  which,  added  to  the  above  time,  gives  the  local 
time  of  transit,  December  12,  9^1  5'".     Adding  the  lunitidal  interval  from  Table  46,  li"^  25'",  the  approximate  time 
of  high  water  will  be  found  to  be,  December  13,  8''  30'"  a.  m. 

Art.  379.  If  the  changes  of  lunitidal  interval  from  half-montlily  inequality  were  the  same  for  all  ports,  it 
would  be  easy  by  a  table  of  a  single  column  to  apply  the  required  correction  to  the  time  of  high  water  when  the 
moon  was  not  at  full  or  change,  but  this  is  not  the  case.  It  has  been  found,  however,  that  the  general  law  of  this 
change  is  the  same,  and  that  by  knowing  the  greatest  and  least  lunitidal  interval  for  any  port  we  can  determine  by 
computation  the  change  of  interval.  The  ports  having  nearly  the  same  difference  of  greatest  and  least  interval  are 
grouped  together,  and  the  correction  to  be  applied  to  the  estabhshment,  according  to  the  age  of  the  moon,  is  given 
in  Table  A. 

The  ports  which  may  thus  be  classed  together  are  the  following :  a.  The  ports  of  England  and  of  the  western 
coast  of  Europe  in  general.  /'.  The  ports  on  the  eastern  or  Atlantic  coast  of  the  United  States,  r.  The  ports  of 
the  western  coast  of  Florida  and  of  the  western  or  Pacific  coast  of  the  United  States. 

This  table  is  arranged  on  the  supposition  that  the  corrected  establishment  is  used,  which  is  the  case  for  the 
more  important  ports  in  Tables  46,  47. 

In  other  parts  of  the  world  than  those  mentioned-  in  Groups  a,  b,  c,  the  half-monthly  inequality  is  little  known. 
The  following  table,  formed  by  averaging  the  three  columns   of  Table  A,  will  probably  give  a  sufficient  approx- 
imation.    The  corrections  are  to  be  applied 
to  the  vulgar  establishment. 

Thus,  in  Example  i,  given  befor^  the 
time  of  the  moon's  meridian  passage  being 
i"  40"',  we  enter  the  table  with  that  quantity 
in  the  column  of  time  of  the  moon's  transit, 
and  under  the  head  of  Group  b,  and  by  an 
easy  proportion  we  find  the  correction  to  the 
lunitidal  interval  to  be  "  subt.  3,"  that  is, 
three  minutes  must  be  subtracted  from  the 
mean  lunitidal  interval  at  Charleston,  making 
it  7''  23'",  which,  added  to  the  time  of  the 
moon's  transit,  would  give  9''  3'",  a.  m.,  as 
a  more  accurate  time  for  the  high  water  of 
November  19,  1880. 

In  Example  2  we  had  the  time  of  the 
moon's  transit  at  Portland  at  9''  5'".  En- 
tering   Table  A   with   9''    in   the   column   of 

moon's  transit  (which  is  near  enough  for  this  purpose),  we  find  in 
the  column  of  Group  b  a  correction  of  "add  16'","  /.  e.,  sixteen 
minutes  must  be  added  to  the  mean  lunitidal  interval,  making  it  li''  41"'',  which,  added  to  the  time  of  the  moon's 
transit,  gives  20''  46"',  or  8''  46"^,  a.  m.,  for  the  time  of  high  water  on  December  13. 

Art.  380.    The  changes  of  the  moon  in  declination  cause  a  tide  once  in  twenty- four  hours,  which  adds  itself 
to  the  morning  high  water,  increasing  it,  and  subtracts  itseK  from  the  next  or  afternoon  high  water,  or  vice  versa. 


Tab 

LE    A. 

Gn 

Time  of 

Group 

Moon's 

■up 

Group 

transit. 

add     41"' 

(''' 

)• 

('-)• 

0" 

add 

19"' 

0 

I 

"       17 

f  ( 

6 

subt.   17 

2 

subt.    II 

subt. 

8 

"      32 

3 

"       27 

t( 

16 

"      44 

4 

"      40 

(C 

22 

"      47 

5 

"      47 

(  ( 

24 

"      35 

6 

"      41 

(  t 

19 

0 

7 

"      17 

(  t 

6 

add      1 7 

8 

ac  d      1 1 

add 

8 

J- 

9 

"       27 

i  i 

16 

"      -14 

10 

"      40 

(( 

22 

"      47 

II 

"      47 

(( 

24 

"      35 

Time  of 

Moon's 

'orrection. 

transit. 

ol' 

0'" 

I 

•ubt.    18 

2 

"      37 

3 

"      49 

4 

"       56 

5 

'•      55 

6 

"      40 

7 

"      22 

8 

"        3 

9 

add       9 

10 

"       16 

II 

"       15 

168 


TIDES. 


This  is  called  the  diurnal  inequality.  It  affects  the  time  and  the  height  of  both  high  and  low  water.  In  most  of> 
the  ports  of  the  (iulf  of  Mexico  this  diurnal  tide  is  the  only  marked  one,  except  when  the  moon  is  near  the  equatoi. 
In  the  ports  of  Great  Britain  and  Ireland,  France,  and  vSpain,  the  diurnal  inequality  in  height  is  marked,  but  in 
time  is  inconsiderable.  On  the  Atlantic  coast  of  the  United  States  it  is  small  both  in  time  and  height.  It  increases 
in  passing  along  the   Straits  of  Florida  to  the  western  coast  of  the   Florida  Peninsula,  and  the  semi-diurnal  tides 

almost  disappear  from  Cape  San  Bias  to  the  mouths  of  the  Mississippi, 
reappearing  only  slightly  between  Isle  I)erniere  and  Galveston,  and 
again  being  merged  in  the  diurnal  tide  from  Aransas  Pass  to  \'era  Cruz, 
and  probably  southward.  The  small  tide  of  the  day  is  frequently  called 
by  Navigators  a  half-tide;  and,  in  speaking  of  the  large  and  small  tides 
of  the  day,  they  say  the  tide  and  half-tide.  On  the  western  coast  of  the 
United  States  this  inequality  is  large  both  in  time  and  height,  amount 
ing  at  San  Francisco,  at  its  greatest  value,  lo  two  and  a  half  hours  of 
time  and  four  feet  cT  height.  It  is  probably  large  on  tlie  whole  western 
coast  of  South  America,  but  observations  are  wanting  to  give  informa- 
tion in  regard  to  the  tides  of  these  localities. 

Table  B  will  give  the  corrections  for  the  daily  inequality  in  time  and 
height  for  the  Pacific  coast  of  the  United  States  to  within  about  eight 
minutes  of  t  me  and  three  inches  of  height. 

The  quantities  in  this  tal:>le  are  the  corrections  to  be  applied  to  the 
tin  es  of  high  or  low  water  obtained  by  means  of  Rule  I  and  corrected 
by  Table  A. 

Rule.  Find  from  the  Nautical  Almanac  the  number  of  days  elapsed 
since  the  moon's  declination  was  greatest,  or,  if  before,  the  number  of 
days  to  come  to  that  time.  With  this  enter  Table  B  in  the  first  column, 
and  opposite  the  number  find  the  correction  in  the  second  column.  When  the  moon's  declination  is  north,  the 
correction  is  to  be  subtracted;  when  south,  it  is  to  be  added.  When  the  moon's  declination  is  nothing,  the  cor- 
rection is  nothing.  The  fourth  and  fifth  columns  give  the  corrections  to  the  heights  of  mean  high  water  and  mean 
low  water  for  the  san;e  days.  The  corrections  for  the  height  of  low  water  follow  the  same  rule  as  those  for  the 
times  of  high  water ;  but  for  the  heights  of  high  water  they  are  the  contrary,  that  is,  they  are  to  be  subtracted 
when  the  former  are  to  be  added,  and  vice  versa. 

The  effects  of  this  inequality  may  be  also  expressed  in  the  follovidng  way  :  The  moon's  declination  being 
north,  the  high  water  next  following  the  moon's  transit  will  be  earlier  and  higher  than  the  average,  <he  next  low 
water  later  and  lower,  the  next  high  water  later  and  lower,  and  the  next  low  water  earlier  and  higher;  when  the 
moon's  declination  is  south  the  first  high  water  is  later  and  lower,  the  next  low  water  earlier  and  liigher,  the  next 
high  water  earlier  and  higher,  and  the  next  low  water  later  and  lower,  by  the  amounts  given  in  the  table. 

Example.  Required  the  time  of  high  water  at  San  Francisco,  October  i6,  iSSo.  By  Rule  I,  we  find  the 
moon's  transit  to  happen  at  3'^  21'"  a.  m.  on  that  day.  The  establishment  for  San  Francisco,  from  Table  46,  is 
I2'>  6'",  which,  added  to  3'^  21'"  gives  15''  27"',  or  3''  27"',  p.m.,  as  the  time  of  high  water,  uncorrected  for  the 
half-monthly  and  diurnal  inequalities.  The  former  is  obtained  from  Table  A,  Group  c,  and  is  45"',  which  is  to 
be  subtracted,  giving  2'' 42'" ;  ihe  second  is  obtained  from  Table  B.  By  referring  to  the  Nautical  Almanac  we 
find  that  on  the  given  day  the  moon  had  her  greatest  declination  north.  Entering,  therefore,  the  table  with  o  day 
from  greatest  declination,  we  find  corresponding  to  it,  in  the  second  column,  64"',  to  be  su])lracted,  as  the  declina- 


Table  B. 

Days  from 

Lunitidal  in- 
tervals. 

Hei 

ghts. 

Moon's 

greatest 

declination. 

1 

High 
wa  er. 

Min. 

Low 
water. 

Min. 

High 
water. 

Low 
water,  j 

Ft. 

Ft. 

0 

64 

38 

i.o 

1.8 

I 

62 

37 

0.9 

1.8  ! 

2 

55 

35 

0.9 

.  1.6 

3 

45 

31 

0.8 

1-4 

4 

33 

23 

0.7 

I.  0 

5 

22 

18 

0.4 

0.7 

b 

9 

6 

0.2 

0.3 

7 

0 

0 

0 

0 

II 


tion  is  north,  giving  i''  T^'i^^ 
nearly  two  hours  in  error. 


as  the  time  of  high  water.  If  the  corrections  had  been  neglected,  we  should  have  been 
The  same  tal)le  tells  us  in  the  other  columns  that  this  high  water  would  be  i.o  foot 
higlier  than  an  average  high  water,  and  the  next  low  water  1.8  foot  lower.  The  next  high  water,  a.  m.  of  the 
1 7th,  would  be  one  foot  lower  than  the  average,  or  two  feet  lower  than  the  above  high  water ;  the  next  low  water 
1.8  feet  higher  than  the  average,  or  3.6  feet  higher  than  the  preceding  one. 


CURRENTS.  169 


CHAPTER    XIV. 

CURRENTS.* 

Al't«  3S1*  A  Current  is  at  present  to  he  understood  to  he  a  stream  on,  or  a  particular  set  in  the  direction 
of,  the  surface  of  the  sea,  occasioned  hy  winds  and  other  impulses,  exclusive  of  (Init  which  mav  I'f  iiijincnccd  by) 
the  causes  of  the  tides.  It  is  an  observation  of  Danipier  \.\\^\.  Currents  are  scarcely  ever  felt  but  at  sea,  and 
Tides  but  upon  the  coasts ;  and  it  is  certainly  an  established  fact  that  currctits  ]irevail  mostly  in  those  parts  where 
the  tides  are  weak  and  scarcely  perceptiljle,  or  where  the  sea,  apparently  little  influenced  by  the  causes  of  the 
tides,  is  disposed  to  a  quiescent  state. 

For  the  probable  causes  of  currents  in  general  the  reader  is  referred  to  the  extracts  from  the  "  Ins'I  RUCTIONS 
FOR  Keeping  the  Ship's  Log-Book,"  Art.  92,  Chap.  II,  Part  I. 

The  .v/of  a  current  is  that  point  of  the  compass  toward  which  the  waters  run,  and  its  drift  \%  the  rate  it  runs 
per  hour. 

Art.  SSti.  Of  Currents  there  are  two  distinctions — the  Drift  Cnnvnt  and  the  Stiratn  Current.  The 
Drii^t  or  Drift  Current  is  the  mere  effect  of  a  constant  or  very  prevalent  wind  on  the  surface  water,  impelling 
it  to  leeward  until  it  meets  with  some  obstacle  which  stops  it  and  occasions  an  accumulation  and  consequent  stream 
of  current.  It  matters  not  whether  the  obstacle  be  land,  or  banks,  or  a  stream  of  current  already  formed.  The 
drift  current  is  generally  shallow,  and  at  a  mean,  perhaps,  of  no  more  than  half  a  mile  an  hour  when  the  wind  is 
constant  and  a  good  breeze. 

Art.  383.  The  Stream  Current  has  been  described  as  an  accumulation  of  the  parts  of  the  drift  into  a 
collective  mass  by  the  intervention  of  some  obstacle;  the  mass  then  running  off  by  means  of  its  own  gravity  and 
taking  the  direction  imposed  on  it  by  the  obstacle  becomes  a  stream  of  current,  and  in  many  cases  a  powerful 
stream,  pursuing  its  way  like  a  vast  river  through  the  ocean. 

In  some  parts  the  current  is  compounded  of  drift  and  stream  :  for  a  stream  already  formed  may  pass  through 
the  region  of  a  prevalent  wind  in  a  direction  according  with  that  of  its  drift  current,  and  receive  an  acceleration  of 
motion  from  it  accordingly. 

Art.  384.  The  usual  method  of  estimating  the  existence,  direction,  and  velocity  of  a  current,  as  is  well 
known,  is  the  comparison  between  the  observed  position  of  a  ship  and  that  obtained  by  dead  reckoning.  It  may 
be  as  well  to  observe,  in  the  outset,  that  this  only  method  of  observations  involves  some  amoun,  of  fallacy,  as  a 
current  will  be  the  general  receiver  of  all  errors  or  imperfections  of  observation;  and  beyond  douljt  the  strt  ngtii  of 
currents  has  been  frequently  exaggerated  from  this  very  cause.  Now,  as  the  latitude  is  obtained  far  moie  easily 
and  accurately  than  the  longitude,  it  follows  that  this  exaggeration  has  been  chiefly  shown  in  those  currents  sup- 
posed to  move  east  and  west.  Still,  by  combining  a  large  number  of  observations,  we  may  safely  conclude  that 
they  will  neutralize  each  other's  errors  and  afford  something  like  an  accurate  conclusion. 

Art.  3§5.  In  the  "Instructions  for  Keeping  the  Ship's  Log-Book,"  Chap  II,  Part  I,  we  fiml  the 
following : 

"When  the  difference  between  the  position  by  observation  and  account  exceeds  5',  and  is  quite  regular  in  both 
direction  and  amount,  especially  if  this  evidence  of  a  current  be  corroborated  Ijy  a  change  in  the  temperature  cr 
density  of  the  water,  then,  AND  ONLY  AFTER  CAREFULLY  weighing  all  the  circumstances,  should  the  Navi- 
gator enter  in  the  Log  that  there  is  a  current." 

Art.  3§6.  The  following  useful  observations  on  this  subject  are  found  in  "The  Admiralty  Manual  of 
.Scientific  Enquiry:" 

"But  it  will  be  proper  further  to  try  the  set  of  the  surface  of  the  water  on  all  favorable  occasions,  hy  the  ordi- 
nary method  of  anchoring  or  of  sinking  a  weight,  endeavoring,  if  possible,  to  get  observations  on  the  same  day  at 
about  six  hours  apart,  in  order  that  it  may  be  seen  whether  the  stream  be  due  to  a  tide  or  not.  If  the  ship  1  e  in 
soundings,  and  the  day  be  calm,  a  very  simple  way  of  effecting  this,  without  the  trouble  of  either  anchoring  or 
lowering  a  boat,  is  to  drop  a  heavy  lead  from  the  quarter,  and  after  it  has  reached  the  bottom,  to  run  out  a  small 
quantity  of  stray  line,  and  then  make  fast  the  'nipper,'  or  a  billet  of  wood,  to  the  line,  and  at  the  same  time  to  fasten 
the  end  of  the  log-line  to  it,  and  veer  away  both  together.  (If  the  lead-line  lie  not  hitched  to  the  nipper,  the  tide 
may  drag  the  line  through  it  and  there  will  be  no  result.)  Then  mark  by  a  watch  the  time  each  knot  is  in  running 
out,  buoying  up  the  line  by  a  chip  of  wood;  when  all  the  line  has  run  out,  take  the  bearing  of  the  nipper  by  a 
compass,  and  haul  all  in  together.  If  currents  be  tried  when  there  are  no  soundings,  the  result  is  merely  the  rela- 
tive motions  of  the  upper  and  lower  strata  of  the  water,  and  it  would  be  difficult  to  say  which  way  either  were 
going;  but  if  we  can  possibly  determine  by  astronomical  observations  the  course  of  the  iifper  surface,  we  shall 
thence  be  able  to  deduce  the  set  of  the  lozver ;  and  if  there  be  found  any  difference  of  moment,  it  will  be  very  desir- 
al'jle  to  ascertain  the  temperature  of  both  upj^er  and  lower  strata  of  the  water,  and  to  record  them  with  the  other 
observations.  These  observations  ought  always  to  be  made  on  calm  days,  and  the  greater  the  depth  to  which  the 
weight  be  sunk  the  better." 

Art.  387.  Bottles. — Maury  says  :  "It  is  a  custom  often  practiced  by  seafaring  people  to  throw  a  bottle 
overboard  with  a  paper,  stating  the  time  and  place  at  which  it  was  done.  In  the  absence  of  other  information  as 
to  currents,  that  afforded  by  these  mute  little  navigators  is  of  great  value.  They  leave  no  tracks  behind  them,  it  is 
true,  and  their  routes  cannot  be  ascertained;   but,  knowing  where  they  were  cast,  and  seeing  where  they  are  found, 

*  By  Lieut.  Charles  H.  Judd. 

In  this  compilation  the  following-named  works  have  been  freely  consulted: 
Maury's  Sailing  Directions. 

Tile  Admiralty  Manual  of  Scientific  Inquiry  ;  by  Sir  John  F.  W .  Herschel,  Bart. 
Kindlay's  Nortli  and  South  Atlantic. 

General  Instructions  for  Hydrogranhic  Surveyors  of  the  U.  S.  Navy;  Bureau  of  Navigation,  Navy  Department,  1868. 
Revised  Instructions  for  Keeping  the  Ship's  Log-Book;  Hydrographic  Office,  Navy  Department,  1877. 
The  Navigation  of  the  Pacific  Ocean,  ('hina  Seas,  &c.  ;  from  tlie  French  of  Mons.  F.  Labrosse.     Translated  by  Lieut. 

J.  W.  Miller,  U.  S.  Navy. 
General  Examination  of  the  Indian  Ocean ;  from  the  French  of  Captain  Ch.  Philippe  de  Kerhallet,  Imperial  Navy. 

Translated  by  Captain  R.  H.  Wyman,  U.  S.  Navy. 
General  Examination  of  the  Meduerranean  Sea  ;  from  the  French  of  Captain  A.  Le  (Jras,  Imperial  Navy.     Translated 

by  Captain  R.  H.  Wyman,  U.  S.  Navy. 


170  CURRENTS. 

some  idea  may  be  formed  as  to  their  course.  Straight  lines  may  at  least  he  drawn  showing  the  shortest  distance 
from  the  beginning  to  the  end  of  the  voyage,  with  the  time  elapsed.  The  late  Admiral  Beechey,  R.  N.,  prepared  a 
chart  some  years  ago  representing,  in  this  way,  the  tracks  of  more  than  one  hundred  bottles.  From  it  it  appears 
that  the  waters  from  every  quarter  of  the  Atlantic  tend  toward  the  Gulf  of  Mexico,  and  its  Stream.  Bottles  cast 
into  the  sea  midway  between  the  Old  and  New  Worlds,  near  the  coasts  of  Europe,  Africa,  and  America,  at  the 
extreme  north  or  furthest  south,  have  been  found  either  m  the  West  Indies  or  within  the  well-known  range  of 
Gulf  Stream  waters." 

Art.  3§§.  Submarine  Currents. — The  following  extract  is  from  the  North  Atlantic  Memoir,  by  A. 
G.  FiNDLAY,  F.  R.  S. : 

"Another  feature  of  ocean  currents  has  been  elicited  in  the  experiments  made  under  the  direction  of  the 
hydrographic  department  of  the  United  States  Coast  Survey  (to  whose  labors  we  have  had  occasion  to  allude  in 
other  places),  and  that  is,  that  the  set  of  the  submarine  currents  does  NOT  correspond  either  in  velocity  or 
DIRECTION  with  those  of  the  surface.  How  far  such  a  singular  fact  will  overturn  our  preconceived  notions  it  must 
be  left  for  more  extended  remarks  to  elicit.  The  following  is  the  account  given  by  Lieutenant  Walsh,  of  the  U.  S. 
brig  Taiii'v,  the  officer  alluded  to:  'The  surface  current  was  first  tried  Ijy  the  usual  mode  (a  heavy  iron  kettle 
being  lowered  from  a  boat  to  the  depth  of  80  fathoms);  then,  for  the  trial  of  the  under  current,  a  large  chip-log, 
of  the  usual  quadrantal  form,  the  arc  of  it  measuring  full  4  feet,  and  heavily  loaded  with  lead  to  make  it  sink  and 
keep  upright,  was  lowered  by  a  light  but  very  strong  cod  line  to  the  depth  of  126  fathoms  (the  length  of  the  line); 
a  barrega  was  attached  as  a  float,  and  a  log-Hne  fastened  to  this  barrega;  and  the  rate  of  motion  of  this  float,  as 
measured  by  this  log-line  ard  glass,  as  well  as  the  direction,  as  shown  by  a  compass,  were  assumed  as  the  velocity 
and  set  of  the  under  current.  No  allowance  was  made  for  the  drag  of  the  barrega,  which  was  always  in  a  different 
direction  from  the  surface  current.  It  was  wonderful,  indeed,  to  see  this  barrega  move  off  against  wind  and  sea, 
and  surface  current,  at  the  rate  of  i  knot  an  hour,  as  was  generally  the  case,  and  on  one  occasion  as  much  as  i3^ 
knots.  The  men  in  the  boat  could  not  repress  exclamations  of  surprise,  for  it  really  appeared  as  if  some  monster 
of  the  deep  had  hold  of  the  weight  below,  and  was  walking  off  with  it.'  " 

The  following  remarks  on  currents  have  been  extracted  from  "General  Instructions  for  Hydro- 
graphic  Surveyors  of  the  United  States  Navy,  Bureau  of  Navigation,  Navy  Department,  1868: 

"Many  efforts  have  been  made  to  ascertain,  and  to  record  for  the  use  of  navigators,  the  prevalent  currents  of" 
the  ocean,  but  hitherto  with  no  very  great  success ;  for  besides  their  own  apparent  inconstancy,  the  observations' 
on  which  current  charts  have  l)een  constructed  were,  till  within  these  few  years,  vitiated  by  the  neglect  of  the 
deviation  of  the  compass.  In  general,  also,  the  daily  error  of  the  reckoning  at  each  following  noon  has  been 
adopted  as  the  effect  of  a  single  current  acting  throughout  the  whole  interval;  whereas  it  is  probable  that  in  every: 
twenty-four  hours  the  vessel  will  have  passed  through  different  streams,  and  have  been  affected  by  different  impulses". 
He,  therefore,  that  is  desirous  of  forming  consistent  views  on  a  subject  so  necessary  in  every  voyage,  and  so  deeply 
interesting  when  considered  on  a  more  extensive  scale,  will  contrive  that  systematic  observations  for  latitude  and 
time  by  the  sun,  moon,  stars,  or  planets  should  be  made  at  different  hours  of  the  day  and  night,  taking  advantage 
of  the  clear  horizon  an  hour  before  sunrise  and  after  sunset,  for  the  express  purpose  of  apportioning  the  whole 
error  of  the  day's  work  into  its  most  likely  periods.  Then,  and  then  Only,  after  a  due  consideration  of  the  prob- 
able effects  of  bad  steering  in  the  different  watches,  of  the  action  of  the  swell  and  sea  upon  the  leeway,  and  of  the 
gradual  but  constant  changes  in  the  variation  and  deviation  of  the  compass,  will  his  arrow  upon  the  current  chart 
be  considered  of  any  authority." 

Art.  389.  Such  is  the  practice  in  every  skillfully  conducted  voyage,  and  as  it  would  therefore  appear  to  be 
a  duty  peculiarly  incumbent  on  all  vessels  of  war,  and  especially  of  surveying  vessels  when  going  out  or  returning 
from  distant  stations,  it  may  be  as  well  to  divide  the  inquiry  into  distinct  heads : 

1.  What  is  the  local  set  and  strength  of  the  current  for  any  specificinterval,  as  shown  by  a  carefully  corrected 
reckoning  when  disentangled  from  all  probable  errors  ? 

2.  Over  what  extent  of  space,  and  at  what  seasons,  does  the  current  appear  to  have  a  certain  degree  of  per- 
manence and  regularity ;  and  how  is  it  modified  by  the  daily  sea  and  land  breezes,  or  by  the  periodic  monsoons, 
or  by  the  varying  issue  of  large  rivers  in  those  changes  of  season  ? 

3.  In  the  vicinity  of  such  rivers  does  any  undertow  exist?  This  maybe  readily  discovered  by  linking  a 
basket  attached  to  a  little  float,  and  tried  at  different  depths. 

4.  To  what  distance  does  the  usual  current  extend  from  the  coast,  and  where  does  any  neutral  space  or  counter 
current  begin  ? 

5.  Is  the  general  direction  of  the  permanent  current  parallel  to  the  shore,  as  in  the  bight  of  Guinea,  or  oblique 
to  it,  as  along  the  coast  of  South  America  ? 

6.  To  what  depth  do  these  currents  extend  downward  ? 

Art.  390.  Submarine  Currents. — And  this  will  open  to  die  inquiring  seaman  the  still  larger  question 
of  the  deep  submarine  currents,  which  it  is  asserted  have  been  found  of  consideral)le  strength — even  \^,\  knots — at 
120  fathoms  below  the  surface.  It  is,  indeed,  difficult  at  first  sight  to  conceive  the  causes  that  can  give  a  horizontal 
impulse  to  a  large  zone  or  stratum  of  water,  at  any  material  depth,  so  as  to  preserve  it  distinct  from  the  water 
above  and  beneath,  and  to  continue  to  it  for  any  length  of  time  an  independent  movement;  but  it  is  not  the  less 
our  duty  to  contribute  our  utmost  to  the  supply  of  honest  and  genuine  observations,  which  can  alone  confirm  or 
refute  that  supposition.  Experiments  for  this  purpose  will  cost  but  little  trouble  in  comparison  with  the  satisfac- 
tion they  will  afford  to  the  Navigator,  or  to  the  light  they  will  throw  on  some  of  the  great  operations  of  nature; 
but  then  they  must  be  conducted  in  such  a  manner  as  to  prevent  all  uncertainty  and  incredulity.  Whenever 
attempted,  three,  if  not  four,  large  current  logs  should  be  sent  down  at  the  same  time,  and  so  buoyed  as  to  be 
kept  at  different  depths — say  at  10,  20,  50,  100  fathoms  or  more — besides  one  which  in  all  cases  should  be  kept 
riding  on  the  surface;  and  it  will  be  still  more  satisfactory  if  two  such  experiments  be  carried  on  at  the  same 
time  and  at  the  distance  of  a  few  miles  apart ;  for  if  such  deep  currents  should  thus  be  proved  really  to  exist 
it  is  possible  that  they  may  be  produced  by  a  kind  of  whirl  or  vortex  of  large  diameter  in  the  superficial  cur- 
rent. The  comparative  temperatures. of  the  atmosphere  and  the  sea  should  be  continually  observed  and  marked 
in  the  log,  with  reference  to  the  current,  for  they  will  often  show  that  it  runs  from  the  northward  to  the  southward. 
On  one  occasion  a  ship  crossing  from  the  Cape  of  Good  Hope  to  the  Rio  de  la  Plata  was  enabled  to  fortell  the 
daily  error  in  her  latitude  by  the  increased  warmth  of  the  water  if  the  current  was  coming  from  the  northward,  or 
by  its  comparative  coolness  if  a  stream  was  setting  up  from  Cape  Horn.  Repeated  series  of  sucli  observations 
will  show  under  what  circumstances  the  thermometer  may  be  expected  to  indicate  the  presence  of  a  current.  The 
trend  and  general  figure  of  fields  and  patches  of  seaweed  should  also  be  noted  with  the  same  view,  as  both  must  be 


CURRENTS.  171 

more  or  less  affected  by  the  direction  and  velocity  of  the  current.  Where  the  patches  are  frequent  or  of  considei- 
able  extent  a  deep  cast  of  the  lead  (say  i,ooo  fathoms)  should  be  obtained,  as  they  may  possibly  indicate  the  prox- 
imity of  lisyiks. 

The  principal  Ocean  Currents  will  now  be  mentioned,  prefacing  their  description  with  a  few  general  observa- 
tions from  Maury :  "  Moreover,  we  may  lay  it  down  as  a  law  in  the  system  of  oceanic  circulation,  that  every  cur- 
rent in  the  sea  has  its  counter-current ;  in  other  words,  that  the  currents  of  the  sea  arc,  like  the  nerves  of  the  human 
system,  arranged  in  jiairs  ;  for  wherever  one  current  is  found  carrying  off  water  from  this  or  that  part  of  the  sea,  to 
the  same  part  must  some  other  current  convey  an  equal  volume  of  water,  or  else  the  first  would,  in  the  course  of 
time,  cease  for  the  want  of  water  to  supply  it."  And,  again,  "It  is  not  necessary  to  associate  with  oceanic  cur- 
rents the  idea  that  they  must  of  necessity,  as  on  land,  run  from  a  higher  to  a  lower  level.  So  far  from  this  being 
the  case,  some  currents  of  the  sea  actually  run  up  hill,  while  others  run  on  a  level.     The  Gulf  Stream  is  of  the  first 

class." 

Currents  of  the  Atlantic. 

Art.  391.  The  principal  current  of  the  Atlantic,  and,  indeed,  the  most  noteworthy  of  all  the  great  ocean 
currents,  is  the  Gulf  Stream. 

Under  the  direction  of  Dr.  Bache,  the  Superintendent  of  the  Coast  Survey,  the  exploration  of  the  Gulf  Stream, 
extending  from  about  42'^  N.  latitude  to  about  28;^^,  and  from  about  65;^"  to  Soj^^  W.  longitude,  has  been 
made,  and  from  his  notes  on  the  same  we  have  extracted  the  following: 

The  ocean  within  the  region  of  the  Gulf  Stream  is  divided  into  several  bands  of  higher  and  lower  tempera- 
ture, of  which  the  ax/s  of  the  Gulf  Stream  is  the  hottest,  the  temperature  falling  rapidly  inshore  and  more  slowly 
outside. 

Thus,  on  a  line  perpendicular  to  the  axis  of  the  stream,  drawn  from  Sandy  Hook,  the  temperature  at  the 
depth  of  15  fathoms  and  100  miles  was  (>i°  ;  at  150  miles,  67°;  at  240  miles,  63^^^  ;  280  miles,  8o>^°. 

The  late  Lieut.  G.  M.  Bache  discovered  a  band  of  water  so  much  colder  than  the  rest  that  he  called  it  the 
"  Cold  Wall,''  the  cold  water  appearing  to  confine  the  hot  water  as  by  a  wall  on  the  iuskore  side.  Its  distance 
from  Sandy  Hook  is  from  230  to  280  miles;  its  distance  from  Cape  May  is  between  132  and  178  miles— the  ther- 
mometer at  15  fathoms  on  the  Sandy  Hook  section  rising  from  62 >^^  to  8o>^,  or  18^  in  50  miles;  on  the  Cape 
May  section,  rising  from  62^  to  83^°,  or  21%"^  in  46  miles  ;  at  Charleston,  at  the  depth  of  20  fathoms,  rising  from 
671^^  to  79^  in  15  miles;  and  at  St.  Simons,  from  70°  to  76°  in  12  miles,  being  at  the  rate  of  4^^  tenths  to  9 
tenths  of  a  degree  to  a  mile.  Besides  this  remarkable  cold  band  there  are  two  outside  ones,  sufficiently  well  defined, 
though  the  difTerences  of  temperature  are  less  marked,  the  existence  of  which  should  be  known  to  the  Navigator, 
that  he  be  not  perplexed  in  crossing  the  stream  and  finding  warm  water,  to  meet  with  cold,  then  warm,  and  then 
cold  again.  The  positions  of  these  bands  may  be  somewhat  changed  when  more  thoroughly  considered.  Iiisule 
of  the  "Cold  Wall"  there  is  a  zvarm  band  z.-nd  then  the  cold  water  of  the  shore.  The  axis  of  the  stream  takes,  in 
general,  the  curve  of  the  coast,  below  rather  than  above  the  water,  being  turned  to  the  eastward  by  the  shoals  off 
the  southern  coast  of  New  England.  The  axis  of  t/ie  cold  band,  the  minimum  of  temperature  which  forms  the 
"Cold  Wall,"  follows  the  shore  and  shoals  in  its  bendings  more  closely  than  the  axis  of  the  Gulf  Stream,  and  is 
traced  with  considerable  probability  to  longitude  66°.  The  warm  water  of  the  Gulf  Stream  rests  on  a  cold  current, 
flowing  toward  Cape  Florida,  the  coldest  water  keeping  near  the  Atlantic  coast,  below  the  surface  if  not  at  it.  By 
observations  at  several  points  along  the  coast  in  400  fathoms,  between  Sandy  Hook  and  Cape  Florida,  the  surface 
temperature  exceeding  80°,  the  thermometer  indicated  46;^^  to  55^  ;  off  Hatteras,  in  1,000  fathoms,  40^. 

The  warm  water  of  the  Gulf  Stream  is  of  very  different  depths  at  different  points  of  its  course,  and  in  differ- 
ent parts  of  any  one  of  the  sections  across  it.  From  the  deepest  portion  in  the  cross  sections  the  warmer  water 
flows  off  toward  the  shore,  and  outward,  overlying  the  cold.  This  thins  out  as  it  approaches  the  shore,  the  cold 
water  which  lies  at  the  bottom  coming  up  in  the  northern  sections,  but  the  warm  water  prevailing  to  the  very 
shore  and  at  considerable  depths  in  the  southern.  When  the  fold  water  is  forced  up  by  a  bank  or  shoal,  or  when 
it  comes  to  the  surface  from  the  thinning  out  of  the  warm,  there  is  of  course  a  considerable  change  of  temperaiure. 
This  cold  water  from  the  north  prevails  on  the  inside  of  the  cold  axis,  at  moderate  depths,  as  far  south  as  Hatteras, 
and  probably  to  the  south  of  it.  Acting  Master  Jones  found  it  50  miles  S.  E.  of  Charleston  light,  running  to  the 
S.  W.,  the  surface  water  being  75°,  and  at  20  fathoms  68"^,  the  axis  of  the  Gulf  Stream  being  82'^,  moderately 
warm  water  extending  to  the  bottom. 

The  direction  of  the  axis  of  the  stream  indicates  the  set  of  the  current  in  that  band.  To  the  right  and  left  of 
it  the  current  is  outward  and  onward,  and  to  the  left,  as  far  as  the  "Cold  Wall,"  is  inward  and  onward.  Inside 
of  the  "  Cold  Wall,"  north  of  Cape  Hattefas,  and  probably  south  of  it,  the  current  is  southerly  along  the  coast. 

The  velocity  of  the  current  in  the  axis  of  the  stream,  on  the  Cape  Canaveral  section,  is  about  3  miles  per  hour ; 
on  the  Cape  Fear  section,  about  2  miles  per  hour;   and  on  the  Sandy  Hook  section,  about  l  mile  per  hour. 

In  the  Charleston  section,  and  to  the  south,  the  bands  of  cold  and  warm  water,  with  scarcely  an  exception, 
zxt  produced  by  the  shape  of  the  bottom.  The  elevated  portions  of  the  bottom,  forcing  up  the  cold  water  into  the 
warm,  cause  cold  streaks,  and  the  division  into  cold  and  warm  bands. 

The  variations  in  temperature  in  different  years  and  at  different  seasons  are  considerable,  the  more  southerly 
sections  in  the  same  season  giving  usually  the  highest  temperature.  But  in  July,  1846,  on  the  axis  of  the  Gulf 
Stream,  the  temperature  was  higher  at  Sandy  Hook  than  in  June,  1853,  at  Canaveral  by  i>^°,  and  higher  than  at 
Charleston  by  5^"-. 

The  low  temperatures  observed  show  that  the  Gulf  Stream  is  comparatively  a  superficial  current  on  the  surface 
of  an  ocean  of  cold  water.  The  temperatures  have  been  observed  from  the  surface  to  the  depth  of  500  fathoms — 
in  a  few  instances  as  low  as  1,300  to  1,500  fathoms. 

Navigators  are  advised  to  make  their  observations  at  the  depth  of  20  fathoms.  Saxton's  metallic  thermometer 
is  highly  recommended.  A  common  Six's  self-registering  thermometer,  or  a  common  thermometer  enveloped  in 
cotton  or  other  bad  conducting  material,  allowed  to  remain  below  the  surface  long  enough  to  take  the  temperature, 
will  answer. 

Mr.  George  W.  Blunt,  in  his  "Atlantic  Memoir,"  remarks: 

"That  in  summer  the  temperature  of  the  Gulf  water,  south  of  Hatteras,  is  about  the  same  as  the  water  on 
soundings.  In  the  months  of  July  and  August,  1845,  the  temperature  of  the  water,  from  the  Mississippi  to  Cape 
Hatteras,  both  in  and  out  of  the  stream,  even  to  the  very  mouth  of  the  Atlantic  rivers,  was  84^  to  82°. 

"The  current  on  the  western  edge  of  the  Gulf  Stream,  from  Sandy  Hook  to  Cape  Hatteras,  sets  south,  a  little 
westerly,  about  20  miles  in  24  hours. 

"The  current  on  the  eastern  edge  of  the  Gulf  Stream,  nearly  down  to  Matanilla  Reef,  sets  to  the  south  and 
west,  almost  opposite  to  the  flow  of  the  Gulf,  at  an  average  of  20  miles  in  24  hours." 


1 72  CURliENTS. 

The  limits  of  this  article  will  not  permit  detailed  descriptions  of  the  other  ocean  currents;  their  general  feat- 
ures only  will  be  mentioned. 

To  return  to  the  Atlantic  Currents  : 

Art.  392.  The  North  Atlantic  Memoir  says : ' 

"Of  the  currents  and  regions  of  the  Atlantic,  the  first  in  order  from  the  Land's  End  of  England  is  Rennell's 
Current,  a  temporary  but  extensive  stream,  which  sets  at  times  from  the  Bay  of  Biscay  to  the  W.  and  N.  W., 
athwart  the  entrance  of  the  English  Channel,  and  to  the  W.  of  Cape  Clear. 

"Second.  The  Easterly  and  S.  E.  Drift  Currents  to  the  coasts  of  Europe  and  Africa,  and  southerly  to 
the  coast  of  Guinea. 

"Third.  The  African  or  Guinea  Current,  an  easterly  stream  across  the  Atlantic  between  5°  and  S'^ 
north,  and  continuing  along  the  coast  of  Africa  into  the  Bights  of  Benin  and  Biafra,  with  a  westerly  outset  from 
the  same. 

"Fourth.  The  Sargossa  Sea,  or  central  area,  between  the  Azores,  Canaries,  and  Bermudas,  &c.,  in  which  it 
seems  that  there  is  no  particular  current,  and  is  covered  with  the  well-known  Sargossa  or  Gulf  weed. 

"Fifth.  The  Equatorial  Currents,  the  vast  streams  caused  by  the  trade-winds.  That  of  the  N.  E.  trade, 
running  from  between  the  tropic  and  Cape  Verde,  on  the  eastern  side,  towards  the  Caribbee  Islands,  having  a  gen- 
eral westward  tendency,  and  that  from  the  S.  E.  trade,  which  is  usually  found  to  the  north  of  the  equator,  passing 
strongly  to  the  westward,  south  of  the  counter  or  easterly  current,  number  three  above,  and  then  strongly  to  the 
W.  IM.  VV.  along  the  Colombian  coast,  joining  the  N.  E.  trade  current  in  the  Caribbean  Sea. 

"Sixth.  The  CURRENTS  of  the  Colombian  or  Caribbean  Sea  and  the  Mexican  Stream,  a  continuation  of 
the  Great  Equatorial  Streams  into  the  Mexican  Sea,  from  the  southeastward  and  eastward. 

"Seventh.  The  Florida  or  Gulf  Stream,  an  outset  from  the  Mexican  Sea,  setting  thence  to  the  northeast- 
ward through  the  Strait  of  Florida,  and  thence  eastward  toward  the  Newfoundland  Bank,  and  Azores,  &c. 

"Eighth  The  Arctic  or  Labrador  Current,  passing  southwards  from  Davis  Strait  down  the  coast  of 
Labrador,  round  Newfoundland,  and  thence  southwestward  past  Nova  Scotia  and  the  coast  of  the  United  States, 
inside  the  Gulf  Stream." 

Art.  393.    Findlay  thus  mentions  the  currents  of  the  South  Atlantic  or  Ethiopic  Ocean: 

"The  prevalent  currents  of  the  Ethiopic  Ocean  may  be  briefly  enumerated: 

"First.  That  remarkable  feature  of  the  ocean  commonly  called  the  Agulhas  (Lagullas)  Current,  which  is 
generated  by  the  great  drifts  of  the  Indian  Ocean,  both  eastward  and  westward  of  Madagascar,  flows  westward, 
and  sets  over  the  edge  of  the  great  Bank  of  Agulhas,  whence,  passing  the  meridian  of  the  Cape  of  Good  Hope,  it 
spreads  both  to  the  north  and  west,  and  a  branch  or  offset  rounds  partially  to  the  southwest,  south,  southeast,  and 
east. 

"Second.  The  South  African  Current  is  a  continuation  of  the  Agul/ias  Citrrcut,  which  sets  along  the 
western  coast  of  Africa  toward  the  equator,  where  it  is  connected  with  the  equatorial  stream.  On  the  parallels  of 
Congo  and  the  River  Zahie  it  exists  as  a  powerful  and  very  extensive  stream,  settmg  to  the  northwestward  and 
westward,  along  the  equator,  whilst  the  Guinea  Cwrcnt,  from  the  North  Atlantic,  meetmg  it,  passes  -ivithin  and 
nearly  brushes  it  on  its  way  to  the  Bight  of  Biafra,  where  it  terminates,  being  barred  up  by  the  lands  to  the  east- 
ward. 

"Third.  The  Guinea  Current. — This  has  been  mentioned  under  the  North  Atlantic  currents. 

"  Fourth.  The  Equatorial  Current. — This  current  has  also  been  referred  to  in  the  North  Atlantic  currents. 

"Fifth.  The  Brazilian  Currents. — On  the  eastern  coast  of  Brazil  the  stream  currents  are  varied  according 
to  the  directions  of  the  winds  or  monsoons  and  the  inclination  of  the  coast. 

"Sixth.  The  Southern  Connecting  Cur'rent. — This  current  flows  eastward  over  the  ocean  between  the 
variable  drifts,  &c.,  in  the  parallel  of  40°  south  and  the  S.  E.  trade-wind,  commencing  in  that  of  25°." 

The  Currents  of  the  Pacific 

Art.  394:.    From  "The  Navigation  of  the  Pacific  Ocean,  China  Seas,  &c.,"*  are  extracted  the  following: 

The  Equatorial  Current. — According  to  the  researches  of  Captain  Duperray,  the  waters  of  the  PacificJ 
Ocean  show  in  the  tropical  regions  a  tendency  to  drift  toward  the  west  with  a  variable  rate,  the  mean  rate  of  this 
movement  being  about  24  miles  per  day.  This  vast  stream,  about  3,000  miles  wide,  is  called  the  equatorial  cnrrcntX 
It  appears  to  have  been  particularly  olxserved  between  the  parallels  of  26"  south  and  24'-  north.  A  counter  current 
lias  been  proved  to  exist,  setting  to  the  eastward,  at  some  distance  to  the  north  of  the  line,  and  especially  in  the 
western  part  of  the  Pacific.  This  counter-current  divides  the  great  equatorial  current  into  two  branches,  which  set 
to  leeward  in  both  the  N.  E.  and  S.  E.  trade  regions,  and  which  are  distinguished  by  the  names  of  the  uort/u-nt 
cqiMtorial  current  and  the  soicthern  equatorial  current. 

The  Equatorial  Counter-Current. — The  Equatorial  Counter-Current  is  an  irregular  stream,  setting 
toward  the  east;  it  is  about  300  miles  wide,  and  lies  between  the  northern  and  southern  equatorial  currents. 

Art.  395.  The  Australian  Currents  (East  Coast). — A  distinction  should  be  made  between  the  great 
ocean  current  and  the  coast  zwxxtxxi.  The  ocean  current  off  the  eastern  coast  of  Australia  is  only  the  prolongation 
of  one  of  the  branches  of  the  Southern  equatorial  current,  which  divides  a  little  to  the  southward  of  the  Fiji  Islands 
and  west  of  178^  W.  One  branch  forms  the  Rossel  Current  and  the  other  the  Australian  Current.  This  latter 
current  first  sets  toward  the  west  and  passes  to  the  southward  of  New  Caledonia,  then  it  turns  to  the  S  W.  and 
passes  to  the  westward  of  Norfolk  Island.  It  continues  to  run  to  the  S.  W.,  setting  toward  Howe  Island  and  to 
about  28^  or  30"  south. 

The  Australian  Current  (South  Coast). — On  the  southern  coast  of  Australia  a  tolerably  regular  current 
exists,  flowing  to  the  eastward.  This  motion  appears  to  be  the  natural  effect  of  the  permanent  winds  which  blow 
from  N.  W.  to  S.  W. 

Art.  396.  The  Rossel  Curreni  .— The  waters  of  the  southern  equatorial  current,  comprised  liotween 
20^  and  26^-  south,  and  to  the  southward  of  the  Fiji  Islands,  divide  into  two  branches.  One  of  these  brandies 
stretches  to  the  S.  VV.,  increasing  the  current  off  the  eastern  coast  of  Australia,  and  the  other  sets  toward  N.  W., 
and  is  called  the  Rossel  Current.  The  waters  of  this  current  pass  between  New  Caledonia  and  the  New  Hebrides, 
and  about  150  miles  to  the  eastward  of  this  group.  They  flow  toward  N.  W.,  and  pass  south  of  Varrikoro  Island 
and  the  Solomon  group,  when  they  change  their  direction  to  W.  and  W.  N.  W.,  and  set  toward  Torres  Strait. 

Art.  39?'.  General  Currents  in  the  "Seas  of  Passage." — In  the  "seas  of  passage,"  that  is,  in 
Java,  Celebes,  Banda,  Timor,  and  Arafura  Seas,  the  currents  generally  set  in  the  same  direction  as  the  monsoons. 

*  Translated  from  the  French  of  Mons.  F.  Labrosse.  ' 


\ 


"  CURRENTS.  173 

The  direction  of  the  current  varies,  not  only  with  the  change  in  direction  of  the  wind,  which  occurs  at  times 
during  a  monsoon,  but  also  in  consequence  of  the  impulse  received  in  the  neighborhood  of  the  straits  from  the 
currents  wltich  run  rapidly  in  all  narrow  channels. 

Ai'l.  398.  The  Great  Antarctic  Drift  Current. — This  name  is  given  in  the  I'acific,  as  well  as  in 
the  Atlantic  and  in  the  Indian  Oceans,  to  the  great  body  of  water  moving  toward  the  east,  between  40'^  and  6o'- 
south,  with  a  constancy  analogous  to  that  of  the  prevalent  westerly  winds.  This  current  is  particularly  noticed  in 
the  Pacific,  between  45^^  and  55"'  soudi,  from  Tasmania  and  the  south  point  of  Stewart  Island  (Xew  Zealand),  t<j 
about  Il8-^  or  108'  west.  At  this  longitude  a  portion  branches  off  and  forms  the  Mentor  Current,  which  flows  to 
the  N.  E.,  toward  St.  Ambrose  Islands,  near  78^'  west  and  26  '  south.  The  greater  part  of  the  main  current  con- 
tinues to  drift  to  the  eastward,  as  far  as  84°  or  86^  west,  where  the  waters  of  this  southern  branch  divide  into  two 
currents,  between  the  parallels  42^  and  47°  south ;  one  bears  to  the  northeast,  in  the  direction  of  Valdivia  and 
Valparaiso,  forming  the  Chile  Current,  and  the  other  tends  to  E.  S.  E.  and  S.  E.,  in  the  direction  of  the  Gulf  of 
Penas  and  the  Strait  of  Magellan,  and  forms  the  Cape  Horn  Current. 

The  Mentor  Current. — It  has  been  seen  above  that  a  part  of  the  Antarctic  Drifl  Current  sets  toward 
E.  N.  K.,  near  11 8"^  or  108*^  west,  in  the  direction  of  St.  Ambrose  Islands.  This  branch,  which  is  called  the 
Mentor  Current,  is  comprised  in  a  zone  of  several  degrees  of  latitude,  lying  to  the  northward  and  southward  of  a 
line  drawn  from  42°  S.  and  128"^  W.  to  30^^  S.  and  85^  W.  Beyond  85  W.  the  waters  shape  their  course  to  the 
northward;  first,  toward  N.  E.,  then  toward  north,  after  they  reach  the  parallel  of  the  St.  Ambrose  Islands. 
Beyond  this  latitude  the  current  bends  rapidly  to  the  N.  W.,  passing  the  parallel  20"  S.  between  83°  and  88^ 
west ;   it  then  bears  to  the  westward  and  becomes  merged  in  the  Southern  Equatorial  Current. 

Art.  3!>0.  The  Currents  of  the  China  Sea.— The  currents  of  the  China  Sea  appear  to  be  caused  by 
the  wind  ;  curing  the  N.  E.  monsoon  they  tend  generally  to  the  S.  W.,  and  during  the  S.  W,  monsoon  to  the  N.  E. 
Space  will  not  permit  the  exceptions  to  this  rule  to  be  mentioned. 

Art.  400.  The  Currents  of  the  Japan  Sea. — The  only  thing  which  can  be  positively  asserted  is  that 
both  wintls  and  currents  in  this  sea  are  variable,  and  that  it  is  necessary  for  Navigators  to  be  extremely  careful 
while  passing  from  Corea  Channel  to  Tsugar  Strait. 

Art.  401.  The  Kuro-Siwo  or  Japan  Current. — One  branch  of  the  Northern  Equatorial  Current,  after 
having  passed  the  Mariana  Islands,  flows  toward  the  eastern  coast  of  Formosa  in  a  W.  N.  \V.  direction.  It  makes 
a  sharp  turn  toward  north  while  passing  between  Formosa  and  the  Meiaco-Sima  Islands.  Next  flowing  toward 
N.  E.  it  makes  the  circuit  of  the  Loo-Choo  Islands;  then  it  passes  between  the  islands  of  Kakai-Sima  and  Ok- 
Sima  to  the  southward  and  the  large  island  of  Kiusiu  to  the  northward.  It  bears  off  along  the  coast  of  Niphon, 
passing  by  the  Bay  of  Jedo,  and  opens  out,  in  a  fan-shaped  manner,  toward  the  different  points  of  the  compass 
between  N.  E.  and  E. ;  after  leaving  South  Island  and  Bayonnaise  Rock,  situated  nearly  on  the  meridian  of  the 
Ray  of  Jedo,  the  current  occupies  nearly  the  whole  sector,  which  extends  from  40^^  N.  to  Moor  Island.  This 
current  "is  called  A'aro-Smv  by  the  Japanese,  that  is,  />/<ic/;  citrroit,  on  account  of  its  dark-blue  waters,  and  presents 
many  analogies  to  the  Gulf  Stream  of  the  Atlantic. 

Near  146-  or  147^  east,  between  Moor  I- land  and  40"^  north,  the  Kuro-Siwo  Current  divides  into  two  parts. 
One,  called  the  Kamtchatka  Cui  rent,  flows  in  a  N.  E.  direction,  having  for  its  axis  a  line  drawn  through  151^  E.  and 
joining  40^  N.  with  Bekring  Strait.  The  other  branch,  which  is  by  far  the  larger,  crosses  the  Pacific  in  a  general 
easterly  direction,  in  the  same  manner  as  the  Antarctic  Drift  Current  in  the  southern  hemisphere.  This  main 
branch  of  the  Kuro-Siwo  is  generally  called  the  Japan  or  Ttssan  Current.  The  waters  of  this  stream  flow  toward 
E.  and  S.  E.,  after  passing  the  meridian  152^  E.,  until  they  reach  172^  E.,  between  the  tropic  of  Cancer  and  40^' 
N.  The  current  Lears  toward  E.  between  172^'  E.  and  163^  W.,  and  particularly  in  the  zone  to  the  westward  of  the 
Sandwich  Islands  included  between  20^  and  24-  N.  On  the  meridian  of  163^  W.,  and  N.  of  the  tropics  as  far  as 
44^'  N.,  the  direction  of  the  current  is  nearly  N.  E. ;  the  southern  part  of  the  current  is  bounded  by  a  line  passing 
through  163^  W  ,  and  joining  the  tropic,  and  40^  N.  at  148^  W.  On  this  meridian  of  148^  W.  the  current  flows 
N.  E.  between  40-^  and  50^  N. ;   it  then  tends  to  E.  and  S.  E.,  and  unites  with  the  current  of  the  coast  of  California. 

Art.  402.  The  Kamtchaika  and  Behring  Currents. — The  waters  of  the  Kuro-Siwo  separate  into 
two  branches,  near  146-  or  147*^  E.,  between  Moor  Island  and  40^  N.  The  least  known,  as  well  as  the  least 
important  of  ihese  branches,  takes  the  name  of  the  Kamchatka  Current.  It  flows  toward  N.  E.,  having  for  an 
axis  a  line  passing  through  151^'  E.,  and  joining  40-^  N.  and  Behring  Strait.  This  current,  about  which  httlc  is 
known,  passes  to  the  west  of  the  Aleutian  Islands,  at  a  distance  of  about  150  miles  from  the  coast  of  Kamtchatka. 
It  may  be  here  stated  that  there  exists  a  cold  polar  counter-current  between  the  current  above-mentioned  and  the 
coast  of  Kamtchatka.  It  comes  from  Behring  Sea,  follows  the  coast  of  Kamtchatka  and  the  direction  of  the  Kurile 
Islands    and  gives  rise  to  currents  which  cease  in  the  southern  part  of  the  sea  of  Okhotsk. 

Behring  Current  is  a  stream  which  appears  to  issue  from  Behring  Strait,  and  bends  first  toward  S.  S.  E., 
afterward  passing  to  the  eastward  of  St.  Lawrence  Island.  It  then  flows  S.  and  S.  S.  \V.,  toward  the  Aleutian 
Islands,  passing  to  the  eastward  of  .St.  Matthew's  Island. 

Art.  403.  I'he  Currents  of  the  Coasts  of  California  and  My.x.ico.— On  the  coast  0/ California, 
from  about  50  N.  to  the  mouth  of  the  Gulf  of  California,  23^  N.,  a  cold  current,  200  or  300  miles  wide,  flows 
with  a  mean  speed  of  0.7  of  a  knot,  being  generally  stronger  near  the  land  than  at  sea.  Usually  it  follows  the 
trend  of  the  land,  that  is,  nearly  S.  S.  E.,  as  far  as  Point  Concepcion  (south  of  Monterey),  when  the  current  begins 
to  bend  toward  S.,  S.  W.,  and  then  to  \V.  S.  W.,  off  Capes  San  Bias  and  St.  Lucas.  On  the  coast  of  Mexico,  from 
Cape  Corrientes  (20^  N.)  to  Cape  Blanco  (Gulf  of  Nicoya)  there  are  alternate  currents  extending  over  a  space  of 
more  than  300  miles  in  width,  which  appear  to  be  produced  by  the  prevailing  winds.  During  the  dry  season, 
January,  l'"ebruary,  and  March,  die  currents  generally  set  toward  S.  E.  During  the  rainy  season,  from  May  to 
October— especially  in  July,  August,  and  September— the  currents  set  to  N.  W.,  particularly  from  Cosas  Island 
and  the  Chilf  of  Nicoya  to  the  parallel  of  IS'-'. 

Art  404.  The  Currents  of  the  Bay  of  Panama. — After  leaving  Cape  San  Lorenzo,  or  the  equator,  a 
current  is  found  along  the  coast  of  South  America,  60  miles  wide  ;  it  follows  the  direction  of  the  land,  and,  enter- 
ing the  Bay  of  Panama,  makes  a  complete  circuit  of  that  gulf.  After  meeting  the  western  coast  of  the  Bay  of 
Panama  the  current  turns  to  the  S.,  and  acquires  considerable  velocity,  especially  during  the  dry  season,  from 
December  to  April,  when  the  winds  are  frequent  from  E.  N.  E.  In  the  Bay  of  Panama,  and  at  its  entrance,  the 
currents  are  far  from  being  regular,  and,  under  certain  circumstances,  are  ([uite  strong. 

Ai"t.  405.  The  Currents  of  the  Coasts  of  Chile  and  Peru.— It  has  been  stated  that  the  Antarctic 
drill-current  is  separated  into  two  branches,  between  42^'  ar  d  47^  S.  One  of  these  branches  flows  toward  N.  E., 
in  the  direction  of^  Valdivia  and  Valparaiso.  This  stream  follows  the  various  sinuosities  of  the  coasts  of  Chile  and 
Peru,  and  forms  the  important  current,  the  existence  of  which  was  first  noted  by  Humboldt.  The  princi])al  char- 
acteristic of  this  current  is  its  relatively  low  temperature,     'ihe  general  direction  of  the  waters  between  Pisco  ami 


y 


1 74  CUKRENTS. 


Payta  is  toward  N.  N.  W.  and  N.  W.  Near  Cape  Blanco  the  current  leaves  the  coast  of  America  and  bears  toward 
the  Galapagos  Islands,  passing  them  on  both  the  northern  and  southern  sides.  Here  it  sets  toward  W.  N.  W.  and 
W.  Beyond  the  meridian  of  the  Galapagos  it  widens  rapidly,  and  the  current  is  lost  in  the  equatorial  current,  near 
108'-' W.  As  often  happens  in  similar  case?,  the  existence  of  a  counter-current  has  been  proved  on  different  occa- 
sions.    This  sets  toward  the  S.,  is  very  irregular,  and  extends  only  a  little  distance  from  shore. 

Art.  406.  The  Cape  Horn  Current. — The  waters  of  the  An  arctic  drift-current  divide,  between  the 
parallels  42°  and  47°  S.,  into  two  branches,  one  of  which  flows  E.  S.  E.  and  S.  E.,  in  the  direction  of  the  Gulf  of 
Peiias  and  the  Strait  of  Magellan,  and  form  the  Cape  Horn  current.  The  stream  follows  the  indentations  of  the 
west  coast  of  Patagonia,  though  with  a  general  S.  E.  and  E.  S.  E.  direction,  being  about  150  or  200  miles  in  width. 
The  current  runs  around  Terra  del  Fuego,  toward  E.,  then  flows  to  N.  E.,  passing  through  the  Strait  of  Le  Maire, 
and  by  Staten  Island.  The  swiftness  of  the  current  is  uncertain  on  account  of  the  great  variation  of  the  winds  i: 
these  quarters. 

Currents  of  the  Indian  Ocean.* 


I 


Art.  407.  General  Currents. — In  the  Indian  Ocean  the  equatorial  current  is  only  found  between  the 
parallels  of  lo"-  S.  and  25°  S.  latitude;  that  is,  in  the  limits  of  the  zone  of  the  S.  E.  trade- winds.  It  commences 
to  be  felt  about  the  meridian  of  j02°  E.,  and  extends  to  the  coast  of  Africa,  with  some  changes,  which  will  be 
mentioned. 

The  traverse  current  of  the  Indian  Ocean,  or  the  counter-current  of  the  Cape  of  Good  Hope,  is  formed  by  two 
currents  ;  the  first  a  branch  of  the  traverse  current  of  the  Atlantic  Ocean,  the  second  a  branch  of  the  Agulhas  Cur- 
rent, which  returns  to  the  Indian  Ocean  a  portion  of  the  waters  taken  to  the  S.  W.  and  S.,  along  the  coast  of 
Africa.  Finally,  in  the  traverse  current  of  the  Indian  Ocean,  returning  to  the  E.,  are  mingled  the  waters  descend- 
ing from  the  south  pole  toward  the  equator,  which,  modifying  its  direction,  causes  it  to  take  that  of  E.  N.  E.  to  N.  E. 

At  Cape  Leeuwin,  the  southwest  point  of  Australia,  the  traverse  current  of  the  Indian  Ocean  is  divided  into 
two  branches,  the  one  going  to  the  north,  along  the  west  coast  of  Australia,  blends  with  the  equatorial  current 
nearly  in  the  latitude  of  the  tropic  of  Capricorn;  the  other,  called  "the  current  of  Australia,"  has  already  been 
mentioned  under  the  head  of  "Currents  of  the  Pacific." 

•  The  equatorial  current,  as  before  stated,  is  not  found  in  the  Indian  Ocean,  except  to  the  south  of  the  equator. 
Its  nonhcrn  limit  follows  nearly  the  equatorial  limits  of  the  S.  E.  trade-winds;  that  is,  the  parallel  of  lo'^  S.  On 
the  meridian  of  102^  E.  its  southern  limit  reaches  often  to  the  parallel  of  25°  S.  ;  but  as  the  equatorial  current 
advances  to  the  W.  this  limit  tends  to  the  north,  diminishing  more  and  more  the  breadth  of  the  bed  of  the  current, 
which,  in  the  meridian  of  the  island  of  Rodriguez,  only  extends  from  the  parallel  of  10^  to  that  of  20°  S.  On  the 
meridian  of  the  island  of  Rodriguez  it  is  divided  into  two  branches;  one,  directed  to  the  S.  W.,  surrounds  the 
island  of  Mauritius  and  its  northern  limit,  passes  to  the  south  of  the  island  of  Reunion,  then  to  the  south  of  Mada- 
gascar, on  the  meri  ian  of  which  this  branch  is  480  miles  broad.  From  this  meridian  it  diminishes  its  breadth 
rapidly,  and,  running  to  the  S.  W.,  it  mixes  with  the  current  of  Agulhas,  a  little  to  the  south  of  Port  Natal.  In 
that  ]wrtion  of  the  sea,  between  the  Agtdhas  Current,  the  S.  W.  branch  of  the  equatorial  current,  and  the  west 
coast  of  Madagascar,  there  are  very  variable  currents. 

The  west  branch  of  the  Equatorial  Current,  which  can  be  regarded  as  a  continuation  of  this  current,  runs  to 
the  N.  W.,  passes  to  the  north  of  Madagascar  and  mingles  with  the  current  of  Mozambique,  which  runs  along  the 
east  coast  of  Africa,  on  the  meridian  of  Madagascar,  in  the  vicinity  of  Cape  Amber,  before  its  junction  with  this 
current.  After  its  junction  with  the  current  of  Mozambique,  the  Equatorial  Current  loses  i  s  name,  and  the  two 
descend  to  the  south  along  the  east  coast  of  Africa,  where,  in  the  latitude  of  Port  Natal,  they  are  called  the  Agul- 
has Current. 

These  are  the  only  currents  in  the  Indian  Ocean  which  can  be  called  general  currents.  In  this  sea,  to  the 
north  of  the  equator,  in  the  "seas  of  passage"  and  the  China  Sea,  the  periodical  winds,  the  alternate  breezes,  and 
the  changes  of  the  monsoon,  produce  currents  which  are  very  variable,  their  direction  depending  upon  that  of  the 
winds  which  produce  them,  the  form  of  the  coast,  and  other  causes. 

Currents  in  the  Red  Sea. 

Art.  40§.    The  currents  in  the  Red  Sea  appear  to  be  entirely  controlled  by  the  prevailing  winds. 

Currents  of  the  MEDiTERRANEAN.t 

Art.  409.  That  progressive  movement  of  the  waters  in  the  Mediterranean  which  is  independent  of  tide, 
and  constitutes  the  current,  is  more  remarkable  for  its  constancy  than  for  its  strength;  these  currents  are  due  prin- 
cipally to  the  constant  differences  of  level  of  this  sea  produced  by  evaporation,  the  precipitation  of  rain,  and  winds. 
The  continual  flow  of  the  waters  of  the  ocean  through  the  Strait  of  Gibraltar,  and  those  of  the  Black  Sea  through 
the  Bosphorus,  would  necessarily  form  two  permanent  currents,  the  one  setting  to  the  east  and  the  other  to  the 
west,  at  the  two  opposite  extremities  of  the  Mediterranean. 

Nearly  all  the  authors  who  have  written  on  the  currents  of  the  Mediterranean  admit  a  general  current  to  the 
east,  which  should  run  along  the  coasts  of  Africa,  Egypt,  and  Syria;  from  there  returning  toward  the  west,  should 
pass  by  the  Archipelago,  uniting  with  that  coming  from  the  Dardanelles,  run  along  the  Morea,  pass  the  Adriatic, 
run  in  part  along  the  coasts  of  Italy,  Provence,  and  Spain,  and  mingle  again  with  the  general  current.  It  is  evident 
ihat  does  this  current  exist  in  all  this  circuit,  as  it  is  only  supplied  at  its  points  of  departure,  it  must  be  very  weak 
and  subject  to  many  perturbations. 

With  the  winds  from  S.  W.  to  N.  W.,  a  greater  body  of  water  enters  the  Mediterranean  than  with  other  winds, 
consequently  the  strength  of  the  current  is  increased  and  its  direction  somewhat  changed;  if  the  wind  is  S.  W.  it 
runs  to  the  N.  E.,  along  the  coasts  of  Spain  and  France,  and  if  N.  W.  it  runs  to  the  E.  and  S.  E, 

If  the  prevailing  wind  is  from  N.  E.  to  S.  E.,  under  their  action  new  currents  are  formed,  and,  combining  with 
the  permanent  current,  take  various  directions;  thus,  with  east  winds,  the  currents  run  into  the  bights  of  the  gulfs 
of  Lyon  and  Valencia,  checking  somewhat  the  general  current  coming  round  Cape  San  Antonio,  mix  with  it, 
taking  a  direction  toward  the  African  coast. 

In  many  parts  of  the  Mediterranean  the  currents  are  as  variable  as  the  winds;  in  certain  localities  the  config- 
uration of  the  coasts  and  the  direction  of  the  channels  change  the  course  of  the  currents  produced  by  the  prevailing 
wind,  and  even  those  caused  by  approaching  winds. 

*  "  General  Examination  of  the  Indian  Ocean,"  translated  from  the  French  of  Ch.  Phillippe  de  Kerhallet. 
1  "  General  Examination  of  the  Mediterranean  Sea,"  translated  from  the  French  of  Capt.  A.  Le  Gras. 


-J 

1 


TO    FACE    PAGE     175. 


-'~»\\-  ! 


SUliVEYlNG.  175 


CHAPTER   XV. 

SURVEYING.* 
DESCRIPTION  OF  INSTRUMENTS. 
THE  PLANE-TABLE.t 

Art.  410.  The  plane-table  at  present  in  use  by  tlie  Coast-Survey  is  composed  of  a  well- seasoned  drawing 
board  about  thirty  inches  in  length,  twenty-four  in  width,  and  three-quarters  of  an  inch  thick,  with  beveled  or 
rounded  edges.  It  is  commt-nly  made  of  several  pieces  of  white  pine,  tongued  and  grooved  together,  with  the 
grain  running  in  different  directions  to  prevent  warping.  It  is  supported  upon  three  strong  brass  arms,  to  which 
it  is  attached  by  screws  passing  through  them  and  entering  the  under  side  of  the  board,  the  three  holes  for  the 
receiition  of  the  screws  being  guarded  by  brass  bushings,  and  situated  equidistant  from  each  other  and  from  the 
centre  of  the  tal)le.  By  means  t)f  tiiese  screws  the  lioard  can  l)e  removed  at  will.  The  arms  rest  upon  the  sloping 
upper  face  of  a  rather  flat  hollow  cone  of  brass,  to  which  they  are  permanently  fixed.  Upon  its  lower  edge  or 
periphery  this  cone  is  fashioned  into  a  horizontally  projecting  rim,  the  inferior  face  of  which  is  as  nearly  as  possible 
a  perfect  plane,  and  this  in  its  turn  rests  upon  a  corresponding  rim  of  a  somewhat  greater  diameter  projecting 
slightly  beyond  it.  This  second  rim  forms  the  upper  and  outer  flange  of  a  circular  metal  disc  in  the  form  of  a  very 
shallow  cylinder.  The  inferior  face  or  plane  of  the  upper  flange  or  ri.Ti  has,  at  its  contact  with  the  superior  face 
of  the  lower,  a  horizontal  rotatory  movement  about  a  common  centre,  which  is  the  centre  also  of  the  instrument, 
and  the  two  are  lield  together  by  means  of  a  solid  conical  axis  of  brass  extending  upward  from  the  centre  of  the 
inner  face  of  the  lower  disc.  A  socket  of  similar  shape  fits  exactly  over  this  axis,  projecting  downwaid  from  the 
inner  side  of  the  apex  of  the  conical  or  upper  disc.  The  two  plates  are  held  together  by  means  of  a  mill-headed 
screw  capping  the  cone  from  the  outside,  and  which  can  be  loosened  or  removed  at  pleasure. 

A  tangent  screw  and  clamp  fastened  to  the  edge  of  the  upper  rim  permit,  when  loose,  the  revolution  of  the 
table  about  its  centre,  and,  when  clamped  to  the  lower  limb,  hold  the  table  firm  while  the  tangent  screw  gives  a 
more  delicate  movement. 

Three  equidistant  vertical  projections  of  brass  grooved  on  the  under  side,  and  cast  in  one  piece  with  the  under 
face  of  the  lower  disc,  extending  from  the  periphery  toward  the  centre,  rest  upon  the  points  of  lliree  large  screws 
which  come  through  a  heavy  wooden  block  below.  This  block,  which  is  the  top  of  the  stand  and  is  approximate 
in  form  to  an  equilateral  triangle,  is  made  of  three  pieces  or  horizontal  layers,  and  is  two  and  a  quarter  inches  thick 
and  very  strong. 

The  three  screws  last  mentioned  have  large  milled  heads,  are  quite  stout,  and  play  through  the  block  from 
below  by  means  of  brass  female  screws  let  into  it.  They  are  the  leveling  screws  of  the  instrument  and  are  e(pii- 
distant  from  its  centre. 

Upon  the  under  side  and  centre  of  the  lower  metal  disc  is  a  socket  containing  a  ball  with  a  brass  arm,  \\  hid; 
projects  through  the  centre  of  the  block  from  beneath.  The  lower  end  of  the  arm  is  threaded,  and  upon  it  plays 
a  female  screw  with  a  large  milled  head,  which  can  be  relaxed  or  tightened  at  pleasure.  This  screw  clamps  the 
whole  upper  part  of  the  instrument  to  the  stand ;  it  is  loosened  only  before  leveling,  and  kept  securely  clamped 
at  all  other  times. 

The  block  is  supported  upon  three  legs,  and  with  them  forms  the  tripod  or  stand  of  the  instrument,  the  legs 
being  of  such  a  length  as  to  brmg  the  table  to  a  convenient  height  for  working,  and  so  arranged  as  to  be  taken  oft 
at  will,  or  closed  so  that  their  iron-shod  and  pointed  ends  can  be  brought  together  or  moved  outward,  as  may  be 
required.  For  lightness  the  legs  are  generally  made  open  through  the  middle  of  their  length,  though  sometimes 
they  are  solid,  and  each  one  is  fashioned  at  the  top  into  a  cylindrical  form  with  an  outer  flange,  the  cylinder  fitting 
into  a  groove  on  the  under  side  and  near  the  edge  of  a  truncated  vertex  of  the  block.  The  flange,  by  coming  in 
contact  with  the  lower  edge  of  the  block,  prevents  a  too  great  spread  of  the  legs.  A  brass  screw,  which  is  con- 
nected at  right  angles  with  the  middle  of  a  movable  bolt  running  through  the  axis  of  the  cylindrical  head  of  the 
leg  and  projecting  through  a  hole  in  the  block,  is  fastened  above  by  a  female  screw  with  a  large  milled  head. 

A  dt'cUnatoirc,  consisting  of  a  rectangular  metal  box  containing  a  needle  so  arranged  that  when  pointing  north 
it  is  parallel  to  the  outer  straight  edge  of  the  box;  a  scale  of  equal  parts  of  brass  or  German  silver;  a  set  of  metal 
clamps  for  fastening  the  map  to  the  table;  a  pair  of  sharp  dividers;  India-rubber,  pencils,  and  a  pen  knife,  com- 
plete the  list  of  essentials  for  prosecuting  plane-table  work. 

Art.  411.    Adjustments. — From  the  nature  of  the  service  in  some  sections  of  the  country  the  plane-tabk' 
is  often  necessarily  subjected  to  rough  usage,  and  there  is  a  constant  liability  to  a  disturbance  of  the  adjustments; 
still,  in  careful  hands,  a  well-made  instrument  may  be  used  under  very  unfavorable  conditions  for  a  long  time  with 
out  ])eing  perceptibly  affected.     One  should  not  fail,  however,  to  make  occasional  examinations,  and  while  at  work 
if  any  difficulty  be  encountered  which  cannot  otherwise  be  accounted  for,  it  should  lead  directly  to  a  scrutiny  of  th 
adjustments. 

1.  The  fiducial  edge  of  the  rule. — This  should  be  a  true,  straight  edge.  Place  the  rule  upon  a  smooth  surfac  ; 
and  draw  a  line  along  the  edge,  marking  also  the  lines  at  the  ends  of  the  rule.  Reverse  the  rule,  and  place  tl,  e 
opposite  ends  upon  the  marked  points,  and  again  draw  the  line.  If  the  two  lines  coincide  no  a' justment  is  nece  ;- 
sary;  if  not,  the  edge  must  be  made  true. 

There  is  one  deviation  from  a  straight  line,  which,  by  a  rare  possibility,  the  edge  of  the  ruler  might  assum :;, 
and  yet  not  be  shown  by  the  above  test ;  it  is  when  a  part  is  convex,  and  a  part  similarly  situated  at  the  other  ei  d 
concave,  in  exactly  the  same  degree  and  proportion.  In  this  case,  on  reversal,  a  line  drawn  along  the  edge  of  the 
rule  would  be  coincident  with  the  o  her,  though  not  a  true  right  line;  this  can  only  be  tested  by  an  exact  straight  edge. 

2.  The  lei'el  attached  to  the  rule.  —  Place  the  instrument  in  the  middle  of  the  table  and  b.ing  the  bubble  to  liie 
centre  by  means  of  the  leveling  screws  of  the  table;  draw  lines  along  the  edge  and  ends  of  the  rule  upon  the 
board  to  show  its  exact  position;  then  reverse  i8o  .  If  the  bubble  remain  central,  it  is  in  adjustment;  if  not, 
correct  it  one  half  by  means  of  the  leveling  screws  of  the  table,  and  the  other  half  by  the  adjusting  screws  attached 

*  By  Lieut   Richard  Wainwright. 

tThe  Plane-Table  and  its  Uses.    United  States  Coast  and  Geodetic  Survey. 


176  SUEVEYING. 

to  the  level.  This  should  be  repeated  until  the  bubble  keeps  its  central  position,  whichever  way  the  rule  may  be 
placed  upon  the  table.  This  presupposes  the  plane  of  the  board  to  be  true.  If  two  levels  are  on  the  rule  they  are 
examined  and  adjusted  in  a  like  manner. 

Great  care  should  be  exercised  in  manipulation,  lest  the  table  be  disturbed. 

3.  Parallax. — Move  the  eye-glass  until  the  cross-hairs  are  perfectly  distinct,  and  then  direct  the  telescope  to 
some  distant  well-define*d  object.  If  the  contact  remain  perfect  when  the  position  of  the  eye  is  changed  in  any 
way,  there  is  no  parallax;  Init  if  it  does  not,  then  the  focus  of  the  object-glass  must  be  changed  until  there  is  no 
displacement  of  the  contact.  When  this  is  the  case  the  cross-hairs  are  in  the  common  focus  of  the  object  and  eye 
glasses. 

4.  To  make  the  line  of  coUimation  perpendicular  to  the  axis  of  i-evoliition  of  the  telescope,  and  the  axis  of  revolu- 
tion parallel  to  the  plane  of  the  rule. — The  instrument  is  set  up  and  carefully  leveled,  and  the  crosshairs  directed  to 
a  plumb  or  other  vertical  line.  If  the  cross-hairs  cover  the  line  when  the  telescope  is  elevated  and  depressed,  the 
adjustments  are  perfect;  should  they  deviate,  however,  from  the  vertical  line,  this  error  may  be  attributable  to  two 
causes:  ist,  the  line  of  collimalion  is  not  perpendicular  to  the  horizontal  axis;  or,  2d,  the  axis  is  not  horizontal, 
and  consequently  not  parallel  to  the  plane  of  the  rule.  In  the  first  case  the  motion  of  the  cross-hairs  will  be  in  a 
curve,  and,  upon  being  made  to  cover  the  vertical  line  when  the  telescope  is  horizontal,  will  deviate  from  it  to  the 
same  side  both  upon  elev  ition  and  depression.  In  the  second  case  the  movement  of  the  cross  hairs  will  be  in  a 
straight  line  oblique  to  the  horizon,  and,  when  made  to  cover  the  vertical  line  when  the  telescope  is  horizontal, 
they  will,  upon  being  elevated  and  depressed,  appear  upon  different  sides  of  the  vertical  line.  These  two  cases 
will  be  Considered  separately. 

W  hen  the  construction  of  the  telescope  admits  of  it,  the  perpendicularity  of  the  line  of  collimation  to  the  axis 
may  be  examined  as  follows:  Direct  the  cross- hairs  to  a  well-defined,  distant  object,  as  nearly  upon  a  level  with  the 
telescope  as  may  be;  draw  a  line  along  the  fiducial  edge;  then  reverse  the  rule  iSo°,  again  placing  the  edge  along 
this  line;  revolve  the  telescope  upon  its  axis  and  again  observe  the  object;  if  the  cross-hairs  cover  it,  the  adjust- 
ment is  perfect;  if  not,  one-half  the  error  must  be  corrected  by  moving  the  cross-hairs  by  means  of  the  adjusting 
screws  of  the  diaphragm,  and  the  other  half  with  the  tangent  screw  of  the  table,  and  the  operation  should  be 
repeated  until  the  adjustment  is  complete. 

In  using  the  method  just  given  it  may  be  taken  for  granted  that  the  line  of  collimation  revolves  in  the  vertical 
plane  of  the  fiducial  edge,  as  any  error  arising  from  this  not  being  the  case  would  be  inappreciable. 

After  this  adjustment  the  horizontality  of  its  axis  should  be  examined.  Direct  the  cross-hairs  to  a  distant, 
well-defined,  elevated  or  depressed  object,  having  the  table  carefully  leveled;  draw  a  line  along  the  fiducial  edge, 
reverse  the  rule,  and  again  direct  toward  the  object ;  if  the  cross-hairs  cover  it  the  axis  is  horizontal ;  if  they  do 
not,  one  half  of  the  deviation  should  be  corrected  by  means  of  the  screws  attaching  the  upper  plate  to  the  top  of 
the  standard,  or  by  means  of  the  screws  attaching  the  standard  to  the  rule.  The  level  attached  to  the  axis  should 
then  be  made  central. 

5.  To  make  the  line  of  collimation  parallel  to  the  vertical  plane  of  the  fiducial  edge. — The  exact  parallelism  of 
these  is  not  absolutely  necessary,  but  it  is  essential  that  the  deviation  should  remain  constant.  This  adjustment 
may  be  examined  by  means  of  two  needles  stuck  in  the  table.  The  table  is  so  turned  that  the  needles  sight  exactly' 
to  some  distant  object ;  the  fiducial  edge  is  then  placed  against  them  and  the  telescope  directed  to  the  ol^ject.  If 
the  cross-hairs  bisect  it  the  adjustment  is  correct,  but  if  they  do  not  it  can  be  corrected  by  means  of  the  screws' 
attaching  the  star.dard  to  the  rule. 

6.  Zero  of  the  vertical  arc. — When  the  line  of  sight  is  horizontal  the  vernier  of  the  vertical  arc  should  read  0°, 
or  the  index  error  should  be  known.  This  may  be  examined  by  means  of  the  distant  sea-horizon,  or  by  setting  up 
the  alidade  so  that  the  centre  of  the  telescope  is  in  the  line  of  sight  of  an  accurately-adjusted  leveling  instrument, 
and  then  directing  lioth  instruments,  while  level,  to  a  distant  object;  if  any  error  be  discovered,  it  may  be  cor- 
rected by  setting  the  vernier  at  o-,  and  adjusting  the  horizontal  wire  to  the  sea-horizon  or  object. 

When  the  above  means  are  not  available  the  following  method  may  be  used :   Set  up  the  instrument  at  a  point, 
measure  the  angle  of  e  evation  or  depression  of  a  distant  object,  remove  the  instrument  to  that  object,  and  measure 
the  angle  of  depression  or  elevation  of  the  first  point.     These  angles  should  be  equal  if  the  adjustment  be  correct;  j 
and,  if  not  equal,  the  index  error  will  be  one  half  the  difference  of  the  two  readings.  \ 

The  following  method  of  making  this  adjustment,  where  you  have  neither  a  separate  level,  a  sea  horizon,  nori 
an  elevation,  may  be  employed:  Set  up  the  table  and  level  it  carefully  on  any  level  piece  of  ground  between  twOi 
equidistant  points,  A  and  B,  say  600  or  800  metres  apart.  Determine,  with  the  table,  the  difference  of  level  of: 
thtse  two  points,  and  remove  the  table  to  A.  Measure  carefully  the  distance  from  the  ground  to  the  centre  of  the, 
axis  of  the  telescope,  and  add  or  subtract  this  from  the  difference  of  level  of  the  point  B,  according  as  it  is  lower 
or  higher  than  A.  Set  up  a  target  or  distinct  point  at  this  height  at  B,  direct  the  cross-hairs  upon  it,  and  correct 
the  verrier  accordingly. 

A  longitudinal  striding  level  placed  upon  the  telescope,  cr  a  level  permanently  fastened  upon  the  top  of  the 
telescope,  parallel  to  the  opli:al  axis,  and  adjusted  to  the  horizontal  wire,  will  give  the  error  at  once.  : 

The  alidade  consists  of  a  brass  rule  about  twenty-two  inchts  long,  having  a  circular  level  on  its  upper  face., 
Near  the  middle  of  the  rule  is  a  perpendicular  cylindrical  column  of  brass,  called  the  "standard,"  surmounted  by 
two  square  brass  plates  joined  by  screws,  and  supporting  horizontally  a  conical  journal,  through  which  extends  a 
closely-fitting  cone  of  brass,  coming  from  and  attached  to  the  side  of  the  telescope.  This  cone  forms  the  axis  of 
the  vertical  movement  of  the  telescope,  and  is  secured  at  the  extremity  by  a  screw  which  holds  it  in  its  place.  The 
telescope  itself  has  the  usual  cross-hairs  and  means  of  focal  adjustment. 

A  transverse  level  is  fastened  to  the  edge  of  the  upper  of  the  two  plates  at  the  top  of  the  standard  by  means 
of  adjusting  screws.  I 

The  telescope  is  so  placed  that  its  line  of  collimation  is  above  and  in  the  same  vertical  plane  with  the  fiducial 
edge  (of  the  rule.  ! 

A  vertical  arc  with  a  tangent  screw  and  clamp  is  attached  to  the  telescopic  side  of  the  lower  brass  plate,  and,  ; 
with  a  vernier  which  moves  in  arc  as  the  teletcope  is  raised  or  depressed,  is  used  in  the  measurement  of  vertical 
angles  for  heights.  i 

TELEMETER. 

Art.  412.  In  consequence  of  some  of  the  disadvantages  resulting  from  the  employment  of  the  chain,  among  : 
which  are  the  necessity  of  frequent  dependence  for  correct  distances  upon  the  chainmen,  the  number  of  persons  \ 
required,  the  lime  consumed  in  its  management,  and  the  impediments  to  its  use  found  in  the  features  of  some  sec- ' 
tiuris  of  country,  another  instrument,  styled  the  telemeter,  has  been  advantageously  introduced  in  the  topogiaphical* 
work  of  the  Coast  Survey,  I 


SURVEYING. 


177 


It  appears  that  instruments  of  this  class  were  at  first  generally  regarded  by  scientific  men  as  merely  ingenious 
inventions,  and  not  as  valuable  in  most  respects  as  the  ordinary  method  of  chaining,  the  filling  in  of  details  form- 
ing a  princ^l^al  exception.  From  the  experience  of  its  use  by  the  officers  of  the  Coast  Survey,  however,  it  has  been 
satisfactorily  ascertained  that  the  rapidity  with  which  the  details  of  a  survey  can  be  determined  and  sketched,  the 
smaller  number  of  men  necessary  to  be  employed,  so  that  whatever  errors  may  occur  rest  with  tiie 
observer  only,  and  the  facility  in  using  it  in  places  where  the  use  of  the  chain  is  impracticable,  or  at 
best  difficult,  render  the  telemeter  a  very  important  acquisition.  It  is  not  considered  that  it  will 
ever  entirely  supersede  the  chain  as  a  measuring  instrument,  but  it  is  undoubtedly  a  facik  and  use- 
ful substitute  under  certain  conditions. 

The  telemeter,  as  used  in  the  Coast  Survey,  is  simply  a  scale  of  equal  parts,  painted  upon  a 
wooden  rod  about  I o  feet  long,  5  inches  wide,  and  \%  inch  thick,  so  graduated  that  the  number  of 
divisions  upon  it,  as  seen  between  the  upper  and  lower  horizontal  wires  of  the  telescope,  is  equal  to 
ilie  numlier  of  units  in  the  distance  between  the  observer's  eye  and  the  rod  held  at  right  angles  to 
the  line  of  sight. 

In  all  cases  the  telemeter  should  be  graduated  experimentally  for  the  particular  insU-ument  and 
eye  of  the  observer  who  has  it  in  use. 

The  horizontal  wires  in  the  diaphragm  ot  the  telescope  should  be  accurately  adjusted,  and  the 
divisions  of  the  telemeter  made  to  correspond  in  length  with  the  distance  included  between  the  uppei 
and  lower  wires  of  the  telescope  at  a  carefully  measured  distance,  and  then  divided  into  as  many 
ecpial  parts  as  there  are  units  in  the  distance  measured. 

For  convenience  of  transportation  it  can  be  hinged  in  the  middle,  and  secured  on  the  side  v-'ben 
in  use  by  a  sliding  bolt;  and  as  it  is  necessary,  when  observed  upon,  that  it  should  be  held  accu- 
rately at  right  angles  to  the  line  of  sight,  a  small  brass  movable  bar,  with  sights  or  a  groove  upon  its 
upper  edge,  should  be  fixed  upon  the  side  of  the  rod  at  a  convenient  height  for  the  eye  of  the  rod- 
man,  and  which,  when  in  position,  will  be  perpendicular  to  the  plane  of  the  telemeter  and  directly 
in  the  line  of  sight  of  the  telescope. 

The  correctness  of  the  telemeter  depends  upon  the  closeness  of  the  reading  and  the  accuracy 
with  which  the  rod  is  held  perpendicularly  to  the  line  of  sight. 

With  ordinary  care  an  error  of  reading  should  not  occur  even  at  the  greatest  distance  denoted 
on  the  rod.  \N'ith  the  observations  carefully  made,  and  the  reading  of  the  rod  reduced  to  a  hori- 
zontal plane,  the  greatest  distance  given  by  it,  as  usually  divided,  can  be  relied  on  as  practically 
correct.  There  is  no  sensible  error  at  any  distance  greater  than  20  metres  and  less  than  260,  and, 
generally  speaking,  the  telescopes  of  the  Coast  Survey  alidade?  have  not  sufficient  reading  power 
beyond  400  metres,  but  it  wi  1  generally  be  safe  to  rely  upon  it  for  any  distance  from  15  to  500 
metres,  beyond  which  it  cannot  be  read  with  accuracy  for  use  in  constructing  a  map  on  a  scale  of 

ToUTIlT' 

The  telemeter  has  been  recommended  for  use  in  a  great  variety  of  cases  where  it  becomes  neces- 
sary to  determine  distances,  in  such  close  filling  in  as  the  corners  of  streets,  wharves,  &c.,  deter- 
mination of  all  classes  of  detail,  in  traverse,  shore  line,  and  even  the  establishment  of  positions,  but 
in  the  latter  it  is  safe  only  to  depend  upon  good  intersections.  It  has  been  employed,  however,  in 
all  mmner  of  detail,  and  is  preferred  by  some  to  the  chain,  in  all  cases  save  on  long  lines,  where 
the  distances  are  so  great  that  the  telescope  will  not  admit  of  the  accurate  reading  of  the  rod,  and  it 
is  maintained  by  some  that  where  only  a  single  point  is  to  be  seen  positions  can  be  readily  and  accu- 
rately determined. 

PORTABLE  MICROMETER-TELESCOPE.* 

Art.  413.  This  instrument  is  constructed  on  the  divided-object-glass  principle,  originated  by 
Dolland,  and  applied  in  the  heliometer  of  the  Konigsberg  Observatory,  described  by  Bessel  in  Astro- 
nomische  Nachrichten,  vol.  viii,  pp.  411-426.  Its  novelty  consists  in  a  new  arrangement  of  the 
slides  and  micrometer  screw,  by  means  of  which  it  is  made  sufficiently  compact  for  a  portable 
■instrument.  Each  one  is  provided  with  an  ordinary  terrestrial  eye-piece,  magnifying  about  fourteen 
(14)  diameters,  for  use  on  shore  or  on  board  ship,  and  an  inverting  eye-piece,  magnifying  about  ten 
(10)  diameters,  especially  designed  for  use  in  boats  or  on  hofseback,  &c.  The  cap,  which  fits  both  eye-pieces, 
has  a  revolving  diaphragm,  with  three  colored  glasses  for  observing  bright  objects. 

Rest  the  tube  nearest  the  object-glass  between  the  thumb  and  palm  of  either  hand,  the  back  of  the  hand 
toward    the    eye,    the    thumb  _ 

clasping  the  telescope,  and  the 
micrometer  head  between  the 
first  two  fingers ;  with  the 
other  hand  hold  the  eye-piece 
up  to  the  eye.  The  microme- 
ter head  is  revolved  by  the 
first  two  fingers. 

To  Read  the  Scale. 

The  reading  consists  of 
four  figures.  The  first  two  are 
taken  from  the  scale  on  the 
face  of  the  object-glass,  the 
last  t7i'o  from  the  micrometer 
head.  The  scale  and  microm- 
eter head  standing  as  in  Fig. 
I,  the  reading  will  be  32  from  the  scale  and  65  from  the  micrometer  head,  or  3265.  Standing  as  in  Fig.  2,  the 
reading  is  1121.  The  micrometer  head  makes  one  complete  revolution  for  each  division  of  the  scale  on  the  face  of 
the  object-glass. 


1 1 1 1 


I  1  I  I  I  I  I  I  I 


310 

1 1 1  I  h  M  I 


I  1 1 1 


\ 


Fig.  I. 


♦Roger's  Portable  Micrometer-Telescope.— Gorringk. 


12    B 


178 


SURVEYING. 


To  find  the  Zero  Reading, 

Tlie  zero  reading  is  that  shown  by  the  scale  and  micrometer  head  when  the  two  images  of  any  object  on  which 

the  telescope  is  directed  exactly  coincide,  one  only  being  seen.     This  is  intended  to  be  when  the  reading  is  2000 ; 

that  is,  when  the  scale 
marks  20  and  the  microm- 
eter head  stands  at  zero. 
To  find  the  zero  reading  : 
direct  the  telescope  to  the 
sun;  revolve  the  microm- 
eter head  in  either  direction 
until  the  upper  and  lower 
edges  of  the  two  images  are 
in  contact ;  read  the  scale 
and  micrometer  head  and 
note  tlie  reading.  Revolve 
the  micrometer  head  in  the 
opposite  direction  until  tlie 
two  images  cross  each  other 
and  their  opposite  edges  are 

in  contact;   read  the  scale  and  micrometer  head  and  note  the  reading.     The  mean  of  these  two  readings  (tliat  is, 

half  their  sum)  is  the  zero  reading. 

Examples.    The  reading  greater  than  2000  being  2528,  and  less  than  2000  being  1482;  then  the  zero  reading  is 

2S28+  1482 

^^ =  2005. 

In  another  instrument  the  reading  greater  than  2000  may  be  2527,  and  that  less  than  2000,  1473;  ^'^'^  the 


zero  reading  would  be 


2527+1473 


=  2000. 


In  another  instrument  the  readings  may  be  2523  and  1471 ;  then  the  zero  reading  would  be 


2523+1471 


:  1997. 


In  measuring  angles,  it  is  convenient  to  apply  the  difference  between  the  zero  reading  and  2000  to  all  readings,' 
calling  it  the  index  correction.  If  the  zero  reading  is  greater  than  2000,  the  index  correction  is  subtractive;  if 
less  than  2000,  it  is  additive. 

To  fijid  the  N^itmbcr  of  Micrometer  Divisions. 

The  difference  between  the  zero  reading  and  scale  reading,  when  the  contact  is  made  of  the  opposite  er  ges  or 
ends  of  any  rbject,  is  the  number  of  micrometer  divisions.  The  index  correction  must  always  be  applied  to  the 
scale  reading  if  the  zero  reading  is  assumed  to  be  2000. 

Example.  The  scale  reading  is  2163,  the  index  correction  — 5;  then  the  required  number  of  micrometer 
divisions  is  2163  —  5  —  2000  =  158.  The  scale  reading  is  1281,  the  index  correction  +  3 ;  then  the  required  num- 
ber of  micrometer  divisions  is  2000  —  1281  -|-3=:  716. 


To  find  the  Value  in  Seconds  ofi  Arc  of  each  Micrometer  Division. 

Find  in  the  Nautical  Almanac  the  sun's  semi-diameter  for  the  day,  and  reduce  it  to  the  hour  of  observation. 
With  the  telescope  bring  the  upper  and  lower  limbs  of  the  sun's  images  in  contact  on  each  side  of  the  zero  reading 
as  many  times  as  convenient,  noting  the  readings.  Take  the  mean  of  all  the  readings  greater  than  the  zero  reading 
and  the  mean  of  all  the  readings  less  than  the  zero  reading;  half  the  difference  between  these  means  is  the  number 
of  micrometer  divisions  in  the  sun's  apparent  diameter.  The  value  in  seconds  of  arc  of  each  division  is  determined 
by  dividing  the  sun's  apparent  diameter  hy  the  number  of  micrometer  divisions.  To  find  the  sun's  apparent  diam- 
eter, subtract  from  the  true  diameter  the  difference  of  refraction  for  the  difference  of  altitude  between  its  upper  and 
lower  limbs. 

Example.    September  i,  1876,  sun's 
twenty-four  hours,  o".23.     Longitude,  5'M3. 


! 


semi-diameter  at  Greenwich,  apparent  noon,  15'  53". 86.     Increase  in 


ence  of  refraction  to  10'  of  altitude,  when  altitude  is  59*^ 

As  24'! :  o".23  : 


Time  of  observation, 
o".23, 


noon.     Altitude  of  sun's  centre,  59°.     Differ- 


As  10'  :  o 


Sun's  semi-diameter, 
Correction  for  increase. 

Sun's  'irue  semi-diameter, 


Sun's  true  diameter. 
Correction  for  refraction. 

Sun's  apparent  diameter 


+ 


15' 53 


23 

"86 
.049 


5"- 13 
=  32' 


.049. 


o".736. 


15'  53' 


.909 

2 


3i'47".8i8 
•736 

31'  47"-o82 
60 


1907"  082 


The  mean  of  eleven  readings  greater  and  less  than 
the  zero  reading  were,  respectively,  2531.83  and  1477.95; 
half  their  difference  is  526  94,  the  number  of  micrometer 
divisions  in  the  sun's  diameter.  Therefore  the  value  of 
each  division  is : 


1907". 082 
526.94 


This  value  is  approximately  determined  for  each  instrument,  and  engraved  on  it. 
the  time  and  by  the  observer  when  very  accurate  results  are  desired. 


3"-6i935- 


It  should  be  determined  at 


SURVEYING. 


179 


To  Measure  the  Angle  Subtended  by  a  Vertical  Object. 

The  inrtrument  having  been  brought  to  focus  and  directed  to  the  object,  revolve  the  micrometer  head  in  either 
direction  until  the  upper  and  lower  edges  or  ends  of  the  two  images  are  in  contact.  The  rclath'e  distiuctness  of 
the  two  images  may  l>c  varied  hv  nun'ing  the  eve  Jroiii  side  to  side  across  the  eyc-pieee  at  right  angles  to  the  direction  of 
the  III ieroineter  screw,  and  it  will  assist  in  making  a  good  contact  to  rock  the  instru*.ient  gently  in  the  hand,  to  the 
right  and  left,  so  as  alternately  to  separate  the  images  laterally  and  Itring  them  together  again.  The  observation 
being  complete,  read  the  scale,  apply  the  index  correction,  and  note  the  number  of  microme'.er  divisions,  which, 
multiplied  by  the  value  of  each  division,  gives  the  angle  subtended  by  the  object. 

Example.  Scale  reading,  2083;  index  correction,  —  5  ;  value  of  each  division,  3". 65  ;  2083  —  5  —  2000=  78, 
th(^  required  number  of  micrometer  divisions  ;   78  X  3' '-65  =  284".  7,  the  angle  required. 

It  would  be  conducive  to  accuracy  to  take  the  mean  of  two  observations,  one  greater,  the  other  less,  than  the 
zero  reading.  The  required  number  of  divisions  would  then  be  half  the  difference  between  the  two  readings,  and 
it  would  be  unnecessary  to  apply  the  index  correction. 

To  find  the  Distance  of  the  Object  Oliserved. 

Find,  as  above,  the  angle  subtended  by  the  object;  then,  if  h  =  its  height,  </ =  the  distance  required,  and 
X  =  the  angle  observed : 


d—h'X. 


tan  X 


;  ox  d^=  h  .  cotan  .r. 


A  small  table  may  be  formed  for  each  instrument  containing  values  of  i ,  with  the  micrometer  readings 

as  the  argument.     Multiply  the  tabular  number  by  the  height  of  the  object  observed;  the  result  will  be  the  distance 
««quired.     The  distances  measured  are  to  be  counted  from  the  object-glass, 

BEAM  COMPASSES. 

Art.  414.    Beam  Compasses  consist  of  an  angular  bar  of  wood  or  me'al,  upon  which  two  instruments  termed 
beam-heads  are  fitted  in  such  a  manner  that  the  bar  may  slide  easily  through  them.     A  clamping-screw  attached  to 

one  side  of  the  beam-head  will  fix  it  in  any  part 
of  its  course  along  the  beam.  Upon  each  head 
a  socket  is  constructed  to  carry  a  plain  poirt, 
exchangeable  for  an  ink  or  a  pencil  point  For 
exact  purposes  the  beam-head  placed  at  the  end  | 
of  the  lieam  has  a  fine  adjustment,  which  moves 
the  point  a  short  distance  to  correct  any  eiror  in 
the  first  rough  setting  of  the  instrument.  Tliis  | 
adjustment  generally  consists  of  a  milled-head 
screw,  which  passes  through  a  nut  fixed  upon  the 
end  of  the  beam  head,  which  it  carries  with  its 
motion. 

PROPORTIONAL  DIVIDERS. 

Art.  415.  Proportional  Dividers  are  prin- 
cipally employed  for  reducing  or  enlarging  draw- 
ings in  any  given  proportion. 

This  instrument  consists  of  two  narrow,  flat 
pieces  of  metal,  each  having  a  dovetail  groove 
up  the  centre  for  the  greater  part  of  its  length, 
and  a  steel  point  at  each  end.  These  two  pieces 
are  united  by  a  pair  of  slides,  fitted  together 
upon  one  pin,  and  also  fitted  in  the  grooves  so  that  they  will  slide  along  them;  a  milled-head  screw 
damps  them  together  upon  the  pin,  which  forms  the  axis  of  the  dividers.  There  is  a  stud  on  one  of  the 
sides,  and  a  corresponding  notch  in  the  other,  which  bring  the  points  over  each  other  when  the  instru- 
ment is  closed,  and  prevent  any  shift  in  the  sides  when  moving  the  slides  to  set  the  instrument.  The 
milled-head  screw  is  sometimes  fitted  to  move  in  a  rack  on  the  sides,  affording  a  finer  adjustment.  On 
one  side  is  the  scale  of  lines  and  on  the  other  the  scale  of  circles.  The  scales  are  read  off  when  the 
instrument  is  closed,  by  bringing  the  line  upon  the  slide  opposite  the  required  division. 


THREE-ARMED  PROTRACTOR.* 

Al't.  416.  The  Station  Pointer  or  Three-Armed  Protractor  is  less  known  than  the  protractor  or 
scale,  though  it  is  an  instrument  that  no  Navigator  should  be  without.  Its  principal  use  in  surveying 
is  to  plot  the  angles  for  soundings,  but  it  is  also  used  for  fixing  the  ship's  position,  &c.  It  is  a  gradu- 
ated circle  with  three  arms;  the  centre  arm  is  fixed,  while  with  the  other  two  the  angles  observed  are 
laid  off;  and,  when  the  edges  of  the  arms  pass  through  the  ihree  stations  between  which  angles  were 
measured,  the  centre  marks  the  position  of  the  observer  at  the  time  the  angles  were  taken.  Adjust- 
able arms  are  provided  which  can  be  fitted  to  the  end  of  the  arms  when  signals  are  distant. 

A  piece  o{  tracing  paper  may  be  made  to  answer  the  purpose.     To  use  the  tracing  paper,  draw  a 
line,  making  a  dot  on  it  to  represent  the  centre  station,  and  with  the  centre  of  the  protractor  on  the  dot, 
lay  off  the  two  observed  angles  right  and  left  of  the  line;   then,  laying  this  on  the  plan,  move  it  about  till  the  three 
lines  pass  exactly  through  the  three  stations  observed.     The  dot  from  which  they  were  laid  off  will  be  on  the 
position  of  the  observer,  and  must  be  pricked  lightly  through  or  marked  underneath  in  pencil. 


*  Marine  Surveying.— Mavne. 


180 


SUEVEYING. 


I 


Art.  417.   Dejinitions.  —  Smveying  is  the  art  of  representing  upon  paper  the  surface  of  the  earth,  eivintr  its 
chaiactenstic  features;  of  land,  the  position  of  prominent  objects,  heights  and  depressions,  &c. ;  and  of  water. 

the  depth,  character  of  Ijottom,  posi- 
tion of  shoals,  &c. 

Topographical  Siii7<eying  deline 
ates  the  characteristic  features  of  the 
land,  and  Hydrographic  Sitri'cv'nig  of 
the  water. 

_  Gcodi'sy  is  a  higher  kind  of  sur- 
veying, which  lakes  into  account  the 
curvature  of  the  earth.     To  points  de-  • 
termined  by  such  a  survey  other  sur- 
veys are  referred. 

In  this  chapter  the  methods  appli- 
cable to  the  use  of  such  instruments  as 
are  generally  supplied  the  Navigator 
will  be  given;  a' so  a  general  sketch 
of  the  methods  of  the  U.  S.  Coast  and 
Geodetic  Survey. 

Art.  4 18.  The  Geodetic  SttiTey 
has  for  its  object  the  determination, 
with  the  nearest  approach  to  accuracy 
possible,  of  points  on  the  surface  of 
the  earth  by  a  process  of  triangulation, 
in  which  all  the  posiuons  are  deter- 
mined trigonometrically  and  astro- 
nomically, and  the  differences  caused 
by  the  curvature  of  the  earth  mathe- 
matically reconciled. 

The  measured  base  from  which 
the  triangulation  commences  is  upon 
ground  selected  as  affording  the  de- 
sired length,  and  as  nearly  level  and 
free  from  obstructions  as  possible. 
The  distance  between  the  extremities 
is  measured  by  a  "Base-measuring 
Apparatus,"  consisting  of  compen- 
sated metallic  rods.  All  precautions 
are  taken  to  insure  the  nearest  possi- 
ble approach  to  the  actual  distance. 

A  reconnaissance  sketch  is  made 
with  a  surveyor's  compass,  showing 
the  relative  positions  of  prominent 
points,  from  which  are  determined  the 
points  that  are  to  be  occupied  as  sta- 
tions. At  the  points  so  selected  sig- 
nals are  erected.  Occupying  each 
station  in  turn,  the  angles  between  all 
the  other  stations  visible  are  observed. 
Observations  with  the  transit  instru- 
ment and  zenith  telescope  are  also 
taken  for  calculating  the  astronomical 
positions.  Dip,  variation,  &c.,  are 
also  determined. 

The  extremities  of  the  base  form 
two  of  these  stations.  The  astronom- 
ical l)earing  of  the  base  line,  as  also  of 
some  of  the  sides  of  the  triangles,  are 
determined. 

At  suitable  points  in  the  triangu- 
lation check  base  lines  are  measured, 
which  serve  to  detect  errors  in  the  cal- 
culated length  of  the  various  s  des  of 
the  triangle ;  and  then  where  the  errors 
are  small  they  are  divided  among  the 
different  triangles. 

The  elements  of  the  various  tri- 


I 


,  1     1   ,    1    ,1         •  ...  ^"^  ticuienis  oi  me  various  tri 

angles  are  calculated,  the  trigonometric  positions  thus  obtained  corrected  for  the  curvature  of  the  earth,  and  recon 
ciled  with  the  positions  as  determined  by  the  astronomical  observations.     The  positions  (or  triangulation  points) 
are  then  plotted  upon  the  projection,  according  to  their  latitudes,  longitudes,  relative  directions,  and  distances. 
.     .^'''^."^  ^'i-^  ^"'"^'■y  i^i-iangulation  a  scheme  of  secondary  and  tertiary  triangulation  is  made  to  determine  sufii- 
cient  points  for  the  Topographer  and  Hydrographer.     In  the  determination  of  Uiese  intermediate  points  much  less 
time  IS  expended.  ^ 

The  7\pog?-apher?,izvii,  with  a  plane-table  sheet  on  which  are  plotted  all  the  triangulation  points  included  in 
the  area  covered  by  the  projection,  which  is  on  a  scale  suitable  to  the  importance  of  the  portion  to  be  surveyed ; 
and  proceeds  to  delineate  all  the  features  of  the  land  which  the  sca'e  of  his  sheet  will  permit,  using  the  plane-{ab]e 
and  telemeter.  '  t=         i 

The  Hydrographer  \%  furnished  with  a  sheet  which  includes  the  water  area  to  l)e  surveyed,  the  coast  line  and 
adjacent  features  as  determined  by  the  topographer,  and  all   triangulation  points  visible  from  the  water.     The 


SURVEYING.  181 

soundings  are  made  along  lines  run  in  such  directions  as  are  best  calculated  to  give  a  good  knowledge  of  the 
bottom.  Along  the  lines  at  regular  intervals  positions  are  determined,  either  by  Ivk^o  sextant  angles  (three-point 
problem),  .w  by  a  range  and  one  sextant  angle,  or  liy  two  theodolite  angles  taken  from  known  points  on  shore,  or 
by  one  theodolite  angle  and  one  sextant  angle. 

The  surroundings  are  reduced  to  mean  low-water  from  the  tidal  data.  The  lines  are  plotted  on  the  pro- 
jection with  a  three-armed  protractor,  or  position-finder,  and  the  reduced  soundings  mapped  on  the  chart  between 
the  stations  by  time  intervals.     Curves  of  equal  depth  drawn,  iS;c. 

After  revision  of  all  the  data  thus  obtained,  a  drawing  of  the  chart,  as  intended  for  publication,  is  made  by  the 
draughtsman ;  it  is  reduced  by  the  photographer,  if  necessary,  and  then  goes  to  the  engraver. 

METHODS    OF  SURVEYING    WITH  INSTRUMENTS   ORDINARILY  PROVIDED    THE 

NA  VIGA  TOR. 

SURVEY  OF  A  HARBOR. 

Art.  4 10.  The  Base  Line. — The  place  to  measure  the  base  line  must  be  selected  with  great  care,  on  a  level 
ipot,  free  from  obstructions,  and  of  sufficient  length.  It  should  be  as  long  as  the  time  allotted  to  the  survey  will 
permit.     It  can  be  measured  by  a  chain,  tape-line,  or  any  graduated  line. 

The  distance  should  be  measured  several  times  and  the  mean  of  the  measurements  taken  as  the  length  of  the 
base  line. 

To  Measure  the  Base  Line. — When  there  is  no  chain  to  be  had  and  only  a  short  tape,  carefully  measure  on 
board' ship  a  distance  of  loo  feet,  marking  each  extremity  with  a  copper  tack,  this  distance  to  be  used  in  verifying 
the  length  of  the  measuring  line.  The  line  should  be  of  stout  cod-line,  well  stretched,  fitted  to  two  staves  pointed 
at  the  end  and  shod  with  iron;  with  iron  rings  sufficiently  large  to  travel  easily  on  the  staves,  to  which  are  fastened 
the  ends  of  the  line.  It  should  be  of  such  length  that  when  stretched  taut  the  shoes  of  the  staves  will  rest  on  the 
tack-heads.     Ten  stakes  or  iron  pins  are  required  for  recording  the  number  of  fleets  with  the  line. 

Place  a  long  pole  with  a  flag  at  each  extremity  of  the  base.  Start  from  Base  No.  I ;  remove  the  pole  and 
put  the  shoe  of  chain-stave  in  place;  the  forward  bearer,  who  carries  the  tally-pins,  stretches  taut  the  line  and  is 
signalled  into  range  witli  Base  No.  2  by  the  rear  man  moving  his  hand  to  right  or  left ;  when  in  position  he  puts  a 
tally-pin  in  place  of  his  stave,  and  moves  ahead,  dragging  the  measuring  line  behind  him.  The  rear  man  replaces 
the  pole  at  Base  No.  i,  and  when  he  readies  the  tally-pin  takes  it  and  puts  the  slioe  of  his  stave  in  its  place,  and 
then  again  lines  the  forward  Ijearer.  So  on  until  the  tally-pins  are  exhausted.  Then  counting  the  pins  to  see  that  he 
has  ten,  tallies  one  in  the  recording  book  and  returns  the  pins  to  the  forward  bearer.  Proceed  as  before  until  Base 
No.  ?  is  reached.  Measure  any  distance  remaining  less  than  lOO  feet  with  a  tape-line.  Record  this  distance 
with  the  odd  number  of  pins,  if  any. 

Then  the  tally  marks  X  looo -f-,  ihe  odd  number  of  pins  X  loo -{-  distance  measured  by  tApe-line  =  Length 
of  Base.     This  should  be  measured  several  times,  and  the  mean  distance  used. 

The  tally-pins  terminate  in  a  ring,  and  if  stakes  are  used  they  should  be  fitted  with  a  becket,  for  convenience 
in  stringing  them  together  to  prevent  loss. 

By  mounting  a  telescope  in  place  of  the  pole  at  Base  No.  i,  pointed  toward  Base  No.  2,  the  chain-bearers  can 
be  kept  in  line  and  a  better  measurement  made.  A  theodolite  is  sometimes  used  for  this  purpose  and  the  pins 
lined  on  the  cross-hairs.  Great  care  must  be  taken  to  keep  the  measuring  line  dry,  and  its  length  should  be 
tested  before  and  after  each  measurement,  and  any  error  recorded  with  the  time  taken,  so  that  it  can  be  allowed 
for  in  the  result. 

The  approximate  time  of  performing  any  operation  during  the  survey  should  be  noted,  as  it  will  often  be 
found  convenient  for  reference. 

ASTRONOMICAL  DETERMINATION  OF  OBSERVATION  SPOT. 

Art.  420.  Take  one  end  of  the  Base  as  the  Ohservaiioii  Spot.  Find  the  latitude  as  in  Chapter  VII,  the 
longitude  as  in  Cliapter  VIII,  using  the  sextant  and  artificial  horizon. 

Find  the  Astroiioinieal  Bearing  of  the  Base  Line  by  the  methods  described  in  Chapter  X,  Arts.  334-336.  For 
the  proper  management  of  the  chronometers  and  for  correcting  the  rates  see  Chapter  II,  Arts.  201-208. 

TRIANGULATION. 

Art.  421.  Selecting  the  Signal  Stations. — The  fewer  the  stations  that  will  cover  the  work  the  better,  as 
more  time  can  be  spent  at  each  station,  and  there  will  be  less  danger  of  errors  creeping  in.  Tiie  sides  of  the 
triangles  adjoining  the  Base  must  be  little  greater  than  the  length  of  the  Base  Line,  and  they  must  be  increased 
gradually  until  they  are  as  long  as  the  ready  use  of  the  sextant  will  permit.  The  triangles  should  be  as  nearly  on 
the  same  level  as  possible,  and  when  the  difference  of  level  is  great  the  angle  observed  may  be  corrected  by  the 
following  formula  :  * 

45*-' j   cot  //  sin  i"  where 

H  ^^  horizontal  angle. 

h  =  observed  angle. 

z  =  90°  —  angle  of  elevation. 

H  —  h  :^  correction  desired. 

This  formula  can  only  be  used  when  2  is  not  smaller  than  87°. 

Art.  422.  .Signals. — Use  natural  objects  for  signals  whenever  possible,  remembering  that  when  the  objects 
ire  large  some  particular  part  must  be  chosen  and  marked  with  a  pole  and  flag,  anil  that  it  must  be  occupied  at  or 
near  the  pole 

A  convenient  signal  is  a  tripod  formed  of  four  scantling,  three  forming  the  legs  and  the  fourth  the  centre  pole. 
The  legs  are  beveled  at  their  heads,  so  as  to  admit  of  their  spreading  out  equally.     An  iron  bolt  passes  through 

•  Nautical  Surveying. — Jeffers. 


182 


SURVEYING. 


the  head  of  the  legs,  and  through  the  centre  pole  at  a  distance  of  one-third  of  its  length  from  the  heel.  The  auger 
hole  should  be  sufficiently  large  to  admit  of  the  legs  moving  freely  on  the  bolt.  A  nut  should  be  screwed  on  the 
end  of  the  bolt  to  prevent  its  drawing.  The  signal  is  bolted,  then  raised  in  place  and  the  feet  secured  (so  that  the 
head  of  the  tripod  is  directly  over  the  triangulation  point);  the  centre  pole  uprighted  by  a  heel  line  and  secured 
by  strips  of  board.  Small  boards  are  nailed  at  right  angles  on  the  centre  pole  and  whitewashed.  When  it  is 
necessary  for  the  signal  to  be  seen  at  a  great  distance  the  intervals  between  the  legs  can  be  filled  with  whitewashed 
boards.  When  a  high  signal  is  not  necessary  a  single  scantling  can  be  used  wiih  small  board  nailed  at  right 
angles.  Always  use  plenty  of  whitewash,  and  place  a  flag  of  white  and  black  cloth  at  the  top  of  the  signals,  as 
the  waving  of  the  flag  will  often  attract  the  eye  when  otherwise  the  signal  would  be  difficult  to  find. 


SPECIMEN  OF  ANGLE  BOOK. 
June  25,  1883. 


No. 


2 

3 

4 

5 
6 

7 
8 

9 
10 


Time. 


9  A.  M. 


Angles. 


5°  13'  30'' 


32  26  00 

59  36  00 

60  25  20 

100  10  10 

10  45  ID 

80  00  00 

95  05  50 

25  06  GO 

105  10  GO 


Objects  Observed. 


Base  No.  II,  and  Wind- 
mill. 

Same  and  Lone  Tree. 

Same  and  Sandy  Pt.  A. 

Sandy  Pt.  A  and  Black 
Hill  A. 

Same  and  Cliff  A* 

Chff  A  and  Long  Pt.  A. 

Same  and  Round  A. 

Same  and  South  Pt.  ^. 

South  Pt.  and  Ship  /^^. 

Same  and  Base  No.  II. 


Station 
Occupied. 


Remarks. 


1 


Base  No.  I. 


Clear  weather,  signals  showing 
plainly. 

Sextant  No.  36. 

I.  C.  =  o 

Observed  by . 


59  36  00 

100  10  10 

95  05  50 

105  IG  OG 

360  G2  GO 


Arf.  4:33.    Observing  the  Angles. — As  near  the  centre  of  the  signal  as  possible  should  be  occupied.     When  I 
the  sextant  is  used  this  can  generally  be  done  so  nearly  as  to  obviate  the  necessity  of  correcting  the  observed  angle; 
but  when  it  is  impossible  the  following  formula  may  be  used:* 

r  —  O  -4-  ^'sin  (0+7)  _    rsinj/ 
■^      D  sin  I"  G  sin  i" 

C  =  corrected  angle. 
O  =  observed  angle. 

r=  distance  from  centre  of  signal  station. 

7  =  angle  between  signal  station  and  left-hand  object  observed. 
D  =  distance  of  right-hand  object. 
G  =  distance  of  left-hand  object. 

D  and  G  are  computed  from  the  observed  angle  and  the  other  angles  of  the  triangle. 

Where  the  position  of  the  signals  will  permit,  observe  a  complete  round  of  angles  with  the  sextant;  then  the 
sum  of  the  angles  should  equal  360°.     But  in  practice  there  will  nearly  always  lie  an  error,  which,  if  small,  divide 
among  the  different  angles  in  proportion  to  their  size.     Take  as  many  rounds  of  angles  as  the  time  will  permit  and , 
use  the  means  of  these  angles.     In  taking  a  round  of  angles  use  one  signal  to  reflect  as  long  as  the  size  of  the-' 
angles  will  permit.     Thus,  with  stations  A,  B,  C,  D,  &c.,  observe  the  angles  AB,  AC,  AD,  xVE;  then  EF,  EG,>j 
EH,  EI;  then  IK,  IL,  IM,  and  MA.     The  angle  BC  =  AC  — AB;  CD  =  AD  — AC,  and  so  on  for  the  other 
angles.     This  method  prevents  an  accumulation  of  errors.     If  the  angles  BC,  CD,  &c.,  are  also  directly  observed 
they  can  be  used  as  checks. 

Each  station  should  be  occupied  and  the  angles  between  all  visible  stations  observed,  as  well  as  on  all  promi- 
nent objects;  but  when  but  little  time  is  allowed  for  the  survey,  only  a  few  stations  need  be  occupied,  and  the 
positions  of  the  remaining  ones  determined  by  the  intersection  of  two  or  more  angles.  If  the  signals  are  all  visible 
from  the  Base  Line,  their  positions  might  all  be  determined  by  the  intersection  of  angles  taken  from  its  extremity, 
but  this  would  be  only  a  rough  approximation. 

When  the  three  angles  of  any  triangle  have  been  observed  they  should  be  added  together;  the  sum  will  sel- 
dom equal  180°.  When  only  differing  slightly  from  this,  divide  the  error  among  the  three  angles;  but  if  differing 
greatly  the  error  must  be  sought  out  and  corrected. 

TOPOGRAPHY. 
The  Use  of  the  Plane-Table  in  Topographical  Surveying. 

Art.  424.  An  extract  from  the  "  Plane-Table  and  its  Uses  "  is  given  here,  as  the  method  afterwards  described 
is  the  same,  only  adapted  to  the  use  of  the  sextant.  Also  a  plant -tjble,  with  the  finer  adjustments  omitted,  might 
readily  be  constructed  on  board  ship,  and  the  work  done  more  rapidly  and  satisfactorily  than  with  a  sextant. 

♦Nautical  Surveying. — Jeffers. 


TO  FACE  PAOE  l§t) 


No.  7. 


SPECIMENS  OF  TOPOGRAPHICAL  SIGNS. 


•■i-:**.%*-^:-.**i^\ 


Oak. 


PXNK. 


Palmetto. 


Mangrove. 


lY  Y  *»>  Y  Y  t 
^Y  Y  V  Y  V 


TTTTTTTTl 
ft  n  1 1  H 

t  n  n  1 1 1 

rm  tin 

Uttt  ft 


Cotton. 


Rice. 


Sugar. 


Grass. 


Cultivation. 


Salt  Marsh. 


Frbsh  Marsh. 


Wooded  Marsh. 


Sand,  High  and  Low 
Water. 


Dwelling,  Bahn, 

AND  OlTHOUSES. 


SURVEYING. 


183 


Arl.  425.  Prr/imiiiaiy  IVoil: — As  an  indispensable  preliminary  to  the  operations  of  field-work,  the  topog- 
rapher must  assure  himself  of  the  correctness  of  the  plotted  points  on  the  sheet,  by  an  examination  of  them  in  the 
field,  either  by  actual 
occupation  of  each  one 
or  of  a  sufficient  number 
to  embrace  them  all  in 
two  or  more  lines  of  ob- 
servation. 

It  is  very  rare  that 
the  number  of  triangu- 
lation  points  furnished, 
or  their  positions,  are 
such  as  to  suffice  for  car- 
rying on  an  extended 
survey  without  the  aid 
of  intermediate  points. 
These  are  to  be  deter- 
mined by  the  plane- 
table  ;  and  this  can  be 
(lone  over  a  whole  or  a 
portion  of  the  sheet, 
either  before  any  filling 
in  of  the  topography  is 
executed  or  during  the 
progress  of  the  work, 
depending  much  upon 
the  character  of  the 
country  and  the  skill 
and  judgment  of  the  to- 
jiographer. 

In  observing  upon 
signals  which  are  not 
perpendicular,  the  sight- 
ing should  be  as  nearly 
as  possible  upon  the 
base  of  the  pole.  ^ 

Art.  426.  FU'Id^ 
practice.  —  Topograph- 
ical points  can  be  determined  by  three  methods,  viz  :  "  prosection,"  "  resection,"  and  measured  distances.  In  the 
first  of  these  the  point  must  be  seen  from  two  or  more  occupied  points  in  suitable  positions,  with  regard  to  the 
point  to  be  determined;  in  the  second,  it  must  be  occupied;  and  in  the  third,  there  must  be  a  direct  measured 
line,  with  an  estab- 
lished   direction 


A 


from 
point. 


the  occupied 
These  meth- 
ods of  determina- 
tion, and  the  inci- 
dental operations 
which  accompany 
them,  will  now  be 
considered. 

Let  O,  P,  Q, 
R,  Fig.  I,  represent 
the  board  of  the 
plane-table,  upon 
which  is  spread 
the  topographical 
sheet ;  the  plotted 
triangulation  point 
a  upon  the  sheet 
representing  the 
signal  A  upon  the 
ground;  /',  the  spire 
B;  c,  the  signal  C; 
and  s,  the  station  S ; 
the  small  letters  on 
the  sheet  represent- 
ing the  centres  of 
the  signals  on  the 
ground,  which  are 
referred  to  by  cor- 
responding large 
letters. 

The  table  is 
first  placed  approx- 
imately level  over 
the  occupied  station 
S,  and  put  in  posi- 


\. 


"H 


184 


SURVEYING. 


lion,  also  approximately,  by  the  eye,  so  that  the  plotted  points  on  the  sheet  are  in  range  with  the  station  S  and 
the  sig^nals  or  objects  they  represent  in  the  field.  Then  plumb  the  point  j  over  the  station  S,  fixing  the  legs  of  the 
table  firmly  in  the  ground;  place  the  alidade  upon  the  table  so  that  the  rule  shall  extend  across  its  centre;  loosen 
the  large  milled-head  screw  projecting  below  the  top  of  the  stand,  and  by  means  of  the  leveling  screws  bring  the 
bubble  of  the  circular  level  on  the  rule  to  the  centre.     Place  the  alidade  at  right  angles  to  its  first  position  upon 

the   board,    repeat  the 


1 


operation,    clamp    the 

.  large  screw  again,  and 

\  ?B  the  table  is  level.    Now 

free  the  tangent  screw 
by  loosening  its  clamp, 
place  the  edge  of  the 
rule  ;-  upon  the  occu- 
pied point  J  and  the 
point  l>,  the  telescope 
being  directed  toward 
the  spire  B,  as  shown 
by  the  arrow-head  in 
the  figure,  and  revolve 
the  table  horizontally 
about  its  centre  with 
the  hands  until  B  is 
seen  in  the  field  of  the 
telescope ;  clamp  the 
tangent  screw  and  turn 
it  till  the  intersection 
of  the  cross-hairs  bisect 
the  top  or  centre  of  the 
spire  B.  The  table  is 
now  "in  position"  if 
the  plotted  points  be 
correct  and  the  proper 
objects  sighted.  In 
other  words,  the  table 
is  "oriented"  when 
the  point  observed 
upon  and  the  point  oc- 
cupied are  in  the  line 
of  sight,  the  edge  of 
the  rule  being  upon  the 
two  plotted  points ;  the 
one,  s,  perpendicularly 
over  the  occupied  sta- 
tion, and  the  other,  //,  the  station  observed  upon.  As  a  test  of  the  correctness  of  this,  place  the  rule  ujwn  the 
point  s  again,  and  upon  the  points  a  and  c  consecutively,  and  if  the  two  signals  A  and  C  are  covered  by  the  vertical 
cross-hair  of  the  telescope,  the  orientation  is  assured,  and  the  meridian  of  the  sheet  is  parallel  to  that  of  the  earth, 
all  the  lines  joining  the  signals  and  their  respective  projections  being  also  parallel. 

The  next  operation  is  to  take  "the  forward  line"  to  the  next  point  which  it  is  desirable  to  occupy  or  deter- 
mine, either  some  natural  object  which  can  be  occupied  or  a  forward  signal  placed  for  that  purpose,  say  the 
signal  D. 

The  edge  of  the  rule  is  placed  upon  the  point  s  and  moved  about  that  point  as  a  centre  until  the  forward  signal 
D  is  covered  by  the  vertical  hair,  and  then  a  line,  /,  is  drawn  along  the  edge  of  the  rule  from  s  sufliciently  far  to 
reach  the  estimated  distance  on  the  sheet  of  the  point  (/,  and  at  each  end  of  the  rule  the  short  checkdines  //  n  are 
drawn.  In  the  same  manner  lines  to  be  afterwards  intersected  should  be  drawn  to  such  objects  as  it  may  be  well 
to  determine.  To  prevent  confusion,  the  ends  of  such  lines  are  marked  as  in  the  diagram:  c/i,  chimney;  /,  tree, 
&c.  Tangent  lines  and  lines  of  radiation  to  objects  comparatively  near  at  hand,  to  be  chained  or  obtained  by  the 
telemeter,  as  fence  corners,  &c. ,  should  be  likewise  taken.  The  necessary  sketching  is  now  done,  omitting 
nothing  that  can  be  completed  from  this  point;  the  alidade  removed,  the  table  raised,  the  signal  put  up,  and  the 
party  leaves  for  the  next  station. 

Now,  let  the  letters  in  Fig.  2  be  the  same  as  in  Fig.  i.  The  table  is  removed  to  the  station  A  and  placed  over 
the  point  on  the  ground,  put  in  approximate  position,  leveled,  clamped,  and  loosened  at  the  tangent  screw,  as  at 
station  S.  The  rule  is  then  placed  upon  the  line  a  s,  the  cross-hairs  of  the  telescope  directed  toward  the  signal  S, 
and  the  table  brought  into  position,  as  before  described.  Then,  keeping  the  edge  of  the  rule  upon  a,  direct  the 
telescope  upon  the  signal  D,  and  draw  the  line  a  d,  interseclingy,  and  determining  the  position  of  the  point  d  upon 
the  sheet,  corresponding  to  D,  and  bearing  the  same  relation  in  position  and  distance  to  the  points  s,  a,  />,  and  c 
as  the  signal  I)  does  to  S,  A,^  B,  and  C.  All  the  other  objects  to  which  lines  were  drawn  from  s,  and  which  can 
be  seen  from  A,  are  intersected  and  determined  in  the  same  manner.  This  is  an  example  of  the  method  of  "  pro- 
section." 

The  necessary  sketching,  determination  of  height,  &c.,  are  executed  here  as  at  S,  and,  indeed,  at  every  point 
occupied,  it  being  desirable,  if  possible,  never  to  occupy  a  station  more  than  once. 

The  intersection  of  two  lines  is  not,  however,  positive  evidence  of  the  correct  determination  of  a  point.  Let 
us,  therefore,  proceed  to  D  and  again  determine  it  by  ''resection"  from  the  point  B.     (vSee  Fig   3.) 

The  table  is  placed  over  the  point  U,  put  in  approximate  position,  leveled,  &c  ,  as  at  Ihe  other  stations.  The 
ride  is  then  pliced  upon  the  forward  line,  /"  (now  called  the  "back  line,"  as  seen  from  D),  passing  through  the 
point  s,  so  that  the  checks  ;/  ;/  are  just  visible  along  the  edge,  and  the  telescope  directed  toward  the  signal  S,  as 
shown  by  the  arrow,  and  the  talkie  oriented.  The  rule  is  then  placed  with  its  edge  liisecting  on;  of  the  pi;  tted 
points,  such  as  b,  which  will  give  a  cleanly-cut  angle  (the  nearer  go'^  the  better)  vvitli  the  line  /",  and  is  moved 
about  that  point  as  a  centre  until  the  spire  15  is  covered  with  the  vertical  hair.  A  line  ii  now  drawn  along  ihc 
edge  of  the  rule,  crossing  the  line  f.     If  this  Hue  inier^ects  /"at  precisely  the  same  point  as  the  lines  f,  <i,  and  d, 


SURVEYING. 


185 


the  position  of  d  upon  the  map  is  assured,  and  a  delicate  hole  with  the  dividers  should  be  pricked  upon  the  sheet 
to  fix  the  point,  surrounded  by  a  small  circle  in  pencil.  The  point  may  bo  still  further  tested  by  resection  from 
C.  If  the  forward  line  from  .c  has  also  been  chained,  the  distance  taken  from  the  scale  and  laid  off  from  s  on 
the  line  /"  will  afford  still  another  test,  and  it  is  quite  ^| 
sufficient  if  it  agree  with  an  intersection  where  only  one 
can  be  obtained. 

Another  forward  line,  /',  is  now  taken,  with  the 
usual  checks,  n'  >i' ,  to  the  next  desirable  station,  and 
lines  of  jirosection  are  also  drawn  from  J  upon  the  chim- 
ney, wind-mill,  cupola,  tree,  and  spire  previously  ob- 
servetl,  as  they  appear  in  the  telescope,  in  succession 
from  left  to  right,  end  their  positions  definitely  fixed 
upon  the  map,  pricked  through  and  marked ;  and  these 
being  well  determined,  can  now  be  used  for  the  deter- 
mination of  other  stations.  New  lines  to  such  other 
objects  as  may  be  thought  necessary  should  be  taken, 
as  well  as  tangent  lines,  and  then  follows  the  sketching 
to  fill  in  the  details  about  the  station. 

The  table  is  now  removed  to  E,  Fig.  4  (which  it  was 
thought  unnecessary  to  mark  on  the  figure),  through 
which  the  forw-ard  line  from  d  is  supposed  to  pass,  and 
is  placed  over  the  station ;  and  the  point  e,  representing 
the  projection  of  the  signal  E  upon  the  map,  is  deter-  q 
mined  by  resections  by  the  use  of  the  line  /'  and  the 

f)oints  s,  a,  b,  and  e,  although  the  latter  two  are  not  abso-  '*^*  4- 

utely  necessary.  The  spire  and  tree  may  also  be  used  for  this  purpose.  Those  points  which,  owing  to  acute 
intersections,  have  been  insufficiently  determined,  as  the  chimney,  cupola,  &c.,  are  again  intersected.  Other  pro- 
secting  lines  are  .taken  from  e  upon  other  points  which  present  themselves,  the  necessary  sketching  made,  and  a 
new  forward  line  taken  to  the  next  station. 

During  all  these  operations  occasional  recurrence  should  be  had  with  the  alidade  to  some  established  point  to 
assure  the  immobility  of  the  table,  or  to  correct  any  deflection  from  the  true  position  which  may  have  taken  place. 


THREE-POINT    PROBLEM. 

Art.  43'7«  It  is  often  expedient  to  set  up  the  table  in  position  at  an  undetermined  point  without  any  back 
line  en  which  to  set.  With  three  signals  in  view,  whose  positions  are  projected  on  the  map,  the  table  can  be 
oriented  and  the  point  determined  by  means  of  the  well  known  "three-point  problem." 

The  table  is  lirought  into  approximate  position  by  the  eye  or  declinatoire,  and,  not  being'properly  oriented,  the 
lines  drawn  from  the  three  projected  points  will  not  intersect  in  one  point;  the  lines  will  form  a  small  triangle, 
called  the  triangle  of  error,  or  two  of  them  will  be  parallel,  intersected  by  the  third.  The  position  of  the  true  point 
can  then  be  determined  geometrically  from  these  several  intersections,  and  is  always  at  the  point  of  intersection  of 
arcs  of  circles  drawn  through  each  two  points  and  the  point  of  intersection  of  the  lines  drawn  from  them;  but 
the  construction  of  these  arcs  is  inconvenient  in  the  field.  More  practicable  modes  of  locating  the  point  sought 
will  be  given  in  their  order. 

In  the  classification  given  below,  based  upon  the  locality  of  the  true  point  in  relation  to  the  triangle  of  error, 
the  triangle  formed  by  the  three  fixed  points  is  called  the  great  triangle,  and  the  circle  passing  through  the  same 
points,  the  great  circle. 

Case  I. — When  the  point  sought  is  within  ihe  great  triangle  the  true  point  is  within  the  triangle  of  error. 

Rule.  If  the  line  from  any  one  of  the  points  falls  to  the  right  of  the  intersection  of  the  other  two,  turn  the 
table  to  the  left,  and  if  to  the  left,  turn  it  to  the  right. 

When  the  point  sought  is  without  the  great  triangle  the  true  point  is  also  without  the  triangle  of  error,  and  is 
situated  to  the  right  or  left  of  it,  according  as  the  table  is  out  of  position  to  the  It/toy  right. 

Case  II — When  the  point  sought  is  without  the  great  triangle  and  within  the  great  circle,  the  true  point  is 
without  the  triangle  of  error,  and  the  line  drawn  from  the  middle  point  lies  between  the  true  point  and  the  intersec- 
tion of  the  other  two  lines.  This  also  includes  Case  III,  which  rarely  occurs  in  practice  where  the  three  points  are 
in  a  straight  line. 

Rule.  If  the  line  from  the  middle  point  is  to  the  right  of  the  intersection  of  the  other  two,  turn  the  table  to 
the  right,  and  if  to  the  left,  turn  it  to  the  left. 

Case  IV. — When  the  point  sought  is  without  the  great  circle,  and  the  middle  point  is  on  the  far  side  of  the 
line  joining  the  other  two  points,  the  true  point  is  without  the  triangle  of  error,  and  upon  the  same  side  of  the 
line  from  the  middle  point  at  the  intersection  of  the  other  two  lines. 

Rule.  If  the  line  from  the  middle  point  is  to  the  right  of  the  intersection  of  the  other  two,  turn  the  table  to 
the  left,  and  if  to  the  left,  turn  it  to  the  right. 

Case  V. — When  the  point  sought  is  without  the  great  circle,  and  the  middle  point  is  on  the  near  side  of  the 
line  joining  the  other  two  points,  the  true  point  is  without  the  triangle  of  error,  and  the  line  drawn  from  the 
middle  point  lies  lietween  the  true  point  and  the  intersection  of  the  other  two  lines. 

RuLi:.  If  the  line  from  the  middle  point  is  to  the  right  of  the  intersection  of  the  other  two,  turn  the  table  to 
the  right,  and  if  to  the  left,  turn  it  to  the  left. 

Case  \T. — When  the  point  sought  is  on  the  range  of  either  two  points,  and  the  table  deflected  from  true 
position,  the  lines  drawn  from  these  points  will  not  intersect,  but  will  be  parallel,  intersected  by  the  line  drawn 
from  the  third  point ;  the  true  point  is  then  between  the  two  parallel  lines. 

Rule.  When  the  line  from  the  right-hand  station  is  uppermost,  turn  the  table  to  the  right,  and  when  that 
from  the  left-hand  is  uppermost,  turn  it  to  the  left. 


TOPOGRAPHY  WITH   THE   SEXTANT. 


Art.  43S.  Mount  a  board  on  tripod  legs.  One  can  readily  be  made  on  board  ship  which  will  fit  the  tripod 
of  the  azimuth  compass,  and  will  aid  in  plotting  the  points  and  sketching  in  the  topography  in  the  field.  Clamps 
of  brass,  to  hold  the  sheet  on  the  board,  can  be  made,  with  the  parts  that  come  in  contact  with  the  sheet  covered 
with  paper. 


186 


SURVEYING. 


Start,  as  with  the  plane  table,  at  station  s,  Fig.  i,  and  take  with  the  sextant  the  angle  DA  or  DB;  with  the 
protractor  lay  off  the  line  /  from  the  station  s  as  plotted  on  the  sheet,  making  the  proper  angle  with  i/a  or  d/>.  In 
the  same  manner  lay  off  lines  to  all  the  prominent  objects,  tangent  lines  and  lines  of  radiation  to  objects  near  at 
hand,  the  distance  to  be  obtained  by  a  measuring  line  or  by  a  vertical  angle  of  a  distance  pole. 

A  long,  light  pole,  fitted  as  follows,  will  be  found  to  answer  very  well  for  measuring  short  distances.  On  the 
pole  AT,  Fig.  5,  fit  two  guides  or  wythes  at  A  and  B,  through  which  pass  the  pole  CD;   at  C  and  I)  fit  two  targets 


JL 


in  the  same  plane;  just  above  D  fit  the  sight-vane  EF  perpendicular  to  the  plane  of  the  targets;  at  G 
fit  an  arm  perpendicular  to  AI,  to  which  attach  the  plumbdine  and  bob  Gil.  Have  a  thumb-screw  at 
B  to  clamp  the  pole  CD  in  place,  which  can  be  fitted  so  as  to  unship  for  convenience  in  carrying. 

When  the  bearer  arrives  at  the  point  designated  by  the  topographer,  he  places  tlie  pole  so  that  the 
targets  are  turned  to  face  the  topographer,  and  holds  it  perpendicular,  being  guided  by  the  plumb-line ; 
then  looking  through  the  sight-vane,  he  raises  the  targets  until  his  line  of  sight  just  touches  the  top  ot 
the  topographer's  head;  this  will  bring  the  centre  of  the  target  D  nearly  on  a  level  with  the  topogra- 
pher.     He  then  clamps  with  the  thumb-screw  at  B. 

The  observer  takes  the  angle  subtended  by  the  two  targets,  from  centre  to  centre.  Having  the 
distance  between  the  centres  of  the  targets,  a  table  can  be  computed  for  the  different  angles  (a  right 
triangle  with  base  and  opposite  angle  given),  and  the  distance  taken  off  the  scale  of  equal  parts  and 
plotted  on  the  sheet. 

After  doing  the  necessary  sketching  proceed  to  station  A,  Fig.  2,  and  take  the  angle  BD ;  with  the 
protractor  lay  off  the  line  uif,  intersectingy",  and  thus  determine  the  position  of  signal  D  at  d.  All  the 
other  objects  to  which  lines  were  drawn  at  station  S,  and  which  can  be  seen  from  A,  are  determined  in 
the  same  manner,  and  lines  drawn  to  other  prominent  objects.     The  necessary  sketching  is  also  done. 

Art.  4  39.   B_y  resection. — Proceed  to  D,  and  take  the  angles  C  and  A,  A  and  S;  ascertain  with 
the  protractor  if  these  angles  correspond  with  those  on  the  sheet  from  d,  as  determined  by  prosection.  ■ 
If  so,  (/  is  determined  correctly,  and  can  be  marked  on  the  sheet  and  used  for  further  work.     Make  fur- ' 
ther  intersections  and  lay  off  other  lines ;  also,  fill  in  with  sketches. 

Art.  430.  By  tlic  three-point  problem. — It  is  often  desirable  to  determine  a  point  on  which  no 
cuts  have  been  made,  especially  when  it  is  desirable  to  finish  the  work  rapidly  and»  use  few  signals. 
With  three  signals  in  view,  properly  situated,  this  can  be  done  by  the  three-point  problem.  Take  the 
right  and  left  hand  angles  and  plot  the  positions  with  the  three-armed  protractor,  or  with  tracing-paper, 
being  careful  to  select  signals  which  will  not  make  the  position  indeterminate.  Draw  lines  to  the 
prominent  objects  as  in  prosection,  and  also  make  the  sketches. 

Art.  431.  By  course  and  distance. — In  a  thickly  wooded  place  where  the  trees  grow  close  to  the 
water's  edge,  and  it  would  require  too  much  time  to  cut  away  sufficiently  to  see  from  one  signal  to 
another,  the  shore  line  can  be  run  in  by  course  and  distance,  taking  the  course  with  the  azimuth  com- 
pass and  measuring  the  distance  with  chain  or  measuring  line ;  sketching  in  between  stations. 

HYDROGRAPHY. 

Art.  432.  First  determine  the  general  scheme  for  the  direction  of  the  sounding  lines.  More 
space  is  covered  with  fewer  lines  when  they  are  parallel.  The  lines  should  be  crossed  at  right  angles. 
If  there  are  long  stretches  of  shoal  water  near  the  shore  line,  the  square  work  can  be  connected  with 
the  shore  line  by  zigzags,  in  a  light-draught  boat,  the  work  being  closed  or  opened  according  to  its 
importance  by  decreasing  or  increasing  the  angle  between  the  lines. 

When  the  different  positions  on  the  sounding  lines  are  determined  from  the  boat,  two  observers 
and  a  recorder  are  required.  One  of  the  observers  can  act  as  recorder,  if  skillful  in  handling  thei 
sextant;  but  he  must  angle  rapidly,  and  take  care  not  to  miss  recording  any  of  the  soundings.  His 
angle  can  be  approximately  set  on  the  sextant  by  the  other  observer.  In  a  small  boat,  where  there 
is  little  room  in  the  stern-sheets  (as  a  dingy,  for  instance),  one  observer  can  steer  ind  angle  while  the 
other  records  and  angles.  This  can  only  be  done  where  the  signals  are  easily  reflected,  and  the 
observers  accustomed  to  taking  horizontal  angles.  It  is  not  advisable  to  stop  the  boat  for  angles,  as 
the  mapping  of  the  soundings  between  determined  positions  is  dependent  upon  time  intervals,  and  if 
the  speed  of  the  boat  were  irregular  the  soundings  could  not  be  mapped  correctly. 

Positions  can  be  determined  by  angles  taken  by  two  observers  on  shore  occupying  known  signal 
points,  or  one  angle  from  the  shore  and  one  from  the  boat  (the  observer  in  the  boat  in  this  case  should 
use  the  occupied  signal  as  one  of  the  objects);  by  two  angles  on  three  known  signals  (three-point 
problem);  or  by  one  angle  and  two  signals  in  range.  In  the  first  two  cases  the  angles  must  be  taken 
simultaneously  on  a  preconcerted  signal  from  the  boat:  the  signal  should  lie  h'-isted  shortly  before  the  time,  and 
the  angle  taken  when  it  is  started  down.  Determining  the  position  by  the  tliree-point  problem  is  generally  to  be 
preferred,  as  mistakes  sometimes  occur  in  the  signals,  and  the  positions  cannot  be  plotted  in  the  boat  when  the 
other  methods  are  used. 

While  the  other  w-ork  is  progressing  on  shore  the  sounding  lines  can  be  run;  but  it  is  best  to  have  the  prin- 
cipal stations  roughly  plotted  before  commencing,  as  without  this  when  mapping  the  soundings  it  will  probably  be 
found  that  seme  places  have  been  gone  over  more  than  once  and  others  omitted ;  therefore  a  sheet  of  points  on  a 
drawing  board,  and  a  small  station- pointer,  if  there  is  one,  should  l^e  provided,  or  if  none,  a  piece  of  tracing-paper. 
Arriving  at  one  end  of  the  line  intended  to  be  run,  determine  the  position  and  start  on  the  course  by  compass^ 
and  run  for  the  next  position.  Take  a  sounding  at  the  position  determined  and  commence  sounding,  recording  all 
the  soundings,  with  the  time  and  course,  the  angles  being  recorded  abreast  the  sounding.  The  recorder  must  make; 
the  leadsman  take  the  casts  regularly  when  in  slowly  changing  bottom,  decreasing  the  number  of  casts  as  the  waterj 
becomes  deeper.  By  counting  the  number  of  casts  for  each  interval  of  time,  the  recorder  can  soon  teach  the  leads- 
man to  be  regular. 

The  time  between  each  position  must  depend  upon  the  circumstances  of  the  case ;  when  in  a  tide-way,  or  where 
the  course  is  likely  to  be  influenced  by  a  current  or  the  wind,  the  angles  must  be  taken  more  frequently  than  wheni 
in  still  water. 

When  the  line  ends  at  or  near  the  shore  and  not  at  too  great  a  distance  for  objects  to  be  seen  with  the  glasses; 
Plot  the  first  position,  and  with  the  protractor  find  out  the  angle  at  this  point,  between  some  signal  on  the  right; 
and  the  intended  direction  of  the  line;  set  the  sextant  to  this  angle;  then,  by  looking  through  the  telescope,  the 
point  where  the  line  should  end  will  be  where  the  signal  is  reflected.  When  this  point  is  found  a  natural  rangel 
can  often  be  picked  up  with  the  glasses. 


X 


\S. 


Fig.  5. 


U 


SURVEYING. 


187 


Tell  the  recorder  at  what  time  the  next  angle  is  to  he  taken,  and  when  the  time  arrives  and  the  signals  selected, 
take  the  angles  simultaneously,  one  observer  marking  when  the  other  is  ready. 

He  cartful  not  to  select  signals  from  which  the  position  will  be  indeterminate  or  the  angles  "swing;"  that  is, 
on  or  nearly  on  the  same  circle.  When  widiin  the  triangle  formtd  by  the  three  signals,  or  when  the  apex  is 
toward  the  observer,  or  when  the  signals  are  in  the  same  straight  line  (if  the  angles  are  not  too  small),  the  angles 
will  be  solid.  If  the  second  jjosition,  when  plotted,  is  found  to  be  off  the  intended  line,  the  course  must  be 
changed,  but  not  too  abruptly ;  shape  it  so  as  to  reach  the  line  at  the  next  position  or  further  on.  Sometimes 
when  very  much  off  ilie  line  it  is  well  to  finish  the  line  parallel  to  the  intended  one,  then  shape  the  course  so  as  to 
allow  for  the  disturbing  cause.  If  every  position  is  not  plotted  the  angles  should  be  plotted  as  olten  as  there  is 
any  liabi  ity  of  being  off  the  course  and  at  least  at  the  extremities  of  the  lines.  By  plotting  frequently  much  can 
be  learned  of  the  currents. 

When  the  lines  begin  or  end  near  the  shore,  if  the  boat  cannot  reach  the  shore-line  its  distance  from  the  boat 
on  a  continuation  of  the  sounding  line  should  be  estimated  and  recorded.  Knowing  the  length  of  the  boat  will 
assist  in  this  estimation.  This  affords  a  check  on  the  topographer.  The  sounding-lines  should  be  drawn  in  as 
finished. 

When  working  in  a  strong  current  it  will  be  found  difficult  to  keep  the  lines  from  running  into  each  other;  so, 
where  natural  ranges  cannot  be  picked  up,  it  will  save  much  time  to  set  up  artificial  ones.  This  can  be  done  by 
setting  up  two  poles  in  the  line  of  the  intended  course  and  determining  the  position  of  one  of  them.  If  it  is  neces- 
sary to  carry  the  range  to  a  great  distance  the  second  pole  must  be  put  in  place  by  compass  and  then  determined 
by  two  or  more  angles ;  or,  better  still,  measure  with  the  protractor  the  angle  made  at  the  first  pole  between  some 
known  signal  and  the  intended  course.  Set  the  sextant  to  this  angle ;  then,  occupying  the  position  of  the  first  pole, 
set  the  second  in  place  where  the  reflection  of  the  signal  falls,  if  one  to  the  right  is  used,  and  place  the  pole  so  that 
its  reflection  will  fall  on  the  signal  if  it  is  to  the  left.  If  the  range  will  be  carried  only  a  short  distance  the  second 
pole  can  be  put  in  line  by  compass. 

Be  careful  in  using  ranges  to  have  them  sufficiently  far  apart;  if  too  near,  the  range  will  open  very  slowly,  and 
the  boat  may  be  some  distance  off"  the  line  before  it  is  detected. 


SPECIMEN  OF  SOUNDING  BOOK. 
Soundings  C. 

Year,  1882;  month,  yimc ;  day  of  mont/i,  25. 


Soundings. 

Red.  for 
Tide. 

Reduced 
Soundings. 

Tlme, 
8. 

Bottom. 

Angles  and 
Ranges. 

Rem.\rks.| 

Feet. 

Tenths. 

Feet. 

Feet. 

Tenths. 

8.30> 

I 

5 

—  0.5 

I 

0 

Sand. 

Lone  Tree. 

2 

0 

I 

5 

(I) 

Sandy  Pt.    29-  30' 

A.  B. 

2 

0 

Chff             50    15  i   B.  C.      '  1 

2 

0 

31 

2 
2 
2 
2 

5 
5 
5 
5 

2 

0 

32 

3 

0 

2 

5 

> 

4 

0 

3 

5 

5 

5 

5 

(2) 

Same            25    30 

A.  B. 

7 

0 

6 

5 

Soft  mud. 

48    00 

B.C. 

33 

9 
9 
9 

0 
0 
0 

8 

5 

34 

9 
9 

10 

0 

5 
0 

9 
9 

0 
5 

35> 

10 

0 

9 

0 

8 

5 

Lone  Tree. 

9 

5 

9 

0 

(3) 

Cliff             30    15      A.  B.         1 

36 

8 

I 

4 

0 
0 
0 
0 

7 
6 

5 
3 

5 
5 
5 
5 

Round         56    10 

B.C. 

37 

3 
3 
3 

5 
0 
0 

3 
2 

0 
5 

2 

5 

2 

0 

Sand. 

38> 

2 

.5 

(4) 

Same           25    00 

A.  B. 

2 

0 

I 

5 

50    30 

B.  C. 

2 

0 

2 

0 

39 

2 

2 

0 
5 

2 

0 

2 

I 

5 

(5) 

Same         {Range.) 

40> 

I 

5 

I 

0 

AS"  15' 

B.C. 

188 


SURVEYING. 


One  angle  on  a  range  is  sufficient  to  plot  the  position,  hut  one  of  the  signals  used  should  be  a  range  mark,  if 
possible. 

The  right-hand  angle  should  always  be  recorded  above  the  left,  and  the  signals  used  recorded — the  right 
above,  and  the  left  below,  the  centre  one.  The  initials  of  ths  observers  should  be  recorded  abreast  their  angles ; 
and,  when  reading,  the  observer  should  call  out  right  or  left,  as  the  case  may  be,  before  the  angle. 

In  all  work  where  the  sextant  is  used  the  index  correction  must  be  taken  frequen'.ly,  and  the  record  so  kept 
that  the  correction  will  be  appHed  to  the  proper  angle. 

Each  day  should  be  given  a  letter  in  the  recording-book,  and  the  positions  numbered  consecutively  as  deter- 
mined, beginning  to  number  afresh  each  day. 

Stern  ranges  are  also  useful  in  keeping  the  boat  on  her  course ;  they  can  be  picked  up  after  the  sounding-line 
has  been  started  in  the  desired  direction. 

TIDES. 

Art.  433.  For  information  about  observing  tides  see  Chapter  XIII.  Be  careful  that  the  clock  used  in 
tidal  observations  agrees  with  that  used  in  sounding. 

To  observe  the  strength  of  the  tide  or  current,  anchor  the  boat  at  the  station  chosen,  and  for  surface  current 
use  a  log-line  and  glass  with  afloat  and  flag.  The  angle  between  the  float  and  some  signal  will  give  the  direction. 
When  subsurface  currents  are  to  be  observed  weight  a  can  and  fasten  it  to  the  float  with  a  line  that  will  permit  it 
to  sink  to  the  desired  depth. 

SPECIMEN  OF  TIDE  BOOK. 


Observations  of  Tides  at  Light-House. 

Vt'iir,  1882;  month,  June;  day  of  month,  25. 


Obs. 


Mean  time'Reading 

Barom- 
eter. 

CLOUDS. 

of  Obser-  '  OF  Tide 

Wind. 

Thermometer. 

vation. 

Staff. 

G 

U 

K 

Ph 

s 

< 

TS 

Course  of — 

u5 

u 

•  r-l 

4-* 

"0 

Q 

d 

Q 

1 

V 

p 

< 

< 

000 

in 

w 
K 

< 

1/1 

< 
Pi 

0 

a, 

Mean 

Low 

Wat 

er, 

V9 

8 

30 

45 

4 
4 

4 
6 

West 

2 

9 

00 

15 

30 
45 

4 
5 

I 

9 
2 
6 

G 

10 

GO 

15 

30 

45 

b 
6 
7 
7 

4 
8 
2 
7 

II 

00 
15 
30 

45 

8 

8 
9 
9 

2 

7 
I 

4 

iJ 

I 

12 

00 
15 
30 
45 

9 
10 
10 

IG 

8 
2 

I 

00 

15 

30 
45 

II 
II 
II 
II 

I 
3 

1 

2 

00 
15 
30 
45 

II 
JI 
II 
II 

b 

5 
4 
I 

3 

GO 

15 

30 

35 

IG 
10 

9 
9 

7 
3 
9 
4 

4 

1 

00 

IS 

30 

45 

9 
8 
8 

7 

G 

5 
I 

7 

5 

GO 
15 

7 
6 

3 
9 

30 

6 

6 

I 


TO    FACE     PA«E     189. 


Oz 


RUNNING    SURVEY. 


SURVEYING.  189 

PLOTTING. 

Art.  434.  The  best  method  is  to  calculate  the  length  of  one  of  the  longest  sides  of  the  triangles  to  start 
with  in  i)lotting.  When  it  is  intended  to  do  this,  also  observe  and  calculate  the  Astronomical  Bearing  of  this  side. 
But  if  there  is  not  time  for  these  calculations,  commence  plotting  with  the  Base  Line.  The  method  is  the  same  for 
both,  but  by  first  plotting  the  large  triangles  and  working  down  to  the  smaller  ones  there  is  less  liability  to  error. 

I)raw  a  meridian,  or  North  and  South  line,  so  that  it  will  pass  through  the  point  from  which  it  is  intended  to 
^commence  plotting;  ilien,  with  the  protractor,  lay  off  aline,  making  the  angle  with  the  meridian  equal  to  the 
.\stronomical  Bearing  of  the  side  or  Base  Line.  From  a  scale  of  equal  parts  take  off  the  length,  with  the  dividers, 
proportioned  to  the  actual  length  according  to  the  intended  scale.  From  i  ach  extremity  lay  off  a  line  according  to 
the  angle  made  with  the  other  extremity  and  a  third  point;  their  intersection  will  l>e  the  position  of  that  ])oint. 
From  ihese  three  points  lay  off  lines  to  all  the  other  points  observed  on,  and,  as  they  are  determined,  lay  off  lines 
from  them.  All  the  cuts  from  different  stations  on  any  one  station  will  rarely  coincide,  and  it  will  require  judg- 
ment to  fix  the  position,  using  those  angles  which  are  the  most  reliable  and  those  lines  which  cut  at  or  near  right 
langles.      Prick  the  triangulation  points  through  the  paper  and  surround  them  with  a  triangle. 

The  sheet  is  now  ready  for  the  topographer,  all  the  plotting  being  done  in  the  field.  The  points,  when  deter- 
mined, are  pricked  through  the  paper  and  surrounded  with  a  circle.  After  the  topography  is  finished  the  work 
should  be  inked  in.  When  the  sounding  is  finished,  plot  the  sounding  positions  on  the  sheet,  marking  them  with 
letter  and  number,  and  draw  the  lines  in  pencil.  Use  the  tracing  as  a  referen'ze.  From  the  tide  books  calculate 
the  mean  low  water,  and  for  corresponding  times  enter  in  the  sounding  books  the  correction  to  be  used.  This  cor- 
rection is  the  difference  between  the  observed  tide  and  the  plane  of  reference,  marked  -\-  if  below  and  —  if  above 
the  plane.  Then  correct  all  the  soundings.  Divide  the  distance  between  the  positions  into  an  equal  number  of  parts. 
Count  the  casts  in  the  book  taken  between  the  positions  and  divide  by  the  number  of  equal  parts;  the  quotient 
will  indicate  which  sounding  to  map — that  is,  every  second,  third,  or  fifth  sounding,  as  the  case  may  be.  This  is 
done  upon  the  assumption  that  an  uniform  rate  of  speed  has  been  maintained  between  the  positions.  Take  a  page 
of  the  sounding  liook  and  number  the  lines  consecutively,  place  i  on  the  sounding  next  after  the  first  position,  and 
the  number  cri  the  next  position  will  give  the  number  of  casts  taken.  In  selecting  the  soundings,  if  there  is  any 
one  that  is  peculiarly  shoal  or  deep,  it  should  be  mapped.  The  figures  aid  abbreviations  should  be  parallel  to  the 
bottom  of  the  sheet.  Write  the  character  of  the  bottom  sufficiently  often  to  be  readily  ascertained  at  a  glance. 
Draw  in  curves  of  equal  depth.  When  the  lines  cross  each  other  if  any  error  has  been  made  in  the  soundings  it 
can  be  detected.  It  is  well  to  map  the  soundings  where  they  cross  first,  and  new  lines  can  be  run  at  once  where 
found  necessary. 

The  time  of  High  and  Low  Water,  the  plane  of  reference,  the  strength  of  current,  the  latitude  and  longitude 
of  observation  spot,  &c.,  should  be  put  on  the  chart;  also  the  scale  used,  and  a  compass-rose  which  agrees  with 
the  Astronomical  Bearings. 

RUNNING    SURVEY. 

Art.  435.  In  a  running  survey  the  points  on  shore  are  determined  from  the  ship  by  prosection,  as  in 
topography,  the  position  of  the  ship  being  determined  by  the  three-point  problem  with  points  already  known,  or 
by  positions  determined  astronomically.  At  important  points,  where  it  Is  possible,  parties  are  sent  on  shore  and 
the  position  determined  astronomically,  also  the  True  Bearing  of  some  other  position.  Except  where  landing 
parties  have  been  sent,  who  will  build  signals  when  necessary,  any  easily  identified  objects  can  be  used  as  signals. 
Great  care  must  be  taken  to  prevent  the  different  observers  from  mistaking  the  signals.  Sketches  must  be  taken 
as  far  ahead  as  possible  and  corrected  as  the  work  is  brought  up,  not  only  for  the  chart,  but  for  identification  of 
the  signals.  Lines  of  sounding  are  run  by  the  ship  and  l)y  the  boats;  negative  soundings  must  be  avoided.  The 
position  of  the  l^oats  can  be. determined  by  the  three-point  prol)lem,  by  an  angle  from  the  boat  and  one  from  the 
ship,  and  by  one  from  the  boat  or  ship  and  the  angle  subtended  l)y  the  ship's  mast  for  distance,  or  even  by  a  bear- 
ing and  distance. 

Where  the  survey  is  not  started  from  two  or  more  determined  points,  a  base  line  must  be  measured  by  sound, 
by  mast-head  angles,  by  distance  run  by  log,  or  by  all. 

The  accompanying  diagram  will  illustrate  some  of  the  methods  to  be  used.  The  vessel  is  anchored  at  I  and 
the  launch  at  A  (it  would  be  better  if  one  extremity  of  the  base  could  be  on  shore).  Determine  the  distance 
between  them  by  sound  ;  determine  position  I  astronomically  and  tie  true  liearing  of  the  line  joining  them.  Angle 
on  all  prominent  objects  from  both  positions  ;  then  proceed  to  station  II ;  at  2,  3,  and  4  hoist  the  signal  for  launch 
to  be  ready  to  determine  positions  A^,  A:i,  and  A^.  At  the  hauling  down  of  the  signal,  determine  the  position  of 
the  ship  by  the  three  points  established  from  I,  and  at  the  same  time  angle  on  the  boat. 

At  II  determine  the  position  astronomically,  by  course  and  distance,  and  by  the  three-point  problem;  also  cut 
in  any  other  objects  that  are  available.  Proceed  then  to  III,  determining  the  position  of  the  launch  at  A5,  Ay,  and 
A',  6  and  7  being  determined  by  distance  run  by  log. 

The  launch  is  started  along  the  coast,  sounding  and  kteping  at  a  certain  distance  from  the  shore,  or  in  about 
the  same  depth  of  water,  according  to  instructions;  determining  the  position  of  the  boat  whenever  signaled  to  do 
so,  and  also  at  intervals  between,  when  possible.  Care  must  be  taken  to  mark  these  independent  stations  differ- 
ently  so  as  to  prevent  confusion.  At  every  position  take  the  angle  subtended  by  the  ship's  mast.  At  Ag  and  A/, 
the  launch  hoists  the  signal  indicating  a  change  of  course,  then  determining  the  position  from  the  ship  by  a  bearing 
at  6  and  an  angle  at  7,  the  launch  taking  the  mast-head  angle. 

Every  opportunity  must  be  used  to  get  the  distance  of  the  ship  and  launch  from  the  shore  line,  when  there 
are  no  objects  on  the  shore  line  that  can  be  directly  determined.  Differences  of  bearing  with  the  distance  run  (see 
(-hap.  IV,  Art.  147),  or  the  angle  from  the  mast-head  between  the  shore  line  and  the  launch,  will  give  this  distance. 

All  the  angles  taken  from  any  one  position  should  be  simultaneous,  but,  as  there  will  often  be  more  angles  to 
be  taken  than  there  are  observers,  the  angles  to  determine  the  position  of  the  vessel  should  be  taken  first  and  the 
others  as  soon  afterwards  as  possible. 

,     To  determine  the  Positions  by  Observation. 

Art.  436.    The  determination  of  the  various  positions  of  the  ship  by  observation  will  require  great  care  and 

judgment.  As  little  dependence  as  possible  must  be  placed  on  the  compass.  Whenever  at  anchor,  observations 
for  current  should  be  taken,  and  where  sufficiently  indicated  allowed  for  in  the  reckoning.  Sumner's  method  should 
be  used,  and  the  lines  brought  both  backwards  and  forwards;  that  is,  the  line  of  position  determined  at  H  brought 


190  SUKVEYING. 


forward  to  III,  and  the  one  at  IV brought  back  to  III;  then  the  intersection  of  the  three  lines  will  give  the  position 
of  III.  Twilight  sights  should  be  taken  when  the  horizon  is  good,  as  by  using  two  stars  with  bearings  differing 
nearly  90°,  the  position  can  be  obtained  at  once  by  the  intersection  of  the  two  lines  of  position,  and  will  not  be 
affected  by  the  current  as  when  an  interval  elapses  between  the  time  of  taking  the  observations. 

If  possible,  when  obliged  to  stop  work  in  the  evening  anchor  or  stop  at  point  where  the  work  can  again  be 
picked  up  by  angling  on  three  known  points.  If  neither  is  possible,  stand  off  and  on,  until  early  dawn,  when 
observations  can  be  taken  for  position.  Endeavor  to  start  from  such  a  point  at  early  dawn  that  the  point  reached 
when  ready  to  commence  angling  and  sounding  may  be  on  the  ground  already  surveyed,  and  not  beyond  tiie  posi- 
tion where  the  work  ceased.     No  good  opportunity  for  ascertaining  the  position  of  the  ship  should  be  omitted. 

V.'hen  time  will  permit  it  will  be  well,  after  astronomically  determining  the  initial  point  of  the  survey,  to  pro- 
ceed to  the  further  end  and  determine  a  point  there;   then  there  will  be  less  error  in  the  difference  of  longitude 

The  work  of  a  running  survey  must  be  plotted  on  a  polyconic  projection. 


I 


TO    MEASURE   A    BASE   LINE    liV    SOUND. 


I 


Art.  ^ST.    The  measiirenient  of  a  base  by  sound,  if  several  trials  are  made  and  the  distance  be  more  than 

mile,  will,  in  most  cases,  be  sufficiently  exact  for  the  above  purposes. 

Fire  alternately  from  ship  and  launch.  Appoint  a  signal  to  be  shown  a  half  or  a  (juarter  of  a  minute  before 
each  di.-- charge,  in  order  that  the  eye  may  rest  between.  When  the  signal  is  made  beg  n  to  note  the  beats,  but  not 
to  count  until  the  flash  is  seen;  and  then  let  the  next  beat  be  one,  and  so  count  up  until  the  report  is  heard.  Let 
this  be  done  several  times,  and  at  the  end  take  the  mean  of  the  beats  and  turn  them  into  seconds  of  time,  by  the 
number  of  strokes  the  watch  makes  in  a  minute;  then,  by  multiplying  this  number  of  seconds  by  1090,  and  adding 
one  foot  for  every  two  degrees  of  the  thermometer  above  freezing  point,  the  length  of  the  base  in  feet  will  be 
obtained. 

SURVEY   OF  A   RIVER. 


Art.  43§.    In  the  accompanying  sketch  is  shown  the  method  by  which  a  river  may  be  surveyed  with  boat: 
using  a  sextant. 

Determine  the  length  of  the  line  between  i  and  2  by  sound.  Make  i  the  observation  spot,  and  determine  its 
position  astronomically  and  the  true  bearing  of  the  line.  Send  a  boat  ahead  to  put  up  signals.  Diminish  the  sides 
of  the  triangles  as  the  river  grows  narrow.  From  I  and  2  cut  in  3  and  the  other  signals  in  sight.  Proceed  to  tri- 
angulate up  the  river  until  the  sides  become  too  short;  then  take  the  distance  pole  (as  described  before,  but  here 
the  height  of  the  targets  can  be  permanently  fixed  at  the  height  of  the  observer  in  the  boat),  send  it  ahead  in  a 
boat  to  the  different  stations.  At  15  set  up  the  pole  in  the  boat,  determine  its  distanqe  from  13  by  the  vertical 
angle,  and  take  the  angle  between  14  and  15;  so  on  until  the  river  grows  so  narrow  that  the  angles  become  too 
small ;   then  uie  the  beaiing  by  compass  and  the  vertical  angle. 

Art.  439.  rio//iiii^.  —  On  the  sheet  draw  a  meridian  passing  through  i;  lay  off  the  side  1-2,  making  an 
angle  with  the  meridian  equal  to  the  True  Beating,  and  the  length  according  to  the  desired  scale.  Plot  the  various 
angles  as  taken  and  sketch  in  between,  or  the  shore  line  can  be  put  in  as  shown  in  topography  after  the  signals  are 
all  plotted.  In  the  narrow  work  it  will  be  found  advisable  to  plot  on  a  larger  scale  than  used  for  the  other  portion, 
to  be  reduced  afterward.  From  13  lay  off  the  line  with  the  protractor,  making  the  angle  with  14  equal  to  the 
observed  angle,  and  take  the  distance  as  found  by  the  vertical  angle  from  the  scale  of  equal  parts.  Sketch  in  as 
the  work  advances. 

In  the  narrow  portion  the  sounding  lines  can  be  run  from  signal  to  signal,  but  in  the  lower  run  regular  sound- 
ing lines. 

*  Admiralty  Manual  of  Scientific  Inquiry. 


J 


TO  FAC  K   PAGE   190. 


v« 


SUliVEY  OK  A  RIVEU. 


EXPLANATION  OF  THE  TABLES. 


TABLES  1,  2. 

TRAVERSE  TABLES,  OR  SOLUTIONS  OF  PLANE  RIGHT  TRIANGLES. 

Tables  l  and  2  were  calculated  by  the  natural  sines  taken  from  the  fourth  edition  of  Sherwin's  Logarithms, 
.vhich  we^re  previously  examined,  by  differences ;  when  the  proof-sheets  of  the  first  edition  were  examined  the 
lumbers  were  again  calculated  by  the  natural  sines  in  the  second  edition  of  Hutton's  Logarithms ;  and  if  any 
jifference  was  found,  the  numbers  were  calculated  a  third  time  by  Taylor's  Logarithms. 

The  first  table  contains  the  difference  of  latitude  and  departure  corresponding  to  distances  not  exceedmg  300, 
ind  for  courses  to  every  quarter-point  of  the  compass.  Table  2  is  of  the  same  nature  and  extent,  but  for  courses 
.-onsisting  of  whole  degrees.  The  manner  of  using  these  tables  is  particularly  explained  under  the  article  of 
Inspection,  in  the  different  Problems  of  Plane,  Middle  Latitude,  and  Mercator's  Sailing. 

These  tables  may  also  be  employed  in  the  solution  of  right-angled  triangles,  as  maybe  seen  in  Art.  112, 
Chap.  Ill,  Part  1. 

TABLE  3. 

MERIDIONAL    PARTS. 

Tliis  talile  contains  the  meridional  parts,  or  increased  latitudes,  for  every  degree  and  minute  to  87^,  calculated 
)y  the  following  formula,  viz  : 

m  =  ^  log  tan  (450  -^  ^  —  a  {e-  sin  \.  ■\- ]A,  e^  sin^  L) 


in  which 


M 

the  Equatorial  radius  a  =  1°^°°   ^  3437'- 74677  log  3-5362739 

M,  the  modulus  of  common  logarithms  ^  0.4342945 

I  =  2.3025851  log  0.3622157 

C,  the  aviiprcssion  or  meridional  eccentricity  of  the  earth  ac- 
cording to  Bessel  =     — ? — j.  =::i  0.003342773  log  7.5241069 
299.1528 

V^^TITTS  =  o.  08 1 6968  log  8. 9 1 22052 


e 


From  which 


^      =    7915'. 7055  log  3.8984896 


ae- 


■2     — 


=        22'.9448  log  1.3606843 

j^«t'«=         o'.o5i0473i  log  8.7079734 

The  results  are  tabulated  to  one  decimal  place,  being  sufficient  for  the  ordinary  problems  of  navigation. 
The  practical  application  of  this  table  is  illustrated  in  Art.  66,  Chap.  II,  Part  I,  and  in  the  various  problems 
of  Mercator's  Sailing,  Chap.  Ill,  Part  I. 

TABLE  4. 

This  table  gives  the  length  of  a  degree  in  both  latitude  and  longitude  at  each  parallel  of  latitude  on  the  earth's 
surface. 

TABLE  5. 

This  table  has  been  calculated  to  facilitate  the  operation  of  finding  the  distance  from  an  object  by  two  bearings, 
Shaving  the  distance  run  and  course.     In  the  first  part  of  the  table  the  arguments  are  given  in  points ;  in  the  second 
Ipart,  in  degrees. 
'        It  is  illustrated  in  Art.  148,  Chap.  IV,  Part  I. 

TABLE  6. 

This  table  contains  the  distances  at  which  any  object  is  visible  at  sea  calculated  by  the  formula 

d=  1.3 1 7  "v/xinfeet, 

in  which  d  is  the  distance  in  statute  miles,  x  the  height  of  the  eye  or  the  object  in  feet. 

The  explanations  and  use  of  this  table  are  given  in  the  Useful  Problems  of  the  Appendix. 

191 


192  EXPLANATION  OF  THE  TABLES. 

TABLE  7. 

To  reduce  Longitude  into  Time,  and  the  contrary. — In  the  first  column  of  this  table  are  contained  degrees  and 
minutes  of  longitude,  in  the  second  the  corresponding  hours  and  minutes,  or  minutes  and  seconds  of  time;  the 
other  columns  are  a  continuation  of  the  first  and  second  respectively.  The  use  of  this  table  will  evidently  appear 
by  a  few  examples. 


Example  I. 
Required  the  time  corresponding  to  50°  31'. 

Opposite  50°  in  col.  i  is 3  20  o 

31'   2  4 


Example  II. 

Required  the  degrees  and  minut&s  corresponding  to 
6'i  33"'  2o^ 

Opposite  6''  32'"   o" in  col.  4  is 98°   o' 

I    20 in  col.  2  is 20 


6    33    20  98   20 


Sought  time 3  22  4 

TABLE  8. 

To  convert  Sidereal  Time  into  Mean  Solar  Time. 

TABLE  9. 

To  convert  Mean  Solar  Time  into  Sidereal  Time. 

TABLE  10 
Contains  the  time  of  true  rising  and  setting  computed  by  the  formula 

cos  H.  A.  =  tan  dec  X  tan  latitude. 

To  find  the  Time  of  the  Sun's  /Using  and  Setting,  and  the  Length  0/  the  Day  and  Night, 

Rule.  Find  the  sun's  declination  at  the  top  of  the  table,  and  the  latitude  in  either  tide  column ;  under  the 
former,  and  opposite  the  latter,  will  lie  the  time  of  the  sun's  setting  if  the  latitude  and  declination  aie  of  the  same 
name,  but  the  time  of  rising  if  of  different  names.  The  time  of  rising,  subtracted  from  12  hours,  will  give  the 
time  of  seating;  or  the  time  of  setting,  subtracted  from  12  hours,  will  give  the  time  of  rising.  The  time  of  rising, 
being  doubled,  will  give  the  length  of  the  night;  and  the  time  of  setting,  being  doubled,  will  give  the  length  of  the 
day. 

For  the  S.UN  the  H.  A.  is  the  app.  time  of  rising  or  setting. 

For  the  Moon  or  a  Star.  Find  the  app.  time  (or  mean  time,  as  required)  of  the  meridian  passage.  Then, 
for  approximate  time  at  rising,  subtract  the  hour  angle  from  the  time  of  meridian  passage  (increased  by  24^  if 
necessary);  for  approximate  time  oi setting  add  them  together,  rejecting  24''  in  the  result  if  it  exceeds  that. 

It  may  be  noted  that  the  numljers  of  Table  10  were  calculated  for  the  moment  the  sun's  centre  appears  in  the 
true  horizon ;  allowance  ought  to  be  made  for  the  dip,  parallax,  and  refraction,  by  which  the  sun  and  stars,  when 
near  the  horizon,  appear  in  general  to  be  elevated  above  half  a  degree  above  their  true  place,  and  the  moon  as 
much  below  her  true  place. 

TABLE  11. 

This  table  was  calculated  by  proportioning  the  daily  variation  of  the  time  of  the  moon's  passing  the  meridian. 
The  numbers  taken  from  this  table  are  to  be  added  to  the  time  at  Greenwich,  in  West  longitude,  but  sub- 
tracted in  East. 

TABLES  12,  13. 

These  are  tables  of  proportional  parts ; 

For  finding  the  variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon's  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page 
in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column  ; — 

.Also,  for  finding  the  variation  of  the  Moon's  Declination  in  seconds  of  time;  the  motio.i  in  one  mmute  beirig 
given  at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds ; 

Also,  for  finding  the  Sun's  Right  Ascension  for  any  given  number  of  hours. 

TABLE  14. 

This  table  contains  the  dip  of  the  sea  horizon,  calculated  by  the  formula 

D  =  58".8  -v/F, 

(n  which  F  =  height  of  the  eye  above  the  level  of  the  sea  in  feet. 
It  is  explained  in  Art.  251,  Chap.  V,  Part  II. 

TABLE  15. 

The  table  contains  the  dip  for  various  distances  and  heights,  calculated  by  this  rule, 

D  =  ^</  + 0.56514  xj, 

in  which  D  represents  the  dip  in  miles  or  minutes,  d  the  distance  of  the  land  in  sea  miles,  and  //  the  heigh  oi  tne  , 
eye  of  the  observer  in  feet. 


EXPLANATION  OF  TABLES.  193 

TABLE  16. 

The  tab^e  contains  the  Sun's  parallax  in  altitude  calculated  by  the  formula 

par.  =  sin  Z  X  8". 75  (0's  Hor.  Par.) 

in  which  Z  =  apparent  zenith  distance. 

It  is  explained  in  Art.  247,  Chap.  V,  Part  II. 

TABLE  17. 

Parallax  in  altitude  of  a  planet  is  found  by  entering  at  the  top  with  the  planet's  horizontal  parallax,  and  at  the 
side  with  the  altitude. 

TABLE  18. 

The  table  gives  the  augmentation  of  the  moon's  semi-diameter  calculated  by  the  formula, 

x=^rs'^  sin  A -\-  }4  c'^  s^  sin^  /^  +  K  <^^  ^> 
i»  which 

/i  =  moon's  apparent  altitude. 
J- =  moon's  horizontal  semi-diameter. 
X  =^  augmentation  of  semi-diameter  for  altitude  /i, 
logc  =  5.25021. 

TABLE  19. 

The  table  contains  the  augmentation  of  the  moon's  horizontal  parallax,  or  the  correction  to  reduce  the  moon's 
equatorial  horizontal  parallax  to  that  point  of  the  earth's  axis  which  lies  in  the  vertical  of  the  observer  in  any  given 
latitude,  computed  by  the  formulas 


A-  =  7r(^— I),  6  = 


■i/(i— ^2sin2  0y 

where     tt  =  equatorial  horizontal  parallax. 
^  =  latitude. 

^  =  eccentricity  of  the  meridian;  log  ^^  =  7.81602. 
A  TT  =  augmentation  of  the  horizontal  parallax  for  the  latitude  ^. 

TABLE  20. 

A/i-(in  refraction,  reduced  from  Bessel's  tables,  to  barometer  30'"  and  thermometer  50°. 

TABLES  21,  22. 

Corrections  of  the  mean  refraction  for  the  height  of  the  barometer  and  thermometer,  deduced  also  from  Bessel's 
,  table. 

.     TABLE  23. 

The  table  contains  the  correction  of  the  moon's  altitude  for  parallax  and  refraction,  corresponding  to  the 
parallax  57'  30". 

TABLE  24. 

This  table  contains  the  correction  to  be  applied  to  the  moon's  apparent  altitude  to  each  minute  of  horizontal 
parallax  and  every  10'  of  altitude  from  5°,  for  height  of  barometer  30'"  and  Fahrenheit  thermometer  50*^. 

For  seconds  of  parallax,  enter  the  table  alsreast  the  approximate  correction  and  find  the  seconds  of  hor.  par- 
allax, viz:  the  tens  of  seconds  at  the  side  and  the  units  at  the  top.  Under  the  latter  and  opposite  the  former  will 
be  the  seconds  to  add  to  the  correction. 

For  minu  es  of  altitude,  take  the  seconds  from  the  extreme  right  of  the  page,  and  apply  them  as  there  directed. 

The  table  was  computed  by  correcting  each  app.  altitude  (of  the  centre)  for  refraction;  then  log.  sec.  alt.  -|-  P. 
L.  Hor.  Par.  =  P.  L.  par.  in  altitude.  From  the  parallax  corresponding  to  this  proportional  logarithm  subtract  the 
refraction;   the  remainder  is  the  correction  of  altitude. 

TABLE  25. 

The  table  gives  the  variation  of  the  altitude  of  any  heavenly  body  arising  from  a  change  of  loo"  in  the  decli- 
nation. It  is  useful  in  finding  the  latitude  by  two  altitudes  of  a  body  when  the  declination  changes  during  the 
interval  of  elapsed  time. 

If  the  change  move  the  body  toward  the  elevated  pole,  apply  the  correction  to  the  altitude  with  the  signs  in 
liie  table;   otherwise  change  the  signs. 

TABLE  26. 

Table  26  contains  the  variation  of  the  altitude  of  any  heavenly  body,  for  one  minute  of  time  from  noon,  for 
various  degrees  of  latitude  and  declination.  The  following  method  was  used  in  constructing  the  table:  A  and  B 
were  calculated  for  each  degree  of  declination  by  these  formulas  : 

Log  A  =:  log  I ".96349  +  2  log  cos  declination  —  20.00000, 
Log  B  :=  log  A  4-  log  tan  tleclination  —  10.00000 ; 

and  then  the  correction  of  the  table  corresponding  to  the  zenith  distance  Z  (  =lat. '^  dec.)  was  found  by  this 
formula:  A  X  cotan  Z  -|-  B.  To  facilitate  the  computation  of  these  numbers,  a  table  of  the  products  of  A  by  the 
whole  numbers  from  i  to  9  was  calculated. 


194  EXPLANATION  OF  TABLES. 

TABLE  27. 


Table  27  contains  the  squares  of  the  minutes  and  parts  of  a  minute  of  tmie  corresponding  to  every  second 
from  o'*  to  12'"  59''.     This  requires  no  explanation. 

The  manner  of  using  tlie  two  preceding  tables  is  exemplified  in  the  body  of  the  work  in  finding  the  latitude 
by  reduction  to  the  meridian,  Art.  278,  Chap.  VII,  Part  II. 

TABLE  28,  A,  B,  C,  D. 

For  finding  the  Latitude  of  a  Place  by  Altitudes  of  Polaris. 

The  formula*  on  which  these  tables  are  based  is 

1 
'L  —  h  —p  cos  t-\-y2p'^  sin  i"  sin-  /  tan  // 

—  YzP^  sin'^  i"  cos  t  sin-  /  +  yi  /'  sin^  i"  siut  t  tan^  h; 

in  which  L  =  the  latitude  of  the  place,  and 

//  =  the  true  altitude, 
p  =  the  polar  distance,  and 
/  =  the  hour  angle  of  the  star. 

Table  A  contains  for  the  declination  88°  40',  or/o  =  1°  20"  =  4800",  \h^  first  correction, 

A  =  —  po  cos  t  —  y^  /'o  sin-  I''  cos  /  sin^  t ; 

Argument,  the  hour  angle  ofi  the  star,  or  24''  —  the  hour  angle. 
Table  B  contains  the  second  correction, 

B  =  )4  p-o  sin  i"  sin2  t  iz.r\  h  -^  y^  p^o  sin^  i"  sin-"  t  tan»  h  ; 

Arguments,  the  true  altitude  ofi  the  star  and  the  hour  angle,  or  24''  —  the  hour  angle.     This  correction 
is  always  additive. 
Table  C  contains  the  third  correction, 

C  —  y  (/-  —p^o)  sin  i"  sin2  /  tan  h; 

Arguments,  B  and  the  declination  ofi  the  star  from  88°  39'  20"  to  88°  41'  20". 
Table  D  contains  the fiourth  correction, 

—  (/  —A)  cos  /  —  >^  (/'  — /^o)  sin2  I"  cos  t  sin^  i; 

Arguments,  A  and  the  declination  of  the  star  from  88'^  39'  20"  to  88'^  41'  20'. 

The  quantities  are  given  to  the  nearest  o".l  :  a  .  placed  after  some  of  them  indicates  a  doubt  between  the 
figure  given  and  the  next  highest,  or  tlaat  the  correct  value  is  o",05  greater  than  that  given.  Thus,  3". 7  .  indicates 
the  actual  value  3". 75.  • 

TABLE  29. 

Mean  Reduced  Refiraction  fior  Lunars,  computed  by  the  formula 

cos  h       sin  /i' 
where 

h  =  the  apparent  altitude, 

r  =  mean  refraction,  barometer  30'",  P'ahrenheit's  thermometer  50°, 
r"  =  mean  reduced  refraction  for  lunars. 

The  refractions  employed  are  Bessel's,  and  were  taken  from  his  table  (Astro/uw/ische  Untersuchungen,  Vol 
I,  p.  200),  which  gives  directly  K  =  r  tan  h. 

The  apphcation  of  this  table  will  be  found  in  "  Lunar  Distances,"  Arts.  301  to  311,  Chap.  VIII,  i'art  II. 

TABLE  30. 

Logs  ofi  A,  By  C,  and  D,  fior  computing  the  First  Coirection  ofi  the  Lunar  Distance,  computed  by  the  formulas 

.  _^,,sin_(^_+J^A^  sin  (H- AH) 

^—  ^  smh  '  ^—  sin  H 

B  —  Y'  ^'"  (2  H  —  A  H)  _  sin  {2  h -\-  /\  h 

sin  2  H  '  sin  2  k        ' 

where 

h  =  moon's  apparent  altitude, 

H  =  sun's,  planet's,  or  star's  apparent  altitude  (denoted  in  the  tables  by  0  or  ^^s  App.  Alt.), 
A  /«  =  difference  of  (J  's  apparent  and  true  altitudes, 
A  H  =  difference  of  Q's  or  ^  's  apparent  and  true  altitudes, 
log  K'  =  .000126, 


*  Chauvenet's  Spherical  and  Practical  Astronomy,  Vol.  I,  p.  256. 


EXPLANATION    OF    TABLES.  195 

and  A  '''j  A  H  were  computed  from  the  arguments  "apparent  altitude"  and  "reduced  parallax  and  refraction" 
by  the  formulas 

/SA  =  {/>~  /)K'  cos/i,  AH  =  (R' -  P)cos  H, 

where 

/>  —  r'  =  ([  's  reduced  parallax  and  refraction, 
R'  —  P  =  O's  or  >fc's  reduced  parallax  and  refraction, 
/  =  (J  's  horizontal  parallax  -f-  A  t  (Table  19), 
P  =  O's  or  ^tc's  horizontal  parallax  (for  a  star  P  =  o), 
r'  =  (I  \s  reduced  refraction  (Table  29), 
R'  =  O's  or  jfc's  reduced  refraction  (Table  29). 

When  A  and  H  become  90°,  the  values  of  B  and  D  assume  the  indeterminate  forms 

o  o 

and,  therefore,  for  computing  their  logarithms  near  the  end  of  the  table,  the  formulas  were  transformed  as  follows: 

B  =  C  K'  [I  +  >^  (R'  —  P)  sin  i"  sin  H], 

A 

D  =  ^^li  —  y^  (J,  —  ,^)  K'  sin  i"  sin  /^]. 

By  means  of  logs  A,  B,  C,  and  D,  the  first  correction  of  the  distance  is  found  by  the  following  formulas: 

(^  =  apparent  distance  of  ({   from  Q  oi"  "X"; 
Ai  (^  =  first  correction, 
A'  —  A  (p  —  t')  sin  /i  cot  i/, 
B'  =  —  B  (/  -    /)  sin  H  cosec  D, 
C  =  —  C  (R'  —  P)  sin  H  cot  d, 
D'  =  D  ( R'  —  P)  sin  k  cosec  d, 
then 

A,</-(A'  +  B')  +  (C'  +  D'), 

and,  in  the  directions  for  using  the  tables,  A'  +  B'  is  called  the  "whole  correction  for  ([,"  and  C  -\-  D'  the 
"whole  correction  for  Q  or  ^." 

TABLE  31. 

Second  Correction  of  the  Lunar  Distance,  computed  by  the  formula 

A2rt'=— ^  Ai(/^  sin  i"  cots'. 
Strictly,  this  formula  should  be 

A2^/  =  —  M  A  d-^  sin  i"  cot  d, 

where  (\d^  whole  correction  of  distance  =  Ai '''+  A3'?'/  so  that  by  entering  the  table  first  with  Ai^'  we  find 
only  an  approximate  value  of  A2"'.  But  if  with  this  approximate  value  we  form  the  approximate  whole  correction 
Airf'+  A:"',  and  enter  with  this  as  the  argument  in  the  place  of  Ai''',  we  have  the  true  value  of  Aj'''-  It  is 
evident,  however,  from  the  table  itself,  that  in  most  practical  cases  this  degree  of  precision  is  unnecessary. 

TABLE  32. 

For  finding  the  Correction  of  the  Lunar  Distance  for  the  Contraction  of  the  Moon's  Semi-diafueter  (by  refrac- 
tion), computed  by  the  formula 

_  (AM-B')^ 

A  -f  -  A  Jo (^_^,)2coFQ' 

where  the  notation  already  employed  is  preserved,  and 

A.ro  =  contraction  of  the  moon's  vertical  semi-diameter  at  the  altitude  //, 
A-s'  =  contraction  of  the  inclined  semi-diameter,  or  of  that  which  hes  in  the  direction  of  the  lunar  distance. 

This  table  is  subdivided  into  Tables  32  A  and  32  B.     If  we  put 

„■  _  AJq 

^~  {p~)-'ycos'^h 
then 


X/, 


aj  =  (A'  +  b')2xC 

where  f  is  an  arbitrary  factor  employed  to  give  g  convenient  integral  values ;  and  in  these  tables  we  have  taken 
/=  18000000,  A  -fii,  A  s,  /  —  ;-',  and  A'  +  B'  being  all  expressed  in  seconds.  Table  32  A  gives  the  value  of^  with 
the  arguments  /  —  r'  and  h  ;  and  Table  32  B  gives  A  J  with  the  arguments  A'  -f-  B   and  g. 

To  find  A-f"  from  the  arguments  p—r'  and  /;,  the  mean  value  of  >■'  for  the  altitude  //  was  added  to  p  —  r',  so 
that  /  became  known ;  whence  also  the  semi-diameter  — ,  and  consequently,  by  means  of  the  refraction  tables,  the 
contraction  A-^d.  The  value  of  A->'  given  by  Table  32  B  is  therefore  that  wliich  corresponds  to  a  mean  state  of  the 
air.  and  in  extreme  cases  may  be  in  error  4"',  but  in  no  probable  case  will  it  be  in  error  more  than  l".  The  true 
value  of  A-f  might,  however,  always  be  found  by  correcting  it,  as  refraction,  by  Tables  21  and  22. 

TABLE  33. 

Forfnding  the  Correction  of  the  Lwiar  Distance  for  the  Contraction  of  the  Sun^s  Setni-diameter  (by  refraction), 
computed  by  the  formula 

^^-^^''(R'-P)2cos2H' 


196  EXPLANATION    OF    TABLES. 

where,  in  addition  to  the  notation  already  employed,  A  So  ^  contraction  of  the  sun's  vertical  semi-diameter  at  the 
altitude  H ;  A  S  =  contraction  of  the  inclined  semi-diameter.  Table  33  A,  with  the  arguments  R'  —  P  and  H, 
gives  a  number 

^       (R'— P)2cos3H       ^ 

""-  ASo X^' 

in  which  A  Sn  is  taken  for  a  mean  value  of  the  sun's  semi-diameter,  P  is  assumed  at  8". 5,  and  F  is  an  arbitrary 
factor  =^-5^;  R' — P,  C'  +  D',  ASo,  and  AS  being  all  expressed  in  seconds.  Table  33  B,  with  the  arguments 
C  +  D'  and  G,  gives 

AS  =  (C'+D')2x^.      • 

This  value  of  A  S  is  that  which  belongs  to  the  actual  state  of  the  air,  but  is  for  a  mean  value  of  the  sun's  semi- 
diameter,  the  variations  of  which  would  not  change  the  tabular  value  by  more  than  o".5  in  any  case. 

TABLE  34. 

Logarithms  of  Seconds. — This  table  contains  the  common  logarithm  answering  to  the  arc  (either  space  or  time) 
in  the  argument.  For  the  convenience  of  the  Navigator  this  table  is  given  with  the  argument,  degrees,  minutes, 
and  seconds,  or  hours,  minutes,  and  seconds,  for  every  ten  seconds,  at  the  side,  the  unit  figure  of  the  seconds 
being  found  at  the  top. 

The  logarithm  is  given  with  the  proper  characteristic  prefixed. 

TABLE  35. 

This  table  contains  the  correction  for  second  differences  of  the  moon's  motion. 

TABLE  36. 

For  finding  the  Va/tte  of  N. — By  this  table  an  approximate  value  of  N  may  be  readily  found,  with  sufficient 
accuracy  for  ordinary  purposes.  In  Table  36  the  moon's  horizontal  parallax  is  assumed  at  its  mean  value  =  57'  30", 
and  the  two  parts  of  N  are  separately  tabulated  by  the  formulas 

a  (  =      first  part  of  N)  ^  —  N'  tt  sin  (5  cotan  (/, 
^  (  =  second  part  of  N)  =:       N'  tt  sin  A  cosec  d ; 

from  which  N  is  found  by  the  formula 

N  =  (?  +  b. 

The  foregoing  Tables  30-36  were  computed  by  Professor  Chauvenet  to  facilitate  the  calculations  by  his  method 
of  Lunar  Distances.     Their  application  will  be  exemplified  in  Chap.  VIII,  Part  II,  Arts.  301  to  311,  inclusive. 

TABLE  37. 

Logarithms  of  A  and  B,  for  computing  the  Equation  of  Equal  Altitudes,  are  calculated  by  the  formulas 

A=-^^ ^-^„,  B=-  ^ 


1800  sin  ^  E  1800  tan  ^  E 

where  E  =  elapsed  time  in  minutes,  and  E  in  the  denominator  is  the  elapsed  time  expressed  in  arc. 

If  we  put 

0    =  latitude  of  the  place  of  observation,  +  north,  —  south, 
&    =  declination  of  the  sun,  -j-  north,  —  south, 

A  =  hourly  change  of  declination,  -f"  north,  —  south, 

;^^   =  correction  to  reduce  the  middle  chronometer  time  to  chronometer  time  of  apparent  nooiif 

algebraically  additive, 
V  =:  the  same  for  midnight. 


I 


we  have 


X  =  —  AAtan0  +  BA  tan  (5 
;<;'  =        A  A  tan  0  -f  ^  A  tan  (i 


This  is  Chauvenet's  table  to  aid  the  solution  of  the  problem  of  Equal  Altitudes,  see  Chap.  VI,  Part  II,  Arts,  i 
265-273. 

TABLE  38. 

Table  38  shows,  nearly,  the  error  in  Longitude  in  miles  and  tenths  of  a  mile,  occasioned  by  an  error  of  one 
mile  in  the  Latitude. 

Thus,  when  the  sun's  altitude  is  30°,  the  Latitude  30°,  and  the  Polar  distance  100',  the  error  is  8-tenths  of  a 
mile. 

The  error  affects  the  Longitude  as  follows  :  ^ 

When  in  West  Long.,  and  <  A.  M.  1    ,     ^  .     (  decreased.  >  When  the  correction  is  marked  (  increased.  ? 

the  time  is  found  in  Col.     \  P.  M.  \  °"S-  '^  ^  increased.    \       X  Uie  Long,  is  \  decreased.  \ 

When  in  East  Long.,  and  (  A.  M.  >    ,      ^  .     (  increased.   \   When  the  correction  is  marked  <  decreased.  ) 

the  time  is  found  in  Col.    \  P.  M.  \    ^     °"S-  is  ^  decreased.  \     X  the  Long,  is  \  increased.   S 


EXPLANATION  OF  TABLES.  197 

TABLE  39. 

The  table  contains  amplitudes  of  heavenly  bodies,  at  rising  and  setting,  for  various  latitudes  and  declinations, 
computed  by  the  formula 

sin  amp.  =  sec  Lat.  X  sin  dec. 

It  is  entered  with  the  declination  at  the  top  and  the  latitude  at  the  side. 
Its  use  is  explained  in  Chap.  X,  Part  II,  Art.  324. 

TABLE  40. 

This  table  gives  a  correction  to  be  applied  to  the  observed  amplitude  to  counteract  the  vertical  displacement 
due  to  refraction,  parallax,  and  dip,  when  the  body  is  observed  with  its  centre  in  the  visible  liorizon. 
Tiie  correction  is  to  be  applied  for  the  Sun,  a  Planet,  or  a  Star. 

At  Rising  in  N.  Lat.   }        ,    ^^^  correction  to  the  right, 
betting  m  S.  Lat.   S 


At 


Rising  in  S.  Lat.   ?         ,      ,     correction  to  the  left. 
Settmgm  N.  Lat.   ^    *^*^ -^ 


For  the  Moon — 

Apply  naZ/the  correction  in  the  contrary  manner. 

TABLE  41. 

Natural  Sines. — This  table  contains  the  natural  sine  and  cosine  for  every  minute  of  the  quadrant  to  the  radius 
looooo,  and  is  to  be  entered  at  the  top  or  bottom  with  the  degrees,  and  at  the  side  marked  M.,  with  the  minutes  ; 
the  corresponding  numbers  will  be  the  natural  sine  and  cosine  respectively,  observing  that  if  the  degrees  are  found 
at  the  top,  the  name  sine,  cosine,  and  M.  must  also  be  found  at  the  top,  and  the  contrary  if  the  degrees  are  found 
at  the  bottom.     Thus,  43366  is  the  natural  sine  of  25^^  42',  or  the  cosine  of  64"^  iS'. 

We  have  given  in  this  edition  of  the  present  table,  in  the  outer  columns  of  the  margin,  tables  of  proportional 
parts,  for  the  purpose  of  finding,  nearly,  by  inspection,  the  proportional  part  corresponding  to  any  number  of  sec- 
onds in  the  proposed  angle ;  the  seconds  being  found  in  the  marginal  column  marked  RL,  and  the  correction  in  the 
adjoining  column.  Thus,  if  we  suppose  that  it  were  required  to  find  the  natural  sine  corresponding  to  25^-42'  19", 
the  difference  of  the  sines  of  25-^  42'  and  25''  43'  is  26;  being  the  same  as  at  the  top  of  the  left-hand  column  of  the 
table;  and  in  this  column,  and  opposite  to  19",  in  the  column  M.,  is  the  correction  8.  Adding  \}m.%  to  the  above 
number  43366,  because  the  numbers  are  increasing^  we  get  43374  for  the  sine  0125^^42'  19".  In  like  manner,  we 
find  the  cosine  of  the  same  angle  to  be  90108  —  4  =  90104,  using  1  he  right-hand  columns,  and  subtracting  because 
the  numbers  aie  decreasing ;  observing,  however,  that  the  number  14  at  the  top  of  this  column  varies  i  from  the 
difference  between  ihe  cosines  of  25"^  42'  and  25°  43',  which  is  only  13 ;  so  that  the  table  may  give  in  some  cases 
a  unit  loo  much  between  the  angles  25-  42'  and  25^  43'  ;  but  this  is,  in  general,  of  but  little  importance,  and  when 
very  great  accuracy  is  required,  the  usual  method  of  proportional  parts  is  to  be  resorted  to,  using  the  actual  tabular 
difference. 

TABLE  42. 

Table  42,  containing  the  common  logarithms  of  numbers,  was  compared  with  Sherwin's,  Hutton's,  and  Tay- 
lor's logarithms. 

TABLE  43. 

Table  43  contains  the  log  sines,  log  tangents,  &c.,  corresponding  to  points  and  quarter  points  of  the  com- 
pass.    This  was  compared  with  Sherwin's,  Hutton's,  and  Taylor's  logarithms. 

TABLE  44. 

Tal:)le  44  contains  the  common  log  sines,  tangents,  secants,  &c.  This  was  compared  with  Sherwin's,  Hutton's, 
an<l  Taylor's  tables.  Two  additional  cf)lumns  are  given  in  this  table,  which  are  very  convenient  in  finding  the 
time  from  an  altitude  of  the  sun  ;  also,  three  columns  of  proportional  parts  for  seconds  of  space,  and  a  small  table 
at  the  bottom  of  each  page  for  finding  the  proportional  parts  for  seconds  of  time.  The  degrees  are  marked  to  180^, 
which  saves  the  trouble  of  subtracting  the  given  angle  from  180°  when  it  exceeds  90'-'. 

The  foregoing  logarithmic  tables  are  fully  explained  in  the  Appendix  in  an  article  on  Logarithms. 

TABLE  45. 

Table  45  contains  the  proportional  logarithms  for  three  hours.  The  numbers  of  this  table  may  be  found  by 
subtracting  the  logarithm  of  tlie  time  in  seconds  from  the  log  of  10800",  or,  which  is  the  same  thing,  by  the  follow- 
ing rule : 

Prop,  log  T  =  4.0334738  —  log  of  T  in  seconds. 

Proportional  Logarithms. — These  logarithms  are  very  useful  in  finding  the  mean  time  at  Greenwich  corre- 
sponding to  the  true  distance  of  the  moon  from  the  sun  or  star,  as  is  explained  in  the  examples  of  working  a  lunar 
observation.  They  may  be  also  used,  like  common  logarithms,  in  working  any  proportion  where  the  terms  are 
given  in  degrees,  minutes,  and  seconds,  or  in  hours,  minutes,  and  seconds,  as  in  the  example  of  taking  a  lunar 
observation  by  one  observer.  The  table  is  extended  only  to  3^  or  3'';  and  if  any  of  the  terms  of  a  given  propor- 
tion exceed  3^  or  3'',  you  may  take  all  the  terms  one  grade  lower;  that  is,  reckon  degrees  as  minutes,  minutes  as 
seconds,  &c.,  and  work  the  proportion  as  before,  observing  to  write  down  the  answer  one  grade  higher;  that  is, 
you  must  estimate  minutes  as  degrees,  seconds  as  minutes,  &c.  Instead  of  taking  all  the  terms  one  grade  lower, 
you  may  change  two  of  the  terms  only,  viz,  one  of  the  middle  terms  and  one  of  the  extreme  terms;  thus,  the  ist 


198 


EXPLANATION    OF    TABLES. 


and  3d  or  the  1st  and  2d  may  be  taken  one  grade  less,  and  the  fourth  term  will  be  given  correctly;  but  if  the  fourth 
term  be  taken  one  grade  less,  you  must,  after  working  the  proportion,  write  it  one  grade  higher,  as  is  evident.  To 
illustrate  this,  we  shall  give  the  following  examples : 


Example  i. 

If  in  15™  10^  of  time  the  sun  rises  2°  40',  how  much 
will  it  rise  in  3™  lo'  at  the  same  rate? 

As  15™  los  Arith.  Comp.,  Prop.  Log  8.9256 


Is  to  2°  40', 
So  is  3™  io% 


Prop.  Log    .0512 
Prop.  Log  1.7547 


To  33'  24", 


Prop.  Log    .7315 


Example  2. 

If  the  sun's  declination  changes  16'  19"  in  24  hours, 
how  much  will  it  change  in  8'*  2"'  ? 

Here  the  ist  and  3d  terms  must  be  taken  one  grade  less. 

As  24'"  o^,             Arith.  Comp.,  Prop.  Log  9.1249 

Is  to  16'  19",  Prop.  Log  1.0426 

So  is  8'"  2%  Prop.  Log  1.3504 


To  5'  28", 


Prop.  Log  1. 5 1 79 


Example  3. 

If  in  12''  the  moon's  longitude  varies  7°  l',  what  will 
it  vary  in  4'^  20'"  ? 

Here  all  the  terms  must  be  taken  one  grade  less. 

As  12™  0%  Arith.  Comp.,  Prop.  Log  8.8239 

Is  to  7'  i",  Prop.  Log  1. 4091  !  Is  to  3'  27", 

So  is  4'"  20%  Prop.  Log  1.6 185  |  So  is  3'"  lo^, 


Example  4. 

If  in  16'"  the  sun  rises  3°  27',  how  much  will  it  rise 
in  3'"  10*^? 

Here  the  2d  and  4th  terms  must  be  taken  one  grade  less. 

As  16'"  o%  Arith.  Comp.,  Prop.  Log  8.9488 

Prop.  Log  1. 71 75 
Prop.  Log  1.7547 


To  2'  32"  2' 


Prop.  Log  1. 85 1 5 


Which,  taken  one  grade  higher,  is  2°  32'  2",  the  an- 
swer required. 


To  o'  41",  Prop.  Log  2.4210 

Which,  taken  one  grade  higher,  is  41',   the  answer 
required. 


TABLES  46,  47.  I 

These  tables  contain  the  times  of  high  water  on  the  full  and  change  of  the  moon,  with  the  vertical  rise  of  the 
tide,  at  many  ports,  harbors,  &c.,  in  the  world. 

TABLE  48.  | 

This  table  gives  the  mean  places  of  the  principal  Fixed  Stars  for  1880,  with  their  annual  variations  in  right 
ascension  and  declination.  1 

TABLE  49.  | 

geographical  positions. 

This  table  gives  the  latitude  and  longitude,  according  to  the  most  recent  authorities,  of  many  places  likely  to  ; 
be  of  use  to  the  Navigator. 

TABLE  50. 

The  Magnetic  Variation  of  the  Compass  in  latitudes  from  70°  N.  to  60'^  S. 


TABLE  I. 

Page  199 

Difference  of  Latitude  and 

Departure  for  ^  Point 

% 

N.X 

E. 

N.  X  W. 

S.  XE. 

s.x^ 

W. 

Dist. 

I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I.O 

0.0 

61 

60.9 

3-0 

121 

120.9 

5-9 

181 

180.8 

!-9 

241 

240.7 

II. 8 

2 

2.0 

0.  I 

62 

61 

•9 

3 

0 

22 

121. 9 

6.0 

82 

181. 8 

8.9 

42 

241.7 

II. 9 

.3 

3-0 

0.  I 

63 

62 

9 

3 

I 

23 

122.9 

6.0 

^^ 

182.8 

9-0 

43 

242.7 

II. 9 

4 

4.0 

0.  2 

64 

b3 

9 

1 

,1 

I 

24 

123.9 

6.1 

84 

183.8 

9.0 

44 

243.7 

12.0 

5 

5-0 

0.  2 

b5 

64 

9 

0 

.■> 

2 

25 

124.8 

6.1 

85 

184.8 

9-  I 

45 

244.7 

12.  0 

6 

6.0 

0.3 

66 

65 

9 

3 

2 

26 

125.8 

6.2 

86  !     185.8 

9-1 

46 

245.7 

12.  I 

7 

7.0 

0.3 

67 

66 

9 

3 

3 

27 

126.8 

6.2 

87  ,     186.8 

9-2 

47 

246.7 

12.  I 

8 

8.0 

0.4 

68 

67 

9 

3 

3 

28 

127.8 

6.3 

88  !     187.8 

9-2 

48 

247.7 

12.  2 

9 

9.0 

0.4 

69 

68 

9 

-^ 

J 

4 

29 

128.8 

(>-3 

89  i     1S8.8 

9-3 

49 

248.7 

12.2 

lO 

10. 0 

0.5 

70 

69 

9 

3 

4 

30 

129.8 

6.4 

90       189. 8 

9-3 

50 

249.7 

12.3 

II 

II. 0 

0-5 

71 

70 

9 

3 

5 

131 

130.8 

6.4 

191 

190.8 

9-4 

251 

250.7 

12.3 

12 

12.0 

0.6 

72 

71 

9 

3 

5 

32 

131-8 

b.5 

92 

191.  8 

9-4 

52 

251-7 

12.4 

13 

13.0 

0.6 

73 

72 

9 

3 

6 

33 

132.8 

6.5 

93 

192.8 

9-5 

53 

252.7 

12.4 

14 

14.0 

0.7 

74 

73 

9 

3 

6 

34 

133-8 

6.6 

94 

193-8 

9-5 

54 

253-7 

12.5 

15 

15.0 

0.7 

75 

74 

9 

3 

7 

35 

134.8 

6.6 

95 

194.8 

9.6 

55 

254-7 

12.5 

I6 

16.0 

0.8 

76 

75 

9 

3 

7 

36 

135-8 

6.7 

96       195. 8 

9.6 

56 

255-7 

12.6 

17 

17.0 

0.8 

77 

76 

9 

3 

8 

37 

136.8 

b-7 

97  1     196.8 

9.7 

57 

256.7 

12.6 

i8 

18.0 

0.9 

78 

77 

9 

8 

38 

137-8 

6.8 

98 

197.8 

9-7 

58 

257-7 

12.7 

19 

19.0 

0.9 

79 

78 

9 

3 

9 

39 

138.8 

6.8 

99 

198.8 

9-^ 

59 

258.7 

12.7 

20 

20.0 

1.0 

80 

79 
"80 

9 

3 

9 

40 

139-8 

6.9 

200 

199.8 

9.8 

60 

259.7 

12.8 

21 

21.0 

1.0 

81 

9 

4 

0 

141 

140.8 

6.9 

201     :       200.  8 

9.9 

261 

260.  7 

12.8 

22 

22.0 

1. 1 

82 

81 

9 

4 

0 

42 

141.  8 

7.0 

02    1       201.8 

9-9 

62 

261.  7 

12.9 

2;> 

23.0 

1. 1 

83 

82 

9 

4 

I 

43 

142.8 

7.0 

03       202. 8 

10.  0 

63 

262.  7 

12.9 

24 

24.  0 

I.  2 

84 

83 

9 

4 

I 

44 

143.8 

7-1 

04       203. 8 

10.  0 

64 

263.7 

13.0 

2S 

25.0 

I.  2 

85 

84 

9 

4 

2 

45 

144.8 

7-1 

05  j     204. 8 

10.  I 

65 

264.7 

13.0 

26 

26.0 

1-3 

86 

85 

9 

4 

2 

46 

145.8 

7-2 

06       205. 8 

10.  I 

66 

265.7 

13-1 

27 

27.0 

1-3 

«7 

86 

9 

4 

1 

47 

146.8 

7-2 

07  '     206. 8 

10.  2 

67 

266.7 

13- I 

28 

28.0 

1.4 

88 

87 

9 

4 

3 

48 

147.8 

7-3 

08 

207.7 

10.  2 

68 

267.7 

13.2 

29 

29.0 

1.4 

89 

88 

9 

4 

4 

49 

148.8 

7-3 

09 

208.7 

10.3 

69 

268.7 

13.2 

30 
31 

30.0 

1-5 

90 

89 

9 

4 

4 

50 

149-8 

7-4 

10 

209.7 

10.3 

70 

269.7 

13.2 

31.0 

1-5 

91 

90 

9 

4 

5 

151 

150.8 

7-4 

211       210. 7 

10.4 

271 

270.7 

13.3 

32 

32.0 

1.6 

92 

91 

9 

4 

5 

52 

151. 8 

7-5 

12  :     211. 7 

10.4 

72 

271.7 

13-3 

33 

33- 0 

1.6 

93 

92 

9 

4 

6 

53 

152.8 

7-5 

13    •       212.7 

10.5 

73 

272.7 

13-4 

34 

34-0 

1-7 

94 

93 

9 

4 

6 

54 

153-8 

7.6 

14       213.7 

10.5 

74 

273.7 

13.4 

35 

35-0 

1-7 

95 

94 

9 

4 

7 

55 

154.8 

7-6 

15       214.7 

10.5 

75 

274.7 

13-5 

36 

36.0 

1.8 

96 

95 

9 

4 

7 

S(^ 

155-8 

7-7 

16  :     215.  7 

10.6 

76 

275.7 

13-5 

37 

37- 0 

1.8 

97 

96 

9 

4 

8 

57 

156.  8 

7-7 

17  :     216. 7 

10.6 

77 

276.7 

13-6 

3« 

38.0 

1.9 

98 

97 

9 

4 

8 

58 

157.8 

7-8 

18  i     217.7 

10.7 

78 

277.7 

13-6 

39 

39- 0 

1.9 

99 

98 

9 

4- 

9 

59 

158.8 

7-8 

19  1     218.  7 

10.7 

79 

278.7 

13-7 

40 
41 

40.0 
41.0 

2.0 

100 

99- 

9 

4 

9 

60 

159-8 

7-9 

20       219.  7 

10.8 

80 

279.7 

13.7 

2.  0 

lOI 

100 

9 

5- 

0 

161 

160.8 

7-9 

221       220.  7 

10.8 

281 

280.7 

13.8 

42 

41.9 

2.  I 

02 

lOl 

9 

5- 

0 

62 

161. 8 

7-9 

22       221.  7 

10.9 

82 

281.  7 

1.3.8 

43 

42.9 

2.  I 

03 

102 

9 

5- 

I 

63 

162.8 

8.0 

23       222.  7 

10.9 

83 

282.7 

13-9 

44 

43-9 

2.  2 

04 

103 

9 

5- 

I 

64 

163.8 

8.0 

24  ,     223.  7 

II. 0 

84 

283-7 

13-9 

45 

44.9 

2.  2 

OS 

104 

9 

5 

2 

&5 

164.8 

8.1 

25  i     224.  7 

II. 0 

85 

284-7 

14.0 

46 

45-9 

2.3 

06 

105 

9 

5 

2 

66 

165.8 

8.1 

26  :     225.  7 

II.  I 

86 

285.7 

14.0 

47 

46.9 

2.3 

07 

106 

9 

5 

3 

67 

166.8 

8.2 

27       226.  7 

n.  I 

87 

2S6.  7 

14.  I 

48 

47-9 

2.4 

08 

107 

9 

S 

■> 

68 

167.8 

8.2 

28  1     227.  7 

II.  2 

88 

287.7 

14.  I 

49 

48.9 

2.4 

09 

108 

9 

5 

3 

69 

168.8 

8-3 

29       228. 7 

II.  2 

89 

288.7 

14.2 

50 

49-9 

2-5 

10 

109 

9 

5 

4 

70 

169.8 

8-3 

30 

229.7 

"•3 

90 

289.7 

14.2 

51 

50-9 

2.5 

III 

no 

9 

5 

4 

171 

170.8 

8.4 

231 

230.7 

11-3 

291 

290.6 

14.3 

52 

51-9 

2.6 

12 

III 

9 

5 

5 

72 

171. 8 

8.4 

32  !    231. 7 

II. 4 

92 

291.  6 

14.3 

S3 

52.9 

2.6 

13 

112 

9 

5 

5 

73 

172.8 

8-5 

33  1    232. 7 

II. 4 

93 

292.  6 

14.4 

54 

53-9 

2.6 

14 

113 

9 

5 

6 

74 

173-8 

8-5 

34  ,     233.  7 

"-5 

94 

293.6 

14.4 

55 

54-9 

2.7 

15 

114 

9 

5 

6 

75 

174-8 

8.6 

35  ;     234.  7 

"-5 

95 

294.6 

14.5 

S^ 

55-9 

2.7 

16 

"5 

9 

5 

7 

76 

175-8 

8.6 

36       235. 7 

II. 6 

96 

295.6 

14.5 

57 

56.9 

2.8 

17 

116 

9 

5 

7 

77 

176.8 

8-7 

37  i     236. 7 

II. 6 

97 

296.  6 

14.6 

5« 

57.9 

2.8 

18 

117 

9 

5 

8 

78 

177-8 

8.7 

38  1     237.  7 

II. 7 

98 

297.6 

14.6 

59 

58.9 

2.9 

19 

118 

9 

5 

8 

79 

178.8 

8.8 

39       238.  7 

II. 7 

99 

298.6 

14-7 

60 

59-9 

2.9 

20 

119.9 

5-9 

80 

179.8 

8.8 

40 

239.7 

II. 8 

300 

299.6 

14.7  , 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  X 

N. 

E.  X 

S. 

w.x^ 

L                   W  X  S. 

[Fc 

)r  7^  Poi 

nts. 

Pag 

6  200 

TABLE  I. 

Difference  of  Latitude  and  Departure  for 

)4  Point 

N.  >^ 

E. 

N.  , 

^  w. 

s 

.>^E 

• 

s 

.  ^w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.o 

0.  I 

61 

60.  7 

6.0 

121 

120.4 

II. 9 

181 

180.  I 

17-7 

241 

239.8 

23.6 

2 

2.0 

0.2 

62 

61.7 

6.1 

22 

121. 4 

12.0 

82 

181.  I 

17.8 

42 

240.  8 

23-7 

3 

3-0 

0-3 

63 

62.  7 

6.2 

23 

122.4 

12.  I 

83 

182.  I 

17.9 

43 

241.8 

23-8 

4 

4.0 

0.4 

64 

63.7 

6.3 

24 

123.4    1    12.2 

84 

183.  I 

18.0 

44 

242.  8 

23-9 

5 

5.0 

0.5 

65 

64.7 

6.4 

25 

124.4  ,  12.3 

85 

184.  I 

18.  I 

45 

243-8 

24.  0 

6 

6.0 

0.6 

66 

65.7 

6-5 

26 

125.4    12.4 

86 

185.  I 

18.2 

46 

244.8 

24.1 

7 

7.0 

0.7 

67 

66.7 

6.6 

27 

126.4  !   12.4 

87 

186.  I 

18.3 

47 

245-8 

24.  2 

8 

8.0 

0.8 

68 

67.7 

6.7 

28 

127.4 

12.5 

88 

187.  I 

18.4 

48 

246.8 

24-3 

9 

9.0 

0.9 

69 

68.7 

6.8 

29 

128.4 

12.6 

89 

188.  I 

18.5 

49 

247.8 

24-4 

lO 

10.  0 

1.0 

70 

69.7 

6-9 

30 

129.4 

12.7 

90 

189.  I 

18.6 

50 

248.8 

24-5 

II 

10.  9 

I.  I 

71 

70.7 

7-0 

131 

130.4 

12.8 

191 

190.  I 

18.7 

251 

"  249.8 

24.  6 

12 

II. 9 

1.2 

72 

71.7 

7-1 

32 

131-4 

12.9 

92 

191.  I 

18.8 

52 

250.8 

24.7 

13 

12.9 

1-3 

73 

72.6 

7-2 

33 

132-4 

13.0 

93 

192.  I 

18.9 

53 

251.8 

24.8 

14 

13-9 

1.4 

74 

73-6 

7-3 

34 

133-4 

13- 1 

94 

193-1 

19.0 

54 

252.8 

24.9 

15 

14.9 

1-5 

75 

74.6 

7-4 

35 

134-3 

13.2 

95 

194.  I 

19.  I 

55 

253-8 

25.0 

i6 

15-9 

1.6 

76 

75-6 

7-4 

36 

135-3 

13-3 

96 

195.  I 

19.2 

56 

254.8 

25-1 

17 

16.  9 

1-7 

77 

76.6 

7-5 

37 

136-3  I   13-4 

97 

196.  I 

19-3 

57 

255-8 

25.2 

i8 

17.9 

1.8 

78 

77.6 

7.6 

38 

137-3  :  13-5 

98 

197-0 

19.4 

58 

256.8 

25-3 

19 

18.9 

1.9 

79 

78.6 

^■l 

39 

138-3 

13-6 

99 

198.  0 

19.5 

59 

257-8 

25-4 

20 

19.9 

2.0 

80 

79.6 

7.8 

40 

139-3 

13-7 

200 

199.0 

19.6 

60 

258.7 

25-_5 

2! 

20.9 

2. 1 

8r 

80.6 

7-9 

141 

140.3 

13-8 

201 

200.  0 

19.7 

261 

259.7 

25.6 

22 

21.9 

2.  2 

82 

81.6 

8.0 

42 

141- 3 

13-9 

02 

201.  0 

19.8 

62 

260.  7 

25.7 

23 

22.9 

2-3 

l^ 

82.6 

8.1 

43 

142.3 

14.  0 

03 

202.0 

19.9 

63 

261.  7 

25.8 

24 

23-9 

2.4 

84 

83.6 

8.2 

44 

H3-3 

14.  I 

04 

203.0 

20.0 

64 

262.  7 

25-9 

25 

24.9 

2-5 

85 

84.6 

!-3 

45 

144-3 

14.2 

05 

204.0 

20.  I 

65 

263.7 

26.0 

26 

25-9 

2.5 

86 

85.6 

8.4 

46 

145-3 

14-3 

06 

205.0 

20.2 

66 

264.7 

26.1 

27 

26.9 

2.6 

87 

86.6 

8-5 

47 

146.3 

14.4 

07 

206.0 

20.3 

67 

265.7 

26.2 

28 

27.9 

2.7 

88 

87.6 

8.6 

48 

147-3 

14-5 

08 

207.0 

20.4 

68 

266.7 

26.3 

29 

28.9 

2.8 

89 

88.6 

f-7 

49 

148.3 

14.  6 

09 

208.0 

20.  5 

69 

267.7 

26.4 

30 

29.9 

2.9 

90 

89.6 

8.8 

50 

149-3 

14.7 

10 

209.0 

20.6 

70 

268.7 

26.5 
26.6^ 

31 

30-9 

3-0 

91 

90.  6 

8.9 

151 

150.3 

14.8 

211 

210.0 

20.  7 

271 

269.7 

32 

31.8 

3-1 

92 

91.  6 

9.0 

52 

151-3 

14- P 

12 

211. 0 

20.8 

72 

270.7 

26.7 

33 

32.8 

3-2 

93. 

92.6 

9.1 

53 

152-3 

15.0 

13 

212.0 

20.9 

73 

271.7 

26,8 

34 

33-8 

3-3 

94 

93-5 

9.2 

54 

153-3 

•5-1 

14 

213.0 

21.0 

74 

272.7 

26.9 

35 

34-8 

3-4 

95 

94-5 

9-3 

55 

154-3 

15-2 

15 

214.0 

21.  I 

75 

273.7 

27.0 

36 

35-8 

3-5 

96 

95-5 

9-4 

56 

155-2 

15-3 

16 

215.0 

21.2 

76 

274.7 

27.1 

H 

36.8 

3-6 

97 

96.5 

9-5 

57 

156.2  j   15.4 

17 

216.  0 

21.3 

77 

275-7 

27.  2 

38 

37-8 

3-7 

98 

97-5 

9.6 

58 

157-2  1  15.5 

18 

217.0 

21.4 

78 

276.7 

27.  2 

39 

38.8 

3.8 

99 

98.5 

9-7 

59 

158.  21  15.  6 

19 

217.9 

21.5 

79 

277.7 

27-3 

40 

39-8 

3-9 

100 

99-5 

9-8 

60 

159.2      15.7 

20 

218.9 

21.6 

80 

278.7 

27.4 

41 

40.8 

4.0 

lOI 

100.5 

9-9 

161 

160.  2 

15.8 

221 

219.9 

21.7 

281 

279.6 

27-5 

42 

41.8 

4.1 

02 

101.5 

10.  0 

62 

161.  2 

15-9 

22 

220.  9 

21.8 

82 

280.6 

27.  6 

43 

42.8 

4.2 

03 

102.  5 

10.  I 

63 

162.  2 

16.  0 

23 

221.  9 

21.9 

83 

281.6 

27.7 

44 

43-8 

4-3 

04 

103-5 

10.2 

64 

163.2 

16. 1 

24 

222.9 

22.0 

84 

282.6 

27.8 

45 

44.8 

4.4 

05 

104.5 

10.3 

65 

164.  2 

16.2 

25 

223.9 

22.  I 

85 

283.6 

27-9 

46 

45-8 

4-5 

06 

105-5 

JO.  4 

66 

165.2 

16.3 

26 

224.9 

22.  2 

86 

284.6 

28.0 

47 

46.8 

4.6 

07 

106.  5 

10.  s 

67 

166.2 

16.4 

27 

225.9 

22.  2 

87 

285.6 

28.1 

48 

47.8 

4-7 

08 

107.5 

10.6 

68 

167.  2 

"16.5 

28 

226.9 

22.3 

88 

286.6 

28.2 

49 

48.8 

4.8 

09 

108.5 

10.  7 

69 

168.2 

16.6 

29 

227.9 

22.4 

89 

287.6 

28.3 

50 

49.8 

4-9 

10 

io9:_5_ 

10.8 

70 

169.  2 

16.7 

30 

228.9 

22.  5 

90 

288.6 

28.4 

51 

50.8 

5-0 

III 

no.  5 

10.9 

171 

170.  2 

16.8 

231 

229.9 

22.6 

291 

289.6 

28.5 

52 

51-7 

5-1 

12 

III. 5 

II. 0 

72 

171. 2 

16.9 

32 

230.9 

22.  7 

92 

290.6 

28.6 

53 

52.7 

5-2 

13 

112.  5 

II.  I 

73 

172.2 

17.0 

33 

231.9 

22.8 

93 

291.6 

28.7 

54 

53-7 

5-3 

14 

113- 5 

II. 2 

74 

173-2 

17. 1 

34 

232.9 

22.  9 

94 

292.6 

28.8 

55 

54-7 

5-4 

15 

1 14. 4 

".3 

75 

174.2 

17-2 

35 

233-9 

23.0 

95 

293.6 

28.9 

56 

55-7 

5-5 

16 

"5-4 

II. 4 

76 

175-2 

17-3 

36 

234-9 

23.1 

96 

294.6 

29.0 

57 

56.7 

5-6 

17 

116. 4 

11-5 

77 

176.  I 

17-3 

37 

235-9 

23.2 

97 

295.6 

29.1 

58 

57.7 

5-7 

18 

"7-4 

II. 6 

78 

177- I 

17.4 

38 

236.9 

23-3 

98 

296.  6 

29.2 

59 

58.7 

5.8 

19 

1 18.  4 

II. 7 

79 

178.  I 

17-5 

39 

"37-8 

23-4 

99 

297.6 

29.3 

60 

59-7 

5-9 

20 

1 19. 4 

II. 8 

80 

179.  I 

17.6 

40 

238.8 

23.5 

300 

298.6 

29.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.>^N. 

I 

i.y^s. 

'W 

^>^N. 

W. 

KS. 

[For 

7}i  Poin 

ts. 

TABLE  I. 

Page  201 

Difference  of  Latitude  and  Departure  for 

^  Point. 

^^N.^E 

N.^  W. 

S.^E. 

d.XW. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep.    1 

I 

I.o 

0.  I 

6l 

60.3 

9.0 

121 

119.7 

17.8 

181 

179.0 

26.6 

241 

238.4     35-4 

2 

2.0 

0-3 

62 

61.3 

9.  I 

22 

1 20.  7 

.17.9 

82 

180.0 

26.7 

42 

239. 4  ,  35-  5 

3 

3-0 

0.4 

63 

62.3 

9.2 

23 

121.  7 

18.0 

!3 

181. 0 

26.9 

43 

240. 4     35.  7 

4 

4.0 

0.6 

64 

63-3 

9-4 

24 

122.  7 

18.2 

84 

182.0 

27.0 

44 

241.4     35.8 

5 

4-9 

0.7 

65 

64.3 

9-5 

25 

123.6 

18.3 

85 

183.0 

27.1 

45 

242.3     35-9 

6 

5-9 

0.9 

66 

65.3 

9-7 

26 

124.6 

18.5 

86 

184.0 

27.3 

46 

243. 3     36.  I 

7 

6.9 

1.0 

67 

66.3 

9.8 

27 

125.6 

18.6 

87 

185.0 

27.4 

47 

244. 3     36.  2 

8 

7-9 

I.  2 

68 

67-3 

10.  0 

28 

126.6 

18.8 

88 

186.0 

27.6 

48 

245.  3      36.  4 

9 

8.9 

1-3 

69 

68.3 

10.  I 

29 

'^Z-^ 

18.9 

89 

187.0 

27.7 

49 

246.3     36.5 

lO 

.    9-9 

1-5 

1.6 

70 

69.2 

10.3 

30 

128.6 

'9.  I„ 

90 

187.9 

27.9 

50 

247. 3     36.  7 

^  iT 

10.  9 

71 

70.2 

10.4 

131 

129.6 

19.  2 

191 

188.9 

28.0 

251 

248.  3      36.  8 

12 

II. 9 

i.S 

72 

71.2 

10.6 

32 

130.6 

19.4 

92 

189.9 

28.2 

52 

249.3     37.0 

13 

12.9 

1-9 

73 

72.2 

10.  7 

33 

131. 6 

19.5 

93 

190.9 

28.3 

53 

250. 3  1  37-  I 

14 

13.8 

2.  I 

74 

73-2 

10.9 

34 

132.5 

19.7 

94 

191.  9 

"^5 

54 

251.3  !  37.3 

15 

14.8 

2.  2 

75 

74.2 

II.  0 

35 

133.5 

19.8 

95 

192.9 

28.6 

55 

252.2  ,  37.4 

i6 

'5.8 

2.3 

76 

75-2 

II.  2 

36 

134. 5 

20.  0 

96 

193.9 

28.8 

56 

253.2  1  37.6 

17 

lb.  8 

2-5 

77 

76.2 

II-3 

37 

135.5 

20.  I 

97 

194.9 

28.9 

57 

254.  2     37.  7 

i8 

17.8 

2.6 

78 

77.2 

II. 4 

38 

136.5 

20.  2 

98 

195.9 

29.1 

58 

255.2     37-9 

19 

18.8 

2.8 

79 

78.1 

II. 6 

39 

137.5 

20.4 

99 

196.8 

29.  2 

59 

256.  2     38.  0 

20 

19.8 

2.9 

80 

79.1 

II. 7 

40 

138.5 

20.5 

200 

197.8 

29.3 

60 

257.2     38.1 

21 

20.8 

3-1 

81 

80.1 

II. 9 

141 

139.5 

20.  7 

201 

198.8 

29.5 

261 

258.2  ;  38.3 

22 

21.8 

3-2 

82 

81. 1 

12.0 

42 

140.5 

20.8 

02 

199.8 

29.  6 

62 

259.2    38.4 

23 

22.8 

3-4 

83 

82.1 

12.2 

43 

141.  5 

21.  0 

03 

200.  8 

29.8 

63 

260.  2    ;    38.  6 

24 

23-7 

3-5 

84 

83.1 

12.3 

44 

142.4 

21.  I 

04 

201.8 

29.9 

64 

261.  I    j    38.  7 

25 

24.7 

3-7 

85 

84. 1 

12.5 

45 

143.4 

21.3 

05 

202.8 

30.1 

65 

262.  I   !  38.  9 

26  , 

25-7 

3-8 

86 

fl-' 

12.6 

46 

144.4 

21.4 

06 

203.8 

30.2 

66 

263. 1  :  39. 0 

27 

26.  7 

4.0 

87 

86.  I 

12.8 

47 

145  4 

21.6 

07 

204.  8 

30.4 

67 

264. 1  1 39. 2 

28 

27.7 

4.1 

88 

87.0 

12.9 

48 

146.4 

21.7 

08 

205.7 

30.5 

68 

265. 1  :  39-  3 

29 

28.7 

4-3 

89 

88.0 

13- I 

49 

147.4 

21.9 

09 

206.  7 

30.7 

69 

266. 1   39. 5 

30 

29.7 

4.4 

90 

89.0 

13.2 

50 

148.4 

22.0 

10 

207.7 

30.8 

70 

267.- 1 

39.6 

31 

30-7 

4-5 

91 

90.0 

13-4 

151 

149.4 

22.  2 

211 

208.7 

31.0 

271 

"268.1 

39.8 

32 

31.7 

4-7 

92 

91.0 

13-5 

52 

150.4 

22.3 

12 

209.7 

31.  I 

72 

269. 1   39. 9 

33 

32.6 

4.8 

93 

92.  0 

13.6 

53 

151. 3 

22.4 

13 

210.  7 

31.3 

73 

270.0 1 40. 1 

34 

33-6 

5-0 

94 

93- 0 

13.8 

54 

152.3 

22.  6 

14 

211.  7 

31.4 

74 

271. 0  40. 2 

35 

34-6 

5-1 

95 

94.0 

13-9 

55 

153.3 

22.7 

15 

212.  7 

31.5 

75 

272. 0  40. 4 

36 

35-6 

5-3 

96 

95- 0 

14. 1 

56 

154.3  i  22.9 

16 

213.7 

31-7 

76 

273.0  40.5 

i7 

36.6 

5-4 

97 

96.0 

14.2 

57 

155.3  i  23.0 

17 

214.7 

31.  8 

77 

274.0  40.6 

38 

37- f 

5-6 

98 

96.9 

14.4 

58 

156.3     23.2 

18 

215.6 

32.0 

78 

275.0  40.8 

39 

38.6 

5-7 

99 

97-9 

14-5 

59 

157.3 

23.3 

19 

216.6 

32.1 

79 

276.0  40.9 

40 

39-6 

5-9 

100 

98.9 

14.7 

60 

158.3 

23.5 

20 

217.6 

32.3 

80 

277.0  i  41. 1 

41 

40.6 

6.0 

1 01^ 

99-9 

14.8" 

T6T 

159.3 

23.6 

221 

'218.6 

32.4 

281 

278.0 ,  41.2 

42 

41.5 

6.2 

02 

100.  9 

15.0 

62 

160.  2     23.  8 

22 

219.  6 

32.6 

82 

278.9  41.4 

43 

42.5 

6.3 

03 

loi.  9 

15. 1 

P 

161.  2     23.  9 

23 

220.6 

32.7 

P 

279.9  41.5 

44 

43-5 

6.5 

04 

102.9 

15-3 

64 

162.  2 

24.1 

24 

221.6 

32.9 

84 

280.9  41. 7 

45 

44-5 

6.6 

05 

103.9 

15-4 

65 

163.  2 

24.  2 

25 

222.6 

33.0 

85 

281.9 

41.8 

46 

45-5 

6.7 

06 

104.9 

15-6 

66 

164.  2 

24.4 

26 

223.6 

33.2 

86 

282. 9 

42.0 

47 

46.5 

6.9 

07 

105.8 

15-7 

67 

165.2 

24-5 

27 

224.5 

33.3 

87 

283.9 

42.1 

48 

47-5 

7.0 

08 

106.8 

15-8 

68 

166.  2 

24.7 

28 

225.5 

33-5 

88 

284.9 

42.3 

49 

48.5 

7-2 

09 

107.8 

16.0 

69 

167.  2 

24.8 

29 

226.  5 

33.6 

89 

285.9 1 42.4  1 

50 

49-5 

7-3 

10 

108.8 

16  I 

70 

168.2 
169.  I 

24.9 

30 

227.5 

33.7 

90 

286.9  42.6  1 

51 

50-4 

7-5 

III 

109.  8 

16.3 

171 

25.1 

231 

228.5 

33-  9 

291 

287.9 

"^'•l 

52 

51-4 

7-^ 

12 

1 10.  8 

16.4 

72 

170.  I 

25.2 

32 

229.5 

34.0 

92 

288.8 

42.8 

53 

52.4 

7.8 

13 

III. 8 

16.6 

73 

171.  I 

25.4 

33 

230.5 

34.2 

93 

289.8  43.0 

54 

53-4 

7-9 

14 

112.8 

16.7 

74 

172.  I 

25.5 

34 

231.5 

34-3 

94 

290.  8     43. 1 

55 

54-4 

8.1 

15 

113.  8 

16.9 

75 

173.  I 

25.7 

35 

232.5 

34.5 

95 

291.8     43.3 

5& 

55.4 

8.2 

16 

114-7 

17.0 

76 

174.  I 

25.8 

36 

233.4 

34-6 

96 

292.8  1  43.4 

H 

56.4 

•    ^-4 

17 

115- 7 

17.2 

77 

175.  I 

26.0 

37 

234.4 

34.8 

97 

293.8     43.6 

58 

57-4 

f-5 

18 

116.  7 

17.3 

78 

176.  I 

26.1 

38 

235.4 

34.9 

98 

294.  8  i  43.  7 

p 

58.4 

^■l 

19 

117.  7 

17-5 

79 

177.  I 

26.3 

39 

236.4 

35.1 

99 

295.8  i  43.9 

60 

59-4 

8.8 

20 

118.  7 

17.6 

80 

178.1 

26.4 

40 

237.4 

35.2 

300 

296.8 

44.0 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

] 

E.|<N. 

E.^S. 

1 

W.^N. 

1 

^.  34  S.                    [Fo 

r  7X  Points.         1 

Page  202 

TABLE  I. 

Difference  of  Latitude  and 

Departure  foi 

•  I  Point. 

N.  by  E. 

N.l 

Dy  W. 

S.by 

E. 

S.byW.                        1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.2 

61 

59.8 

II. 9 

121 

118.  7 

23.6 

181 

177-5 

35-3 

241 

236.4 

47.0 

2 

2.0 

0.4 

62 

60.8 

12.  I 

22 

119-7 

23.8 

82 

178.5 

35-5 

42 

237-4 

47.2       1 

3 

2.9 

0.6 

63 

61.8 

12.3 

23 

120.  6 

24.0 

83 

179.5 

35-7 

43 

238.3 

47.4 

4 

3-9 

0.8 

64 

62.8 

12.5 

24 

121.  6 

24.2 

84 

180.5 

35-9 

44 

239.3 

47.6 

5 

4.9 

1.0 

65 

63.8 

12.7 

25 

122.  6 

24.4 

85 

181. 4 

36.1 

45 

240.3 

47.8 

6 

1-9 

1.2 

66 

64-7 

12.9 

26 

123.6 

24.6 

86 

182.4 

36.3 

46 

241.3 

48. 0 

7 

6.9 

1.4 

67 

65.7 

13-1 

27 

124.6 

24.8 

87 

183.4 

36.5 

47 

242.3 

48.2 

8 

^f 

1.6 

68 

66.7 

^3-3 

28 

125-5 

25.0 

88 

184.4 

36.7 

48 

243.2 

48.4 

9 

8.8 

1.8 

69 

^^•7 

13-5 

29 

126.  5 

25.2 

89 

185.4 

36.9 

49 

244.2 

48.6 

lO 

9.8 

2.0 

70 

68.7 

13-7 

30 

127.5 

25.4 

90 

186.3 

37.1 

50 

245.2 
246.2 

48.8 
49- 0 

II 

10.8 

2.  I 

71 

69.6 

13-9 

131 

i28.y' 

25."6 

191 

187.3 

37.3 

251 

12 

II. 8 

2.3 

72 

70.6 

14.0 

32 

129.5 

25.8 

92 

188.3 

37.5 

52 

247.2 

49.2 

13 

12.8 

2.5 

73 

71.6 

14.2 

33 

130.4 

25.9 

93 

189.3 

37-7 

53 

248.  I 

49.4 

14 

13-7 

2.7 

74 

72.6 

14.4 

34 

131-4 

26.  I 

94 

190.3 

37-8 

54 

249.1 

49.6 

15 

14.7 

2.9 

75 

73-6 

14.  6 

35 

132.4 

26.3 

95 

191.3 

38.0 

55 

250.  I 

49.7 

16 

'1-7 

3-1 

76 

74.5 

14.8 

36 

133.4 

26.5 

96 

192.2 

38-2 

56 

251.  1 

49.9 

17 

16.7 

3-3 

77 

75-5 

15.0 

37 

134.4 

26.7 

97 

193.2 

38.4 

57 

252.  I 

50.1 

18 

17-7 

3-5 

78 

76.5 

15.2 

38 

135.3 

26.9 

98 

194.2 

38.6 

58 

253.0 

50.3 

19 

18.6 

3-7 

79 

77-5 

15-4 

39 

136.3 

27.1 

99 

195.2 

38.8 

59 

254.0 

50.5 

20 

19.  6 

3-9 

80 

.  78.  5 

15-6 

40 

137.3 
138.3 

27.3 

200 

196.2 

39- 0 

60 

255.0 

50.7 

21 

20.6 

4.1 

81 

79.4     15-8 

141 

27.5 

201 

197.1 

39-2 

261 

256.0 

50.9 

22 

21.6 

4.3 

82 

80. 4     16. 0 

42 

139.3 

27.7 

02 

198.  I 

39.4 

62 

257.0 

51- I 

23 

22.6 

4-5 

P 

81.4     16.2 

43 

140.3 

27.9 

03 

199.1 

39.6 

^J 

257-9 

51-3 

24 

23-5 

4-7 

^4 

82.4  1  16.4 

44 

141. 2 

28.1 

04 

200.  I 

39-8 

64 

258.9 

51-5 

25 

24.5 

4-9 

85 

83.4     16.6 

45 

142. 2 

28.3 

05 

201.  I 

40.0 

65 

259-9 

51-7 

26 

^^•5 

5-1 

86 

84.3 

16.8 

46 

143.2 

28.5 

06 

202.0 

40.  2 

66 

260.9 

51-9 

27 

26.5 

5-3 

87 

85.3 

17.0 

47 

144.2 

28.7 

07 

203.0 

40.4 

67 

261.9 

52.1 

28 

27.5 

5-5 

88 

86.3 

17.2 

48 

145-2 

28.9 

08 

204.0 

40.6 

68 

262.9 

52.3 

29 

28.4 

5-7 

89 

87.3 

17.4 

49 

146. 1 

29.  I 

09 

205.  0 

40.8 

69 

263.8 

52.5 

30 

29.4 

5-9 

90 

88.3 

17.6 

50 

147- 1 

.29.3 

10 

206.0 

41.0 

70 

264.8 

52.7 

31 

30.4 

6.0 

91 

89.3 

17.8 

151 

148. 1 

29.5 

211 

206.9 

"41.2" 

271 

265.8 

52.9 

32 

31-4 

6.2 

92 

90.2 

17.9 

52 

149-1 

29.7 

12 

207.9 

41.4 

72 

266.8 

53.1 

33 

32-4 

6.4 

93 

91.2 

18. 1 

53 

150.  I 

29.8 

13 

208.9 

41.  6 

73 

267.8 

5j-  j 

34 

33-3 

6.6 

94 

92.2     18.3 

54 

151. 0 

30.0 

14 

209.9 

41.7 

74 

268.7 

53-5 

35 

34.3 

6.8 

95 

93-  2      18.  5 

55 

152.  0 

30.2 

15 

210.9 

41.9 

75 

269.7 

53-6 

36 

35  3 

7.0 

96 

94.2 

18.7 

56 

153-0 

30.4 

16 

211. 8 

42.1 

76 

270.7 

53-8 

H 

36.3 

7-2 

97 

95-1 

18.9 

57 

154.0 

30.6 

17 

212.8 

42.3 

77 

271.7 

54.0 

38 

37.3 

7-4 

98 

96. 1 

19.  I 

58 

155-0 

30.8 

18 

213.8 

42.5 

78 

272.7 

54.2 

39 

38.3 

7.6 

99 

97-1 

19-3 

59 

155-9 

31,0 

19 

214.8 

42.7 

Z9 

273.6 

54-4 

40 

39-2 

7.8 

100 

98.1 

19-5 

60 

156.9 

31.2 

20 

215.8 

42.9 

80 

274.6 

54.6 

41 

40.2 

8.0 

loi 

99.1 

19.7 

161 

157-9 

31-4 

221 

216.8 

43-1 

281 

275.6 

54.8 

42 

41.2 

8.2 

02 

100.  0 

19.9 

62 

158-9 

31.6 

22 

217.7 

43-3 

82 

276.6 

55.0 

43 

42.2 

8.4 

03 

lOI.O 

20.  I 

63 

159-9 

31-8 

23 

218.  7 

43.5 

83 

277.6  i  55-2    1 

44 

43-2 

8.6 

04 

102.0 

20.3 

64 

160.8 

32-0 

24 

219.7 

43-7 

84 

278.5  !  55-4    1 

45 

44.1 

8.8' 

05 

103.0 

20.  5 

65 

161.  8 

32-2 

25 

220.  7 

43-9 

85 

279.5 

55-6 

46 

45.1 

9.0 

06 

104.0 

20.  7 

66 

162,8 

32.4 

26 

221.  7 

44-  1 

86 

280.5 

55-8 

47 

40.  I 

9.2 

°7 

104.9 

20.  9 

67 

163.8 

32.6 

27 

222.  6 

44-3 

87 

281.5 

56.  0 

48 

47.1 

9-4 

08 

105.9 

21.  I 

68 

164.8 

32.8 

28 

223.6 

44.5 

88 

282.5 

56.2 

49 

48.  I 

9.6 

09 

106.  9 

21.3 

69 

165.8 

33-0 

29 

224.6 

44.7 

89 

283.4 

56.4 

50 

49.0 

9.8 

10 

J_°7._?_ 

21.5 

70 

166.7 

33-2 

30 

225.  6 

44.9 

90 

284.4 

56.6 

51 

50.  0 

9-9 

III 

108.  9 

21.  7 

171 

167-7 

33-4 

231 

226.6 

45.1 

291 

285.4 

56.8 

52 

51.0 

10.  I 

12 

109.  8 

21.9 

72 

168.7 

33-6 

32 

227.5 

45-3 

92 

286.4 

57- 0 

53 

52.0 

10.3 

13 

no.  8 

22.0 

73 

169.7 

33-8 

33 

228.5 

45-5 

93 

^!Z-4 

57.2 

54 

53- 0 

10.5 

14 

III. 8 

22.  2 

74 

170.7 

33-9 

34 

229.5 

45.7 

94 

288.4     57.4 

5| 

53-9 

10.7 

15 

112.  8 

22.4 

75 

171. 6 

34.1 

35 

230.5 

45-8 

95 

289.3     57.6 

56 

54-9 

10.  9 

16 

113.  8 

22.  6 

76 

172.  6 

34-3 

36 

231-5 

46.0 

96 

290.3     57.7 

5^ 

55  9 

II   I 

17 

114.  8 

22.8 

77 

173-6 

34.5 

37 

232.4 

46. 2 

97 

291-3     57-9 

58 

56.9 

"•3 

18 

115-7 

23.0 

78 

174-6 

34.7 

38 

233.4 

46.4 

98 

292.3 

58.1 

59 

57-9 

II. 5 

19 

116.  7 

23.2 

79 

175-6 

34.9 

39 

234.4 

46.6 

99 

293.3 

58.  3 

60 

58.8 

II. 7 

20 

117.7 

23-4 

80 

176.5 

35-1 

40 

235-4 

46.8 

300 

294.2 

58.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E. 

byN. 

E.  by  S. 

W.by 

N. 

W.  byS 

. 

;For  7  Points.      1 

TABLE  I. 

Page  203 

Difference  of  Latitude  and  Departure  for 

1%  Points. 

'N.  1 

by  E.  %  E. 

] 

f^.  by  W.  % 

W.                  S.  by  E.  } 

<E.                 S. 

byW 

.  XW. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

58.6 

I 

I.O 

0.2 

61 

59.2 

14.8 

121 

II7.4 

.29.4 

181 

175-6 

44.0 

241 

233.8 

2 

1-9 

0.5 

62 

60.  I 

15-1 

22 

1 18.  3 

29.  6 

82 

176.5 

44.2 

42 

234-7 

58.8 

3 

2.9 

0.7 

63 

61.  I 

15.3 

23 

1 19- 3 

29.9 

^3 

177.5 

44.5 

43 

235-7 

59.0 

4 

3-9 

1.0 

64 

62.  I 

15.6 

24 

120.3 

30.1 

84 

178.5  ,  44.7 

44 

236.7 

59.3 

5 

4.9 

I.  2 

65 

63.1 

15.8 

25 

121. 3 

30.4 

85 

179.5  i  45-0 

45 

237-7 

59.5 

6 

5-8 

1-5 

66 

64.0 

16.  0 

26 

122.2 

30.6 

86 

180.4 

45.2 

46 

238.6 

59.8 

7 

6.8 

1-7 

67 

65.0 

16.3 

27 

123.2 

30.9 

87 

181,4 

45-4 

47 

239.6 

60.  0 

S 

7-8 

1-9 

68 

66.0 

16.5 

28 

124.2 

31.  I 

88 

182.4 

45-7 

48 

240.6 

60,3 

9 

8.7 

2.2 

69 

66.9 

16.8 

29 

125.  I 

31.3 

89 

183.3  ;  45-9 

49 

241.5 

60.  5 

lO 

9-7 

2.4 

70 

67.9 

17.0 

30 

126.  I 

31.6 
31-8 

90 
191 

184. 3    46. 2 

50 

242.5 
243-5 

60.  7 
61.0 

II 

10.7 

2.7 

71 

68.9 

17-3 

»3i 

127.7^ 

185. 3  i  46.4 

251 

12 

II. 6 

2.9 

72 

69.8 

17-5 

32 

128.0 

32.1 

92 

186. 2    46. 7 

52 

244-4 

61.  2 

13 

12.  6 

3-2 

73 

70.8 

17.7 

33 

129.0 

32.3 

93 

187.2    46.9 

53 

245.4 

61.5 

14 

13.6 

3-4 

74 

71.8 

18.0 

34 

130.0 

32.6 

94 

188. 2  i  47. 1 

54 

246,4 

61.7 

15 

14.6 

3-6 

75 

72.8 

18.2 

35 

131. 0 

32.8 

95 

189.2   ;  47.4 

55 

247,4 

62.  0 

i6 

15-5 

3-9 

76 

73-7 

18.5 

36 

131-9 

33.0 

96 

190,  I   j  47.  6 

56 

248.3 

62.2 

17 

16.5 

4.  I 

77 

74-7 

18.  7 

21 

132.9 

33-  3 

97 

191.  1      47.9 

57 

249.3 

62.4 

i8 

17-5 

4.4 

78 

7^-1 

19.  0 

38 

133-9 

33-5 

98 

192.  I   i  48.  I 

58 

250.3 

62.  7 

19 

18.4 

4.6 

79 

76.6 

19.  2 

39 

134.8 

33-8 

99 

193.0 

48.4 

59 

251.2 

62.  9 

20 

L9i4^ 

4-9 

80 

77.6 

19.4 

40 

135-8 

34-0 

200 

194.0 

48.6 

60 

252,2 

63-2 

21 

20.4 

5-1 

81 

78.6 

19.7 

141 

136.8 

34-3 

201 

195.  0 

48.8 

261 

253-2 

63-4 

22 

21.3 

5-3 

82 

79-5 

19.9 

42 

137-7 

34-5 

02 

195-  9  i  49.  I 

62 

254-1 

63-7 

23 

22.3 

5-f 

f3 

80.5 

20.  2 

43 

138.7 

34-7 

03 

196.9  1  49.3 

^J> 

255-1 

63-9 

24 

23-3 

5-8 

84 

81.5 

20.4 

44 

139-7 

35-0 

04 

197.  9  1  49-  6 

64 

256.  1 

64.  I 

25 

24-3 

6.  I 

85 

82.5 

20.  7 

45 

140.7 

35-2 

05 

198.9  ;  49.8 

65 

257.1 

64.4 

26 

25.2 

6.3 

86 

83-4 

20.  9 

46 

141.  6 

35-5 

06 

199.  8     50.  I 

66 

258.0 

64.6 

27 

26.2 

6.6 

87 

84.4 

21.  I 

47 

142.  6 

35-7 

07 

200.  8     50.  3 

67 

259.0 

64.9 

28 

27.  2 

6.8 

88 

85-4 

21.4 

48 

143.6 

36.0 

08 

201.8     50. 5 

68 

260.  0 

65.1 

29 

28.1 

7.0 

89 

86.3 

21.6 

49 

144.5 

36.2 

09 

202.  7     50.  8 

69 

260.9 

65.4 

30 

29. 1 

7-3 

90 

87.3 

21.9 

50 

145-5 

36.4 

10 

203,7 

51-0 

70 

261.9 

65.6 

31 

30.1 

7-5 

91 

88.3 

22.  I 

151 

146.  5 

36.7 

211 

204.7 

51-3 

271 

262.  9 

65.8 

32 

31.0 

7.8 

92 

89.2 

22.4 

52 

147.4 

36.9 

12 

205.6 

51-5 

72 

263.8 

66.1 

33 

32.0 

8.  0 

93 

90.  2 

22.  6 

53 

148.4 

37-2 

13 

206.  6 

51.8 

73 

264.8 

66.3 

34 

33-0 

^•3 

94 

91.  2 

22.8 

54 

149.4 

37-4 

14 

207.6 

52.0 

74 

265.8 

66.6 

35 

34-0 

8.5 

95 

92.  2 

23.1 

55 

150.4     37-7 

15 

208.6 

52.2 

75 

266.8 

66.8 

36 

34-9 

8.7 

96 

93-1 

23-3 

56 

151-3     37-9 

16 

209.5 

52.5 

76 

267.7 

67.  I 

37 

35-9 

9.0 

97 

94.1 

23.6 

H 

152.3     38.1 

17 

210,  5 

52.7 

77 

268.7 

67.3 

38 

36-9 

9.2 

98 

95-1 

23.8 

58 

153-3  i  38.4 

18 

211.  5 

53-0 

78 

269.7 

67.5 

39 

37-8 

9-5 

99 

96.0 

24.1 

59 

154.  2  1  38.  6 

19 

2T2.  4 

53-2 

79 

270.6 

67.8 

40 

38.8 

9-7 

100 

97.0 

24-3 

60 

155.2  i  38.9 

20 

213.4 

53-5 

80 

271.6 

68.0 

41 

39.8 

10.  0 

lOI 

98.  0 

24-5 

161 

156.  2     39.  I 

221 

214.4 

53-7 

281 

272.6 

68.3 

42 

40.7 

10.2 

02 

98.9 

24.8 

62 

157- 1     39.4 

22 

215.3 

53-9 

82 

273.5 

68.5 

43 

41-7 

10.4 

03 

99-9 

25.0 

63 

158.  I  1  39.  6 

23 

216.3 

54-2 

83 

274.5 

68.8 

44 

42.7 

10.7 

04 

100.9 

25-3 

64 

159.  I  [  39.8 

24 

217.3 

54-4 

84 

275.5 

69,0 

45 

43-7 

10.9 

05 

101.9 

25-5 

65 

160.  I     40.  I 

25 

218.  3       54.  7 

85 

277.5 

69.  2 

46 

44.6 

II. 2 

06 

102.8 

25.8 

66 

161.  0     40.  3 

26 

219,2       54.9 

86 

277.4 

69.5 

47 

45-6 

II. 4 

07 

103.8 

26.  0 

67 

162.  0  i  40.  6 

27 

220.  2    i    55.  2 

87 

278.4 

69.7 

48 

46.6 

II. 7 

08 

104.8 

26.  2 

68 

163.  0     40.  8 

28 

221.2        55.4 

88 

279.4 

70.0 

49 

47.5 

II. 9 

09 

105.7 

26.5 

69 

163.9 

41.  I 

29 

222.1    ,    55.6 

89 

280.3 

70.2 

50 

48.5 

12.  I 

10 

106.  7 

26.  7 

70 

164.9 

41-3 

30 

223,1 

55-9 

90 

281.3 

70.5 

51 

49-5 

12.4 

III 

107.  7 

27.0 

171 

165.9 

41.5 

231 

224.  I 

56.1 

291 

282,3 

70,7 

52 

50-4 

12.6 

12 

108.  6 

27.2 

72 

166.8 

41.  a 

32 

225,0 

56.4 

92 

283.2 

71.0 

53 

51.4 

12.9 

13 

109.6 

27-5 

73 

167.8 

42.0 

33 

226,  0     56.  6 

93 

284.2 

71,2 

54 

52.4 

13- I 

H 

no.  6 

27.7 

74 

168.8 

42.3 

34 

227,0     56,9 

94 

285.2 

71,4 

55 

53-4 

13-4 

15 

III. 6 

27.9 

75 

169,8 

42.5 

35 

228,0 

57.1 

95 

286.2 

71,7 

56 

54-3 

13.6 

16 

112.  5 

28.2 

76 

170.7 

42.8 

36 

228,9 

57.3 

96 

287.1 

71,9 

57 

55-3 

13-8 

17 

"3-5 

28.4 

77 

171-7 

43.0 

?>1 

229,  9 

57.6 

97 

288.1 

72,2 

58 

56.3 

14.  I 

18 

114- 5 

28.7 

78 

172.7 

43-3 

38 

230.9 

57.8 

98 

289.  I 

72,4 

59 

57-2 

14-3 

19 

115-4 

28.9 

79 

173-6 

43-5 

39 

231.8 

58.1 

99 

290.9 

72.7 

60 

58.2 

14.6 

20 

116,4 

29.2 

80 

174.6 

43-7 

40 

232.8 

58-3 

300 

291.0 

72.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.      Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  N.  E 

^E.           E 

:.  s.  E. 

%^.           W 

.  N,  W.  %.  W.           V 

I.  s.  w,  %  w. 

[F 

or  6%  P( 

nnts. 

Page  204 

TABLE 

I. 

Difference  of  Latitude  and  Departure  for 

i}^  Point. 

N. 

byE. 

y^E. 

N.  by 

w.  >^ 

W. 

S.  by  E.  } 

4  E.                S.  by  W. 

Kw. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0-3 

61 

58.4 

17.7 

121 

II5.8 

35-1 

181 

173-2 

52.5 

241 

230.6 

70.0 

2 

1-9 

0.6 

62 

59-3 

18.0 

22 

116.  7 

35.4 

82 

174-2 

52.8 

42 

231.6 

70.  2 

3 

2.9 

a.  9 

63 

60.3 

18.3 

23 

117.  7 

35.7 

83 

175- I 

53-1 

43 

232.5 

70.5 

4 

3-8 

'.2 

64 

61.2 

18.6 

24 

118.  7 

36.0 

84 

176.  I 

53-4 

44 

233.5 

70.8 

5 

4.8 

^•5 

65 

62.  2 

18.9 

25 

119.  6 

36.3 

85 

177.0 

53.7 

45 

234.5 

71.  I 

6 

5-7 

1-7 

66 

63.2 

19.2 

26 

120.6 

36.6 

86 

178.0 

54.0 

46 

235.4 

71.4 

7 

6.7 

2.0 

67 

64.  I 

19.4 

27 

121.  5 

36-9 

^ol 

178.9 

54.3 

47 

236.4 

71.7 

8 

7-7 

2-3 

68 

65.1 

19.7 

28 

122.  5 

37-2 

88 

179.9 

54.6 

48 

237.3 

72.0 

9 

8.6 

2.6 

69 

66.0 

20.0 

29 

123.4 

37-4 

89 

180.  9 

54.9 

49 

238.3 

72.3 

lO 

9.6 

2.9 

70 

67.0 

20.3 

30 

124.4 

37-7 

90 

181.8  j  55.2 

50 

239.2 

72.6 

II 

10.5 

3-2 

71 

67.9 

20.6 

131 

125.4 

38-0 

191 

182.8  j  55.4 

251 

240.2 

72.9 

12 

"•5 

3-5 

72 

68.9 

20.9 

32 

126.  3 

3^-3 

92 

183.7 

55.7 

52 

241.  I 

73-2 

13 

12.4 

3-8 

73 

69.9 

21.2 

33 

127.3 

38.6 

93 

184.7 

56.0 

53 

242.  I 

73-4 

14 

13-4 

4.1 

74 

70.8 

21.  5 

34 

128.2 

38.9 

94 

185.6 

5^3 

54 

243.1 

73-7 

15 

14.4 

4.4 

75 

71.8 

21.  8 

35 

129.  2 

39.2 

95 

186.6 

56.6 

55 

244.0 

74-0 

16 

15-3 

4.6 

76 

72.7 

22.  I 

36 

130.  I 

39-5 

96 

187.6  '  56.9 

56 

245-0 

74-3 

17 

16.3 

4-9 

77 

73-7 

22.4 

37 

131.  I 

39-8 

97 

188.5   ^  57.2 

H 

245-9 

74-6 

18 

17.2 

5-2 

78 

74.6 

22.  6 

38 

132.  I 

40.  I 

98 

189.5 

57.5 

58 

246.9 

74-9 

19 

18.2 

5-5 

79 

75-6 

22.9 

39 

133.0 

40.3 

99 

190.4 

57.8 

59 

247.8 

75-2 

20 

19. 1 

5-8 

80 

76.6 

23,2 

40 

134.0 

40.  6 

200 

191.4 

58.1 

60 

248.8 

75-5 

21 

20. 1 

6.1 

'JT 

77-5 

23-5 

141 

134.9 

40.9 

201 

192.  3     58.  3 

261 

249.8 

>5-8 

22 

21. 1 

6.4 

82 

78.5 

23.8 

42 

135-9 

41.2 

02 

193.  3     58-  6 

62 

250.7 

76.1 

23 

22. 0 

6.7 

83 

79-4 

24.1 

43 

136.8 

41.5 

03 

194-3  i  58.9 

63 

251.7 

76.3 

24 

23.0 

7.0 

84 

80.4 

24.4 

44 

137.8 

41.8 

04 

195-2     59-2 

64 

252.6 

76.6 

25 

23-9 

7.3 

85 

81.3 

24.7 

45 

138.8 

42.1 

°5 

196.  2 

59.5 

65 

253-6 

76.9 

26 

24.9 

7-5 

86 

82.3 

25.  0 

46 

139.7 

42.4 

06 

197.1 

59.8 

66 

254-5 

77.2 

27 

25.8 

7.8 

87 

83-3 

25-3 

47 

140.7 

42.7 

07 

198. 1 

60.  I 

67 

255-5 

77.5 

28 

26.8 

8.1 

88 

84.2 

25-5 

48 

141.  6 

43-0 

08 

199.0     60.4 

68 

256.5 

77.8 

29 

27.8 

8.4 

89 

85.2 

25.8 

49 

142.6 

43-3 

09 

200. 0 

60.  7 

69 

257.4 

78.1 

30 
31 

28.7 

8.7 

90 

86.1 

26. 1 

50 

143-5 

43-5 

10 

201.0 

61.  0 

70 

258.4 

78.4 

29.7 

9.0 

91 

87.1 

26.4 

151 

144.5 

43-8 

211 

201.9 

61.3 

271 

259.3 

78.7 

32 

30.6 

9-3 

92 

88.0 

26.  7 

52 

145.5 

44-1 

12 

202.9 

61.5 

72 

260.3 

79-0 

33 

31.6 

9.6 

93 

89.0 

27.0 

53 

146.4 

44-4 

13 

203.8 

61.8 

73 

261.2 

79-2 

34 

32.5 

9.9 

94 

90.  0 

27-3 

54 

147.4 

44-7 

14 

204.8 

62.  I 

74 

262.  2 

79.5 

35 

10.  2 

95 

90.9 

27.6 

55 

148.3 

45- 0 

15 

205.7 

62.4 

75 

263.2 

79-8 

36 

34-4 

10.5 

96 

91.9 

27.9 

56 

149-3 

45-3 

16 

206.  7 

62.  7 

76 

264. 1 

80.  I 

37 

35-4 

10.  7 

97 

92.8 

28.2 

57 

150.2 

45-6       17 

207.7 

63.0 

77 

265. 1 

80.4 

38 

36.4 

II. 0 

98 

93-8 

28.4 

58 

151. 2 

45-9       18 

2od.  6 

63-3 

78 

266.0 

80.  7 

39 

37-3 

"•3 

99 

94-7 

28.7 

59 

152.2 

46. 2       19 

209.  6 

63.6 

P 

267.0 

81.0 

40 

38.3 

II. 6 

100 

95-7 

29.0 

60 

153- I 

46. 4       20 

210.5  1  63.9 

80 

267.9 

81.3 

41 

39-2 

II. 9 

lOI 

96.7 

29-3 

161 

154.  I 

46.7 

221 

211.  5  i  64.2 

281 

268.9 

81.6 

42 

40.2 

12.  2 

02 

97.6 

29.6 

62 

155-0 

47.0 

22 

212.4  1  64.4 

82 

269.9 

81.9 

43 

41. 1 

12.5 

03 

98.6 

29.9 

63 

156.0 

47-3 

23 

213.4     64.7 

^3 

270.8 

82.2 

44 

42.1 

12.8 

04 

99.5 

30.2 

64 

156.9 

47.6 

24 

214.4 

65.0 

f4 

271.8 

82.4 

45 

43-1 

13-1 

OS 

100.  5 

30.5 

65 

157-9 

47-9 

^5 

215-3 

65-3 

85 

272.7 

82.  7 

46 

44.0 

13-4 

06. 

lOI.  4 

30.8 

66 

158.9 

48.2 

26 

216.3 

65.6 

86 

273-7 

83.0 

47 

45.0 

13.6 

07 

102.4 

31- I 

67 

159.8 

48.5 

27 

217.  2 

65-9 

^7 

274.6 

^3-3 

48 

45-9 

13-9 

08 

103.3 

31-4 

68 

160.8 

48.8 

28 

218.2  :  66.2 

88 

275.6 

83.6 

49 

46.9 

14.2 

09 

104.3 

31.6 

69 

161.  7 

49.1 

29 

219. 1 

66.5 

89 

276.  6 

S3.  9 

50 

47.8 

14-5 

10 

105.  3_ 

31-9 

70 

162.  7 

49-3 

30 

220. 1 

66.8 

90 

277.5 

84.2 

51 

48.8 

14.8 

iiF 

106.  2 

32  2 

171 

163.6 

49.6 

231 

221. 1 

67.  I 

291 

278.5 

84.5 

52 

49.8 

15- I 

12 

107.  2 

32-5 

72 

164.6 

49-9 

32 

222. 0     67. 3 

92 

279.4 

84.8 

53 

50.7 

15.4 

13 

108.  I 

32.8 

73 

165.6 

50.  2 

33 

223.  0  i  67.  6 

93 

280.4 

85.1 

54 

51-7 

15-7 

H 

109.  I 

33-1 

74 

r66.  5 

50.5 

34 

223.9  !  67.9 

94 

281.3 

85-3 

55 

52.6 

16.0 

15 

no.  0 

33-4 

75 

167.5 

50.8 

35 

224.  9     68.  2 

95 

282.3 

85.6 

56 

53-6 

16.3 

16 

III.  0 

33-7 

76 

168.4 

51-1 

36 

225.8  ,  68.5 

96 

283.3 

f|-9 

57 

54-5 

16.5 

17 

112. 0 

34- 0 

77 

169.4 

51-4 

37 

226.  8  !  68.  8 

H 

284.2 

86.2 

58 

55-5 

16.8 

18 

112.  9 

34-3 

78 

170.3 

51-7 

38 

227.8 

69.  I 

98 

285.2 

86.5 

59 

56.5 

17.  I 

19 

113-9 

34-5 

79 

171.3 

52.0 

39 

228.  7 

69.4 

99 

286.  I 

86.  8 

60 

57-4 

17.4 

20 

1 14.  8 

34-8 

80 

172.  2 

52.3 

40 

229.  7 

69.7 

300 

287.  I 

87.1 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

E.  N.  P 

:.  ^E. 

E.  S.  E 

.  KE. 

W.  N.  W 

'•/zW. 

W.  S.  W.  '4  W. 

:For  6}4 

Points. 

TABLE  I. 

- 

Page  205  1 

% 

Difference  of  Latitude  and  Departure  for 

I^  Points. 

N.  1 

jy  E.  ^  E.                  N.  by  W.  j4 

W.                   S.  by  E. 

^E.                 S 

.  by  W.  %  W. 

Dist. 

I 

Lat. 

Dep. 
0.3 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
40.8 

Dist. 
181 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 
81.2 

0.9 

61 

57.4 

20.6 

121 

II3-9 

170.4 

61,0 

241 

226.9 

2 

1-9 

0.7 

62 

58.4 

20.9 

22 

1 14.  9 

41.  I 

82 

171. 4 

61.3 

42 

227.9 

81.5 

3 

2.8 

I.O 

63 

59-3 

21.2 

23 

115.8 

41.4 

83 

172.3 

61.  7 

43 

228.8 

81.9 

4 

3-8 

1-3 

64 

60.3 

21.6 

24 

1 16.  8 

41.8 

84 

173-2 

62.  0 

44 

229.7 

82.2 

5 

4.7 

1-7 

65 

61.2 

21.9 

25 

117.  7 

42.1 

85 

174.2 

62.3 

45 

230.7 

.     82.5 

6 

5-6 

2.0 

66 

62.  I 

22.  2 

26 

1 18.  6 

42.4 

86 

175.1 

62.  7 

46 

231- '» 

82.9 

7 

6.6 

2.4 

67 

63.1 

22.6 

27 

119.  6 

42.8 

87 

176.  I 

63.0 

47 

232.6 

83.2 

8 

7-5 

2.7 

68 

64.0 

22.9 

28 

120.5 

43.1 

88 

177.0 

63-3 

48 

233-5 

83.5 

9 

8.5 

3-0 

69 

65.0 

23.2 

29 

121. 5 

43.5 

89 

178.0 

63.7 

49 

234.4 

83.9 

lO 

II 

9-4 
10.4 

3-4 
3-7 

70 
71 

65-9 
66.8 

23.6 
23.9 

30 
131 

122.4 
123.3 

43-8 
44.  I 

90 
191 

178.9 

64.0 

50 

235-4 

84.2 

179.8 

~^H-Y 

251 

236.3 

84.  6 

12 

"•3 

4.0 

72 

67.8 

24-3 

32 

124.  3     44.  5 

92 

180.  8  j  (4.  7 

52 

237-3 

84.9 

13 

Ii2.  2 

4.4 

73 

68.7 

24.6 

33 

125.2     44.8 

93 

181.  7  1  65.0 

53 

238.2 

85-2 

14 

13.2 

4.7 

74       69. 7 

24.9 

34 

126.  2     45.  I 

94 

182.7     65.4 

54 

239.2 

85.6 

15 

14.  I 

5-1 

75       70.6 

25-3 

35 

127. 1 

45-5 

95 

183.  6     65.  7 

55 

240.1 

85-9 

i6 

15- 1 

5-4 

76       71.6 

25.6 

36 

128.0 

45.8 

96 

184.  5  !  66.  0 

56 

241.0 

86.2 

17 

16.0 

5-7 

77       72. 5 

25-9 

37 

129.0 

46.  2 

97 

185.5     66.4 

57 

242.0 

86.6 

i8 

16.9 

6.1 

78 

73-4 

26.3 

38 

129.9 

46.5 

98 

186.4  1  66.7 

58 

242.9 

86.9 

19 

17.9 

6.4 

79 

74-4 

26.6 

39 

130.9 

46.8 

99 

187.4  1  67.0 

59 

243-9 

87-3 

20 
21 

18.8 
19.8 

6.  7 
7-1 

80 

75-3 

27.0 

"27.3 

40 

131.8     47-2 

200 

188.3     67.4 

60 

244.  8 

87.6 
L7-9 

81  !    7673 

141 

132.  8     47.  5 

201 

189.  3     67.  7 

261 

245-7 

22 

20.  7 

7.4 

82      77. 2 

27.  6 

42 

133.7 

47.8 

02 

190.  2  i  68.  I 

62 

246.7 

88.3 

23 

21.7 

83      78. 1 

28.0 

43 

134.6 

48.2 

03 

191.  I      68.4 

63 

247.6 

88.6 

24 

22.6 

8.  I 

84       79- 1 

28.3 

44 

135.6     48.5 

04 

192.  I   :  68.  7 

64 

248.6 

88.9 

25 

23-5 

8.4 

85 

80.0 

28.6 

45 

136.  5 

48.8 

05 

193.  0  I  69.  I 

65 

249-5 

89-3 

26 

24.5 

8.8 

86 

81.0 

29.0 

46 

137.5 

49.2 

Ob 

194.0  1  69.4 

66 

250.5 

89.6 

27 

25-4 

9-1 

87 

81.9 

29-3 

47 

138.4 

49.5 

07 

194. 9  !  69.  7 

67 

251.4 

89.9 

28 

26.4 

9.4 

88 

82.9 

29.6 

48 

139.3 

49.9 

08 

195.  8  !  70.  I 

68 

252.3 

90-3 

29 

27.3 

9.8 

89 

83.8 

30.0 

49 

140.3 

50.  2 

09 

196.  8     70.  4 

69 

253-3 

90.6 

30 
31 

28.2 
29.  2 

10.  I 
10.4 

90 
91 

84.7 
"85.  7 

30.3 
30.7 

50 

141. 2     50.5 

10 

197.  7  i  70.  7 

70 
271 

254.2 

91.0 

151 

142.2     50.9 

2rr 

198.7     71.  I 

255-2 

91-3 

32 

30.1 

10.8 

92 

86.6 

31.0 

52 

143.  I     51.2 

12 

199.6  I  71.4 

72 

256. 1 

91.6 

33 

31-1 

II.  I 

93 

87.6 

31-3 

53 

144. 1     51-5 

13 

200.  5  1  71.  8 

73 

257-0 

92.  0 

34 

32.0 

"•5 

94 

88.5 

31-7 

54 

145.0     51.9 

14 

201.  5  '  72.  I 

74 

258.0 

92.3 

35 

33- 0 

II. 8 

95 

89.4 

32.0 

55 

145.9     52.2 

15 

202.  4  !  72.  4 

75 

258.9 

92.6 

36 

33-9 

12.  I 

96 

90.4 

32.3 

56 

146.9     52.6 

16 

203.4  '  72.8 

76 

259-9 

93-0 

37 

34-8 

12.5 

97 

91-3 

32.7 

57 

147.8     52.9 

17 

204.  3      73.  1 

77 

260.8 

93-3 

38 

35-8 

12.8 

98 

92.3 

33- 0 

58 

148.8     53.2 

18 

205.3  :  73-4 

78 

261.  7 

93-7 

39 

36.7 

13- I 

99 

93-2 

33-4 

59 

149.  7     53-  6 

19 

206.  2  1  73.  8 

79 

262.  7 

94.0 

41 

37-7 
38.6 

13-5 

13.8 

100 

94.2 
95-1 

33-7 

34- 0 

60 

16Y' 

150.6     53.9 

20 

207.  I      74.  I 

80 

263.6 

94-3 

lOI 

151-6     54-2 

221 

208.  I  '  74.  5 

281 

264.6 

94.7 

42 

39-5 

14.  I 

02 

96.0 

34-4 

62 

152.5     54-6 

22 

209.  0   :    74.  8 

82 

^^^•5 

95- 0 

43 

40.5 

14.5 

03 

97.0 

34-7 

P 

153.5     54.9 

23 

210.0       75.  I 

83 

266.5 

95-3 

44 

41.4 

14.8 

04 

97.9 

35- 0 

64 

154.4     55-2 

24 

210.9  '  75-5 

84 

267.4 

95-7 

45 

42.4 

15-2 

05 

98.9 

35-4 

65 

155-4     55.6 

25 

211.  8  ;  75.8 

85 

268.3 

96.0 

46 

43-3 

15-5 

06 

99.8 

35-7 

66 

156.3     55-9 

26 

212.8  1  76.  I 

86 

269.3 

96.4 

47 

44-3 

15.8 

07 

100.7 

36.0 

67 

157-2     56.3 

27 

213-  7  '  76.  5 

87 

270.2 

96.7 

48 

45-2 

16.2 

08 

loi.  7 

36.4 

68 

158.2     56.6 

28 

214. 7     76.8 

88 

271.2 

97.0 

49 

46.  I 

16.5 

09 

102.6 

36.7 

69 

159.  I     56.9 

29 

215.6     77.1 

89 

272.1 

97-4 

59 
51 

47.1 
48.0 

16.8 
17.2 

10 

103.  6 

37.1 

37-4 

70 

160. 1     57.3 

30 

216.6     77.5 

90 

273.0 

97-7 

III 

104.5 

171 

161.  0    !     57.6 

231 1 

217,5     77.8 

291 

274-0 

98.0 

52 

49- 0 

17-5 

12 

105.5 

37.7 

72 

161.9         57.9 

32 

218.4  !  78.2 

92 

274-9 

98-4 

53 

49-9 

17.9 

13 

106.4 

38.1 

73 

162.9         58.3 

33 

219.4  t  78.5 

93 

275-9 

98.7 

54 

50.8 

18.2 

14 

107.3 

38.4 

74 

163.8         58.6 

34 

220.3  i  78.  8 

94 

276.8 

99.0 

55 

51.8 

18.5 

15 

108.3 

38.7 

75 

164.8         59.0 

35 

221.3  :  79-2 

95 

277.8 

99-4 

5^ 

52.7 

18.9 

16  ; 

109.2 

39-1 

76 

165.7         59.3 

36 

222.  2        79.  5 

96 

278.7 

99-7 

57' 

53-7 

19.  2 

17  ; 

no.  2 

39-4 

77 

166.7         59.6 

37 

223.1 

79.8 

97 

279.6 

100.  I 

58  1 

54.6  ; 

19-5 

18 

III.  I 

39-8 

78  j 

■167.  6     60.  0 

38! 

224.  I 

80.2 

98 

280.6 

100.4 

59  : 

55.6  ■ 

19.9 

19  j 

112. 0 

40.  I 

79  I 

168.  5     60.  3 

39  i 

225.0 

80.5 

99 

281.  5 

100.  7 

60  \ 

56.5 
Dep. 

20.2 

20  ! 

Dist. 

113.0 

40.4 

80 

169.  5     60.  6 

40  : 

1 

226.0 

80.9 

300 

282.5  , 

lOI.  I 

1  Dist. 

Lat. 

1 

Dep. 

Lat. 

Dist. 

Dep.    1    Lat. 

Dist. 

Dep. 

Lat. 

Dist.  i 

1 

Dep. 

Lat. 

!     E. 

N.  E.  X 

E.             E.  S.  E.  l{  E. 

W. 

N.  W.  X  W.              '^ 

kV.  s.  w.  X  w. 

1 

_For  6X 

Points. 

Page  206 

TABLE  I. 

Difference  of  Latitude  and  Departure  for  2  Points. 

N.N. 

E. 

N.  N.  W 

s.  s. 

E. 

s.s. 

W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.4 

61 

56.4 

23.3 

121 

III.  8     46.  3  1 

181 

167.2 

69-3 

241 

222.  7 

92.2 

2 

1.8 

0.8 

62 

57.3 

23.7 

22 

112.  7 

46.7 

82 

168.  I 

69.6 

42 

223.6 

92.6 

3 

2.8 

I.  I 

63 

58.2 

24.1 

23 

113.  6 

47.1 

83 

169.  I 

70.0 

43 

224.5 

93-0 

4 

3-7 

1-5 

64 

59.1 

24.5 

24 

1 14.  6     47.5 

84 

170.  0 

70.4 

44 

225.4 

93-4 

5 

4.6 

1-9 

65 

60.  I 

24.9 

25 

"5-5     47-8 

85 

170.9 

70.8 

45   ' 

226.4 

93-8 

6 

5-5 

2.3 

66 

61.0 

25-3 

26 

116. 4     48.2 

86 

171.  8 

71.2 

46  ! 

227.3 

94-1 

7 

6.5 

2.7 

67 

61.9 

25.6 

27 

117.3  1  48.6 

87 

172.8 

71.6 

47 

228.2 

94-5 

8 

7-4 

3-1 

68 

62.8 

26.  0 

28 

118. 3     49.0 

88 

173-7 

71.9 

48 

229.  I 

94-9 

9 

8.3 

3-4 

69 

63.7 

26.4 

29 

119. 2     49.4 

89 

174.6 

72-3 

49 

230.0 

95-3 

10 

9.2 

3-8 

70 

64.7 

26.8 

30 

120.  I     49.  7 

90 

175-5 

72.7 
73-1 

50 

231.0 

95.7 

II 

10.2 

4.2 

71 

65.6 

27.2 

131 

121.  0  I  50. 1 

191 

176.5 

251 

231.9 

96. 1 

12 

II.  I 

4.6 

72 

66.5 

27.6 

32 

122.0  :  50.  5 

92 

177.4 

73-5 

52 

232.8 

96.4 

13 

12.0 

5-0 

12, 

67.4 

27.9 

33 

122.9     ;     50.9 

93 

178.3 

73-9 

53 

233.7 

96.8 

14 

12.9 

5-4 

74 

68.4 

28.3 

34 

123.8          51-3 

94 

179.  2 

74-2 

54 

234.7 

97.2 

15 

13-9 

5-7 

75 

69-3 

28.  7 

35 

124.7         51-7 

95 

180,2 

74-6 

55 

235-6 

97-6 

16 

14.8 

6.1 

76 

70.2 

29.  I 

36 

125.  6  i  52.  0 

96 

181. 1 

75-0 

56 

236-5 

98.0 

17 

15-7 

6.5 

77 

71.  I 

29.5 

37 

126.6     52.4 

97 

182.0 

75-4 

57 

237.4 

98.3 

18 

16.6 

6.9 

78 

72.  I 

29.8 

38 

127.  5     52.  8 

98 

182.9 

75-8 

58 

238.4 

98.7 

19 

17.6 

7-3 

79 

73- 0 

30.2 

39 

128.4  i  53-2 

99 

183.9 

76.2 

59 

239.3 

99.1 

20 
21 

18.5 
19.4 

7-7 

80 

73-9 

30.6 

40 

129.3  i  53-6 

200 

184.8 

76-5 

60 

240.  2 

99.5 

8.0 

81 

74.8 

31.0 

141 

130.3  1  54.0 

201 

185.7 

76.9 

261 

241.  I 

99.9 

22 

20.3 

8.4 

82 

75.8 

31-4 

42 

131.2  1  54.3 

02 

186.6 

77-3 

62 

242.  I 

100.3 

23 

21.2 

8.8 

^3 

76.7 

31.8 

43 

132.  I  !  54.  7 

03 

187.5 

77-7 

63 

243.0 

100.6 

24 

22.2 

9.2 

84 

77.6 

32.1 

44 

133.0  '  55-1 

04 

188.5 

78.1 

64 

243.9 

lOI.O 

25 

23.  I 

9.6 

85 

78.5 

32.5 

45 

134.  0^55.5 

°5 

189.4 

78-5 

^A 

244.8 

101.4 

26 

24.0 

9-9 

86 

79-5 

32-9 

46 

134.9     55.9 

06 

190.3 

78.8 

66 

245.8 

101.8 

27 

24.9 

10.3 

87 

80.4 

33-3 

47 

135.8  !  56.3 

07 

191.  2 

79-2 

67 

246.7 

102.2 

28 

25-9 

10.7 

88 

81.3 

33-7 

48 

136.7 

56.6 

08 

192.2 

79-6 

68 

247.6 

102.6 

29 

26.8 

II.  I 

89 

82.2 

34.1 

49 

137.7 

57.0 

09 

193- I 

80.0 

69 

248.5 

102.9 

30 

27.7 

"•5 

90 

83.1 

34.4 

50 

138.6     57.4 

10 

194.0 

80.4 

70 

249.4 

103.3 

31 

28.6 

II. 9 

91 

84.1 

34.8 

151 

139-5     57.8 

211 

194.9 

80.  7 

271 

250.4 

103.7 

32 

29.6 

12.  2 

92 

85.0 

35-2 

52 

140. 4     58.  2 

12 

195-9 

81.  I 

72 

251.3 

104.  I 

33 

30-5 

12.  6 

93 

85.9 

35-6 

53 

141. 4     58.6 

13 

196.8 

81.5 

73 

252.  2 

104.5 

34 

31-4 

13.0 

94 

86.8 

36.0 

54 

142.3     58.9 

14 

197.7 

81.9 

74 

253-1 

104.9 

35 

32.3 

13-4 

95 

87.8 

36.4 

55 

143.  2     59-  3 

15 

198.6 

82.3 

75 

254.1 

105.2 

36 

33-3 

13-8 

96 

88.7 

36.7 

56 

144.  I     59.  7 

16 

199.6 

82.7 

76 

255.0 

105.6 

37 

34-2 

14.2 

97 

89.6 

37-1 

57 

145.0     60.  I 

17 

200.  5 

83.0 

77 

255.9 

106.  0 

38 

35-1 

14-5 

98 

90.5 

37.5 

58 

146. 0     60.  5 

18 

201.4 

83-4 

78 

256.8 

106.4 

39 

36.0 

14.9 

99 

91-5 

37-9 

59 

146.  9     60.  8 

19 

202.3 

83-8 

79 

257.8 

106.8 

40 

37- 0 

15.3 

100 

92.4 

38.3 

60 

147.8  '  61.2 

20 

203.3 

84.2 

80 

258.7 

107.2 

41 

37-9 

15-7 

lol 

'  93-3 

38.7 

161 

148.7  !  61.6 

221 

204.2 

84.  6 

281 

259.6 

107.5 

42 

38.8 

16.  I 

02 

94.2 

39.0 

62 

149.  7  1  62.  0 

22 

205.  I 

85.0 

82 

260.  5 

107.9 

43 

39-7 

16.5 

03 

95-2 

39.4 

63 

150. 6     62.4 

23 

206.0 

85-3 

^3 

261.5 

108.3 

44 

40.7 

16.8 

04 

96. 1 

39-8 

64 

151. 5     62.8 

24 

206.9 

85-7 

84 

262.4 

108.7 

45 

41.6 

17.2 

05 

97- 0, 

40.2 

65 

152.4     63.1 

25 

207.9 

86.1 

85 

263.3 

'  109.  I 

46 

42.5 

17.6 

06 

97-9 

40.6 

66 

153.4  :  63.5 

26 

208.8 

86.5 

86 

264.2 

109.4 

47 

43-4 

18.0 

07 

98.9 

40.9 

67 

154.3    63.9 

27 

209.7 

86.9 

87 

265.2 

109.  8 

48 

44-3 

18.4 

08 

99.8 

41-3 

68 

155.2  i  64.3 

28 

210.  6 

87.3 

88 

266. 1 

no.  2 

49 

45-3 

18.8 

09 

100.  7 

41.7 

69 

156. 1    64. 7 

29 

211. 6     87.6 

89 

267.0 

no.  6 

50 

46.2 

19.  I 

10 

Id. 6 

42.1 

70 

157. 1 

65.1 

30 

212. 5     88.0 

90 

267.9 

III.O 

51 

47.1 

19.5 

III 

102.6 

42.5 

171 

158.0 

65.4 

231 

213.4  :  88.4 

291 

268. 8 

~iii74 

52 

48.0 

19.9 

12 

103.5 

42.9 

72 

158.9    65.8 

32 

214.3     88.8 

92 

269.8 

III.  7 

53 

49.0 

20.3 

13 

104.4 

43-2 

73 

159.8  j  66.2 

33 

215.3  :  89.2 

93 

270  7 

112.  I 

54 

49-9 

20.  7 

14 

105.3 

43-6 

74 

160.8     66.6 

34 

216.  2     89.  5 

94 

271.6 

112.5 

55 

50.8 

21.0 

15 

106.2 

44.0 

75 

161.  7     67.  0 

35 

217.  I      89.9 

95 

272.5 

112. 9 

56 

51-7 

21.4 

16 

107.2 

44.4 

76 

162.6     67.4 

36 

.   218.  0     90.  3 

96 

273-5 

\  "3-3 

57 

52.7 

21.8 

17 

108.  I 

44.8 

77 

163.  5  1  67.  7 

37 

219.  0     90.  7 

H 

274.  4 

"3-7 

58 

53-6 

22.  2 

18 

109.0 

45-2 

78 

164.  5     68.  I 

38 

219.9     91.  I 

98 

275-3 

114.  0 

59 

54-5 

22.6 

19 

109.9 

45-5 

79 

165.4     68.5 

39 

220.  8     91.  5 

99 

276.2 

114. 4 

60 

55-4 

23.0 

20 

no.  9 

45-9 

80 

166.3      ^ 

68.9 

40 

221.  7 

91.8 

300 

277.2 

1 14.  8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

LaU 

Dist. 

Dep. 

Lat. 

E. 

N.  E. 

E.  5 

?.  E. 

W.  N.  W. 

W.  S.  W. 

[For  6  I 

^oints. 

TABLE  I. 

Page  207 

Difference  of  Latitude  and 

3eparture  for 

2%  Points. 

£  N.  E.  %  E. 

N.  N.  W.  % 

w. 

S. 

S.  E. 

XE. 

S. 

s.  w.  %  w. 

Dist. 

I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  i     Lat. 

Dep. 

0.9 

0.4 

61 

55.1 

26.  I 

121 

109.4 

51.7 

181 

163.6 

77-4 

241 

217.9 

103.0 

2 

1.8 

0.9 

62 

56.0 

26.5 

22 

no.  3 

52.2 

82 

164.5 

77-8 

42 

218.8 

103.5 

3 

2.7 

1-3 

^3 

57- 0 

26.9 

23 

III. 2 

52.6 

f3 

165.4 

78.2 

43 

219.7 

103.9 

4 

3-6 

1-7 

64 

57-9 

27.4 

24 

1X2.  I 

53-0 

84 

166.3 

78.7 

44 

220.6 

104.3 

5 

4-5 

2.  I 

65 

58.8 

27.8 

25 

II3.0 

53-4 

^5 

167.2 

79-1 

45 

221.5 

104.  8 

6 

5-4 

2.6 

66 

59-7 

28.2 

26 

113-9 

53-9 

86 

168.  I 

79-5 

46 

222.4 

105.2 

7 

(^.3 

3-0 

67 

60.  6     28.  6 

27 

1 14.  8 

54.3 

87 

169.0 

80.0 

47     223. 3 

105.6 

8 

7-2 

3-4 

68 

61.  5  !  29.  I 

28 

"5-7 

54-7 

88 

169.9 

80.4 

48 

224.2 

106.0 

9 

8.1 

3-8 

69 

62. 4  i  29.  5 

29 

116. 6 

55-2 

89 

170.9 

80.8 

49 

225.  I 

106.5 

10 

II 

9.0 

43 

70 

63-3  i  29.9 

30 

II7-5 

J5-^ 

90 

171. 8 

81.2 

5o_ 

226.0 

106.9 

9-9 

4.7 

71 

64.  2      30.  4 

131" 

1 18. 4 

56.0 

191 

172.7 

81.7 

251      226.9 

^07:3 

12 

10.8 

^■l 

72 

65.  I 

30.8 

32 

1 19- 3 

56.4 

92 

173.6 

82.1 

52     227. 8 

107.7 

13 

II. 8 

5.6 

73 

66.0 

31.2 

33 

120.  2 

56.9 

93 

174-5 

82.5 

53     228. 7 

108.2 

14 

12.7 

6.0 

74 

66.9 

31.6 

34 

121.  I 

57.3 

94 

175-4 

82.9 

54 

229.  6 

108.6 

15 

13-6 

6.4 

75 

67.8 

32.  I 

35 

122.  0 

57-7 

95 

176.3 

l^-i 

55     230. 5 

109.0 

16 

14.5 

6.8 

76 

68.7 

32.5 

36 

122.9 

5H 

96 

177.2 

83.8 

56     231.4 

109-5 

17 

15-4 

7-3 

77 

69.6 

32-9 

37 

123.8 

58.6 

97 

178.  I 

84.2 

57     232.3 

109.9 

.    18 

16.3 

7-7 

78 

70-  5     33-  3  1 

38 

124.8 

59- 0 

98 

179.0 

84.7 

58     233.2 

no.  3 

19 

17.2 

8.  I 

79 

71.4 

33-8 

39 

125.7 

59-4 

99 

179.9 

85.1 

59  '  234. I 

no.  7 

20 
21 

18. 1 
19.0 

8.6 

80 

72.3 

34-2 

40 

126.6 

59-9 

200 

180.8 

85-5 

60     235. 0 

III.  2 

9.0 

81 

73-2 

34-6 

141 

127.5 

60.3 

201 

181.  7 

85-9' 

261     235.9 

III. 6 

22 

19.9 

9-4 

82 

74. 1  !  35-  I 

42 

128.4 

60.  7 

02 

182.6 

86.4 

62  1  236,8 

112.  0 

23 

20.8 

9.8 

83 

75- 0  1  35-5 

43 

129.3 

61. 1 

03 

183.5 

86.8 

63  1  237.  7 

112. 4 

24 

21.7 

10.3 

84 

75-  9     35-  9 

44 

130.  2 

61.6 

04 

184.4 

87.2 

64  i  238.  7 

112.9 

25 

22.6 

10.7 

85 

76.8 

36-3 

45 

131.  I 

62.0 

05 

185.3 

87.6 

65  ,  239.6 

"3-3 

26 

23-5 

II.  I 

86 

77.7 

36.8 

46 

132.0 

62.4 

06 

186.2 

88.1 

66  ;  240,  5 

113- 7 

27 

24.4 

II-5 

87 

78.6 

37-2 

47 

132.9 

62.9 

07 

187.  I 

88.5 

67     241.4 

1 14.  2 

28 

25-3 

12.  0 

88 

79.6     37-6  1 

48 

133-8 

63-3 

08 

188.0 

88.9 

68  i  242.3 

1 14.  6 

29 

26.  2 

12.4 

89 

80.5 

38.1 

49 

134-7 

63.7 

09 

188.9 

89.4 

69     243.2 

115. 0 

30 

27.1 

12.8 

90 

81.4 

38.5 

50 

135-6 

64.  I 

10 

189.8 

89.8 

70  j  244.  I 

"5-4 

31 

28.0 

13-3 

91 

82.3 

38-9 

151 

136-5 

^64:6- 

211 

190.7 

90.  2 

271  i  245.0 

"5-9 

32 

28.9 

13-7 

92 

83.2 

39.3 

52 

137.4 

65.0 

12 

191. 6 

90.6 

72 

245-9 

1 16. 3 

33 

29.8 

14. 1 

93 

84.  I  1  39.  8 

53 

138.3 

65-4 

13 

192.5 

91.  I 

73 

246.8 

116.  7 

34 

30-7 

14-5 

94 

85.0  i  40.2 

54 

139.2 

65.8 

14 

193-5 

91.5 

74 

247.7 

117.  2 

35 

31.6 

15.0 

95 

85.  9     40.  6 

55 

140.  I 

66.3 

15 

194.4 

91.9 

75  i  248.6 

117.  6 

36 

32.5 

15-4 

96 

86.8     41.0 

56 

141.  0 

66.7 

16 

195-3 

92.4 

76     249. 5 

118.  0 

37 

33-4 

15.8 

97 

87.7  1  41.5 

57 

141-9 

67.1 

17 

196.2 

92.8 

77      ;      250.4 

1 18. 4 

38 

34-4 

16.2 

98 

88.6  i  41.9 

58 

142.8 

67.6 

18 

197.1 

93.2 

78    ;     251.3 

1 18.  9 

39 

35-3 

16.7 

99 

89-5 

42.3 

59 

143-7 

68.0 

19 

198.0 

93-6 

79 

252.2 

"9-3 

40 

36.2 

17. 1 

100 

90.4 

42.8 

60 

144.6 

68.4 

20 

198.9 

94-1 

80 

253.1 

1 19.  7 

120.  I 

41 

37-1 

17-5 

lOI 

91-3 

43-2 

161 

145-5 

68.8 

221 

199.8 

94-5 

281 

254.0 

42 

38.0 

18.0 

02 

92.2  !  43.6 

62 

146.4 

69.3 

22 

200.  7 

94-9 

82  !  254.9 

120.  6 

43 

38.9 

18.4 

03 

93. 1    44. 0 

63 

147.4 

69.7 

23 

201.6 

95-3 

83  1  255-8 

121. 0 

44 

39-8 

18.8 

04 

94. 0    44. 5 

64 

148.3 

70.  I 

24 

202.  5 

95.8 

84     256. 7 

121. 4 

45 

40.7 

19.2 

05 

94. 9    44. 9 

65 

149.2 

70.5 

25 

203.4 

96.  2 

85     257.6 

121.9 

46 

41.6 

19.7 

06 

95-  8     45-  3 

66 

150. 1 

71.0 

26 

204.3 

96.6 

86  1  258.5 

122.  3 

47 

42.5 

20. 1 

07 

96.  7     45-  7 

67 

151.0 

71.4 

27 

205.2 

97.1 

87     259.4 

122.7 

48 

43-4 

20.  5 

08 

97.  6     46.  2 

68 

151-9 

71.8 

28 

206.  I 

97-5 

88  1  260.3 

123.  I 

49 

44-3 

21,0 

09 

98.5     46.6 

69 

152.8 

72.3 

29 

207.0 

97.9 

89  ;  261.3 

123.  6 

50 
51 

45-_2 
46.  I 

21.4 
21.8 

10 

99.4     47.0 

70 

153.7 

72.7 

30 

207.9 

98.3 

90     262. 2 

124.0 

III 

IOO-3  !  47-5 

171 

154.6 

7?,-^ 

231 

208.8 

98.8 

291  ^  263.  I 

124.4 

52 

47.0 

22.  2 

12 

101.2  1  47.9 

72 

155-5 

73.5 

32 

209.7 

99.2 

92     264. 0 

124.8 

53 

47-9 

22,  7 

13 

102.  2     48.  3 

73 

156.4 

74.0 

33 

210.  6 

99.6 

93     264. 9 

125-3 

54 

48.8 

23.1 

14 

103.  I  i  48.  7 

74 

157.3 

74.4 

34 

211. 5 

100.  0 

94     265.8 

125-7 

55 

49-7 

23-5 

15 

104.0 

49.2 

75 

158.2 

74.8 

35 

212.4 

100.5 

95  •  266. 7 

126.  I 

56 

50.6 

23-9 

16 

104.9 

49.6 

76 

159- 1 

75-2 

36 

213.3 

100.  9 

96  '.  267.  6 

126.6 

57 

51-5 

24.4 

17 

105.8 

50.0 

77 

160.0 

75.7 

37 

214.2 

101.3 

97  1  268.  5 

127.0 

58 

52.4 

24.8 

18 

106.  7 

50.5 

78 

160.9 

76.1 

38 

215. 1 

101.8 

98 

269.4 

127.4 

59 

53.3 

25.2 

19 

107.6 

50-9 

79 

161. 8 

76.5 

39 

216.  I 

102.2 

99 

270.3 

127.8 

60 
Dist. 

54.2 

25.7 

20 

108.5 

51-3 

80 

162.  7 

77.0 

40 

217.0 

102.6 

300 

271.2 

128.3 

I 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

^ 

r.  E.  by  ] 

i.  U  E.         S 

E.  by  E.  34:  E. 

N 

W.  by  \ 

V  34:  w 

c 

.  W.  by  V 

^.  u  w. 

[F01-5M 

Points. 

Pag 

e208] 

TABLE  I. 

Difiference  of  Latitude  and  Departure  for 

2)4  Points. 

N.  N 

.  ^.J4 

E. 

N.  N.  W.  }i  W,                   S. 

S.  E. 

/2E. 

S 

.  s.  w.  ^  w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.5 

61 

53.8 

28.8 

121 

106.7     57- 0 

181 

159.6 

^5-3 

241 

212.5 

1 13.  6 

2 

1.8 

0.9 

62 

54-7 

29.2 

22 

107.6  i  57.5 

82 

160.  5  ! 

85.8 

42 

213.4 

114.  I 

3 

2.6 

1.4 

63 

55. 6     29.  7 

23    i    108.5    i    58-0 

83 ! 

161. 4  t 

86.3 

43 

214.3 

114-5 

4 

3-5 

1-9 

64 

56.4  ,  30.2 

24     109. 4  :  58.  5 

84 1 

162.3 

86.7 

44 

215.2 

115.0 

5 

4-4 

2.4 

65 

57.3     30-6 

25     no.  2     58.9 

85 

163.2 

87.2 

45 

216.  I 

115. 5 

6 

5-3 

2.8 

66 

58.2     31. 1 

26  I  III.  I  j  59.4 

86 

1 64.  0 

87.7 

46 

217.0 

116.0 

7 

6.2 

3-3 

67 

59.1     31.6 

27     :      112.  0     1     59.9 

87 

164.9 

88.2 

47 

217.8 

116.4 

8 

7-  I 

3-8 

68 

60. 0     32.  I 

28  ^  112.  9     60.3 

88 

165.8 

88.6 

48 

218.7 

116.9 

9 

7-9 

4.2 

69 

60. 9     32.  5 

29      113.  8  ■  60.  8 

89  1 

166.7 

89.  I 

49 

219.6 

117.4 

lO 

8.8 

4-7 

70 

61.7 
62.6 

33- 0 

30      114.  6  ; 

61-3  1 
61.8 

90^ 
191  i 

167.6 
168.4 

89.6 
90.0 

50 

220.  5 

117.8 

II 

9-7 

5-2 

71 

33-5 

131      115.  5  , 

251 

221.4 

118.  3 

12 

10.6 

5-7 

72 

63.5 

33-9 

32  '   116.  4     62.  2  1 

92 

169.3 

90.5 

52 

222.  2 

118.8 

13 

"•5 

6.1 

73 

64.4 

34-4 

33  \  "7-3     62.7 

93 

170.2 

91.0 

53 

223.1 

119.  3 

14 

12.3 

6.6 

74 

65.3 

34.9 

34  :   1 18.  2      63.2 

94 

171-1  : 

91-5 

54 

224.0 

119.  7 

'5 

13.2 

7-1 

75 

66.  I 

35-4 

35  i  "9-1     63.6 

95 

172.0  ] 

91.9 

55 

224.9 

120.2 

i6 

14. 1 

7-5 

76 

67.0 

35  8 

36     119. 9     64.  I 

96  i 

172.9 

92.4 

56 

225.8 

120.  7 

17 

15.0 

8.0 

77 

67.9 

36-3 

37  i  120. 8  :  64. 6 

97 

173-7  : 

92.9 

57 

226.7 

121. 1 

i8 

15-9 

8.5 

78 

68.  8     36.  8 

38  j  121.  7    65.1 

98 

174.6 

93-3 

58 

227.5 

121.6 

19 

16.8 

9.0 

79 

69.  7  '  37.  2 

39  I  122.6  t  65.5 

99 

175-5 

93-8 

59 

228.4 

122.  I 

j 

20 

17.6 

9.4 

80 

70.6 

37-7 

40     123. 5     66. 0 

200 

176.4 

94-3 

60 

229.3 

122.6 

21 

18.5 

9-9 

81 

71.4 

38.2- 

141      124.  4  i  66.  5 

201 

177-3    : 

94.8 

261 

230.2 

123.0 

22 

19.4 

10.4 

82 

72.3 

38.7 

42      125.2     66.9 

02  1 

178.  I 

95-2 

62 

231.  I 

123.5 

23 

20.3 

10.8 

83 

73-2 

39-1 

43  '  126.  I  !  67. 4 

03  '• 

179.0 

95-7 

63 

231-9 

124.0 

24 

21.2 

"•3 

84 

74.  I     39-  6 

44  '  127.0  !  67.9 

04 

179.9 

96.  2 

64 

232.8 

124.4 

25 

22.0 

II. 8 

85 

75.  0  j  40.  I 

45    :    127.9   ;   68.4 

05 

180.8 

96.6 

65 

233-7 

124.9 

26 

22.9. 

12.3 

86 

75. 8  :  40.  5 

46  !   128.8  1  68.8 

06 

181.  7 

97.1 

66 

234-6 

125.4 

27 

23.8 

12.7 

87 

76.7     41.0 

47  :  129.6     69.3 

07 ; 

182.6 

97-6 

67 

235-5 

125.9 

28 

24.7 

13.2 

88 

77.6 

41-5 

48  j  130-  5 

69.8 

08 

183.4 

98.  I 

68 

236.4 

126.3 

29 

25.6 

13-7 

89 

78.5 

42.0 

49  1  131-4 

70.  2 

09 

184.3 

98.5 

69 

237.2 

126.8 

30 
31 

26.5 

14. 1 

90 

79-4 

42.4 

50     132. 3      70. 7 

10 1 

185.2 

99.0 

70 

238.1 

127.3 

27.3 

14.6 

91 

80.  3  I  42. 9 

151  !  133-2  1  71-2 

^11    ; 

186.  I 

99-5 

271 

239.0 

127.7 

32 

28.2 

15- 1 

92 

81. 1  ;  43.4 

52    1    134.  I    !    71-7 

12 

187.0 

99-9 

72 

239-9 

128.2 

33 

29. 1 

15.6 

93 

82.0  ,  43.8 

53     134-  9     72.  I 

13 

187.8 

100.  4 

73      240. 8 

128.7 

34 

30.0 

16.0 

94 

82.9 

44-3 

54     135.8     72.6 

14 

188.7 

100.9 

74 

241.6 

129.2 

35 

30-9 

16.5 

95 

83.8 

44.8 

55  i  136.  7  :  73-1 

15 

189.6 

101.4 

75 

242.5 

129.6 

36 

31-7 

17.0 

96 

84.7 

45-3 

56  i  137-6  '  73-5 

16 

190.5 

101.8 

76 

243-4 

130.  1 

37 

32.6 

17.4 

97 

85.  5  i  45-  7 

57  :    138.5      74-0 

17 

/9I.4 

102.3 

77     244. 3 

130.  6 

38 

33-5 

17.9 

98 

86.4  !  46.2 

58  :  139-3    74.5 

18 

192.3 

102.  8 

78     245. 2 

131.0 

39 

34-4 

18.4 

99 

87.  3  1  46.  7 

59  !  140-2     75-0 

19 

193- I 

103.  2 

79 

246.  I 

131.5 

40 

35-3 

18.9 

100 

88.2 

47.1 

60  1  141. 1     75-4 

20 

194.0 

J°3-7^ 

80 

246.9 

132.0 

41 

36.2 

19.3 

lOI 

89.1 

47.6 

161      142.0     75.9 

221 

194.9 

104.  2 

281 

247-8 

132.5 

42 

37- 0 

19.8 

02 

90.0 

48.  I 

62     142.9  :  76.4 

22 

195.8 

104.7 

82 

248.7 

132.9 

43 

37-9 

20.3 

03 

90.8  1  48.6 

63  ;  143-  8     76. 8 

23 

196.7 

105. 1 

83      249. 6 

133.4 

44 

38.8 

20.7 

04 

91.7     49.0 

64  j  144. 6  1  77.  3 

24 

197.6 

105.6 

84     250. 5 

133-9 

45 

39-7 

21.  2 

05 

92.6  \  49.5 

65  !  145-5  1  77-8 

25 

198.4 

106. 1 

85      251.3 

134-3 

46 

40.  6 

21.7 

06 

93-5  1  50.0 

66  ;   146.  41  78.  3 

26 

199-3 

106.5 

86     252.2 

134.8 

47 

41-5 

22.  2 

07 

94.4  1  50-4 

67  ;   147-  3  1   78-  7 

27 

200.  2 

107.0 

87     253.  1 

135-3 

48 

42.3 

22.6 

08 

95-2  I  50.9 

68     148.  2  !  79.  2 

28 

201.  I 

107-5 

88     254.0 

135.8 

49 

43-2 

23.1 

09 

96.1 

51-4 

69  !  149-  0  ;  79-  7 

29 

202.0 

107.9 

89 

254-9 

136.2 

50 

44.  I 

23.6 

10 

97.0 

51-9 

70  ]  149. 9  !  80.  I 

30 

202.8 

108.4 

_„9° 

255-8 

136.7 

-■ 

51 

45.0 

24.  0 

III 

97-9 

52-3 

171 

150.8  j  80.6 

231 

203.  7 

108.9 

291 

256.6 

137.2 

52 

45-9 

24-5 

12 

98.8 

52.8 

72     151. 7     81. 1 

32 

204.6 

109.4 

92 

257-5 

137-6 

53 

46.7 

25  0 

13 

99.  7     53-  3 

73     152.6     81.6 

33 

205-  5 

109. 5i 

93 

258.4 

138. 1 

54 

47.6 

25.5 

14 

100.  5     53.  7 

74  ;  153-5  1  82.0 

34 

206.4 

1 10.  3 

94 

259-3 

138.6 

55 

48.5 

25-9 

15 

101.4     54.2 

75  :  154-3  1  82.5 

35 

207.3 

no.  8 

95 

260.2 

139- I 

56 

49.4 

26.4 

16 

102. 3 :  54. 7 

76  ,  155.2  '  83.0 

36 

208.1 

III. 2 

96 

261.0 

139-5 

57 

50.3 

26.  9 

17 

103.2  55.2 

77  '  156.  I  j  83.4 

37 

209. 0 

HI. 7 

97 

261.9 

140.0 

58 

51-2 

27.3 

18 

104. 1  1 55.6 

78  :  157.0  !  83.9 

38 

209.9 

112.  2 

98 

262.8 

140.5 

59 

52.0 

27.8 

19 

104. 9 1 56. 1 

79     157-9  i  84.4 

39 

210.8 

112.  7 

99 

263.7 

140.9 

60 

52.9 

28.3 

20 

105.8  56.6 

1 

80 

1  158.  7 

84.9 

40 

211.  7 

113.1 

300 

264.6 

141.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.         Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

N. 

E.  byE 

KE. 

s. : 

E.  by  E.  }i  E. 

N.  W.  by  W.  >^  W 

^     s 

.  W.  by  A 

A^.  >^  W 

^        [For  S'A 

Points. 

TABLE  I. 

Page  209  | 

Difference  of  Latitude  and  Departure  for 

2^  Points. 

N.  N.  E.  ^  E. 

N.  N.  W.  ^ 

w.             s 

S.E. 

XE. 

s.  s.  w.  ^  w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
52.3 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.5 

61 

31.4 

121 

103.8 

62.2 

181 

155-2 

93-1 

241 

206.  7 

123.9 

2 

I.  7         I.O 

62 

53-2 

31-9 

22 

104.  6     :     62.  7 

82 

156. 1 

93-6 

42 

207.  6 

124.4 

3 

2.6        1.5 

63 

54-0 

32.4 

23 

105.  5     63.  2 

^3 

157-0 

94-1 

43 

208.4 

124.9 

4 

3.4    !       2.1 

64 

54.9 

32.9 

24 

106.  4     63.  7 

84 

157-8 

94-6 

44 

209.3 

125.4 

5 

4-3  !     2.6 

65 

55-8 

33-4 

25 

107.  2     64.  3 

85 

158.7 

95-1 

45 

210.  I 

126.0 

6 

5-  I       3-  I 

66 

56.6 

33-9 

26 

108.  I  I  64.  8 

86 

159-5 

95-6 

46 

211. 0 

126.  5 

7 

6.0       3.6 

67 

57.5 

34-4 

27 

108.9  '  65.3 

87 

160.4 

96.  I 

47 

211.  9 

127.0 

8 

6. 9  j    4.  I 

68 

58.3 

35- 0 

28 

109,8     65. 8 

88 

161.  3 

96.7 

48 

212.  7 

127.5 

9 

7.  7  :    4.  6 

69 

59.2 

35-5 

29 

no.  6  ;  66.3 

89 

162. 1 

97-2 

49 

213.6 

128.  0 

lO 

8.6       5.1 

70 

60.0 

36.  0 

30 

III. 5 
112. 4 

66.8 

90 

163.0 

97-7 

50 

214.4 

128.5 

II 

9-4 

5.7 

71 

60,  9 

36.5 

131 

67.3 

191 

163.8 

98.2 

251 

215-3 

129.0 

12 

10.  31     6.  2 

72 

61.8 

37- 0 

32 

113. 2     67.9 

92 

164.7 

98.7 

52 

216.  I 

129.  6 

13 

II. 2       6.7 

73 

62.6 

37-5 

33 

114.  I 

68.4 

93 

165-5 

99-2 

53 

217.  0 

130-1 

14 

12.  0       7.  2 

74 

63-5 

38.0 

34 

1 14.  9 

68.9 

94 

166.4 

99-7 

54 

217.9 

130.  6 

15 

12.9  I     7.7 

75 

64.3 

38.6 

35 

115.  8 

69.4 

95 

167.3 

100.  3 

55 

218.  7 

131-1 

i6 

13.7       8.2 

76 

65.2 

39-1 

36 

116.  7 

69.9 

96 

168. 1 

100.  8 

56 

219.  6 

131-6 

17 

14.  6       8.  7 

77 

66.0 

39-6 

37 

117.5 

70.4 

97 

169.0 

101.3 

57 

220.  4 

132.  I 

i8 

15-4       9-3 

78 

66.9 

40.  I 

38 

118.  4 

70.9 

98 

169.8 

101.8 

58 

221.3 

132.6 

19 

16.3       9.8 

79 

67.8 

40.  6 

39 

119.  2 

71-5 

99 

170.7 

102.3 

59 

222.  2 

133-2 

20 

17.2      10.3 

80 

68.6 

41.  I 

40 

120.  I 

72.0 

200 

171-5 

102.8 

60 

223.0 

133-7 

21 

18.0  .  10. '8 

81 

69.5 

41.6 

141 

120.  9 

72'.  5~ 

201 

172.4 

103.3 

261 

223.9 

134.2 

22 

18.9      II. 3 

82 

70.3 

42.2 

42 

121. 8 

73-0 

02 

173-3 

103.8 

62 

224.7 

134-7 

23 

19.7  1  II.  8 

!^ 

71.2 

42.7 

43 

122.  7 

73-5 

03 

174. 1 

104.4 

^3 

225.  6 

135-2 

24 

20.  6      12.  3 

84 

72.  0 

43-2 

44 

123-5 

74-0 

04 

175-0 

104.9 

^ 

226.  4 

135-7 

25 

21.4      12.9 

85 

72.9 

43-7 

45 

124.4 

74-5 

05 

175-8 

105.4 

65 

227.3 

136.  2 

26 

22.3      13.4 

86 

73.8 

44.2 

46 

125.  2 

75-1 

06 

176.7 

105.9 

66 

228.  2 

136.8 

27 

23-  2  .  13.  9 

87 

74.6 

44-7 

47 

126.  I 

75-6 

07 

177-5 

106.4 

67 

229.  0 

137-3 

28 

24.  0  ,  14.  4 

88 

75-5 

45-2 

48 

126.9 

76. 1 

08 

178.4 

106.9 

68 

229.  9 

137-8 

29 

24.9      14.9 

89 

76.3 

45-8 

49 

127.8 

76.6 

09 

179-3 

107.4 

69 

230.7 

138.3 

30 

25-7  1  15-4 

90 

77.2 

46.3 

50 

128.7 

77.1 

10 

180.  I 

108.0 

70 

231-6 

138.8 

31 

26.  6  '  15.9 

91 

78. 1 

46.8 

151 

129.  5 

77-6 

2tl 

181. 0 

108.5 

271 

232.4 

139-3 

32 

27.4      16.5 

92 

78.9 

47-3 

52 

130.4 

78.1 

12 

181. 8 

109.0 

72 

233-3 

139-8 

33 

28.3      17.0 

93 

79.8 

47.8 

53 

131-2 

78.7 

13 

182.7 

109-5 

73 

234.2 

140.4 

34 

29.2  I  17.5 

94 

80.6 

48.3 

54 

132.  I 

79-2 

14 

183.6 

no.  0 

74 

235-0 

140.9 

35 

30.  0  '  18.  0 

95 

81.5 

48.8 

55 

132.9 

79-7 

15 

184.4 

no.  5 

75     235. 9 

141-4 

36 

30.9      18.5 

96 

82.3 

49-4 

56 

133-8 

80.2 

16 

185.3 

IIl.O 

70     236.  7 

141.9 

37 

31.7  ,  19.0 

97 

83.2 

49.9 

57 

134.7 

80.  7 

17 

186.  I 

III. 6 

77     237.6 

142.4 

38 

32-6  1  19.5 

98 

84.1 

50.4 

58 

135-5 

81.2 

18 

187.0 

112.  I 

78 

238.4 

142.9 

39 

33-  5     20.  I 

99 

84.9 

50.9 

59 

136.4 

81.7 

19 

187.8 

112.  6 

79 

239-3 

143-4 

40 

34.3     20.6 

100 

85.8  ,  51.4  1 

60 

137.2 

82.3 

20 

188.7 

113-1 

80 

240.  2 

143-9 

41 

35.2        2[.I 

lOI 

86.6  •  51.9  1 

161 

138.  I 

82.8 

221 

189.6 

113-6 

281 

241.0 

144-5 

42 

36.  0  !  21.  6 

02 

87.5     52. 

62 

139.0 

83-3 

22 

190.4 

114.  I 

82 

241.9 

145.0 

43 

36.9  '  22.  I 

03 

88.3     53.0 

f^ 

139-8 

83.8 

23 

191-3 

114.  6 

^3 

242.7 

145-5 

44 

37.  7     22.  6 

04 

89.  2     53-  5 

64 

140.7 

84-3 

24 

192.  I 

115-  2 

84 

243.6 

14O.  0 

4^ 

38. 6     23.1 

05 

90.  I     54. 0 

65 

141-5 

84.8 

^5 

193-0 

115-7 

85 

244-5 

146.5 

46 

39-5     23.6 

06 

90.  9     54-  5 

66 

142.4 

85-3 

26 

193-8 

116.  2 

86 

245-3 

147.0 

47 

40.3  :  24.2 

07 

91.8  '  55.0 

67 

143-2 

85-9 

27 

194-7 

116.  7 

87 

246.  2 

147-5 

48 

41.2     24.7 

08 

92.  6 

55-5 

68 

144.  I 

86.4 

28 

195-6 

117.  2 

88 

247.0 

148.  I    i 

49 

42.  0     25.  2 

09 

93-5 

56.0 

69 

145.0 

86.9 

29 

196.4 

117.7 

89 

247.9 

148.6 

50 

42.9 

25.7 
26.  2 

10 
III 

94-4 
95-2 

56.6 

70 

145-8 

87-4 

30 

197-3 

118.2 

^.90 

248.7 

149.1 

51 

43-7 

57.  I 

171 

146.7 

!^-9 

231 

198.  I 

118.  8 

291      249. 6 

149.6 

52 

44.  6  1  26.  7 

12 

96.1      57.6 

72 

147-5 

88.4 

32 

199-0 

119-3 

92     250.5 

150.  I 

53 

45.  5     27.  2 

13 

96.9     58.1 

73 

148.4 

88.9 

33 

199-9 

1 19.  8 

93     251.3 

150.6 

54 

46.  3     27.  8 

14 

97-  8     58.  6 

74 

149.2 

89.5 

34 

200.  7 

120.3 

94     252. 2 

151-1 

55 

47.  2     28.  3 

15 

98.  6     59.  I 

75 

150.  I 

90.  0 

35 

201.6 

120.8 

95     253.0 

151.7 

56 

48.  0     28.  8 

16 

99-  5     59-6 

76 

151.  0     90.  5 

36 

202.  4 

121.3 

96     253. 9 

152.  2 

57 

48.9     :     29.3 

17 

100.  4 

60.  2 

77 

151. 8     91.0 

37 

203-3 

121. 8 

97  ,  254-  7 

152-7 

58 

49.   7    ;    29.  8 

iS 

lOI.  2 

60.  7 

7^ 

152-7 

91-5 

38 

204.  I 

122.4 

98     ;    255.  6 

153-2 

59 

50.  6     30.  3 

19 

102.  I 

61.2 

79 

153-5 

92.0 

39 

205.  0 

122.  9 

99     256. 5 

153-7 

60 

Si-5 

30.8 

20 

102.9 

61.  7 

80 

154-4 
Dep. 

92.5 
Lat. 

40 

205-9 

123-4 

300     257.3 

154.2 

Dist. 

Dep.         Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dist. 

Dep. 

Lat. 
V.  )i  W. 

Dist.  1     Dep. 

Lat. 
oints. 

^ 

r.  E.  by  E.  X  E.        S 

E.by  E.  >4:  E. 

N. 

W.  by  W.  X  W 

'_           c 

>.  W.  by  \ 

[F 

or  5X  r 

14   B 


Pag 

e210 

TABLE  I. 

Difference  of  Latitude  and 

Departure  for  3  Points 

>• 

N. 

E.  by  N. 

N.  "W 

\  by  N. 

S.  E. 

byS. 

S.  W.  by  S. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist, 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

50-7 

33.9 

121 

100.6 

P-l 

181 

150-5 

100.6 

241 

200.4 

133.9 

2 

1.7 

I.  I 

62 

51.6 

34-4 

22 

101.4 

67.8 

82 

151-3 

lOI.  I 

42      201.2 

134-4 

3 

2-5 

1-7 

63 

52.4 

35- 0 

23 

102.3 

68.3 

83 

152.  2 

lOi.  7 

43  1  202.0 

135-0 

4 

3-3 

2.2 

64 

53-2     35-6  1 

24 

103.  I 

68.9 

84 

153-0 

102.2 

44 

202.9 

135-6 

5 

4.2 

2.8 

^5 

54-0 

3&.I 

25 

103.9 

69.4 

^5 

153-8 

102.8 

45 

203.7 

136.1 

6 

5-2 

3-3 

66 

54-9 

36.7 

26 

104.8 

70.0 

86 

154-7 

103.3 

46 

204.5 

136.7 

7 

5-8 

3-9 

67 

55-7 

37-2 

27 

105.  6 

70.6 

87 

155-5 

103-9 

47 

205.4 

137.2 

8 

6.7 

4.4 

68 

56.5     37.8 

28 

106.4 

71.  I 

88 

156.3 

104.4 

48     206. 2 

137.8 

9 

7-5 

5-0 

69 

57.4  !  38.3 

29 

107.3 

71.7 

89 

157.  I 

105.  0 

49 

207.0 

138.3 

lO 

8.3 

5-6 

70 

58.2 

3W-9 

30 

108.  I 

72.  2 

90 

158.0 

105.6 

50 

207.9 

138.9 

II 

9.1 

6.1 

71 

59- 0 

39-4 

131 

108.  9 

72.8 

191 

158.8 

io67i 

251 

208.7 

139.4 

12 

10. 0 

6.7 

72 

59-9 

40.0 

32 

109.  8 

73-3 

92 

159.6 

106.  7 

52 

209-5 

140.0 

13 

10.8 

7.2 

73 

60.  7 

40.6 

33 

no.  6 

73-9 

93 

160.5 

107.2 

53 

210.4 

140.6 

14 

II. 6 

7.8 

74 

61.5 

41.  I 

34 

III. 4 

74-4 

94 

161. 3 

107.8 

54 

211.  2 

141.  1 

15 

12.5 

8.3 

75 

62.4     41.7 

35 

112.  2 

75-0 

95 

162.  I 

108.3 

55  j  212.0 

141.7 

16 

^3-3 

8.9 

76 

63.2  ,  42.2 

36 

113. 1 

75-6 

96 

163.0 

108.  9 

56     212. 9 

142.  2 

17 

14.  I 

9-4 

77 

64.0 

42.8 

37 

113- 9 

76.1 

97 

163.8 

109.4 

57  1  213.7 

142.8 

18 

15.0 

10. 0 

78 

64.9 

43-3 

38 

114.  7 

76.7 

98 

164.6 

no.  0 

58  \  214.5 

143.3 

19 

15.8 

10.6 

79 

65.7 

43-9 

39 

115.6 

77-2 

99 

165.5 

no.  6 

59 

215.4 

143-9 

20 

16.6 

II.  I 

80 

66.5 

44.4 

40 

1 16. 4 

77-8 

200 

166.3 

in.  I 

60 

216.2 

144.4 

21 

17.5 

II. 7 

81 

67.3 

45.0 

141 

117.  2 

78.3 

201 

167.  I 

111.7 

261 

217.0 

145. 0 

22 

18.3 

12.2 

82 

68.  2  i  45.  6 

42 

118.  I 

78.9 

02 

168.0 

112.  2 

62 

217.8 

145.6 

23 

19.  I 

12.8 

83 

69.0 

46. 1 

43 

118.9 

79-4 

03 

168.8 

112.8 

63  1  218.  7 

146.  I 

24 

20.0 

13-3 

84 

69.8 

46.7 

44 

119-7 

80.0 

04 

169.  6 

^^3-3 

64  1  219.5 

146.7 

25 

20.8 

13-9 

85 

70.7 

47.2 

45 

120.6 

80.6 

05 

170.5 

"3-9 

65 

220.3 

147.2 

26 

21.6 

14.4 

86 

71-5 

47.8 

46 

121. 4 

81.  I 

06 

171-3 

114.4 

66 

221.2 

147.8 

27 

22,4 

15.0 

87 

72.3 

48.3 

47 

122.2 

81.7 

07 

172.  I 

115. 0 

67 

222.0 

148.3 

28 

23-3 

15-6 

88 

73-2 

48.9 

48 

123. 1 

82.2 

08 

172.9 

115.6 

68 

222.8 

148.9 

29 

24.1 

16.  I 

89 

74.0 

49.4 

49 

123.9 

82.8 

09 

173-8 

116.  I 

69 

223.7 

149.4 

30 

24.9 

16.  7 

90 

74.8 

50.0 

50 

124.7 

83-3 

10 

174.6 

116.  7 

70 

224.5 

150.0 

31 

25.8 

17.2 

91 

75-7 

50.6 

151 

125.6 

"83.9 

211 

175-4 

117.  2 

271 

225.3 

150.6 

32 

26.6 

17.8 

92 

76.5 

51. 1 

52 

126.4 

84-4 

12 

176.3 

117.8 

72 

226.2 

151.  I 

33 

27.4 

18.3 

93 

77-3 

51-7 

53 

127.  2 

85.0 

13 

177. 1 

118.3 

73 

227.0 

151-7 

34 

28.3 

18.9 

94 

78.  2  ,  52.  2 

54 

128.0 

85.6 

14 

177.9 

118.9 

74  :  227,8 

152.2 

35 

29.  I 

19.4 

95 

79- 0  .  52.8 

55 

128.9 

86.1 

15 

178.8 

119.4 

75  ;  228.  7 

152.8 

36 

29.9 

20.0 

96 

79-8  i  53-3 

56 

129.7 

86.7 

16 

179.6 

120.  0 

76     229. 5 

153.3 

37 

30.8 

20,6 

97 

80.7 

53-9 

57 

130-5 

87.2 

17 

180.4 

120.6 

77  1  230.3 

153.9 

38 

31.6 

21.  I 

98 

81.5 

54-4 

58 

131-4 

U-^ 

18 

181. 3 

121.  1 

78     231. 1 

154.4 

39 

32.4 

21.7 

99 

82.3  ,  55- 0 

59 

132.2 

88.3 

19 

182. 1 

121.  7 

79     232. 0 

155.0 

40 

33-3 

22.2 

100 

83.1 

55.6 

60 

133-0 

88.9 

20 

182.9 

122.2 

80     232. 8 

155.6 

41 

34-1 

22.8 

lOI 

84.0 

56.1 

161 

133-9 

89.4 

221 

183.8 

122.8 

281  1  233.6 

156.  I 

42 

34-9 

23-3 

02 

84.  8  i  56.  7 

62 

134-7 

90.0 

22 

184.6 

123-3 

82  ':  234.  5 

156.7 

43 

35.8 

23-9 

03 

85.6  j  57.2 

63 

135-5 

90.6 

23 

185.4 

123-9 

83  :  235.3 

157.2 

44 

36.6 

24.4 

04 

86.5      57.8 

64 

136.4 

91. 1 

24 

186.2 

124.4 

84     236.  I 

157.8 

45 

37-4 

25.0 

05 

87.  3  i  58.  3 

65 

137-2 

;  91-7 

25 

187.  I 

125.0 

85  '  237.0 

158.3 

46 

38.2 

25.6 

06 

88.  I  :  58.  9 

66 

138.0 

92.2 

26 

'     187.9 

125.6 

86     237.8 

158.9 

47 

39-1 

26.  I 

07 

89.  0     59.  4 

67 

138.9 

92.8 

27 

188.  7 

126.  I 

87  ;  238.6 

159.4 

48 

39-9 

26.  7 

08 

89.8     60.0 

68 

139-7 

93-3 

28 

189.  6 

126.  7 

88     239.5 

160.0 

49 

.    40.7 

27.2 

09 

90.  6     60.  6 

69 

140-5 

93-9 

29 

1     190. 4 

127.  2 

89     240. 3 

160.6 

50 

41.6 

27.8 

10 

91.  5  ,  61.  I 

70 

141- 3 

94-4 

30 

191.  2 

127.8 

90  ,  241.  1 

161.  1 

51 

i     42. 4 

28.3 

III 

92.3 

61.7 

171 

142.2 

1  95-0 

231 

192. 1 

128.3 

291      242. 0 

161,  7 

52 

!     43-2 

28.9 

12 

93-1 

62.2 

72 

143.0 

95-6 

32 

192.9 

128.9 

92     242. 8 

162.2 

53 

:  44- 1 

29.4 

13 

94.0 

62.8 

73 

i  143-8 

96. 1 

33 

193-  7 

129.4 

93  1  243.6 

162.8 

54 

44-9 

30.0 

14 

1     94.8 

63.3 

74 

144.7 

96.7 

34 

194.6 

130.0 

94     244. 5 

163.3 

55 

45-7 

30.6 

15 

95-  6     63.  9 

75 

145-5 

97-2 

35 

195.4 

130.6 

95  :  245.3 

163.9 

.56 

'     46.6 

31- I 

16 

96. 5     64. 4 

76 

146.3 

97.8 

36 

196. 2 

131.  I 

96     246.  I 

164.4 

57 

47-4 

31-7 

17 

97.3     65.0 

77 

147.2 

98-3 

37 

197.  I 

131- 7 

97     246. 9 

165.0 

58 

48.2 

32.2 

18 

98.  I      65.  6 

78 

148.0 

98.9 

38 

197.9 

132.2 

98     247. 8 

165.6 

59 

49.1 

32.8 

19 

1     98.  9  ;  66.  I 

79 

148.8 

99-4 

39 

198.7 

132.8 

99     248.6 

166.  I 

60 

!     49-9 

33-3 

20 

99-8 

66.7 
Lat. 

80 

149.7 

100.  0 

40 

199.6 

133-3 

300     249. 4 

166.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

i    Lat. 

1 

Dist. 

j     Dep. 

Lat. 

Dist.      Dep. 

Lat. 

N.  E.  1 

jy  E. 

S.  E.  by  E. 

N.  W.  b 

yW. 

S.  W.  by 

W.                [For  5  Po 

ints. 

TABLE  I. 

[Page  211  j 

Difference  of  Latitude  and  Departure  for  ^X  Points. 

'N 

E.U 

N. 

N.  W 

■  H^ 

r. 

S. 

E.)( 

s. 

( 

5.  W. 

3JS. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

49.0 

36.3 

121 

97.2 

72.1 

181 

145-4 

107.8 

241 

193.6 

143.6 

2 

1.6 

I.  2 

62 

49.8 

36.9 

22 

98.0 

72.7 

82 

146.2 

108.4 

42 

194.4 

144.2 

3 

2.4 

1.8 

63 

50.6 

37-5 

23 

98.8 

73.3 

83 

147.0 

109.0 

43 

195.2 

144.8 

4 

3-2 

2.4 

64 

51-4 

38.1 

24 

99.6 

73-9 

84 

147.8 

109.6 

44 

196.0 

145.4 

5 

4.0 

3-0 

65 

52.  2 

38.7 

25 

100.4 

74.5 

8S 

148.6 

no.  2 

45 

196.8 

145.9 

6 

4.8 

3.6 

66 

53- 0 

39-3 

26 

loi.  2 

75-1 

86 

149-4 

no.  8 

46 

197-6 

146.5 

7 

5-6 

4.2 

67 

538 

39-9 

27 

102.  0 

75.7 

87 

150.2 

III. 4 

47 

198.4 

147.  I 

8 

6.4 

4.8 

68 

54-6 

40  5 

28 

102.8 

76.  2 

88 

151.0 

112. 0 

48 

199.2 

147.7 

9 

7-2 

5-4 

69 

55-4 

41. 1 

29 

103.6 

76.8 

89 

151. 8 

112.6 

49 

200.0 

148.3 

lO 

8.0 

6.0 

70 

56.2 

41.7 

30 

_I04^ 

77-4 

90 

152.6 

113-2 

SO 

200.8 

148.9 

II 

8.8 

6.6 

71 

57- 0 

42.3 

131 

105.  2 

78.0 

191 

^153.4 

113-8 

251 

201.6 

149.  5 

12 

9.6 

7.1 

72 

57.8 

42.9 

32 

106.0 

78.6 

92 

154.2 

114.4 

52 

202.4 

150. 1 

13 

10.4 

7-7 

73 

58.6 

43-5 

33 

106.8 

79.2 

93 

155-0 

115.0 

53 

203.  2 

150.7 

14 

II. 2 

8-3 

74 

59-4 

44.1 

34 

107.6 

79-8 

94 

155-8 

115.6 

54 

204.0 

151.3 

'5 

12.0 

8.9 

75 

60.  2 

44.7 

'35 

108.4 

80.4 

95 

156.6 

116.  2 

55 

204.  8 

151.9 

i6 

12.9 

9-5 

76 

61.0 

45-3 

36 

109.  2 

81.0 

96 

157.4 

1 16.  8 

56 

205.6 

152.5 

17 

13-7 

10.  I 

77 

61.8 

45-9 

37 

no.  0 

81.6 

97 

158.2 

117.4 

57 

206.4 

153.1 

i8 

14-5 

10.7 

78 

62.  7 

46.5 

38 

1 10.  8 

82.2 

98 

159-0 

117.9 

58 

207.  2 

153.7 

'9 

15-3 

II-3 

79 

63.5 

47.1 

39 

III. 6 

82.8 

99 

159.8 

118.5 

59 

208.  0 

154-3 

20 

16. 1 

II. 9 

80 

64-3 

47-7 

40 

112. 4 

83.4 

200 

160.  6 

119.  I 

60 

208.8 

154.9 

21 

16.9 

12.5 

81 

65.1 

48.3 

J41 

113-3 

84.0 

201 

161. 4 

119.7 

261 

209.6 

155-5 

22 

17.7 

13-1 

82 

65-9 

48.8 

42 

114.  I 

84.6 

02 

162.2 

120.3 

62 

210.4 

156. 1 

23 

18.5 

13-7 

83 

66.7 

49-4 

43 

1 14. 9 

^^ 

03 

163.  I 

120.9 

P 

211.  2 

156.7 

24 

19.3 

14-3 

84 

67.5 

50.0 

44 

"5-7 

85.8 

04 

163.9 

121. 5 

64 

212.0 

157-3 

25 

20.  I 

14.9 

85 

68.3 

50.6 

45 

116.  5 

86.4 

05 

164.7 

122.  I 

65 

212.8 

157.9 

26 

20.9 

IS- 5 

86 

69.  I 

51-2 

46 

"7-3 

87.0 

06 

165.5 

122.  7 

66 

213-7 

158.5 

27 

21.7 

16.  I 

87 

69.9 

51.8 

47 

118. 1 

87.6 

07 

166.3 

123.3 

67 

214.5 

159.1 

28 

22.5 

16.  7 

88 

70.7 

52.4 

48 

1 18. 9 

88.2 

08 

167.  I 

123.9 

68 

215-3 

159.  6 

29 

23-3 

17-3 

89 

71-5 

53-0 

49 

119.  7 

88.8 

09 

167.9 

124.5 

69 

216.  I 

160.2 

30 

24.1 

17.9 

90 

72.3 

53.6 

50 

120.  5 

89.4 

10 

168.7 

125  I 

70 

216.9 

160.8 

31 

24.9 

18.5 

91 

73-1 

54-2 

151 

121.  3" 

90.0 

211 

169.  5 

125.7 

271 

217.7 

161. 4 

32 

25- 7 

19. 1 

92 

73-9 

54.8 

52 

122.  I 

90.5 

12 

170.3 

126.3 

72 

218.5 

162.0 

33 

26.  5 

19.7 

93 

74.7 

55-4 

53 

122.  9 

91.  I 

T  1 

171.  I 

126.9 

73 

219.3 

162.6 

34 

27-3 

20.3 

94 

75-5 

56.0 

54 

123-7 

91.7 

14 

171. 9 

127.5 

74 

220.  I 

163.2 

35 

28.1 

20.8 

95 

76.3 

56.6 

55 

124.5 

92.3 

15 

172.7 

128.  I 

75 

220.9 

163.8 

36 

28.9 

21.4 

96 

77.1 

57-2 

56 

125.3 

92.9 

16 

173.  5 

128.7 

76 

221.  7 

164.4 

37 

29.7 

22.0 

97 

77.9 

57.8 

57 

126.  I 

93.5 

17 

174-3 

129.3 

77 

222.  5 

165.0 

3S 

30-5 

22  6 

98 

78.7 

58.4 

58 

126.9 

94. 1 

18 

17s- I 

129.9 

78 

223.3 

165.6 

39 

31-3 

23.  2 

99 

79-5 

59- 0 

59 

127.7 

94-7 

19 

175-9 

130.5 

79 

224.  I 

166.2 

40 

32.1 

23.8 

100 

80.3 
81.  I 

59-6 

60 

128.5 
129.  3 

95-3 

20 

176.7 

131.  I 

131.6 

80 

224.9 

166.8 

41 

32.9 

24.4 

lOI 

60.  2 

161 

95.9 

221 

177-5 

281 

225.7 

167.4 

42 

33-7 

25.0 

02 

81.9 

60.8 

62 

130.  I 

96.5 

22 

178.3 

132.2 

82 

226.5 

168.0 

43 

34-5 

25.6 

03 

82.7 

61.4 

63 

130.9 

97.1 

23 

179.  I 

132.8 

83 

227.3 

168.6 

44 

35-3 

2O.  2 

04 

83.5 

62.  0 

64 

131.  7 

97.7 

24 

179-9 

133.4 

84 

228.  I 

169.2 

45 

36.1 

26.8 

"5 

84.3 

62.5 

65 

132.5 

98.3 

25 

180.7 

134.0 

^5 

228.9 

169.8 

46 

36.9 

27.4 

06 

85.1 

63.1 

66 

133-3 

98.9 

26 

181. 5 

134.6 

86 

229.7 

170.4 

47 

37.8 

28.0 

07 

85.9 

63.7 

67 

134- 1 

99-5 

27 

182.3 

135.2 

87 

230.5 

171. 0 

48 

38.6 

28.6 

08 

86.7 

64-3 

68 

134.9 

100.  I 

28 

183. 1 

135-8 

88 

231-3 

171. 6 

49 

39-4 

29.  2 

09 

87.5 

64.9 

69 

135-7 

100.  7 

29 

183.9 

136.4 

89 

232.1 

172.  2 

SO 

40.  2 

29.8 
30-4 

10 

88.4 

65-5 

70 
171 

136.5 
137.3 

101.3 
101.9 

30 

184.7 

137.0 

90 

232.9 

172.8 

5' 

41.0 

III 

89.2 

66.1 

231 

185.5 

137.6 

291 

233.7 

173.3 

52 

41.8 

31.0 

12 

90.0 

66.  7 

72 

138.2 

102.5 

32 

186.3 

138.2 

92 

234.5 

173-9 

53 

42.6 

31.6 

13 

90.8 

67.3 

73 

139.0 

103.  I 

33 

187. 1 

138.8 

93 

235.3 

174.5 

54 

43-4 

32.2 

14 

91.6 

67.9 

74 

139.8 

103.7 

34 

188.0 

139.4 

94 

236.1 

175.1 

55 

44.2 

32.8 

15 

92.4 

68.5 

75 

140.6 

104.2 

35 

188.8 

140.  0 

95 

236.9 

175.7 

56 

45- 0 

33-4 

16 

93-2 

69.  I 

76 

141.4 

104.8 

36 

189.6 

140.  6 

96 

237.  7 

176.3 

57 

45.8 

34- 0 

17 

94.0 

69.7 

77 

142.  2 

105.4 

37 

190.4 

141.2 

97 

238.6 

176.9 

5« 

46.6 

34-6 

18 

94.8 

70.3 

78 

143.0 

106.  0 

38 

191.  2 

141. 8 

98 

239.4 

177.5 

59 

47-4 

35-1 

19 

95.6 

70.9 

79 

143.8 

106.6 

39 

192.0 

142.4 

99 

240.  2 

178.  I 

60 

48.2 

35-7 

20 

96.4  j  71.5 

80 

144.6 

107.2 

40 

192.8 

143.0 

300 

241.0 

178.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

X.  E. 

V  K. 

S.  E.  U  E. 

N. 

W.  ^  V 

V. 

s.  ^^ 

■.  ',  w. 

[ 

For  4 

i4  Point 

s. 

Page  212 

TABLE  I. 

Difference  of  Latitude  and 

Departure  for 

1%  Points. 

N.  E.  K 

N. 

N.  W.  }^  N. 

S 

.E.  > 

^S. 

s.  w.  %  s. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
114.  8 

Dist. 

241 

Lat. 

Dep. 

152-9 

I 

0.8 

0.6 

61 

47-2 

38.7 

121 

93-5 

76.8 

181 

139-9 

186.3 

2 

1-5 

1-3 

62 

47-9 

39-3 

22 

94-3 

77-4 

82 

140.7 

"5-5 

42 

187,  I 

153-5 

3 

2.3 

1.9 

^3 

48.7 

40.  0 

•23 

95-1 

78.0 

83 

141- 5 

116.  I 

43 

187.8 

154-2 

4 

3.1 

2.5 

64 

49-5 

40.6 

24 

95-9 

78.7 

84 

142.  2 

116.  7 

44 

188.6 

154.8 

5 

^•t 

^■l 

il 

50.  2 

41.2 

25 

96.6 

79-3 

^5 

143.0 

117.4 

45 

189.4 

155-4 

6 

4.6 

3-8 

66 

i   51-0  :  41-9 

26 

97-4 

79-9 

86 

143-8 

118. 0 

46 

190,2 

156.  I 

7 

5-4 

4-4 

67 

51.8  i  42.5 

27 

i     98.2 

80.6 

87 

144.6 

118.  6 

47 

190.9 

156-  7 

•  8 

6.2 

5-1 

68 

52.6 

43-1 

28 

98.9 

81.2 

88 

145-3 

"9-3 

48 

191-7 

157-3 

9 

7.0 

^•7 

69 

53-3 

43.8 

29 

99-7 

81.8 

89 

146. 1 

"9-9 

49 

192.  5 

158.0 

lO 

7.7 

6.3 

70 
71 

54.1 

44.4 

30 

100.5 

82.5 

90 

146.9 

120.5 

50 

J93^3_ 
194.0 

158.6 
159.2  " 

II 

8.5 

7.0 

54.9 

45- 0 

131 

101.3 

83.1 

191 

147.6 

121.  2 

251 

12 

9-3 

7.6 

72 

55-  7  ;  45-  7 

32 

102.0 

!3-  7 

92 

148.4 

121. 8 

52 

194.8 

159.9 

13 

10. 0 

8.2 

73 

56.4  ,,  46.3 

33 

102.8 

84.4 

93 

149.2 

122.4 

53 

195.6 

160.  5 

14 

10.8 

8.9 

74 

57.2 

46.9 

34 

103.6 

85.0 

94 

150.0 

123.  I 

54 

196.3 

161. 1 

15 

II. 6 

9-5 

75 

58.0 

47.6 

35 

104.4 

85.6 

95 

150-7 

123-7 

55 

197. 1 

161.8 

i6 

12.4 

10.2 

76 

58.7^ 

48.2 

36 

105.  I 

86.3 

96 

151-5 

124-3 

56 

197.9 

162.4 

17 

13- I 

10,8 

77 

59.5 

48.8 

37 

105.9 

86.9 

97 

152-3 

125.0 

57 

198.7 

163.0 

i8 

13-9 

II. 4 

78 

60.3 

49-5 

38 

106.  7 

87.5 

98 

153-1 

125.  6 

58 

199.4 

163.7 

19 

14.7 

12. 1 

79 

61. 1 

50.1 

39 

107.4 

88.2 

99 

153-8 

126.  2 

59 

200.2 

164.3 

20 

15-5 

12.  7 

80 

61.8 

50.8 

40 

108.2 
109.0 

88.8 
89-4 

200 

154.6 

126.9 

60 

201.0 

164.9 

21 

16.2 

13-3 

81 

62.6 

51-4 

141 

201 

155-4 

"^27.  5 

261 

201.  8 

165.6 

22 

17.0 

14.0 

82 

63.4 

52.0 

42 

109.8 

90.  I 

02 

156. 1 

128.  I 

62 

202.5 

166.2 

23 

17.8 

14.6 

f3 

64.  2 

52.7 

43 

no.  5 

90.7 

03 

156.9 

128.8 

63 

203.3 

166.8 

24 

18.6 

15.2 

84 

64.9  1  53-3 

44 

III. 3 

91.4 

04 

157-7 

129.4 

64 

204.  1 

167.  5 

25 

19-3  1  15-9 

^5 

65-7  !  53-9 

45 

112.  I 

92.0 

05 

158-5 

130.  I 

65 

204.8 

168. 1 

26 

20.  I 

16.5 

86 

66.  5  ,  54.  6 

46 

112.  9 

92.  6 

06 

159-2 

130.7 

66 

205.6 

168.7 

27 

20.9 

17.  I 

87 

^7-3 

55-2 

47 

113.6 

93-3 

07 

160.0 

131-3 

67 

206.4 

169.4 

28 

21.6 

17.8 

88 

68.0 

55-8 

48 

1 14. 4 

93-9 

08 

160.8 

132.0 

68 

207.2 

170.0 

29 

22.4 

18.4 

89 

68.  8     56.  5 

49 

115.  2 

94-5 

09 

161. 6 

132.6 

69 

207.9 

170.7 

30 

_23-  2 

19.0 
~i9.T 

90 

69.6     57.1 

50 

116.  0 

95.2 
95-8 

10 

162.3 

133-  2 

70 

208.7 

171. 3 

31 

24.0 

91 

70.3  i  57-7 

151 

116.  7 

211 

163.  I 

133-9 

271 

^09-5 

171.  9 

32 

24.7 

20.3 

92 

71. 1  i  58.4 

52 

II7-5 

96.4 

12 

163.9 

134-5 

72 

210,3 

172.6 

33 

25.  5  ,  20.9 

93 

71.9     59.0 

53 

1 18. 3 

97-1 

13 

164.7 

135- I 

73 

211. 0 

173.2 

34 

26.3  1  21.6 

94 

72.  7     59-  6 

54 

119. 0 

97-7 

14 

165.4 

135-8 

74 

211. 8 

173-8 

35 

27. 1     22.  2 

95 

73-  4     60.  3 

55 

119.8 

98.3 

15 

166.  2 

136.4 

75 

212.6 

174-5 

36 

27.8 

22.8 

96 

74.  2     60.  9 

56 

120.6 

99.0 

16 

167.0 

137-0 

76 

213.4 

175.  I 

37 

28.6 

23-5 

97 

75.0     61.5 

57 

121. 4 

99-6 

17 

167.7 

137-7 

77 

214.  I 

175-7 

38 

29. 4  i  24. 1 

98 

75.  8  i  62.  2 

58 

122.  I 

100.2 

18 

168.5 

138-  3 

78 

214.9 

176.4 

39 

30. 1     24.  7 

99 

76.  5     62.  8 

59 

122.  9 

100.  9 

19 

169.3 

138.9 

79 

215.7 

177.0 

40 
41 

30-9 
31-7 

25.4 
26.0 

100 

lOI 

77.3 

78.  r 

^•3:4 
64.  I 

60 
i6i 

123-7 
124.5 

loi.  5 
102. 1 

20 
221 

1 70.  I 

139.  6 

80 
281 

216.4 

177.6 

1 70.  8  1 

140.2 

217,2 

178.3 

42 

32.5 

26.6 

02 

78.8 

64.7 

62 

125.2 

102.8 

22 

171. 6 

140.8 

82 

218.0 

178.9 

43 

33-2 

27.3 

03 

79.6 

65.3 

63 

126.0 

103.4 

23 

172.4  : 

141- 5 

83 

218.8 

179-5 

44 

34- 0 

27.9 

04 

80.4 

66.0 

64 

126.8 

104.0 

24 

173-2 

142.  I 

84 

219-5 

180.2 

45 

34-8 

28.5 

05 

81.2 

66.6 

65 

127.5 

104.7 

25 

173-9 

142.7 

85 

220.3 

180.8 

46 

35-6 

29.2 

06 

81.9 

67.2 

66 

128. 3 

105-3 

26 

174-7 

143-4 

86 

221.  I 

181.4 

47 

36.3 

29.8 

07 

82.7 

67.9 

67 

129. 1 

105.9 

27 

175-5   i 

144.0 

87 

221.9 

182.  I 

48 

37.1 

30.5 

oS 

83.5 

68.5 

68 

129.9 

106.  6 

28 

1 76.  2 

144. 6       88 

222.6 

182.  7 

49 

37-9 

31- I 

09 

84.3 

69.  I 

69 

130.6 

107.2 

29 

177.0 

145-3       89 

223.4 

183-3 

50 

38.7 

31-7  1 

10 

85.0 

69.8 

70 

JJ^-A. 

107.8 

30 

177-8  1 

145.9       90 

224.2 

184.0 

51 

39-4 

32.4 

III 

85.8 ,  70.4! 

171 

132.2 

108.5 

231 

178.6 

146.5 

291 

224.9 

184.^6^ 

52 

40.  2 

33- 0 

12 

86.6 

71.  I 

72 

133-0 

109.  I 

32 

179-3 

147.2 

92 

225.7 

185.2 

53 

41.0 

33-6 

13 

87.4 

71-7 

73 

133-7 

109.8 

33 

180.  I 

147.8 

93 

226.5 

185.9 

54 

41.7 

34-3 

14 

88.1 

72.3 

74 

134-5 

no.  4 

34 

180.  9 

148.4 

94 

227-3 

186.5 

5§ 

42.5 

34-9 

15 

88.9 

73- 0 

75 

135-3 

III.O 

'    35 

181.  7  i 

149- I 

95 

228.0 

187.1 

56 

43-3 

35-5 

16 

89.7 

73-6 

76  1 

136.0 

III.  7 

36 

182.4 

149.7 

96 

228.8 

187.8 

57 

44.1 

^^/l 

17 

90.4 

74.2 

77 

136.8 

112.3 

37 

183.2 

150.4 

97 

229.6 

1 88. 4 

58 

44.8 

36.8 

18 

91.2 

74-9 

78 

137.6 

112.  9 

38 

184.0 

151. 0 

98 

230.4 

1S9. 0 

59 

45-6 

37.4 

19 

92.0 

75-5 

79 

138.4 

113.6 

39 

184.7 

151.6 

99 

231.  I 

189.7 

60 
Dist. 

46.4 

38.1 

20 

92.8 

76.1 

80 

139- I 

114.  2 

40 

185-5 

152-3 
Lat. 

300 
Dist. 

231.9 
Dep. 

190.3 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

N.  E.  X  E. 

S 

.  E.  ;^  E. 

N. 

vf.'A' 

W. 

S. 

W.  >^  V 

. 

[Fo 

r4K  Po 

ints          1 

TABLE  I. 

Page  213 

Difference  of  Latitude  and  Departure  for  ^}{  Points. 

N.  E.  X  N. 

N.  W.  X  N.                        S.  E.  %  S. 

s.  w. 

Xs. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.7 

0.7 

61 

45-2 

41.0 

121 

89.7 

81.3 

181 

134- I 

121. 6 

241 

178.0 

iei.8 

2 

>-5 

1-3 

62 

45-9 

41.  0 

22 

90.4 

81.9 

82 

134-9 

122.  2 

42 

179.3 

1O2.  5 

3 

2.2 

2.  0 

63 

46.7 

42.3 

23 

91.  I 

82.0 

83 

•35-6 

122.9 

43 

180.  I 

163.2 

4 

3-0 

2.7 

64 

47-4 

43- 0 

24 

91.9 

8.3.3 

84 

136.  3 

123.6 

44 

180.8 

163.9 

5 

3-7 

3-4 

05 

48.2 

43-7 

25 

92.0 

83.9 

85 

137- 1 

124.  2 

45 

181.  5 

164.5 

6 

4.4 

4.0 

00 

48.9 

44-3 

20 

93-4 

84.0 

80 

137-8 

124.9 

46 

182.3 

1O5.2 

7 

5-2 

4.7 

67 

49.6 

45- 0 

27 

94.1 

85.3 

87 

138.0 

125.0 

47 

183.0 

165.9 

8 

5-9 

5-4 

08 

50.4 

45-7 

28 

94.8 

80. 0 

88 

139-3 

12O.3 

48 

183.8 

1OO.5 

9 

6.7 

6.0 

09 

51- I 

46.3 

29 

95-6 

80.0 

89 

140.0 

12O.  9 

49 

184.5 

1O7.  2 

lO 

II 

7.4 
8.2 

6.7 
7.4 

70 
71 

51-9 
52.6 

47.0 
47-7 

30 

96.3 

87.3 

90 

140,  8 

127.0 

50 
251 

185.2 
186.0 

167.9 
1 08.0 

131 

97.1 

88.0 

191 

141- 5 

128.3 

12 

8.9 

8.1 

72 

53-3 

48.4 

32 

97.8 

88.0 

92 

142.8 

128.9 

52 

18O.  7 

1O9.  2 

13 

9.0 

8.7 

73 

54- « 

49.0 

33 

98.5 

89-3 

93 

143.0 

129.  6 

53 

187.5 

1O9.9 

14 

10.4 

9-4 

74 

54.8 

49-7 

34 

99-3 

90.0 

94 

143-7 

130-3 

54 

188.2 

170.0 

15 

II.  I 

10.  I 

75 

55-6 

50-4 

35 

100. 0 

90.7 

95 

144-5 

131. 0 

55 

188.9 

171. 2 

i() 

II. 9 

10.7 

7b 

5^.3 

51.0 

3^ 

100.8 

91-3 

90 

145-2 

131-6 

56 

189.7 

171. 9 

17 

12.6 

II. 4 

77 

57-1 

51-7 

•\7 

101.5 

92.0 

97 

146.  0 

132-3 

57 

190.4 

172.0 

18 

U-3 

12.  I 

78 

57-8 

52.4 

38 

102.3 

92.7 

98 

146.7 

133-0 

58 

191. 2 

173.3 

19 

14.  I 

12.  8 

79 

58.5 

53-1 

39 

103.0 

93-3 

99 

147.4 

133-6 

59 

191.9 

173.9 

20 

14.8 

13-4 

80 

59-3 
60.0 

53-7 

40 

103.7 

94.0 

200 

148.2 

134-3 

Oo 
261 

192.0 
193.4 

174.0 
175-3 

21 

15.6 

14.  I 

81 

54-4 

141 

104.5 

94-7 

201 

148.9 

135-0 

22 

lb.  3 

14.8 

82 

60.8 

55-1 

42 

105.2 

95-4 

02 

149-7 

135-7 

02 

194.  I 

175-9 

23 

17.0 

15-4 

83 

01.  5 

55-7 

43 

106.0 

96.0 

03 

150.4 

136.  3 

63 

194.9 

17O.O 

24 

17.8 

16.  I 

84 

62.  2 

56.4 

44 

106.  7       96.  7 

04 

151.  2 

137.0 

•    04 

195.0 

177-3 

25 

18.5 

16.8 

85 

63.0 

57-1 

45 

107.4 

97-4 

05 

151. 9 

137-7 

65 

I9O.4 

178.0 

26 

19-3 

17.5 

8b 

63.7 

57.8 

40 

108.2 

98.0 

oO 

152.0 

138-3 

60 

197.  I 

178.0 

27 

20.0 

18.  I 

87 

64.5 

.58.4 

47 

108.9 

98.7 

07 

153-4 

139.0 

07 

197.8 

179.3 

28 

20.  7 

18.8 

88 

65.2 

59.1 

48 

109.7 

99.4 

08 

154- I 

139-7 

68 

198.0 

180.0 

29 

21.5 

19-5 

89 

65.9 

59.8 

49 

no.  4 

100.  I 

09 

154-9 

140.4 

69 

199-3 

180.0 

30 

22.2 

20. 1 
20T8 

90 

60.7 

Oo.  4 

50 

III.  I 

100.  7 

10 

155-6 

141. 0 
141-7 

70 
271 

200.  I 
200.8 

181.3 

31 

23.0 

91 

67.4 

61.  I 

151 

III. 9 

101.4 

211 

156.3 

182.0 

32 

23-7 

21.5  j    92 

68.2 

O1.8 

52 

112. 0 

102.  I 

12 

157- I 

142.4 

72 

201.5 

182.7 

33 

24-5 

22.2  I 

93 

08.  9 

b2.S 

53 

"3-4 

102.  7 

13 

157.8 

143.0 

73 

202.3 

183-3 

34 

25.  2 

22.8 

94 

69.6 

03.1 

54 

114. 1 

103.4 

H 

158.0 

143-7 

74 

203.0 

184.0 

35 

25-9 

23-  5 

95 

70.4 

03.8 

55 

1 14.  8 

104.  I 

15 

159-3 

144.4 

75 

203.8 

184.7 

3b 

26  7 

24.2 

9b 

71.  I 

64.5 

5b 

115. 0 

104.  8 

lO 

lOo.  0 

145- I 

70 

204.5 

1 8c;.  4 

37 

27.4 

24.8 

97 

71.9 

05.1 

57 

11O.3 

105.4 

17 

1O0.8 

145-7 

77 

205.2 

18O.0 

3^^ 

28.2 

25-5 

98 

72.6 

65.8 

58 

117.  I 

106.  I 

18 

1O1.5 

146.4 

78 

20O.  0 

18O.  7 

39 

28.9 

26.2 

99 

73-4 

00.5 

59 

117.8 

106.8 

19 

162.3 

147.  I 

79 

20O.  7 

187.4 

40 

29.6 

26. 9     100 

74.1 

O7.  2 

Oo 

1 18.0 

107.4 

20 

163.  0 

147-7 

80 

207.5 

188.0 

41 

30.4 

27.5  I 

lOI 

74.8 

O7.  8 

lOi 

"9-3 

108.  I 

221 

163.8 

148.4 

281 

208.  2 

188.7 

42 

31- I 

28.2 

02 

7.5.  & 

08.  5 

02 

120.0 

108.8 

22 

164-5 

149.  I 

82 

208.9 

189.4 

43 

31-9 

28.9 

03 

76.3 

O9.  2 

63 

120.8 

109.  5 . 

23 

165.  2 

149.  8 

P 

209.7 

190. 1 

44 

32.6 

29.5 

04 

77.1 

O9.8 

04 

121. 5 

no.  I 

24 

166.0 

150.4 

84 

210.4 

190.7 

45 

00-  6 

30.2 

05 

77.8 

70.5 

b5 

122.3 

no.  8 

25 

16O.  7 

151.  I 

85 

211. 2 

191-4 

46 

34.1 

30-9 

Ob 

78.5 

71.2 

00 

123.0 

III. 5 

20 

167-5 

151.  8 

86 

211. 9 

192.  I 

47 

34.8 

31.6 

07 

79-3 

71.9 

07 

123.7 

112.  2 

27 

168.2 

152.4 

87 

212.  7 

192-7 

48 

35-6 

32.2 

08 

80.0 

72.5 

08 

124.5 

112.8 

28 

168.9 

153-  I 

88 

213.4 

193-4 

49 

36.3 

32.9  ; 

09 

80.8 

73-2 

09 

125.2 

113-5 

29 

169.7 

I.S3.8 

89 

214. 1 

194-1 

50 
51 

37-0 
37.8' 

33-6  i 

10 

81.5 

73-9 

70 

126.0 

114. 2 

30 

170.4 

154-5 

90 
291 

214  9 

194.8 

34-2  1 

III 

82,2 

74-5 

171 

126.  7 

114.  8 

231 

171.  2 

155- I 

215.6 

•  195-4 

52 

38.5 

34-9 

12 

83.0 

75-2 

72 

127.4 

"5.5 

32 

171. 9 

155.8 

92 

21O.  4 

19O.  I 

53 

39-3 

.S5.6 

13 

83.7 

75-9 

73 

128.2 

116.  2 

33 

172.6 

156-5 

93 

217. 1 

19O.8 

54 

40.0 

36.3 

M 

84-5 

76.0 

74 

128.9 

116.  9 

34 

173-4 

157- I 

94 

217.8 

197.4 

55 

40.8 

36.9 

15 

85.2 

77.2 

75 

129.7 

"7-5 

35 

174.1 

157-8 

95 

218.0 

198. 1 

5(^ 

41-5 

37.6       16 

80.  0 

77-9 

70 

130.4 

118. 2 

3b 

174.9 

158-5 

96 

219.3 

198.8 

57 

42.2 

.38.3 

^7 

80.  7 

78.0 

77 

131.  I 

118. 9 

37 

175.6 

159.2 

97 

220. 1 

199.5 

5« 

43- 0 

39-0 

18 

87.4 

79.2 

78 

131-9 

"9-5 

38 

176.3 

159.8 

98 

220.8 

200.  I 

59 

43-7 

39-6 

19 

88.2 

79-9 

79 

132.0 

120.  2 

39 

177.  I 

160.5 

99 

221.  5 

200.8 

60 

44-5 

40.3 

20 

88.9 

80.0 

80 

133.4 

120.9 

40 

177.8 

1O1.2 

300 
Dist. 

222.3 

201.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dep. 

Lat. 

N.  E.  «4:  E.                S 

.E.  Xl 

E. 

N. 

w.  X  w.            S. 

w.  X  V 

f. 

[Fo 

r  4X  Points.         1 

Pag 

e214] 

TABLE  I. 

Difference  of  Latitude  and 

Departure  for 

4  Points. 

N.  E. 

IS 

r.  w. 

S.  E. 

s.  w. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.7 

0.7 

61 

43.1 

43-  I 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170,4 

2 

1.4 

1.4 

62 

43.8 

43-8 

22 

86.3 

86.3 

82 

128.7 

128.  7 

42 

171.  I 

171.  I 

3 

2.  I 

2.  I 

63 

44.5 

44-5 

23 

87.0 

87.0 

83 

129.4 

129.4 

43 

171.8 

171. 8 

4 

2.8 

2.8 

64 

45-3 

45-3 

24 

87.7 

L7-7 

84 

130.  I 

130.  I 

44 

172.5 

172.5 

5 

3-5 

3-5 

65 

46.0 

46.0 

25 

88.4 

88.4 

85 

130.8 

130.8 

45 

173.2 

173-2 

6 

4.2 

4.2 

66 

46.7 

46.7 

26 

89.  I 

89.  I 

86 

131. 5 

131.  5 

46 

173.9 

173-9 

7 

4.9 

4.9 

67 

47-4 

47-4 

27 

89.8 

89.8 

87 

132.  2 

132.2 

47 

174.7 

174-7 

8 

5-7 

5-7 

68 

48.1 

48.1 

28 

90.5 

90.5 

88 

132.9 

132.9 

48 

175.4 

175-4 

9 

6.4 

6.4 

69 

48.8 

48.8 

29 

91.2 

91.  2 

89 

133.6 

133.6 

49 

176.  I 

176.. 

10 

7.1 

7-1 

70 

49-5 

49.5 

30 

91,9 

_9i.9 

90 

134.4 

134.4 

50 

176,8 

176.8 

II 

7.8 

7.8 

71 

50.2 

50.  2 

131 

92.6 

92.6 

191 

135. 1 

135.  I 

251 

177.5 

177.5 

12 

8.5 

8.5 

72 

50.9 

50.9 

32 

93-3 

93.3 

92 

135.8 

135.8 

52 

178.2 

178.2 

13 

9.2 

9.2 

73 

51-6 

51.6 

a 

94.0 

94.0 

93 

13*^.5 

136.5 

53 

178.9 

178-9 

14 

9-9 

9.9 

74 

52.3 

52.3 

34 

94.8 

94.8 

94 

137.2 

137.2 

54 

179.6 

179.6 

15 

10.6 

10.6 

75 

53- 0 

53- 0 

35 

95-5 

95.5 

95 

137.9 

137.9 

55 

180.3 

180.3 

16 

"•3 

"•3 

76 

53-7 

53-7 

36 

96.  2 

96.  2 

96 

138.6 

138.6 

56 

181,0 

181. 0 

17 

12.0 

12.0 

77 

54-4 

54-4 

31 

96.9 

96.9 

97 

139.3 

139.3 

57 

181.  7 

181.7 

18 

12.  7 

12.7 

78 

55-2 

55-2 

38 

97.6 

97.6 

98 

140.  0 

140. 0 

58 

182.4 

182.4 

19 

13-4 

13-4 

79 

55-9 

55-9 

39 

98.3 

98.3 

99 

140.7 

140.7 

59 

183.  I 

183.  I 

20 

14.  I 

14. 1 

80 

56.6 

56.6 

40 

99.0 

99.0 

200 

141.4 

141. 4 

60 

183.8 

183.8 

21 

14.8 

14.8 

81 

57.3 

57.3 

141 

99-7 

99.7 

201 

142. 1 

142.  I 

261 

184.6 

184.6 

22  • 

15-6 

15-6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185.3 

185-3 

23 

16.3 

16.3 

P 

58.7 

58.7 

43 

lOI.  I 

lOI.  I 

03 

143.5 

143.5 

63 

186.0 

186.0 

24 

17.0 

17.0 

84 

59-4 

59-4 

44 

101.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.  I 

60.  I 

45 

102.  5 

102.  5 

05 

145.0 

145.0 

65 

187.4 

187.4 

26 

18.4 

18.4 

86 

60.8 

60.8 

46 

103.  2 

103.2 

06 

145-7 

145.7 

66 

188.  I 

188.  I 

27 

19.  I 

19. 1 

87 

61.5 

61.5 

47 

103.9 

103.9 

07 

146.4 

146.4 

67 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.  2 

62.  2 

48 

104.7 

104.7 

08 

147.  1 

147.  I 

68 

189.5 

189.5 

29 

20.  5 

20.  5 

89 

62.9 

62.9 

49 

105.4 

105.4 

09 

147.8 

147.8 

69 

190,2 

190.  2 

30 

21.2 

21.  2 

90 

63.6 

63.6 

50 

106.  I 

106.  I 

10 

148.5 

148.5 

70 

190.9 

190.9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

ro6.  8 

211 

149.2 

149.2 

271 

191. 6 

191. 6 

32 

22.6 

22.6 

92 

^>l 

!>; 

52 

107-5 

107.5 

12 

149.9 

149.9 

72 

192.3 

192.3 

33 

23-3 

23-3 

93 

^A-^ 

65.8 

53 

108.2 

loS.  2 

13 

150.6 

150.6 

n 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

54 

108.9 

108.  9 

14 

151.3 

151. 3 

74 

193.7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

55 

109.  6 

109.6 

15 

152.  0 

152.  0 

75 

194.5 

194.5 

36 

25-5 

25-5 

96 

67.9 

67.9 

56 

no.  3 

no.  3 

16 

152-7 

152.7 

76 

195-2 

195.2 

37 

26.  2 

26.2 

97 

68.6 

68.6 

57 

III.  0 

III.O 

17 

153.4 

153.4 

77 

195.9 

195.9 

38 

26.9 

26.9 

98 

69-3 

69-3 

58 

III. 7 

III. 7 

18 

154-1 

154.  I 

78 

196.  6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

59 

112. 4 

112.4 

19 

154-9 

154-9 

79 

197.3 

197.3 

40 

.28^3^ 

28.3. 

100 

70.7 

70.7 

60 

113. 1 

113.1 

113.8 

20 

155-6 

155.6 

80 

198.0 

198.0 

41 

29.0 

29.0 

lOI 

71.4 

71.4 

161 

113.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

02 

72.  I 

72.1 

62 

114.  6 

114.  6 

22 

157.0 

157.0 

82 

199.4 

199.4 

43 

30.4 

30-4 

03 

72.8 

,72.8 

63 

II5-3 

115.3 

23 

157.7 

157.7 

l^ 

200.  I 

200.  I 

44 

31- I 

31-1 

04 

73-5 

73-5 

64 

116. 0 

116.0 

24 

158.4 

158.4 

f4 

200.8 

200.8 

45 

31.8 

31.8 

°5 

74.2 

74.2 

65 

116.  7 

116.  7 

25 

159.1 

159.1 

ll 

201.  5 

201.  5 

46 

32.5 

32.5 

06 

75- 0 

75- 0 

66 

117.4 

1 1 7.  4 

26 

159.8 

159.8 

86 

202.  2 

202.  2 

47 

33-2 

33-2 

07 

75-7 

75-7 

67 

118. 1 

118.  1 

27 

160.  5 

160.  5 

87 

202.9 

202.9 

48 

33-9 

33-9 

08 

76.4 

76.4 

68 

1 18.  8 

118.8 

28 

161.  2 

161.  2 

88 

203.6 

203.6 

49 

34-6 

34-6 

09 

77-' 

77.1 

69 

1 19.  5 

119.  5 

29 

161.9 

161.9 

89 

204.4 

204.4 

50 

__35-_4_ 

35-4 

10 

77.8 

77.8 

70 

120.  2 

120.  2 

30 

162.6 

162.6 

90 

205.  I 

205.  I 

51 

36.  I 

36.1 

III 

78.5 

78.5 

171 

120.9 

120.9 

231 

163.3 

163.3 

291 

205.8 

205.8 

52 

36.8 

36.8 

12 

79.2 

79.2 

72 

121. 6 

121. 6 

32 

164.0 

164.0 

92 

206.  5 

206,  5 

53 

37-5 

37-5 

13 

79-9 

79-9 

73 

122.3 

122.3 

33 

164.8 

164.  8 

93 

207,2 

207.  2 

54 

38.2 

38.2 

14 

80.6 

80.6 

74 

123.0 

123.0 

34 

165.5 

165.5 

94 

207.9 

207.9 

55 

38.9 

38.9 

15 

81.3 

81.3 

75 

123.7 

123.7 

35 

166,  2 

166.2 

95 

208,6 

208.6 

56 

39-6 

39.6 

16 

82.0 

82.0 

76 

124.5 

124.5 

36 

166.9 

166.9 

96 

209,3 

209.3 

57 

40.3 

40-3 

17 

82.7 

82.7 

77 

125.2 

125.  2 

37 

167.6 

167.6 

97 

210.  0 

210.0 

58 

41.  0 

41.0 

18 

83.4 

83.4 

78 

125.9 

125.9 

38 

168.3 

168.3 

98 

210.  7 

210.  7 

59 

41.7 

41.7 

19 

84.1 

84.1 

79 

126.6 

126.  6 

39 

169.  0 

169.0 

99 

211. 4 

211. 4 

60 

42.4 

42.4 

20 

84.9 

84.9 

80 

127.3 

127.3 

40 

169.  7 

169.7 

300 

212. 1 

212. 1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

N.  I 

- 

N.  W 

S.  E. 

s.  ■' 

\N. 

[ 

For  4 

Points. 

TABLE  2. 

[Page  215  | 

»> 

Difference  of  Latitude  and  Departure  for 

I  Degree. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.0 

61 

61.0        I 

121 

121. 0 

2.  I 

181 

181.  0 

3-2 

241 

241.0 

4.2 

2 

2.0 

0.0 

62 

62.0        I 

22 

122.0 

2.  I 

82 

182.0 

3  2 

42 

242.0 

4-2 

3 

3-0 

0.  I 

63 

63.0        I 

23 

123.0 

2.  1 

P 

183.0 

3-2 

43 

243.0 

4.2 

4 

4.0 

0.  I 

64 

64.0        I 

24 

124.0 

2.2 

84 

184.0 

3 

2 

44 

244.0 

4-3 

5 

5-0 

0.  I 

65 

65.0        I 

25 

125.  0 

2.2 

85 

185.0 

3 

2 

45 

245.0 

4-3 

6 

6.0 

0.  I 

66 

66.0        I 

2 

26 

126.0 

2.  2 

86 

186.0 

3 

2 

46 

246.  0 

4-3 

7 

7.0 

0.  I 

67 

67.0        I 

2 

27 

127.0 

2.2 

87 

187.0 

3 

3 

47 

247.0 

4-3 

8 

8.0 

0.  I 

68 

68.0        I 

2 

28 

128.0 

2.2 

88 

188.0 

3 

48 

248.0 

4.3 

9 

9.0 

0.2 

69 

69.0        I 

2 

29 

129.0 

2-3 

89 

189.0 

3 

3 

49 

249.0 

4-3 

10 

10. 0 

0.  2 

0.2 

70 

70. 0        I 

2 

30 

130.0 

2.3 

90 

190.0 

3 

3 

50 

250.0 

4.4 

II 

1 1.0 

71 

^  71-0  r  I 

2 

131 

131.0 

2.3 

191 

191.0 

0 

3 

251 

251.0 

4-4 

12 

12.0 

0.  2 

72 

72.0  !    I 

3 

32 

132.0 

2.3 

92 

192.0 

3 

4 

52 

252.  0 

4.4 

13 

13.0 

0.2 

73 

73- 0  i     I 

3 

33 

133-0 

2.3 

93 

193.0 

3 

4 

53 

253-0 

4-4 

14 

14.0 

0.  2 

74 

74- 0       I 

3 

34 

134.0 

2.3 

94 

194.0 

3 

4 

54 

254.0 

4-4 

'5 

15.0 

0.3 

75 

75- 0       I 

35 

135-0 

2.4 

95 

195-0 

3 

4 

55 

255-0 

4-5 

i6 

16.0 

0.3 

76 

76. 0       I 

3 

36 

136.0 

2.4 

96 

196.0 

3 

4 

56 

256.0 

4-5 

17 

17.0 

0-3 

77 

77.0       I 

3 

37 

137-0 

2-4 

97 

197.0 

3 

4 

57 

257.0 

4.5 

i8 

18.0 

0-3 

78 

78.0  i     I 

4 

38 

138.0 

2-4 

98 

198.0 

3 

5 

58 

258.0 

4-5 

19 

19.0 

0-3 

79 

79.0       I 

4 

39 

139.0 

2.4 

99 

199.0 

3 

5 

59 

259.0 

4-5 

20 

20,0 

0.3 

80 

80.0       I 

4 

40 

140.0 

2.4 

200 

200.0 

3 

5 

60 

260.0 

4-5 

21 

21.0 

0.4 

81 

81.0       I 

4 

141 

141.0 

2-5 

201 

201.0 

3 

5 

261" 

261.  0 

4-6 

22 

22.0 

0.4 

82 

82.0       I 

4 

42 

142.0 

2-5 

02 

202.0 

3 

5 

62 

262.0 

4.6 

23 

23.0 

0.4 

P 

83.0       I 

4 

43 

143.0 

2-5 

03 

203.0 

3 

5 

P 

263.0 

4.6 

24 

24.0 

0.4 

84 

84.0       I 

5 

44 

144.0 

2-5 

04 

204.0 

3 

6 

64 

264.0 

4.6 

25 

25.0 

0.4 

85 

85.0       I 

5 

45 

145.0 

2.5 

05 

205.  0 

3 

6 

65 

265.0 

4.6 

26 

26.0 

0-5 

86 

86.0       I 

5 

46 

146.  0 

2-5 

06 

206.  0 

3 

6 

66 

266.0 

4.6 

27 

27.0 

0.5 

87 

87.0       I 

5 

47 

147-0 

2.6 

07 

207.0 

3 

6 

67 

267.0 

4.7 

28 

28.0 

0.5 

88 

88.0       I 

5 

48 

148.0 

2.6 

08 

208.0 

3 

6 

68 

268.0 

4-7 

29 

29.0 

0.5 

89 

89.0       I 

6 

49 

149.0 

2.6 

09 

209.0 

3 

6 

69 

269.0 

4-7 

30 

30.0 

0-5 

90 

90. 0       I 

6 

50 

150.0 

2.6 

10 

210.0 

3 

7 

70 

270.0 

4-7 

31 

31.0 

0.5 

91 

91.0       I 

6 

151 

151. 0 

2.6 

211 

211. 0 

3 

7 

271 

271.0 

4.7 

32 

32.0 

0.6 

92 

92.0       I 

6 

52 

152.0 

2.7 

12 

212.0 

3 

7 

72 

272.0 

4-7 

33 

33.0 

0.6 

93 

93- 0       I 

6 

53 

153-0 

2.7 

13 

213.0 

3 

7 

73 

273.0 

4-8 

34 

34.0 

0.6 

94 

94.0       I 

6 

54 

154.0 

2.7 

14 

214.0 

3 

7 

74 

274.0 

4.8 

35 

35- 0 

0.6 

95 

95.0        I 

55 

155.0 

2.7 

15 

215.0 

3 

8 

75 

275.0 

4.8 

36 

36.0 

0.6 

96 

96.0       I 

56 

156.0 

2.7 

16 

216.0 

3 

8 

76 

276.0 

4.8 

37 

37-0 

0.6 

97 

97- 0  ,     I 

57 

157.0 

2-7 

17 

217.0 

3 

8 

77 

277.0 

4.8 

38 

38.0 

0.7 

98 

98.  0  i     I 

58 

158.0 

2.8 

18 

218.0 

3 

8 

78 

278.0 

4-9 

39 

39- 0 

0.7 

99 

99.0       I 

59 

159.0 

2.8 

19 

219.0 

3 

8 

79 

279. 0 

4.9 

40 

40.0 

0.7 

100 

100. 0       I 

60 

160.0 

2.8 

20 

220.0 

3 

8 

80 

280.0 

4-9 

41 

41.  0 

0.7 

lOI 

lOI.O           I 

X 

161 

161.0 

2.8 

221 

221.0 

3 

9 

281 

281.0 

4-9 

42 

42.0 

0.7 

02 

102. 0        I 

8 

62 

162.0 

2.8 

22 

222.0 

3 

9 

82 

282.0 

4-9 

43 

43- 0 

0.8 

03 

103.0       I 

8 

63 

163.0 

2.8 

23 

223.0 

3 

9 

P 

283.0 

4-9 

44 

44.0 

0.8 

04 

104. 0       I 

8 

64 

164.0 

2.9 

24 

224.0 

3 

9 

84 

284.0 

5-0 

45 

45- 0 

0.8 

05 

105.0  1     I 

8 

65 

165.0 

2.9 

25 

225.0 

3 

9 

85 

285.0 

5-0 

46 

46.0 

0.8 

06 

106.0  1     I 

8 

66 

166.0 

2.9 

26 

226.  0 

■^ 
J 

9 

86 

286.0 

5-0 

47 

47.0 

0.8 

07 

107.0        I 

9 

67 

167.0 

2.9 

27 

227.0 

4 

0 

87 

287.0 

5-0 

48 

48.0 

0.8 

08 

108. 0        I 

9 

68 

168.0 

2.9 

28 

228.  0 

4 

0 

88 

288.0 

5-0 

49 

49.0 

0.9 

09 

109. 0       I 

9 

69 

169.  0 

2.9 

29 

229.  0 

4 

0 

89 

289.0 

5-0 

50 
51 

50.0 

0.9 

10 

1 10.0       I 

9 

70 

170.0 

3-0 

30 

230.0 

4 

0 

90 

290.0 

5- 1 

51.0 

0.9 

III 

III.O          I 

9 

171 

171. 0 

3-0 

231 

231.0 

4 

0 

291 

291.0 

5-1 

52 

52.0 

0.9 

12 

II2.0          2 

0 

72 

172.0 

3-0 

32 

232.0 

4 

0 

92 

292.0 

5-1 

53 

53.0 

0.9 

13 

113. 0          2 

0 

73 

173-0 

3-0 

3i 

233-0 

4 

93 

293-0 

5-1 

54 

54.0 

0.9 

14 

1 14.0    1       2 

0 

74 

174.0 

3-0 

34 

234.0 

4 

94 

294.0 

5-1 

55 

55- 0 

I.  0 

15 

115. 0           2 

0 

75 

175-0 

3-1 

35 

235-0 

4 

95 

295-0 

5-1 

56 

56.0 

1.0 

16 

116.  0          2 

0 

76 

176.0 

3-1 

36 

236.0 

4 

96 

296.  0 

5-2 

57 

57.0 

I.  0 

17 

1 1  7.  0          2 

0 

77 

177.0 

3-1 

37 

237-0 

4 

97 

297.0 

5-2 

58 

58.0 

1.0 

18 

118.  0          2 

I 

78 

178.0 

3-1 

38 

238.0 

4 

2 

98 

298.  0 

5-2 

19 

59- 0 

1.0 

19 

119.  0          2 

I 

79 

179.0 

3-1 

39 

239-0 

4 

2 

99 

299.0 

5-2 

60 

60.0 

1.0 

20 

120.0          2 

I 

80 

180.0 

3.1 

40 

240.0 

4 

2 

300 

300.0 

5.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.        La 

t. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 



[Foi 

-  89  Degr 

ees. 

Pag 

e216] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

2  Degrees 

• 

Dist, 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.0 

61 

61.0 

2.  I 

121 

120.9 

4.2 

181 

180.9 

6.3 

241 

240.9 

8.4 

2 

2.0 

0.  I 

62 

62.0 

2.2 

22 

121. 9 

4- 

3 

82 

181. 9 

6.4 

42 

241.9 

8.4 

3 

3-0 

0.  I 

63 

63.0 

2.2 

23 

122.9 

4- 

3 

^i 

182.9 

6.4 

43 

242.9 

8.5 

4 

4.0 

0.  I 

64 

64.0 

2.2 

24 

123.9 

4- 

3 

84 

183.9 

6.4 

44 

243-9 

8.5 

5 

5-0 

0.2 

65 

65.0 

2-3 

25 

124.9 

4- 

4 

85 

184.9 

6-5 

45 

244-9 

8.6 

6 

6.0 

0.  2 

66 

66.0 

2-3 

26 

125-9 

4- 

4 

86 

185-9 

6.5 

46 

245-9 

8.6 

7 

7.0 

0.  2 

67 

67.0 

2-3 

27 

126.9 

4- 

4 

87 

186.9 

6.5 

47 

246.8 

8.6 

8 

8.0 

0-3 

68 

68.0 

2.4 

28 

127.9 

4- 

5 

88 

187.9 

6.6 

48 

247.8 

8.7 

9 

9.0 

0-3 

69 

69.0 

2.4 

29 

128.9 

4- 

5 

89 

188.9 

6.6 

49 

248.8 

^•7 

lo 

10. 0 

0-3 

70 

70.0 

2.4 

30 

129.9 
130.9 

4- 
4- 

5 
6 

90 

189.9 

6.6 

50 

249.8 

8.7 

II 

II. 0 

0.4 

71 

71.0 

2-5 

131 

191 

190.9 

6.7 

251 

250.8 

8.8 

12 

12.0 

0.4 

72 

72.0 

2.5 

32 

13I-9 

4 

6 

92 

191.  9 

6.7 

52 

251.8 

8.8 

13 

13.0 

0.5 

73 

73- 0 

^•5 

33 

132.9 

4 

6 

93 

192.9 

6.7 

53 

252.8 

8.8 

14 

14.0 

0-5 

74 

74.0 

2.6 

34 

133-9 

4 

7 

94 

193-9 

6.8 

54 

253-8 

8.9 

15 

15.0 

0.5 

75 

75- 0 

2.6 

35 

134-9 

4 

7 

95 

194.9 

6.8 

55 

254.8 

8.9 

16 

16.0 

0.6 

76 

76.0 

2.7 

36 

135-9 

4 

7 

96 

195-9 

6.8 

56 

255-8 

8.9 

17 

17.0 

0.6 

77 

77.0 

2.7 

37 

136.9 

4 

8 

97 

196.9 

6.9 

57 

256.8 

9.0 

18 

18.0 

0.6 

78 

78.0 

2.7 

38 

137-9 

4 

8 

98 

197.9 

6.9 

58 

257-8 

9.0 

19 

19.0 

0.7 

79 

79.0 

2.8 

39 

138.9 

4 

9 

99 

198.9 

6.9 

59 

258.8 

9.0 

20 

20.0 

0.7 

80 

80.0 

2.8 

40 

139-9 

4 

9 

200 

199.9 

7.0 

60 

259.8 

9.1 
9-1 

21 

21.0 

0.7 

8f 

81.0 

2.8 

141 

140.9 

4 

9 

201 

200  9 

7.0 

261 

260.8 

22 

22.0 

0.8 

82 

82.0 

2.9 

42 

141.  9 

5 

0 

02 

201.9 

7.0 

62 

261.8 

9-  I 

23 

23.0 

0.8 

^3 

82.9 

2.9 

43 

142.9 

5 

0 

03 

202.9 

7-1 

63 

262.8 

9.2 

24 

24.0 

0.8 

84 

83.9 

2.9 

44 

143-9 

5 

0 

04 

203.9 

7-1 

64 

263.8 

9-2 

25 

25.0 

0.9 

85 

84.9 

3-0 

45 

144.9 

5 

I 

05 

204.9 

7-2 

65 

264.8 

9-2 

26 

26.0 

0.9 

86 

85.9 

3-0 

46 

145-9 

5 

I 

06 

205.9 

7-2 

66 

265.8 

9-3 

27 

27.0 

0.9 

87 

86.9 

3-0 

47 

146.9 

5 

I 

07 

206.9 

7-2 

67 

266.8 

9-3 

28 

28.0 

1.0 

88 

87.9 

3-1 

48 

147.9 

5 

2 

08 

207.9 

7-3 

68 

267.8 

9.4 

29 

29.0 

1.0 

89 

88.9 

3-1 

49 

148.9 

5 

2 

09 

208.9 

7-3 

69 

268.8 

9-4 

30 

30.0 

1.0 
I.  I 

90 

89.9 

3-1 

50 

149-9 

5 

2 

10 

209.9 

7.3 

70 

269.8 

9-4 

31 

31.0 

91 

90.9 

3-2 

151 

150.9 

5 

3 

211 

210.9 

7-4 

271 

270.8 

9-5 

32 

32.0 

I.  I 

92 

91.9 

3-2 

52 

151-9 

5 

3 

12 

211.9 

7-4 

72 

271.8 

9-5 

33 

33- 0 

I.  2 

93 

92.9 

3-2 

53 

152.9 

5 

3 

13 

212.9 

7-4 

73 

272.8 

9-5 

34 

34-0 

1.2 

94 

93-9 

3-3 

54 

153-9 

5 

4 

14 

213.9 

7-5 

74 

273.8 

9.6 

35 

35- 0 

1.2 

95 

94.9 

3-3 

55 

154-9 

5 

4 

15 

214.9 

7-5 

75 

274.8 

9.6 

36 

36.0 

1-3 

96 

95-9 

3-4 

56 

155-9 

5 

4 

16 

215.9 

7-5 

76 

275-8 

9.6 

37 

37- 0 

1-3 

97 

96.9 

3-4 

57 

156.9 

5 

5 

17 

216.  9 

7-6 

n 

276.8 

9-7 

38 

38.0 

1-3 

98 

97-9 

3-4 

58 

157-9 

5 

5 

18 

217.9 

7-6 

78 

277.8 

9-7 

39 

39- 0 

1.4 

99 

98.9 

3-5 

59 

158-9 

5 

5 

19 

218.9 

7-6 

79 

278.8 

9-7 

40- 
41 

40.0 
41.0 

1.4 

100 

99.9 

3-5 

60 

159-9 

5 

.6 

20 

219.9 

7-7 

80 
281 

279.8 
280.8 

9.8 
9-8 

1.4 

lOI 

100.9 

3-5 

161 

160.9 

5 

.6 

221 

220.9 

7-7 

42 

42.0 

1-5 

02 

101.9 

3-6 

62 

161. 9 

5 

•7 

22 

221.9 

7-7 

82 

281.8 

9.8 

43 

43- 0 

1-5 

03 

102.9 

3-6 

63 

162.9 

5 

-7 

23 

222.9 

7-8 

l^ 

282.8 

9-9 

44 

44.0 

1.5 

04 

103.9 

3-6 

64 

163.9 

5 

-7 

24 

223.9 

7.8 

84 

^3-8 

9-9 

45 

45- 0 

1.6 

05 

104.9 

3-7 

65 

164.9 

5 

8 

25 

224.9 

7-9 

85 

284.8 

9.9 

46 

46.0 

1.6 

06 

105.9 

3-7 

66 

165-9 

5 

.8 

26 

225.9 

7-9 

86 

285.8 

10.  0 

47 

47.0 

1.6 

°l 

106.9 

3-7 

67 

166.9 

5 

.8 

27 

226.9 

7-9 

87 

286.8 

10.  0 

48 

48.0 

1-7 

08 

107.9 

3-8 

68 

167.9 

5 

-9 

28 

227.9 

8.0 

88 

287.8 

10.  I 

49 

49.0 

1.7 

09 

108.9 

3-8 

69 

168.9 

5 

-9 

29 

228.9 

8.0 

89 

288.8 

10.  I 

50 

50.  0 

1-7 

10 

109.9 

3.8 

70 

169.9 

5 

•9 

30 

229.9 

8.0 

90 

289.8 

10.  I 

51 

SiTo" 

1.8 

III 

no.  9 

3-9 

171 

170.9 

6 

.0 

231 

"^23079" 

8.1 

291 

290.8 

10.  2 

52 

52.0 

1.8 

12 

III. 9 

3-9 

72 

171. 9 

6 

.0 

32 

231.9 

8.1 

92 

291.8 

10.  2 

53 

53-0 

1.8 

13 

112. 9 

3-9 

73 

172.9 

6 

.0 

33 

232.9 

8.  I 

93 

292.8 

10.  2 

54 

54-0 

1.9 

14 

1 13- 9 

4.0 

74 

173-9 

6 

.  I 

34 

233-9 

8.2 

94 

293.8 

10.3 

55 

55- 0 

1.9 

15 

1 14. 9 

4.0 

75 

174.9 

6 

.  I 

35 

234-9 

8.2 

95 

294.8 

10.3 

56 

56.0 

2.0 

16 

115-9 

4.0 

76 

175-9 

6 

.  I 

36 

235-9 

8.2 

96 

295-8 

10.3 

57 

57- 0 

2.0 

17 

116.  9 

4-1 

77 

176.9 

6 

.  2 

37 

236.9 

f-3 

97 

296.8 

10.4 

58 

58.0 

2.0 

18 

117-9 

4.1 

78 

177.9 

6 

.  2 

38 

237-9 

^•3 

98 

297.8 

10.4 

59 

59. 0 

2. 1 

19 

1 18. 9 

4.2 

79 

178.9 

6 

.2 

39 

238.9 

!-3 

99 

298.8 

10.4 

60 

60.0 

2. 1 

20 

"9-9 

4.2 

80 

179.9 

6 

•3 

40 

239-9 

8.4 

300 

299.8 

10.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Foi 

-  88  Degr 

ees. 

TABLE  2. 

Page  217 

^» 

Diffei 

rence  0: 

"  Latitude  and  Departure  for 

3  Degrees 

i« 

Dist. 

1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
121 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

r.o 

0.  I 

61 

60.9 

3-2 

120.8 

6.3 

181 

180.8 

9.5 

241 

240.7 

12.6 

2 

2.0 

0.  I 

62 

61.9 

3-2 

22 

121. 8 

6.4 

82 

181. 8 

9.5 

42 

241.7 

12 

7 

3 

3-0 

0.  2 

63 

62.9 

3-3 

23 

122.8 

6.4 

^3 

182.7 

9.6 

43 

242.7 

12 

7 

4 

4.0 

0.  2 

64 

63-9 

3-3 

24 

123.8 

6.5 

84 

183-7 

9.6 

44 

243.7 

12 

8 

5 

5-0 

0.3 

65 

64.9 

3-4 

25 

124.8 

6.5 

85 

184.7 

9.7 

45 

244.7 

12 

8 

6 

6.0 

0-3 

66 

f>5-9 

3-5 

26 

125.8 

6.6 

86 

185.7 

9.7 

46 

245.7 

12 

9 

7 

7.0 

0.4 

67 

66.9 

3-5 

27 

126.8 

6.6 

87 

186.7 

9.8 

47 

24b.  7 

12 

9 

8 

8.0 

0.4 

68 

67.9 

3-6 

28 

127.8 

6.7 

88 

187.7 

9.8 

48 

247.7 

13 

0 

9 

9.0 

0-5 

69 

68.9 

3.6 

29 

128.8 

6.8 

89 

188.  7 

9.9 

49 

248.7 

13 

0 

10 

10.0 

0-5 
0.6 

70 
71 

69.9 
70.9 

3-7 
3-Z 

30 

129.8 

6.8 

90 

189-7 

9.9 

50 

249.7 

13 

I 

It 

II. 0 

131 

130.8 

6.9 

191 

190.7 

10.  0 

251 

250.7 

13 

I 

12 

12.0 

0.6 

72 

71.9 

3-! 

32 

131.8 

6.9 

92 

191.  7 

10.  0 

52 

251-7 

13 

2 

13 

13.0 

0.7 

73 

72.9 

3-8 

33 

132.8 

7.0 

93 

192.7 

10.  I 

53 

252-7 

13 

2 

'4 

14.0 

0.7 

74 

73-9 

3-9 

34 

133-8 

7.0 

94 

193-  7 

10.  2 

54 

253-  7 

13 

3 

15 

15.0 

0.  8 

75 

74-9 

3-9 

'  35 

134.8 

7-1 

95 

194.7 

10.2 

55 

254-7 

13 

-* 

10 

16.0 

0.8 

76 

75-9 

4.0 

36 

135-8 

7.1 

96 

195-7 

10.3 

56 

255-6 

13 

4 

17 

17.0 

0.9 

77 

76.9 

4.0 

37 

136.8 

7-2 

97 

196.7 

10.3 

57 

256.6 

13 

5 

1 8 

!8.0 

0.9 

78 

77-9 

4.1 

38 

137-8 

7-2 

98 

197.7 

10.4 

58 

257.6 

13 

5 

19 

19.0 

I.O 

79 

78.9 

4.1 

39 

138.8 

7-3 

99 

198.7 

10.4 

59 

258.6 

13 

6 

20 

20.0 

I.  0 

80 

79-9 

4.2 

40 

139-8 

7-3 

200 

199-7 

10.5 

60 

_259^6 

13 

6 

21 

21.0 

I.  I 

81 

80.9 

4.2 

141 

140.8 

7-4 

201 

200.  7 

10.5 

261 

260. 6 

13" 

7 

22 

22.0 

I.  2 

82 

81.9 

4-3 

42 

141. 8 

7-4 

02 

201.  7 

10.6 

62 

261.6 

13 

7 

23 

23.0 

I.  2 

83 

82.9 

4-3 

43 

142.8 

7-5 

03 

202.  7 

10.6 

^3 

262.  6 

13 

8 

24 

24.  0 

1-3 

84 

83.9 

4.4 

44 

143.8 

7-5 

04 

203.7 

10.7 

64 

263.  6 

13 

8 

25 

25.0 

1-3 

85 

84.9 

4.4 

45 

144.8 

7-6 

05 

204.7 

10.7 

65 

264.  6 

13 

9 

26 

26.0 

1.4 

86 

85.9 

4.5 

46 

145.8 

7-6 

06 

205.7 

10.8 

66 

265.6 

13 

9 

27 

27.0 

1.4 

87 

86.9 

4.6 

47 

146.8 

7-7 

07 

206.  7 

10.8 

67 

266.  6 

14 

0 

28 

28.0 

1-5 

88 

87.9 

4.6 

48 

147.8 

7.7 

08 

207.7 

10.9 

68 

267.6 

14 

0 

29 

29.0 

1-5 

89 

88.9 

4-7 

49 

148.8 

7.8 

09 

208.7 

10.9 

69 

268.6 

14 

I 

30 

30.0 

1.6 

_90 

89.9 

4.7 

50 

149-8 

7-9 

10 

209.7 

II. 0 

70 

269.6 

14 

I 

31 

31.0 

1.6 

qi 

90.9 

4.8 

151 

150.8 

7-9 

211 

210.  7 

II. 0 

271 

270.6 

14 

2 

32 

32.0 

1-7 

92 

91.9 

4.8 

52 

151.8 

8.0 

12 

211.  7 

II.  I 

72 

271.  6 

14 

2 

33 

33- 0 

1-7 

93 

92.9 

4-9 

53 

152.8 

8.0 

13 

212.  7 

II.  I 

73 

272.6 

14 

3 

34 

34- 0 

1.8 

94 

93-9 

4.9 

54 

153-8 

8.  I 

14 

213.7 

II.  2 

74 

273.6 

14 

35 

35-0 

1.8 

95 

94-9 

5-0 

55 

154.8 

8.1 

15 

214.7 

II. 3 

75 

274.6 

14 

4 

36 

36.0 

1.9 

96 

95-9 

5-0 

56 

155.8 

8.2 

16 

215.7 

II. 3 

76 

275.6 

14 

4 

37 

36-9 

1.9 

97 

96.9 

5-1 

57 

156.8 

8.2 

17 

216.  7 

II. 4 

77 

276.6 

14 

5 

38 

37.9 

2.0 

98 

97-9 

5-1 

58 

157-8 

8-3 

18 

217.7 

II. 4 

78 

277.6 

14 

5 

39 

38.9 

2.0 

99 

98.9 

5-2 

59 

158.8 

8.3 

19 

218.7 

II. 5 

79 

278.6 

14 

6 

40 

41 

39-9 

2. 1 

100 

99.9 

5-2 

60 

159.8 

8.4 

20 

^_2^9-_7_ 

"-S 

80 
281 

279.6 
280.6 

14 

14 

7 

7 

40.9 

2.  I 

lOI 

100.9 

5-3 

161 

160:8 

8.4 

221 

220.  7 

II. 6 

42 

41.9 

2.  2 

02 

101.9 

5-3 

62 

161.  8 

8.5 

22 

221.  7 

II. 6 

82 

281.6 

14 

8 

43 

42.9 

2.3 

03 

102.9 

5-4 

63 

162.8 

^•5 

23 

222.  7 

II. 7 

83 

282.6 

14 

8 

44 

43-9 

2.3 

04 

103.9 

5-4 

64 

163.8 

8.6 

24 

223.7 

II. 7 

84 

283.6 

14 

9 

45 

44-9 

2.4 

05 

104.9 

5-5 

65 

164.8 

8.6 

25 

224.7 

II. 8 

85 

284.  6 

14 

9 

46 

45-9 

2.4 

06 

105.9 

5-5 

66 

165.8 

8.7 

26 

225.7 

11.8 

86 

285.6 

15 

0 

47 

46.9 

2-5 

07 

106.9 

5-6 

67 

166.8 

8.7 

27 

226.  7 

II. 9 

87 

286.6 

15 

0 

48 

47-9 

2-5 

08 

107.9 

5-7 

68 

167.8 

8.8 

28 

227.7 

II. 9 

88 

287.6 

15 

I 

49 

48.9 

2.6 

09 

108.9 

5-7 

69 

168.8 

8.8 

29 

228.7 

12.  0 

89 

288.6 

15 

I 

50 

49-9 

2.6 

10 

109.8 

5.8 

70 

169.8 

8.9 

30 

229.7 

12.0 

90 

289.6 

15 

2 

51 

50.9 

2.7 

Tii 

1 10.  8 

~5.8^ 

171 

170.8 

8.9 

231 

230.7 

12.  I 

291 

290.  6 

15 

2 

52 

51-9 

2.7 

12 

III. 8 

5-9 

72 

171. 8 

9.0 

32 

231.7 

12.  I 

92 

291.  6 

15 

3 

53 

52.9 

2.8 

13 

1 12.  8 

5-9 

73 

172.8 

9.1 

33 

232.7 

12.2 

93 

292.  6 

15 

3 

54 

53-9 

2.8 

14 

113.8 

6.0 

74 

173-8 

9.1 

34 

233-7 

12.  2 

94 

293.6 

15 

4 

55 

54.9 

2.9 

15 

1 14.  8 

6.0 

75 

174.8 

9.2 

35 

234-7 

12.3 

95 

294.6 

15 

4 

56 

55.9 

2.9 

16 

115.8 

6.1 

76 

175-8 

9.2 

36 

235-7 

12.4 

96 

295-6 

15 

5 

57 

56.9 

3-0 

17 

1 16.  8 

6.1 

77 

176.8 

9.3 

37 

236.7 

12.4 

97 

296.6 

15 

5 

58 

57-9 

3-0 

18 

1 17.  8 

6.2 

78 

177.8 

9.3 

38 

237-7 

12.5 

98 

297.6 

15 

6 

59 

58.9 

3-1 

19 

118.  8 

6.2 

Z9 

178.8 

9-4 

39 

238.7 

12.5 

99 

298.6 

15 

6 

60 
Dist. 

59-9 

3-1 

20 

1 19.  8 

6.3 

80 

179-8 

9.4 

40 

239-7 

12.6 

300 

299.  6 

15-7 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fo 

r  87  Degr 

ees. 

Pag 

•e  218j 

TABLE  2. 

Diffei 

ence  of  Latitude  and  Departure  for  4  Degrees. 

Dist. 
I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
120.  7 

Dep. 

Dist. 

Lat. 
180.6 

Dep. 

Dist. 

Lat. 

Dep. 

I.O 

0.  I 

61 

60.9 

4.3 

121 

8.4 

181 

12.6 

241 

240.4 

16.8 

2 

2.0 

0.  I 

62 

61.8 

4-3 

22 

121.  7 

8.5 

82 

181.6 

12.7 

42 

241.4 

16.9 

3 

3-0 

0.  2 

63 

62.8 

4.4 

23 

122.  7 

8.6 

83 

182.6 

12.8 

43 

242.4 

17.0 

4 

4.0 

0.3 

64 

63.8 

4-5 

24 

123.7 

8.6 

84 

183.6 

12.8 

44 

243.4 

17.0 

5 

5-0 

0-3 

65 

64.8 

4-5 

25 

124.7 

8.7 

85 

184.5 

12.9 

45 

244.4 

17.  I 

6 

6.0 

0.4 

66 

65.8 

4.6 

26 

125.7 

8.8 

86 

185.5 

13.0 

46 

245.4 

17.2 

7 

7.0 

0-5 

67 

66.8 

4.7 

27 

126.  7 

8.9 

87 

186.5 

13.0 

47 

246.4 

17.2 

8 

8.0 

0.6 

68 

67.8 

4.7 

28 

127.7 

8.9 

88 

187.5 

13.1 

48 

247.4 

17.3 

9 

9.0 

0.6 

69 

68.8 

4.8 

29 

128.7 

9.0 

89 

188.5 

13.2 

49 

248.4 

17-4 

lO 

10.  0 

0.7 

70 
71 

69.8 
70.8 

4.9 

30 

129.7 

9.1 

90 

189.5 

13.3 

50 

249.4 

17.4 
17.5 

11 

II. 0 

0.8 

5.0 

131 

130.7 

9.1 

191 

190.  5 

13.3 

251 

250.4 

12 

12.0 

0.8 

72 

71,8 

5.0 

32 

131.7 

9.2 

92 

191.5 

13.4        52 

251.4 

17.6 

13 

13.0 

0,9 

73 

72.8 

5-1 

33 

132.7 

9.3 

93 

192.5 

13.5       53 

252.4 

17.6 

14 

14.0 

1.0 

74 

73.8 

5-2 

34 

133.7 

9-3 

94 

193.5 

13-5       54 

253.4 

17.7 

15 

15.0 

I.  0 

75 

74.8 

5.2 

35 

134.7 

9-4 

95 

194.5 

13.6 

55 

254.4 

17.8 

i6 

16.0 

1. 1 

76 

n-l 

5-3 

36 

135.7 

9-5 

96 

195.5 

13.7 

56 

255.4 

17.9 

17 

17.0 

1.2 

77 

76.8 

5.4 

37 

136.7 

9.6 

97 

196.5 

13.7 

57 

256.4 

17.9 

i8 

18.0 

1-3 

78 

77.8 

5-4 

38 

137.7 

9.6 

98 

197.5 

13.8 

58 

257.4 

18.0 

19 

19.0 

1-3 

79 

78.8 

5-5 

39 

138.7 

9.7 

99 

198.5 

13.9       59 

258.4 

18.  I 

20 

20.0 

1.4 
1-5 

80 
81 

79.8 
80.8' 

5-6 
5-7 

40 

139.7 

9.8 

200 

199.5 

14. 0       60 

_^59:_4_ 

18.  I 

21 

20.9 

141 

140.7 

9.8 

201 

200.  5 

14.0 

261 

260.4 

18.2 

22 

21.9 

1-5 

82 

81.8 

5.7 

42 

141.  7 

9.9 

02 

201.  5 

14. 1 

62 

261.4 

18.3 

23 

22.9 

1.6 

^3 

82.8 

5.8 

43 

142.7 

10. 0 

03 

202.  5 

14.2 

63 

262.4 

18.3 

24 

23-9 

1-7 

84 

83.8 

5.9 

44 

143.6 

10.  0 

04 

203.5 

14.2 

64 

263.4 

18.4 

25 

24.9 

1-7 

85 

84.8 

5-9 

45 

144.6 

10.  I 

05 

204.5 

14.3 

65 

264.4 

18.5 

26 

25-9 

1.8 

86 

85.8 

6.0 

46 

145.6 

10.  2 

06 

205.5 

14.4 

66 

265.4 

18.6 

27 

26.9 

I  9 

87 

86.8 

6.1 

47 

146.6 

10.3 

07 

206.  5 

14.4 

67 

266.  3 

18.6 

28 

27.9 

2.0 

88 

87.8 

6.1 

48 

147.6 

10.3 

08 

207.5 

14.5 

68 

267.3 

18.7 

29 

28.9 

2.0 

89 

88.8 

6.2 

49 

148.6 

10.4 

09 

208.5 

14.6 

69 

268.3 

18.8 

30 
31 

29.9 
30.9 

2.  I 

2.  2 

90 

91 

89.8 

6.3 

50 

149.  6  , 

10.5 

10 

209.5 

14.6 

70 

269.3 
270.3 

18.8 
18.9 

90:8 

6.3 

151 

150.6 

10.5 

211 

210.  5 

14.7 

271 

32 

31-9 

2.2 

92 

91.8 

6.4 

52 

151.  6 

10.6 

12 

211.  5 

14.8 

72 

271-3 

19.0 

33 

32.9 

2.3 

93 

92.8 

!-5 

53 

152.6 

10.7 

13 

212.  5 

14  9 

n 

272.3 

19.0 

34 

33-9 

2.4 

94 

93-8 

6.6 

54 

153.6 

10.7 

14 

213.5 

14.9 

74 

273.3 

19.1 

35 

34-9 

2.4 

95 

94.8 

6.6 

55 

154.6 

10.8 

15 

214.5 

15.0 

75 

274.3 

19.2 

36 

35-9 

2.5 

96 

95-8 

6.7 

56 

155.6 

10.9 

16 

215.5 

15.1 

76 

275.3 

19.3 

37 

36.9 

2.6 

97 

96.8 

6.8 

57 

156.6 

II. 0 

17 

216.  5 

15.  I 

n 

276.3 

19.3 

38 

37.9 

2.7 

98 

97.8 

6.8 

58 

157.6 

II. 0 

18 

217.5 

15.2 

78 

277.3 

19.4 

39 

38.9 

2.7 

99 

98.8 

6.9 

59 

158.6 

II.  I 

19 

218.5 

15.3 

P 

278.3 

19.5 

40 

39-9 
40.9 

2.8 

100 

,^99.8 

7.0 

60 

159.6 

11.2 

20 

2i9:_5_ 
220.  5 

15.3 
15.4 

80 
"281 

279.3 
'   280.3 

19.5 
19.6 

41 

2^9^ 

lOI 

100.  8 

7.0 

161 

160.6 

11.  2 

221 

42 

41.9 

2.9 

02 

101.8 

7-1 

62 

161.  6 

11-3 

22 

221.5 

15.5 

82 

281.3 

19.7 

43 

42.9 

3-0 

03 

102.  7 

7.2 

63 

162.6 

II. 4 

23 

222.5 

15.6 

f^ 

282.3 

19.7 

44 

43-9 

3-1 

04 

103.7 

7.3 

64 

163.6 

II. 4 

24 

223.5 

15.6 

84 

283.3 

19.8 

45 

44.9 

3-1 

OS 

104.7 

7.3 

65 

164.  6 

11-5 

25 

224.5 

15.7 

85 

284.3 

19.9 

46 

45-9 

3-2 

06 

105.7 

7.4 

66 

165.6 

II. 6 

26 

225.4 

15.8 

86 

285.3 

20.0 

47 

46.9 

3-3 

07 

106.  7 

7.5 

67 

166.6 

II. 6 

27 

226.4 

15.8 

87 

286.3 

20.0 

48 

47-9 

3-3 

08 

107.6 

7-5 

68 

167.6 

II. 7 

28 

227.4 

15.9 

88 

^ll-^ 

20.  I    , 

49 

48.9 

3-4 

09 

108.7 

7.6 

69 

168.6 

II. 8 

29 

228.4 

16.0 

89 

288.3 

20.2 

50 

49-9 

3.5 
3-6 

10 

109.7 

7.7 
7-7 

70 
1 7.1 

169.6 

II. 9 

30 

229.4 

16.0 

90 

_289.3 

20.  2 

51 

50.9 

III 

no.  7 

170.6 

II. 9 

231 

230.  4 

16.  I 

291 

290.  3 

20.3 

52 

51-9 

3-6 

12 

III. 7 

7.8 

72 

171.6 

12.0 

32 

231.4 

16.2 

92 

291.3 

20.4 

53 
54 

52.9 

3-7 

13 

112.  7 

7.9 

73 

172.6 

12.  I 

32, 

232.4 

16.3 

93 

292.3 

20.4 

53-9 

3-8 

14 

113- 7 

8.0 

74 

173.6 

12.  I 

34 

233.4 

16.3 

94 

293.3 

20.5 

55 

54.9 

3-8 

15 

114.7 

8.0 

75 

174.6 

12.2 

35 

234.4 

16.4 

95 

294-3 

20.6 

56 

55-9 

3-9 

16 

115.7 

8.1 

76 

175.6 

12.3 

36 

235.4 

16.5 

96 

295.3 

20.  6 

57 

56.9 

4.0 

17 

116.  7 

8.2 

77 

176.6 

12.3 

37 

236.4 

16.5 

97 

296.3 

20.  7 

58 

57.9 

4.0 

18 

117.7 

8.2 

78 

177.6 

12.4 

38 

237.4 

16.6 

98 

297.3 

20.8 

59 

58.9 

4-1 

19 

118.  7 

8.3 

79 

178.6 

12.5 

39 

238.4 

16.7 

99 

298.3 

20.9 

60 
Dist. 

59-9 

4.2 

20 

119.7 

8.4 

80 

179.6 

12.6 

40 

239.4 

16.7 

300 

299.3 

20.9 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Foi 

•  86  Degr 

ees. 

TABLE  2. 

Page  219 

» 

Difference  of  Latitude  and  Departure  for 

5  Degrees 

'• 

Dist. 
I 

Lat. 

I.O 

Dep. 
0.  I 

Dist. 
61 

Lat. 
60.8 

Dep. 

5-3 

Dist. 
121 

Lat. 
120.  5 

'   Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

10.5 

181 

180.3 

15.8 

241 

240.  I 

21.0 

2 

2.0 

0.  2 

62 

61.8 

5-4 

22 

121.  5        10 

.6 

82 

181.  3 

15-9 

42 

241.  I 

21.  I 

3 

3.0 

0-3 

63 

62.8 

5-5 

23 

122.5      10 

-7 

83 

182.3 

15-9 

43 

242.  I 

21.2 

4 

4.0 

0.3 

64 

63.8 

5-6 

24 

123.5    10 

.8 

84 

183-3 

16.0 

44 

243.1 

21-3 

5 

5-0 

0.4 

65 

64.8 

5-7 

25 

124.5    10 

.9 

85 

184.3 

16.  I 

45 

244.1 

21.4 

6 

6.0 

0-5 

66 

65.7 

5.8 

26 

125.5    II 

.0 

86 

185.3 

16.2 

46 

245.1   1  21.4     1 

7 

7.0 

0.6 

67 

66.7 

5.8 

27 

126.5     II 

.  I 

87 

186.3 

16.3 

47 

246.  I 

21.5 

8 

8.0 

0.7 

68 

67.7 

5-9 

28 

127.5    II 

.  2 

88 

187-3 

16.4 

48 

247.1 

21.6 

9 

9.0 

0.8 

69 

68.7 

6.0 

29 

128. 5     II 

2 

89 

188.3 

16.5 

49 

248.1 

21.7 

10 

II 

10.  0 
II. 0 

0^9 

70 

69.7 

6.1 

30 

129.5    " 

-3 

90 

189.3 

16.6 

50 
251 

249.0 

21.8 

1.0 

71 

70.7 

6.2^ 

131 

130-5    II 

4 

191 

190.3 

16.6 

250.0 

21.9 

12 

12.0 

I.  0 

72 

71-7 

6.3 

32 

131-5    II 

5 

92 

191. 3 

16.7 

52 

251.0      22.0     1 

'3 

13.0 

I.  I 

73 

72.7 

6.4 

33 

132.5    II 

6 

93 

192.3 

16.8 

53 

252.0  1  22.  I     1 

14 

13-9 

1.2 

74 

73-7 

6.4 

34 

133-5    II 

7 

94 

193-3 

16.9 

54 

253.0 

22.  I 

15 

14.9 

1-3 

75 

74-7 

6.5 

35 

134.5    II 

8 

95 

194.3 

17.0 

55 

254.0 

22.  2 

i6 

15-9 

1.4 

76 

75-7 

6.6 

36 

135-5   II 

9 

96 

195.3 

17.  I 

56 

255.0 

22.3 

17 

16.9 

1-5 

77 

76.7 

6.7 

37 

136.5    II 

9 

97 

196.3 

17.2 

57 

256.0 

22.4 

i8 

17.9 

1.6 

78 

77.7 

6.8 

38 

137.5        12 

0 

98 

197.2 

17.3 

58 

257.0      22.5 

19 

18.9 

1-7 

79 

78.7 

6.9 

39 

138.5        12 

I 

99 

198.2 

17-3 

59 

258.0     22. 6 

20 
21 

19.9 
20.  9 

1-7 

80 

79-7 

7.0 

40 

139-5        12 

2 

200 

_i99.2 

17.4 

60 

259.  0     22.  7 

1.8 

81 

80.7 

7-1 

141 

140.5    ,    12 

3 

201 

200.2 

17-5 

261 

260.0 

22.  7 

22 

21.9 

1.9 

82 

81.7 

7-1 

42 

141.5        12 

4 

02 

201.  2 

17.6 

62 

261.0 

22.  8 

23 

22. 9 

2.0 

83 

82.7 

7.2 

43 

142.5    1    12 

5 

03 

202.2 

17.7 

63 

262.0 

22.9 

24 

23-9 

2.  I 

84 

83.7 

7-3 

44 

143.5    i     12 

6 

04 

203.2 

17.8 

64 

263.  0  '  23.  0 

25 

24.9 

2.  2 

85 

84.7 

7-4 

45 

144.4        12 

6 

°5 

204.2 

17.9 

65 

264.  0     23.  I 

26 

25-9 

2.3 

86 

85.7 

7-5 

46 

145.4    ,     12 

7 

06 

205.  2 

18.0 

66 

265.  0     23.  2 

27 

26.9 

2.4 

87 

86.7 

7.6 

47 

146.4   .    12 

8 

07 

206.  2 

18.0 

67 

266. 0  :  23. 3 

28 

27.9 

2.4 

88 

87.7 

7-7 

48 

147.4 

12 

9 

08 

207.  2 

18.  I 

68 

267,0    23.4 

29 

28.9 

2.5 

89 

88.7 

7.8 

49 

148.4 

13 

0 

09 

208.2 

18.2 

69 

268.0 

23-4 

30 
31 

_29^9 

2.6 

90 

89.7 

7.8 

50 

149-4 

13 

I 

10 

209.2 

18.3 

70 

269.0 

23-5 

30-9 

2.7 

91 

90.7 

7-9 

151 

150.4       13 

2 

211 

210.  2 

18.4" 

271 

270.0 

23.6 

32 

31-9 

2.8 

92 

91.6 

8.0 

52 

151.4   i    13 

2 

12 

211.  2 

'^•1 

72 

271.0    23. 7 

33 

32.9 

2.9 

93 

92.6 

8.1 

53 

152.4 

13 

3 

13 

212.  2 

18.6 

73 

272.0    23.8 

34 

33-9 

3-0 

94 

93-6 

8.2 

54 

153.4 

13 

4 

14 

213.  2 

18.7 

74 

273-0    23.9 

35 

34.9 

3-1 

95 

94.6 

8.3 

55 

154.4   '    13 

5 

15 

214.  2 

18.7 

75 

274.0    24.0 

36 

35-9 

3-1 

96 

95-6 

8.4 

56 

155-4  ;   13 

6 

16 

215.2 

18.8 

76 

274. 9    24. 1 

37 

36.9 

3-2 

97 

96.6 

8.5 

57 

156.4      13 

7 

17 

216.  2 

18.9 

77 

275.9  ■  24.1 

38 

37.9 

3-3 

98 

97.6 

8.5 

58 

157-4      13 

8 

18 

217.2 

19.0 

78 

276. 9    24. 2 

39 

38.9 

3-4 

99 

98.6 

8.6 

59 

158.4      13 

9 

19 

218  2 

19.  I 

79 

277-9    24.3 

40 
41 

39-8 
40.8 

3-5 

100 

99.6 

8.7 

60 

159-4      13 

9 

20 
221 

219.  2 

19.2 

80 

278.9    24.4 

3-6 

lOI 

100.6 

8.8 

161 

160.4      14 

0 

220.2 

19.3 

281 

279.9    ;    24.5 

42 

41.8 

3-7 

02 

101.6 

8.9 

62 

161. 4      14 

I 

22 

221.  2 

19.3 

82 

280.  9     24.  6 

43 

42.8 

3-7 

03 

102.6 

9.0 

63 

162.4      14 

2 

23 

222.2 

19.4 

83 

281.9     24.  7 

44 

43-8 

3-8 

04 

103.6 

9.1 

64 

163.4  1   14 

3 

24 

223.1 

19-5 

84 

282,  9     24.  8 

45 

44.8 

3-9 

05 

104.6 

9.2 

65 

164.4  i   14 

4 

25 

224.  I 

19.6 

85 

283.  9     24.  8 

46 

45-8 

4.0 

06 

105.6 

9.2 

66 

165.4 

14 

5 

26 

225.  I 

19.7 

86 

284.  9     24.  9 

47 

46.8 

4.  I 

07 

106.6 

9-3 

67 

166.4 

14 

6 

27 

226.  I 

19.8 

ll 

285.9  i  25.0 

48 

47.8 

4.2 

08 

107.6 

9-4 

68 

167.4 

14 

6 

28 

227.  I 

19.9 

88 

286.  9    !    25.  I 

49 

48.8 

4-3 

09 

108.6 

9-5 

69 

168.4 

14 

7 

29 

228.1 

20. 0 

89 

287.9       25.2 

50 
5' 

49.8 
50.8 

_4-4 
4.4 

10 

109.6 

9.6 

70 

169.4 

14 

8 

30 

229.  I 

20.  0 

90 

288.9       25.3 

^11 1 

1 1076^ 

9-7 

171 

170.3 

14 

9 

231 

^23o.r 

20.  I 

291 

289.9        25.4 

52 

SI. 8 

4-5 

12 

III. 6 

9.8 

72 

171. 3      15 

0 

32 

231. 1 

20.  2 

92 

290.9       25.4 

53 

-52.8 

4.6 

13 

112.6 

9.8 

73 

172.3 

15 

I 

33 

232.1 

20.3 

93 

291.9       25.5 

54 

53.8 

4-7 

14 

1 13.  6 

9-9 

74 

173.3 

15 

2 

34 

233-1 

20.4 

94 

292.  9     25.  6 

55 

54.8 

4.8 

15 

114.  6 

10.  0 

75 

174-3 

15 

3 

35 

234. 1 

20.  5 

9^ 

293.  9  '  25.  7 

56 

55.8 

4.9 

16 

115.6 

10.  I 

76 

175-3  i  15 

3 

36 

235.1 

20.  6 

96 

294.9     25.8 

57 

56.8 

5-0 

17 

1 16.  6 

10.  2 

77 

176.3     15. 

4 

37 

236. 1 

20.  7 

97 

295.9     25.9 

58 

57.8 

5-1 

18 

117. 6 

10.3 

78 

177.3     15 

5 

38 

237.1 

20.  7 

98 

296.  9     26.  0 

59 

58.8 

5-1 

19 

118.  5 

10.4 

79 

178.3     15- 

6 

39 

238. 1 

20.8 

99 

297.  9     26.  I 

60 

59.8 

5-2 

20 

1 19.  5 

10.5 

80 

179-3 

15- 

7 

40 

239.1 

20.9 

300 

298.9 

26. 1 

Dist. 

Dep. 

Lat.    1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.    1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Foi 

'  85  Degrees.         1 

Page  220 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  6  Degrees. 

1 

II 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Depll 

I 

I.O 

0.  I 

61 

60.  7 

6.4 

121 

120.3 

12.6 

181 

180.0 

18.9 

241 

239.7 

25.  2I 

2 

2.0  1     0.2 

62 

61.7 

6.5 

22 

121. 3 

12.8 

82 

181. 0 

19.0 

42 

240.7 

25.39 

3 

3.0  1     0.3 

P 

62.7 

6.6 

23 

122.3 

12.9 

^3 

182.0 

1    19.  I 

43 

241.7 

25. 4I 

4 

4.  0       0. 4 

64 

f^-^ 

6.7 

24 

123-3 

13.0 

84 

183.0 

19.2 

44 

242.7 

25.  5I 

5 

5.  0        0.  5 

^5 

t     64.6 

6.8 

25 

124-3 

13-1 

85 

184.0 

1   19-3 

45 

243.7 

25.6V 

6 

6.  0       0.  6 

66 

'     65.6 

6.9 

26 

125-3 

13-2 

86 

185.0 

19.4 

46 

244.7 

25.  7B 

7 

7.  0       0.  7 

67 

1     66.6 

7.0 

27 

126.  3 

13-3 

87 

186.0 

19-5 

47 

245.6 

25.8 1 

8 

8.0       0.8 

68 

:     67.6 

7-1 

28 

127.3 

13-4 

88 

187.0 

19-7 

48 

246.6 

25.9  M 

9 

9. 0       0. 9 

69 

68.6 

7.2 

29 

128.3 

13-5 

89 

188.0 

19.8 

49 

247.6 

26.0     ; 

lO 

iT 

1      ^-^ 
!     10.9 

I.  0 
I.  I 

70 
71 

69.6 
70.6 

7-3 
7-4 

30 
131 

129.3 

13.6 

90 

189.0 

19.9 

50 
251 

248.6 

26.  I 

130.3 

13-7 

191 

190.0 

20.0 

249.6 

26.2 

12 

i     "-9 

1-3 

72 

71.6 

7-5 

32 

131.  3 

13-8 

92 

190.9 

20.  I 

52 

250.  6 

26.3 

13 

12.9 

1.4 

73 

'     72.6 

7.6 

33 

132-3 

1  13-9 

93 

I9I-9 

20.2 

53 

251.6 

26.4 

14 

13-9 

'•^ 

74 

73-6 

7-7 

34 

133-3 

i  14.0 

94 

192.9 

20.3 

54 

252.6 

26.6 

15 

14.9 

1.6 

75 

74.6 

7.8 

35 

134-3 

14.  I 

95 

193-9 

20.4 

55 

253-6 

26.7 

i6 

15.9 

1-7 

76 

75.6 

7-9 

36 

135-3 

14.2 

96 

194-9 

20.  5 

56 

254.6 

26.8 

17 

16.9 

1.8 

77 

76.6 

8.0 

37 

136.  2 

14-3 

97 

195-9 

20.6 

57 

255-6 

26.9 

i8 

17  9 

1.9 

78 

77.6 

8.2 

38 

137-2 

14.4 

98 

196.9 

20.  7 

58 

256.6     27.0    1 

19 

18.9 

2.0 

l^ 

78.6 

l-^ 

39 

138.2 

14.5 

99 

197-9 

20.8 

59 

257.6 

27.1 

20 
21 

19.9 

2. 1 

80 
81 

79.6 
80.6 

8.4 

8:5" 

40 
141 

139.2 
140.2 

14.  6 

200 

198.9 

20.  9 
21.0 

60 
261 

25S.6 
259.6 

27.  2 

27.  3 

20. 9       2.2 

"14.  T 

201 

199.9 

22 

21.9       2.3 

82 

81.6 

8.6 

42 

141.  2 

14.8 

02 

200.9 

21.  I 

62 

260.6 

27.4 

23 

22.9       2.4 

83 

82.5 

8.7 

43 

142.  2 

14.9 

03 

201.  9 

21.2 

63 

261.6 

27.5 

24 

23.9 

^•^ 

84 

83.5 

8.8 

44 

143.2 

15-1 

04 

202.  9 

21.3 

64 

262.  6 

27.  6 

25 

24.9 

2.6 

^5 

84.5 

8.9 

45 

144.2 

15.2 

05 

203.9 

21.4 

65 

263-5 

27.7 

26 

25-9 

2.7 

86 

85.5 

9.0 

46 

145-2 

15-3 

06 

204.9 

21-5 

66 

264.5 

"27.8 

27 

26.9 

2.8 

87 

86.  5 

9-1 

47 

146.  2 

15-4 

07 

205.9 

21.6 

67 

265.5 

27.9 

28 

27.8 

2.9 

88 

87.5 

9.2 

48 

147.2 

15-5 

08 

206.9 

21.7 

68 

266.  5 

28.0 

29 

28.8 

3-0 

89 

88.5 

9-3 

49 

148.2 

15-6 

09 

237-9 

21.8 

69 

267.5 

28.1 

30 
31 

29.8 

3-1 

90 
91 

89.5 
90.5 

9-4 

50 

149.2 

15-7 

10 

2X1 

208.8 

22.0 

70 

268.  5      28.  2 

269.  5      28.  3 

30.  8  I     3.  2 

9-5 

151 

150.2 

15.8 

209.8 

22.  1 

271 

32 

31.8       3-3 

92 

91-5 

9.6 

52 

151.  2 

15-9 

12 

210.8 

22.2 

72 

270.5      28.4 

33 

32.8 

3-4 

93 

92.5 

9.7 

53 

152.  2 

16.0 

13 

211. 8 

22.3 

73 

271-5 

28.  5 

34 

33-8 

3-6 

94 

93-5 

9.8 

54 

153-2 

16. 1 

14 

212.8 

22.4 

74 

272.5 

28.6 

35 

34.8 

3-7 

95 

94-5 

9-9 

55 

154-2 

16.2 

15 

213.8 

22.  5 

75 

273-5 

28.  7 

36 

35-8       3.8 

96 

95-5  I 

10.  0 

56 

155-1 

16.3 

16 

214.8 

22.6 

76 

274.5      28.8     1 

37 

36.8       3.9 

97 

96.5  ! 

10.  I 

57 

156. 1 

16.4 

17 

215.8 

22.  7 

77 

275-5      29.0     \ 

38 

37.8 

4.0 

98 

97-5 

10.  2 

58 

157- 1 

16.5 

18 

216.8 

22.8 

78 

276.5 

29.1     1 

39 

38.8 

4.1 

99 

98.5 

10.3 

59 

158. 1 

16.6 

19 

217.8 

22.9 

79 

277.5 

29.2    1 

40 
41 

39-8 
40.8 

4.2 

100 

99-  5_  1 
100.4 

J°-5„ 
10.6 

60 

_'59^i 

16.7 

20 
221 

218.8 
219.8 

23.0 

80 

278.5      29.3     1 

4.1I 

ToF 

161 

160. 1 

16.8 

23.1 

23^" 

279.5 

29.4    1 

42 

41.8       4.41 

02 

101.4 

10.7 

62 

161. 1 

16.9 

22 

220.8 

23.2 

82 

280.  5      29.  5 

43 

42.  8       4.  5 

03 

102.4 

10.8 

P 

162. 1 

17.0 

23 

221.  8 

23-3 

83 

281.4      29.6 

44 

43.  8       4.  6 

04 

103.4 

10.  9 

64 

163. 1 

17. 1 

24 

222.8 

23-4 

84 

282.  4      29.  7 

"^5 

44. 8       4-7 

05 

104.4 

II.  0 

65 

164. 1 

17.2 

25 

223.8 

23-5 

85 

283.4 

29.8 

46 

45.  7       4-  8 

06 

105.4 

II.  I 

66 

165. 1 

17.4 

26 

224.8 

23.  6 

86 

284.  4      29.  9 

47 

46.7 

4-9 

07 

106.4  i 

II.  2 

67 

166. 1 

17-5 

27 

225.8 

23-7 

87 

285.  4      30.  0 

48 

47-7 

5-0 

08 

107.4 

11-3 

68 

167.  I 

17.  6 

28 

226.8 

23.8 

88 

28b.  4      30.  I 

49 

48.7 

5-1 

09 

108.4 

II. 4 

69  i 

168. 1 

17.7 

29 

227.7 

23-9 

89 

2S7.4      30.2 

50 
51 

49-7 

5-2 

10 

"iii"1 

X09  4 
no.  4 

"-5 

70  1 

169, 1 

17.  s 

30    i 

228.7 

24.0 

90 

288.  4      30.  3 

50-  7       5-  3  i 

II. 6 

171  1 

170. 1 

17.9 

231 

229.7 

24.1 

291 

289.4      30.- 4 

52 

51-7       5-4 

12  ! 

III. 4 

II. 7 

72 

171.  I 

18.0 

32 

230.7 

24-3 

92 

290.4 

30.5    1 

53 

52. 7       5-5 
53-7       5-6  1 

13  ! 

112. 4 

II. 8 

73 

172.  I 

18.  I 

33 

231-  7 

24-4 

93 

291.4 

30.6 

54 

14 

113. 4  \ 

II. 9 

74 

173.0 

18.2 

34 

232.  7 

24-5 

94 

292.  4      30  7 

55 

54-7 

5-7 

15 

114-4 

12.  0 

75 

174.0 

18.3 

35 

233-  7 

24.6 

95 

293.  4      30.  8 

56 

55-7  : 

5-9  I 

16 

115-4 

12.  I 

76 

175-0 

18.4 

36 

234-  7 

24.7 

96 

294-  4     30.  9 

57 

56.  7        6.  0 

17 

116.  4 

12.2 

77  1 

176.0 

18.5 

37 

235-  7 

24.8 

97 

295-4 

31.0 

58 

57.7        6.1 

18  1 

117.4 

12.3 

78  ! 

177- 0  1 

18.6 

38 

236.  7  : 

24-9 

98 

296.4 

31.1 

59 

58.  7  ,     6.  2 

19 

118.  3 

12.4 

79 

178.0 

18.7 

39 

237-  7 

25.0 

99 

297.4 

31-3 

60 

59-  7  1     6. 3 

20 

1 19- 3 

12.5 

80  1 

179-0 

18.8 

40 

238.  7 

1 

25.1 

300 

298.4 

31   4 
Lat. 

Dist. 

Dep. 

Lat.    1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.    j 

Dist. 

Dep. 

[For 

84  Degrees.         1 

TABLE  2. 

Page  221 

Di&erence  0 

"  Latitude  and  Departure  for 

7  Degrees. 

Dist. 

Lat.' 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.  I 

61 

60.5 

7-4 

121 

120.  I       14.  7 

179.7 

22.  I 

241 

239.2 

29.4 

2 

2.0 

0.  2 

62 

61.5 

7.6 

22 

121.  I        14.9 

82 

180.6 

22.2 

42 

240.2 

29.5 

3 

3-0 

0.4 

63 

62.5 

7-7 

23 

122.  I        15.0 

P 

181. 6 

22.3 

43 

241.  2       29.6 

4 

4.0 

0.5 

64 

63.5 

7.8 

24 

123.  I        15.  I 

84 

182.6 

22.  4 

44 

242.  2       29.  7 

5 

5-0 

0.6 

65 

64.5 

7-9 

25 

124.  I        15.2 

!5 

183.6 

22.5 

45 

243.  2       29.  9 

6 

6.0 

0.7 

66 

65-5 

8.0 

26 

125.  I        15.4 

86 

184  6. 

22.  7 

46 

244.2       30.0 

7 

6.9 

0.9 

67 

66.5 

8.2 

27 

126.  I        15.5 

87 

185.6 

22.8 

47 

245.  2    f  30.  I 

8 

7-9 

1.0 

68 

67.5 

8.3 

28 

127.0        15.6 

88 

186.6 

22.9 

48 

246.  2       30.  2 

9 

8.9 

I.  I 

69 

68.5 

8.4 

29 

128.0        15.7 

89 

187.6 

23.0 

49 

247.  I      30.  3 

10 

_9^9_ 

1.2 

70 

<^9-5 
70-5 

8.5 

30 

129.  0      15.  8 

90 

188.6 

23.2 

50 

248.1 
249.1 

30.5     1 

10.9 

1-3 

71 

8.7 

131 

130.0      16.0 

191 

189.6 

23-3 

251 

30.6 

12 

II. 9 

1-5 

72 

7'-5 

8.8 

32 

131. 0      16.  I 

92 

190.6 

23-4 

52 

250.  I    i    30.  7 

'3 

12.9 

1.6 

73 

72.5 

8.9 

33 

132.0     16. 2 

93 

191. 6 

23-5 

53 

251.1        30.8 

H 

13-9 

1-7 

74 

73-4 

9.0 

34 

133-0      16.3 

94 

192.6 

23.6 

54 

252. 1  :  31.0 

15 

14.9 

1.8 

75 

74-4 

9-1 

35 

134.0      16.5 

95 

193-5 

23-8 

55 

253. 1     31. 1 

16 

15.9 

1.9 

76 

75-4 

9-3 

36 

135.0     16.6 

96 

194-5 

23-9 

50 

254.1     31.2 

17 

16.9 

2.  I 

77 

76.4 

9-4 

37 

136.0      16.  7 

97 

195-5 

24.0 

57 

255-1  \  31.3 

18 

17.9 

2.2 

78 

77.4 

9-5 

38 

137.0      16,8 

98 

196.5 

24.1 

58 

256.1  j  31.4 

19 

18.9 

2.3 

79 

78.4 

9.6 

39 

138.0      16.9 

99 

197-5 

24-3 

59 

257.1  1  31.6 

20 
21 

19.9 

2.4 

80 
81 

79-4 
80.4 

9-7 

40 

139.0      17.  I 
139.9  '  17.2 

200 
201 

198.5 
199.5 

24-4 

60 

258.1 

31.7 
31.8 

20.8 

2.6 

9.9 

141 

24-5 

261 

259. 1 

22 

21.8 

2.7 

82 

81.4 

10.  0 

42 

140.9  1  17.3 

02 

200.5 

24.  6 

62 

260.0 

31.9 

23 

22.8 

2.8 

83 

82.4 

4lO.    I 

43 

141-9      17-4 

03 

201.  5 

24.7 

63 

261.0 

32.1 

24 

23.8 

2.9 

84 

83.4 

10,2 

44 

142.9     17-5 

04 

202.5 

24-9 

64 

262. 0  i  32. 2 

2t 

24.8 

3-0 

^5 

84.4 

10.4 

45 

143-9      17-7 

°5 

203.5 

25-0 

^5 

263.0    32.3 

26 

25.8 

3.2 

86 

85. 4 

10.5 

46 

144.9      17.8 

06 

204.5 

25.1 

66 

264.0  1  32.4 

27 

26.8 

3-3 

87 

86.4 

10.6 

47 

145-9      17-9 

07 

205.5 

25.2 

67 

265.0  1  32.5 

2S 

27.8 

3.4 

88 

87-3 

10.7 

48 

146.9      18.0 

08 

206.4 

25-3 

68 

266.0 

32.7 

29 

28.8 

3-5 

89 

88.3 

10.8 

49 

147.9      18.2 

09 

207.4 

25-5 

69 

267.0 

32.8 

30 
31 

29.8 

30.8 

3-7 

90 
91 

89.3 
90.3 

II. 0 

50 
151 

148.9 
149.9 

18.3 

10 

208.4 

25.6 

70 

268.0 
269. 0 

32.9 

3-8 

II.  I 

18.4 

211 

2097^ 

25-7 

271 

33.0 

32 

31.8 

3-9 

92 

91-3 

II.  2 

52 

150.9      18.5 

12 

210.  4      25.  8 

72 

270.0 

33-1 

33 

32.8 

4.0 

93 

92.3 

"•3 

53 

151. 9      18.6 

13 

21 1.  4      26.0 

73 

271.0 

33.3 

34 

33-7 

4.1 

94 

93-3 

II. 5 

54 

152.9      18.8 

14 

212.4      26.  I 

74 

272.0 

33-4 

35 

34-7 

4-3 

95 

94.3 

II. 6 

55 

153.8      18.9 

15 

213.4  1  26.2 

75 

2730    33.5    1 

36 

o5-7 

4.4 

96 

95-3 

II. 7 

56 

154.8 

19.  0 

16 

214.4  :   26.3 

76 

273.9     33-^ 

37 

36.7 

4-5 

97 

96.3 

II. 8 

57 

155-8 

19.  I 

17 

215.4      26.4 

77 

274.9  1  33-8 

3H 

37-7 

4.6 

98 

97-3 

II. 9 

58 

156.8 

19-3 

18 

216.4      26.6 

78 

275-9     33-9 

39 

5^-7 

4.8 

99 

98.3 

12.  I 

59 

'^l-l 

19-4 

19 

217.4  1   26.7 

79 

276.  9     34. 0 

40^ 
41 

39-7 

4.9 

100 

99-3 

12.2 

60 

158.8 

19-5 

20 

218.4 

26.8 

80 

277. 9     34. 1 

40.7 

5-0 

lOI 

100.  2 

12.3 

T61 

159-8^ 

19.6 

221 

219.4 

26.9 

281 

278.  9     34.  2 

42 

41.7 

5-1 

02 

101.2 

12.4 

62 

160.8 

19.7 

22 

220.  3      27.  I 

82 

279.9  1  34-4 

43 

42.7 

5-2 

03 

102.  2 

12.6 

63 

161.  8 

19.9 

23 

221.  3        27.  2 

P 

280.9  i  34.5 

44 

4J-7 

5-4 

04 

103.2 

12.7 

64 

162.8 

20.  0 

24 

222.3  !  27.3 

84 

281.9     34.6 

45 

44-7 

5-5 

05 

104.2 

12.8 

65 

163.8 

20.  I 

25 

223.3    1    27.4 

85 

282.  9     34.  7 

46 

45-7 

5-6 

06 

105.2 

12.9 

66 

164.8 

20.  2 

26 

224.3    1    27.5 

86 

283.  9     34.  9 

47 

46.6 

5-7 

07 

106.2 

13.0 

67 

165.8 

20.4 

27 

225.3    i    27.7 

87 

284.  9     35.  0 

48 

47.6 

5-8 

08 

107.2 

13.2 

68 

166.7 

20.5 

28 

226.  3  1  27.  8 

88 

285.9     35-1 

49 

48.6 

6.0 

09 

108.2 

13-3 

69 

167.7 

20.  6 

29 

227.3  !  27.9 

89 

286.  8     35.  2 

50 
51 

49.6 
50.6 

6.1 
6.2 

10 

109.2 

13-4 

70 

168.7 

20.  7 

30 

22S.  3     28. 0 

90 

287.8     35-3 

III 

no.  2 

'3-5 

171 

169.7 

20.8 

231 

229.3" 

28.2 

291 

288. 8     35.  5 

52 

51.6 

6.3 

12 

III. 2 

13.6 

72 

170.7 

,21.0 

32 

230.3 

28.3 

92 

289.8  '  35.6 

53 

52.6 

6.5 

13 

112. 2 

13-8 

73 

171.  7 

21.  I 

33 

231.3 

28.4 

93 

290.  8     35.  7 

54 

53.6 

6.6 

14 

1 13. 2 

13-9 

74 

172.7 

21.  2 

34 

232.3 

28.5 

94 

291.8     35.8 

55 

54.6 

^•7 

IS 

114. 1 

14.0 

75 

173-7 

21.3 

35 

233-2 

28.6 

95 

292.  8  1  36.  0 

56 

55-6 

6.8 

16 

115.  I 

14.  I 

76 

174-7 

21.4 

36 

234.2     28. 8 

96 

293.  8     36.  I 

57 

56.6 

6.9 

17 

116. 1 

14-3 

77 

175.7 

21.  6 

37 

235.2  ;  28.9 

97 

294.8     36.2 

58 

57.6 

7.1 

18 

117. 1 

14.4 

78 

176.7 

21.7 

38 

236.2 

29.0 

98 

295-8  :  36.3 

59 

58.6 

7.2 

19 

118.  I 

14-5 

79 

177-7 

21.8 

39 

237-2 

29.  I 

99 

296.  8     36. 4 

00 
Dist. 

59.6 
Dep. 

7-3 

20 

119. 1 

14.6 

80 

178.7 

21.9 

40 

238.2 

Dep. 

29.2 

300 

297.  8     36.  6 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Lat. 

Dist. 

Dep. 

Lat.    1 

[Fo 

r  83  Degrees.         1 

Page  222 

TABLE  2. 

1, 

Difference  of  Latitude  and  Departure  for  8  Degrees. 

1', 

Dist. 

Lat. 

1  " 

I.O 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat, 

Dep. 

I 

0.  I 

61 

60.4 

H 

121 

119.  8 

16.8 

181 

179.2 

25.2 

241 

238.7 

33-5 

2 

2.0 

0.3 

62 

61.4 

8.6 

22 

120.8 

17.0 

82 

180.2 

25-3 

42 

239.6 

33-7 

3 

3-0 

0.4 

63 

62.4 

8,8 

23 

121. 8 

17.  I 

83 

181. 2 

25-5 

43 

240.6 

33.8 

4 

4.0 

0.6 

64 

63-4 

8.9 

24 

122.8 

17.3 

84 

182.2 

25.6 

44 

241.  6 

34-0 

5 

5-0 

0.7 

65 

64.4 

9.0 

25 

123.8 

17.4 

85 

183.2 

25.7 

45 

242.  6 

34-1 

6 

5-9 

0.8 

66 

65.4 

9.2 

26 

124.8 

17.5 

86 

184.2 

25.9 

46 

243.6 

34-2 

7 

6.9 

1.0 

67 

66.3 

9-3 

^7 

125.8  1  17.7 

87 

185.2 

26.0 

47 

244.6 

34.4 

S 

7-9 

I.  I 

68 

67-3 

9-5 

28 

126.8  j  17.8 

88 

186.2 

26.  2 

48 

245.6 

34-5 

9 

8.9 

1-3 

69 

68.3 

9.6 

29 

127.  7  1  18.  0 

89 

187.2 

26.3 

49 

246.6 

34-7 

lO 

9-9 

1.4 

70 

69-3 

9-7 

30 

128.7 

18.  I 
18.2" 

90 
191 

188.2 
189.  I 

26.4 
^26.6 

50 
251 

247.6 
248.6 

34.8 
34.  9 

II 

10.9 

1-5 

71 

70.3 

9-9 

131 

129.7 

12 

II. 9 

1-7 

72 

71-3 

10.  0 

32 

130.7 

18.4 

92 

190.  I 

26.7 

52 

249.5 

35-1 

13 

12.9 

1.8 

73 

72.3 

10.2 

33 

131-7 

'^•5 

93 

191.  I 

26.9 

53 

250.5 

35-2 

14 

13-9 

1-9 

74 

73-3 

10.3 

34 

132.7 

18.6 

94 

192.  I 

27.0 

54 

251.5 

35-3 

15 

14.9 

2.  I 

75 

74.3 

10.4 

35 

133-7 

18.8 

95 

193.  I 

27.1 

55 

252.5 

35-5 

i6 

'to 

2.2 

76 

75-3 

IC.6 

36 

134-7  i  18.9 

96 

194.  I 

27.3 

56 

253-5 

35-6 

17 

16,8 

2.4 

77 

76.3 

10.7 

37 

135-7 

19. 1 

97 

195.  I 

27.4 

57 

254-5 

35-8 

i8 

17.8 

^•5 

78 

77.2 

10  9 

38 

136-7 

19.  2 

98 

196.  I 

27.6 

58 

255-5 

35-9 

19 

18.8 

2.6 

79 

78.2 

II  0 

39 

137-7 

19.3 

99 

197.1 

27.7 

59 

256.5 

36.0 

20 

19.8 
20.8' 

2.8 

2^9 

80 

79.2 

II   I 

_4°„ 

138.6 
139.6 

19-5 

200 

198.  I 

27.8 

60 

257.5 

36.2 
36-3 

21 

81 

80.2 

"•3 

141 

19.6 

201 

199.0 

28.0 

261 

258.5 

22 

21.8 

3-1 

82 

81.2 

II. 4 

42 

140.6 

19.8 

02 

200.  0 

28.1 

62 

259.5 

36-5 

23 

22.8 

3-2 

P 

82.2 

II. 6 

43 

141.  6 

19.9 

03 

2«I.O 

28.3 

63 

260.4 

36  6 

24 

23.8 

3-3 

84 

83.2 

II. 7 

44 

142.6 

20.  0 

04 

202.0 

28.4 

64 

261.  4 

36-7 

25 

24.8 

3-5 

85 

84.2 

II. 8 

45 

143-  6 

20.  2 

05 

203.0 

28.5 

65 

262.4 

36-9 

26 

25-7 

3-6 

86 

85.2 

12.0 

46 

144.6 

20.3 

06 

204.0 

28.7 

66 

263.4 

37-0 

27 

26.7 

3-8 

87 

86.2 

12.  I 

47 

145.6 

20.  5 

07 

205.0 

28.8 

67 

264.4 

37-2 

28 

27.  7 

3-9 

88 

87.1 

12.  2 

48 

146.6 

20.  6 

08 

206.0 

28.9 

68 

265.4 

37-3 

29 

28.7 

4.0 

89 

88.1 

12.4 

49 

147-  5 

20.  7 

09 

207.0 

29.  I 

69 

266.4 

37.4 

30 
31 

29.7 
30-7 

4.2 

4-3 

90 
91 

89, 1 
90.  I 

12.5 
12.7 

50 

148.5 

20.9 

10 

208.0 

29.2 
29^4 

70 

271 

267.4 
268.4 

37-6 

37-7 

151 

149-5 

21.0 

211 

208.9 

32 

31-7 

4-5 

92 

91. 1 

12  8 

52 

150.5  {  21.2 

12 

209.9 

29.5 

72 

269.4 

37-9 

33 

32.7 

4.6 

93 

92. 1 

12.9 

53 

151-5 

21-3 

13 

210.  9 

29.  6 

73 

270.3 

38.0 

34 

33-7 

4-7 

94 

93-1 

13- I 

54 

152.5 

21.4 

14 

211.  9 

29.8 

74 

271.3 

38.1 

^ 

34-7 

4.9 

9| 

94.1 

13.2 

55 

153-5 

21.6 

15 

212.9 

29.9 

75 

272.3 

38.3 

36 

35-^ 

5-0 

96 

95-1 

13-4 

56 

154.5     21.7 

16 

213.9 

30.1 

76 

273-3 

38-4 

37 

36.6 

5-1 

97 

96. 1 

13.5 

57 

155-5     21.9 

17 

214.9 

30.2 

77 

274-3 

38.6 

38 

37-6 

5-3 

98 

97- 0 

13.6 

58 

156.5 

22.0 

18 

215-9 

30-3 

78 

275-3 

38-7 

39 

38.6 

5-4 

99 

98.0 

13-8 

59 

157-5 

22.  I 

19 

216.9 

30-5 

79 

276.3 

38-8 

40 
41 

39-6 

5-6 

100 

-_99iO_ 

13-9 

60 

158.4     22.3 

20 

217.9 

30.6 

80 
281 

277.3 
278.3 

39-0 
39-1 

40.6 

5-7 

lOI 

100.  0 

14.  I 

161 

159-4 

22.4 

221 

218.8 

30.8 

42 

41.6 

5.8 

02 

lOI.O 

14.2 

62 

160.4 

22.  5 

22 

2IQ,8 

30-9 

82 

279.3 

39-2 

43 

42.6 

6.0 

03 

102.0 

14-3 

P 

161. 4 

22.  7 

23 

220.8 

31.0 

83 

280.  2 

39-4 

44 

43-6 

6.  I 

04 

103.  0 

14-5 

64 

162.4 

22.8 

24 

221.8 

31.2 

84 

281.2 

39-5 

45 

44.6 

6.3 

05 

104.0 

14.6 

65 

163.4 

23.0 

25 

222.  8 

31.3 

85 

282.  2 

39-7 

46 

45-6 

6.4 

06 

105.0 

14.8 

66 

164.4 

23-1 

26 

223.8 

31.5 

86 

283.2 

39.8 

47 

46.5 

6.5 

07 

106.0 

14.9 

67 

165.4 

23-2 

27 

224.8 

31.6 

87 

284.2 

39-9 

48 

47.5 

6.7 

08 

106.9 

15.0 

68 

166.4 

23-4 

28 

225.8 

31.7 

88 

285.2 

40.  I 

49 

48.5 

6.8 

09 

107.9 

15.2 

69 

167.4 

23-5 

29 

226.8 

31.9 

89 

286.2 

40.2 

50 
51 

49-5 
50-5 

7.0 
7-1 

10 

108.9 

15-3 

70 

168.3 

23-7 

30 

227.8 

32.0 

90 

287.2 

40.4 
40.5 

III 

109.9 

15-4 

171 

169.3 

23.8 

231 

228.8 

32.1 

291 

'  288.  2 

52 

51-5 

7.2 

12 

no.  9 

15.6 

72 

170.3 

23-9 

32 

229.7 

32.3 

92 

2S9.  2 

40.  6 

53 

52-5 

7-4 

13 

III. 9 

15-7 

73 

171-3 

24.1 

33 

230.7 

32.4 

93 

290.  I 

40.8 

54 

53-5 

7-5 

14 

112. 9 

15-9 

74 

172.3 

24.  2 

34 

231-7 

32.6 

94 

291.  I 

40.9 

55 

54.5 

^■l 

15 

113-9 

16.0 

75 

173-3 

24.4 

35 

232.7 

32.7 

95 

292.  I 

41. 1 

56 

55-5 

7.8 

16 

1 14. 9 

16. 1 

76 

174-3 

24.5 

36 

233-7 

32.8 

96 

293.1 

41.2 

57 

56.4 

7-9 

17 

115.9 

16.3 

77 

175.3 

24.6 

37 

234-7 

33.0 

97 

294.1 

41.3 

58 

57.4 

8.  I 

18 

116.  9 

16.4 

78 

176.3 

24.8 

38 

235-7 

33-1 

98 

295-1 

41.5 

59 

58.4 

8.2 

19 

117.  8 

16.6 

79 

177.3 

24.9 

39 

236-7 

33-3 

99 

296.  I 

41.  6 

60 

59-4 

8.4 

20 

1 18.  8 

16.7 

80 

178.2 

25.1 

40 

237-7 

33-4 
Lat. 

300 
Dist. 

297.1 
Dep. 

41.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For 

82  Degrees.        1 

TABLE  2. 

Page  223 

%^ — 

Difference  of  Latitude  and  Departure  for  9  Degrees 

• 

Dist. 

Latl 

Dep. 

1 

'     0.2 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
238.0 

Dep. 

37-7 

I 

I.O 

61 

60.2 

9-5 

121 

1 19. 5 

18.9 

181 

178.8 

28.3 

241 

2 

2.0 

0.3 

62 

61.2 

9-7 

22 

120.  5 

19.  I 

82 

179.8 

28.5 

42 

239.0 

37-9 

3 

3-0 

0.5 

63 

62.2 

9.9 

23 

121.  5 

19.  2 

83 

180.  7 

28.6 

43 

240.0 

38.0 

4 

4.0 

0.6 

64 

63.2 

10.  0 

24 

122.5 

19.4 

84 

1S1.7 

28.  S 

44 

241.0 

38-2 

5 

4.9 

o.S 

65 

64.2 

10.2 

25 

123.5 

19.  6 

85 

182.7 

28.9 

45 

242.0 

38-3 

6 

5-9 

0.9 

66 

65.2 

10.3 

26 

124.4 

19.7 

86 

183.7 

29.  I 

46 

243.0 

38-5 

7 

6.9 

I.  I 

67 

66.2 

10.5 

27 

125.4 

19.9 

87 

184.7 

29-3 

47 

244.0 

38.6 

8 

7-9 

1-3 

68 

67.2 

10.6 

28 

126.4 

20.0 

88 

185.7 

29-4 

48 

244-9 

38.8 

9 

8.9 

1.4 

69 

68.2 

10.8 

29 

127.4 

20.2 

89 

186.7 

29.6 

49 

245-9 

39-0 

10 

II 

9.9 
10.9 

1.6 
1-7 

70 

71 

72 

69.  I 
70.1 

II. 0 
II.  I 

30 

128.4 

20.3 

90 

187.7 

29.7 

50 

246.9 
247-9 

39-1 
39-3 

131 

129.4 

20.  5 

191 

188.6 

29-9 

251 

12 

II. 9 

1.9 

71.  I 

"•3 

32 

130.4 

20.6 

92 

189.6 

30.0 

52 

248.9 

39  4 

'3 

12.8 

2.0 

73 

72.1 

II. 4 

33 

131. 4 

20.8 

93 

190.6 

30.  2 

53 

249-9 

39-6 

14 

13.8 

2.  2 

74 

73-1 

II. 6 

34 

132.4 

21.0 

94 

191. 6 

30.3 

54 

250.9 

39-7 

15 

14.8 

2-3 

75 

74.1 

II. 7 

35 

133-3 

21.  1 

95 

192.6 

30-5 

55 

251.9 

39-9 

16 

15.8 

2-5 

76 

75-1 

II. 9 

36 

134.3 

21.3 

96 

193-6 

30-7 

56 

252.8 

40.0 

17 

16.8 

2.7 

77 

76.1 

12.0 

37 

135.3 

21.4 

97 

194.6 

30.8 

57 

253-8 

40.2 

18 

17.  8 

2.8 

78 

77.0 

12.  2 

38 

136.3 

21.  6 

98 

195.6 

31.0 

58 

254.8 

40.4 

19 

18.8 

3-0 

79 

78.0 

12.4 

39 

137.3 

21.7 

99 

196.5 

31- I 

59 

255-8 

40.5 

20 

19.8 

3-1 
3-3 

80 
81 

79.0 

12.5 

40 

138.3 

21.9 

200 

197.5 

31.3 

60 

256.8 

40.7 
40.8 

21 

20.  7 

80.0 

12.7 

141 

139-  3 

22.  I 

201 

198.5 

3 '-4 

261 

^57- f 

22 

21.7 

3-4 

82 

81.0 

12.8 

42 

140.3 

22.2 

02 

199.5 

31.6 

62 

258.8 

41.  0 

23 

22.7 

^■t 

!^ 

82.0 

13.0 

43 

141.  2 

22.4 

03 

200.5 

31.8 

63 

259-8 

41.  I 

24 

23-7 

3-8 

84 

83.  0 

13- I 

44 

142.  2 

22.5 

04 

201.  5 

31-9 

64 

260.  7 

41.3 

25 

24.7 

3-9 

85 

84.0 

13-3 

45 

143.2 

22.  7 

OS 

202.  5 

32.1 

65 

261.  7 

41.5 

26 

25.7 

4.1 

86 

84.9 

13-5 

46 

144.2 

22.8 

06 

203.5 

32.  2 

66 

262.  7 

41.6 

27 

26.  7 

4.2 

87 

85.9 

13-6 

47 

145.2 

23.0 

07 

204.5 

32.4 

67 

263.7 

41.8 

28 

27.7 

4.4 

88 

86.9 

13-8 

48 

146.  2 

23.2 

08 

205.4 

32-5 

68 

264.7 

41.9 

29. 

28.6 

4-5 

89 

87.9 

13-9 

49 

147.2 

23-3 

09 

206.4 

32.7 

69 

265.7 

42.1 

30 
31 

29.  6 
?o.  6 

4-7 
4.8 

90 
91 

88.9 
'89.9- 

14.  I 

50 

148.2 

23-5 

10 

207.4^ 

32.9 

70 

266.7 

42.2 

14.  2 

151 

149.  I 

23.6 

211 

208.4 

33.0 

271 

267.7 

42.4 

32 

31.6 

5-0 

92 

90.9 

14.4 

52 

150. 1 

23-8 

12 

209.4 

33-2 

72 

268.7 

42.6 

33 

32.6 

5-2 

93 

91.9 

14-5 

53 

151. 1 

23-9 

13 

210.4 

33-  3 

73 

269.6 

42.7 

34 

33-6 

5-3 

94 

92.8 

14.7 

54 

152.  I 

24.1 

14 

211. 4 

33-5 

74 

270.6 

42.9 

35 

34-6 

5-5 

95 

93.8 

14.9 

55 

153.  I 

24.  2 

15 

212.4 

33-6 

75 

271.6 

43-0 

36 

35-6 

5-6 

96 

94.8 

15.0 

56 

154.  I 

24.4 

16 

213.3 

33.8 

76 

272.6 

43-2 

37 

36.5 

5-8 

97 

95.8 

15.2 

57 

155.1 

24.  6 

17 

214.3 

33.9 

77 

273.6 

43-3 

38 

^^Z-5 

5-9 

98 

96.8 

15-3 

58 

156.  I 

24-7 

18 

215-3 

34-1 

78 

274-6 

43-5 

39 

38.5 

6.1 

99 

97.8 

15-5 

59 

157.0 

24.9 

19 

216.3 

34.3 

79 

275.6 

43-6 

40 
41 

39-5 

6.3 

100 

lOI 

98.8 
99.8 

15.6 

60 

158.0 

25.0 

25.  2 

20 
221 

217-3 
218.3 

34.4 
34-6 

80 

281 

276.6 

27775 

43-8 

40.5 

6.4 

15.8 

161 

159-0 

44.0 

42 

41-5 

6.6 

02 

100.  7 

16.0 

62 

160.0 

25.3 

22 

219.3 

34-7 

82 

278.5 

44.  I 

43 

42.5 

6.7 

03 

loi.  7 

16.  I 

63 

161.  0 

25.5 

23 

220.3 

34-9 

!^ 

279.5 

44.3 

44 

43-5 

6.9 

04 

102.  7 

16.3 

64 

162.0 

25.7 

24 

221.2 

35-0 

84 

280.5 

44.4 

45 

44.4 

7.0 

05 

103-7 

16.4 

65 

163.0 

25.8 

25 

222.  2 

35-2 

85 

281.5 

44.6 

46 

45-4 

7.2 

06 

104.7 

16.6 

66 

164.  0 

26.0 

26 

223.2 

35.4 

86 

282.5 

44.7 

47 

46.  4 

7-4 

07 

los.  7 

16.7 

67 

164.9 

26.  I 

27 

224.  2 

35.5 

87 

283.5 

44-9 

4S 

47-4 

7.5 

08 

106.  7 

16.9 

68 

165.9 

26.3 

28 

225.  2 

35.7 

88 

284.5 

45-1 

49 

48.4 

7-7 

09 

107.7 

17.  I 

69 

166.  9 

26.4 

29 

226.  2 

35.8 

89 

285.4 

45-2 

50 
51 

49-4 
50.4 

7.8 
8.0 

10 
III 

108.6 

17.2 

70 

167.9 
168.9 

26.6 

30 

227.2 

36.0 

_9°_ 

286.4 

45-4 
45-5 

109.6 

17.4 

171 

26.  8" 

231 

228.2 

36.1 

291 

287:4" 

52 

5f-4 

8.1 

12 

no.  6 

17.5 

72 

169.9 

26.9 

32 

229.  I 

36.3 

92 

288.4 

45-7 

53 

52.3 

8.3 

13 

£11.6 

17.7 

73 

170.9 

27.1 

33 

230.  I 

36.4 

93 

289.4 

45-8 

54 

53-3 

8.4 

14 

112. 6  1 

17.8 

74 

171. 9 

27.2 

34 

231-1 

36.6 

94 

290.4 

46.0 

55 

54-3 

8.6 

15 

113. 6 

18.0 

75 

172.8 

27.4 

35 

232.  1 

36.8 

95 

291.4 

46.  I 

56 

55-3 

8.8 

16 

114.  6 

18.  I 

76 

'73-8 

27.5 

36 

233.1 

36.9 

96 

292.4 

46-3 

57 

56.3 

8.0 

17 

115.  6 

18.3 

77 

174.8 

27.7 

37 

234.1 

37.1 

97 

293-3 

46.5 

5!^ 

57.3 

9.1 

18 

.16.5 

18.5 

78 

175.8 

27.8 

38 

235.1 

37-2 

68 

294-3 

46.6 

59 

58.3 

9.2 

19 

"7-5 

18.6 

176.8 

28.0 

39 

236.1 

37-4 

99 

295-3 

46.8 

60 

59-3 

9.4 

ao 

1 18.  5 

18.8 

80 

177.8 

28.2 

40 

237.0 

37-5 

300 

296.3 
Dep. 

46.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Lat. 

[Foi 

81  Degrees.         1 

Page  224 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

10  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.2 

61 

60.  I 

10.6 

121 

119.  2 

21.0 

178.3 

31-4 

241 

237.3 

41.8 

2 

2.0 

0.3 

62 

61.  I 

10.8 

22 

120.  I 

21.  2 

82 

179.2 

31.6 

42 

238.3 

42.0 

3 

3-0 

o-S 

63 

62.0 

10.9 

23 

121.  I        21.4 

83 

180.2 

31.8 

43 

239.3 

42.2 

4 

3-9 

0.7 

64 

63.0 

II.  I 

24 

122.  I        21.  5 

84 

l8l.2 

32.0 

44 

240.3 

42.4 

5 

4-9 

0.9 

65 

64.0 

II-3 

25 

123.  I        21.7 

85 

182.2 

32.1 

45 

241.3 

42.5 

6 

5.9 

1.0 

66 

65.0 

11-5 

26 

124.  X  I  21.9 

86 

183.2 

32.3 

46 

242.3 

42.7 

7 

6.9 

I.  2 

67 

66.0 

II. 6 

27 

125.  I        22.  I 

87 

184.2 

32-5 

47 

243.2 

42.9 

8 

7-9 

1.4 

68 

67.0 

II. 8 

28 

126.  I        22.2 

88 

185.  I 

32.6 

48 

244.2 

43-1 

9 

8.9 

1.6 

69 

68.0 

12.0 

29 

127.0        22.4 

89 

186.  I 

32.8 

49 

245.2 

43-2 

lO 

II 

9.8 
10.8 

1-7 

70 

68.9 

12.2 

30 

128.0        22.6 

90 

187.  I 

33- 0 

50 

246.2 

43-4 

1.9 

71 

69.9 

12.3 

131 

129.0       22.7 

191 

188.  I 

33-2 

251 

247.2 

43-6 

12 

II. 8 

2.  I 

72 

70.9 

12.5 

32 

130.0       22.9 

92 

189.  I 

33-3 

52 

248.2 

43-8 

13 

12.8 

2.3 

73 

71.9 

12.7 

33 

131.  0    1    23.1 

93 

190.  I 

33.5 

53 

249.2 

43-9 

14 

13.8 

2.4 

74 

72.9 

12.8 

34 

132.0 

23-3 

94 

191.  I 

33-7 

54 

250.  I 

44-  I 

15 

14.8 

2.6 

75 

73-9 

13.0 

35 

132.9 

23-4 

95 

192.0 

33-9 

55 

251.  I 

44-3 

1 6 

15.8 

2.8 

76 

74.8 

13.2 

36 

133-9 

23.6 

96 

193.0 

34-0 

56 

252.  I 

44-5 

17 

16.7 

3-0 

77 

75-^ 

13-4 

37 

134-9 

23.8 

97 

194.0 

34-2 

57 

253-1 

44.6 

iS 

17.7 

3-1 

78 

76.8 

13-5 

38 

135-9 

24.0 

98 

195-0 

34-4 

58 

254-1 

44-8 

19 

18.7 

3-5 

79 

77.8 

13-7 

39 

136.9        24.1 

99 

196.0 

34-6 

59 

255-1 

45-0 

20 
21 

19.7 
20.  7 

3-5 
3-^ 

80 

78.8 

13-9 

40 

137.9       24.3 

200 

197.0 

34.7 

60 

256.  I 

45-1 
45-3 

81 

79.8 

14.  I 

141 

138.9       24.5 

201 

197-9 

34-9 

261 

^257:  o~ 

22 

21.7 

3-8 

82 

80.  8 

14.2 

42 

139.8       24.7 

02 

198.9 

35-1 

62 

258.0 

45-5 

23 

22.  7 

4.0 

83 

81.7 

14.4 

43 

140.8       24.8 

03 

199.9 

35-3 

63 

259.0 

45-7 

24 

23.6 

4.2 

84 

82.7 

14.6 

44 

141. 8     25.0. 

04 

200.9 

35-4 

64 

260.0 

45.8 

25 

24.6 

4-3 

85 

83.7 

14.8 

45 

142.  8     25.  2 

05 

201.  9 

35-6 

65 

261.  0 

46.  0 

26 

25.6 

4-5 

86 

84.7 

14.9 

46 

143.8     25.4 

06 

202.9 

35.8 

66 

262.0 

46.2 

27 

26.6 

4.7 

87 

85.7 

15-1 

47 

144.8     25.4 

07 

203.9 

35-9 

67 

262.9 

46.4 

28 

27.6 

4-9 

88 

86.7 

15-3 

48 

145-  8  i  25.  7 

08 

204.8 

36.1 

68 

263.9 

46.5 

2,9 

28.6 

5-0 

89 

87.6 

15-5 

49 

146.7 

25-9 

09 

205.8 

36.3 

69 

264.9 

46.7 

30 
31 

29-5 

30-5 

5-2 

5-4 

90 
91 

88.6 
89.6" 

15.6 

50 

147-7 

26.0 

10 

206.8 

36.5 

70 

265^9^ 

46.9 
'47.1"" 

15.8 

151 

148.  7  1  26.  2 

211 

■  207.  8 

36.6 

271 

266.  9 

32 

31-5 

5.6 

92 

90.  6 

16.0 

52 

149.  7  1  26. 4 

12 

208.8 

36.8 

72 

267.  9 

47.2 

33 

32.5 

5-7 

93 

91.6 

16. 1 

53 

150.  7  :  26. 6 

13 

209.  8 

37.0 

73 

268.9 

47-4 

34 

33-5 

5-9 

94 

92.6 

16.3 

54 

151-7  i  26.7 

14 

210.  7 

37.2 

74 

269.8 

47-6 

35 

34-5 

6.1 

95 

93-6 

16.5 

55 

152.6 

26.9 

15 

211.  7 

37.3 

75 

270.8 

47.8 

36 

35-5 

6.3 

96 

94-5 

16.7 

56 

153-6 

27.  I 

16 

212.  7 

37.5 

76 

271.8 

47-9 

37 

36.4 

6.4 

97 

95-5 

16.8 

57 

154.6 

27-3 

17 

213-7 

37.7 

77 

272.8 

48.1 

38 

37-4 

6.6 

98 

96.5 

17.0 

58 

155.6    27.4 

18 

214.7 

37-9 

78 

273-8 

48.3 

39 

38.4 

6.8 

99 

97-5 

17.2 

59 

156.6  :  27.6 

19 

215-7 

38.0 

79 

274.8 

48.4 

40 

39-4 

6.9 
7.1 

100 

98.5 

17.4 

60 

157.6  !  27.8 

20 

216.  7 

38.2 

80 

275-7 

48.6 
48.8 

41 

40.4 

Toi 

99-5 

17-5 

161 

158.6  i  28.0 

221 

217.6^ 

38.4 

281 

276.7 

42 

41.4 

7-3 

02 

100.  5 

17.7 

62 

159.  5   1   28.  I 

22 

218.6 

38.5 

82 

277.7 

49.0 

43 

42.3 

7-5 

03 

101.4 

17.9 

63 

160.  5   i  28.  3 

23 

219.  6 

38.7 

83 

278.7 

49.1 

44 

43-3 

7.6 

04 

102.4 

18. 1 

64 

161.  5   1  28.5 

24 

220.  6 

38.9 

84 

279.7 

49-3 

45 

44-3 

7.8 

05 

103.4 

18.2 

65 

162.  5   :  28.  7 

25 

•    221.6 

39-1 

85 

280.  7 

49-5 

46 

45-3 

8.0 

06 

104.4 

18.4 

66 

163.  5      28.  8 

26 

222.  6 

39-2 

86 

281.  7 

49.7 

47 

46.3 

8.2 

07 

105.4 

18.6 

67 

164.5 

29.0 

27 

223.  6 

39.4 

87 

282.  6 

49.8 

48  , 

47-3 

8.3 

08 

106.4 

18.8 

68 

165-4 

29.  2 

28 

224.5 

39.6 

88 

283.6 

50.0 

49: 

48.3 

8.5 

09 

107.3 

18.9 

69 

166.  4     29.  3 

29 

225.5 

39.8 

89 

284.6 

50.2 

50 

_49-2 

8.7 
8.9 

10 
III 

108.3 
109.3 

19. 1 

70 

167.  4     29.  5 

30 

226.  5 

39.9 

_90. 

285.6 

50.4 
50.5 

51 

50.  2 

19.3 

171 

168. 4  1  29.  7 

231 

227.5 

40.  I 

291 

286.6 

52 

51-2 

9.0 

12 

no.  3 

19.4 

72 

169.4     29.9 

32 

228.  5 

40.3 

92 

287.6 

50-7 

53 

52.2 

9.2 

13 

III. 3 

19.6 

73 

170.4     30.0 

33 

229.5 

40.5 

93 

28S.  5 

50-9 

54 

53-2 

9.4 

14 

112.  3 

19.8 

74 

171. 4 

30.2 

34 

230.4 

40.  6 

94 

2S9.  5 

51-I 

55 

54.2 

9.6 

15 

"3-3 

20.0 

75 

172.3 

30-4 

35 

231.4 

40.8 

95 

290.5 

51-2 

56 

55-1 

9-7 

16 

114.  2 

20. 1 

76 

173-3     30-6 

36 

.232.  4 

41.0 

96 

291.5 

51-4 

57 

56.1 

9-9 

17 

115.2 

20.3 

77 

174-3     30-7 

37 

233-4 

41.2 

97 

292.5 

51.6 

5^ 

57-1 

10.  I 

18 

116.  2 

20.  5 

78 

175-3     30-9 

38 

234-4 

41-3 

q8 

293-5 

51-7 

59 

58.1 

10.2 

19 

117.  2 

20.  7 

79 

176.3 

31-1 

39 

235-4 

41-5 

99 

294-5 

51-9 

60 
')ist. 

59-1 

10.4 

20 

1 18.  2 

20.8 

80 

177-3 

31-3 

40 

236-4 

41.7 

300 

295.4 

52.1 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Foi 

80  Degn 

;es. 

TABLE  2. 
nifference  of  Latitude  and  Departure  for  ii  Degrees. 


[Page  225 


Dist.       Lat. 


I 

2 

4 

5 

b 

7 
S 

9 

ID 
II 
12 

13 

14 

1=; 

i6 

•7 

iS 

19 

20 
21 

22 
23 
24 
25 
26 

27 
2S 

29 


31 

32 

34 
35 
36 
37 
38 
39 

41 
42 

43 
44 

45 
46 

47 
48 

49 
50 

51 

52 
53 
54 
55 
56 

57     ; 

58! 

59  : 

60  1 


i.o 
2.0 
2.9 

3-9 

4.9 

5-9 
6.9 

7-9 
8.8 

__?:.?_ 
10.8 
II. 8 
12.8 
13-7 
14.7 
15-7 
16.  7 

17.7 
18.7 

19.  6 

20.  6 
21.6 
22.6 
23.6 

24-5 

25-5 
26.  5 
27.5 
28.  5 
29.4 


Dep. 


0.  2 
0.4 
0.6 
o.S 
1.0 

1.  I 
13 
1-5 
1-7 

2. 1 
2.3 

2.5 

2.7 
2.9 

3-1 

3-2 

3-4 
3.8 


Dist. 


Lat.        Dep. 


61 
62 

63 
64 

65 
66 
67 
68 
69 
70 

71 

72 

73 

74 

75 
76 

77 
78 

79 
80 


59-9 
60.9 
61.8 
62.8 
63.8 
64.8 
65.8 
66.8 
67.7 
^8^7_ 
69.7 
70.7 
71.7 
72.6 
73-6 
74.6 
75.6 
76.6 
77-5 
78.5 


4.0 
4.2 

4-4 
4.6 
4.8 
5-0 

5-2 

5-3 
5-5 
5-7 


81 

82 

84 

85 
86 

87 

88 

89 

90 


79-5 
80.5 
81.5 
82.5 

83.4 
84.4 
85.4 
86.4 
87.4 
88.3 


30-4 

31-4 
32.4 
33-4 
34-4 
35-3 
36.3 
37-3 
38.3 
39-3 

40.  2 

41.  2 

42.  2 
43-2 
44-2 
45.2 
46.  I 
47.1 
48.1 
49-1 
50.1 
51.0 
52.  o 

53- o 
54.0 

55.  o 
56.0 
56.9 

57-9 
58-9 


Dist.  I    Dep. 


5-9 
6.1 

6.3 

6.5 
6.7 

6.9 

7-1 

7.3 

7-4 

7.8 
8.0 
8.2 

8.4 
8.6 
8.8 
9.0 
9.2 

9-3 
9.5_ 

9-7 
9.9 
10.  I 
10.3 
10.5 
10.  7 

10.  9 

11.  I 

"•3 
II. 4 

Lat. 


91 

92 
93 
94 

95 
96 

97 
98 

99 
100 

lOI 

02 

03 
04 

05 
06 

07 

08 

09 

10 

III 

12 

'3 
14 

15 
16 

17 
18 

19 
20 

Dist. 


89-3 
90.3 


91 

92 

93 

94 

95-2 

96.2 

97.2 

98.  2 

99.1 

GO.  I 

01.  I 

02.  I 

03.  I 

04.  I 
05.0 

06.  O 

07.  o 

08.0 

09.  o 

09.9 

10.  9 
II 
12 

13 
14 

15 

16.8 

17.8 


1.6 

1.8 
2.  o 

2.2 
2.4 
2.6 
2.8 

3-0 
3-2 
3^ 
3-5 


5-3 


5-5 

5-8 
6.0 
6.2 
6.4 
6.6 
6.8 
7.0 
7.2 


7-4 

7.6 

7-7 
7-9 

8.1 

8.3 
8.5 
8.7 
8.9 
9-  I 


9-3 

9-5 

9-7 
9.8 

20.  o 

20.  2 

20.4 

20.  6 
20.8 
21.0 

21.  2 
21.  4 

21.  6 
21.8 
21.9 

22.  I 
22.3 
22.5 
22.  7 
22.9 


Dep.         Lat. 


Dist. 


121 

22 

23 

24 

26 
27 
28 
29 

3£_ 
131 

32 
33 
34 
35 
36 
37 
38 
39 

^°. 
141 

42 
43 
44 
45 
46 

47 
48 

49 
50 


151 

52 
53 
54 
55 
56 
57 
58 

59 
60 

161 
62 

63 
64 

65 
66 

67 

68 

69 

70 


171 

72 

73 
74 

75 
76 

77 
78 

79 
80 

Dist. 


Lat. 


18.8 
19.8 

20.  7 

21.  7 

22.  7 

23-7 
24.7 

25.  6 

26.6 

27.6 

2876" 

29.  6 

30.6 

31-5 

32.5 

33-5 

34-5 

35-5 

36.4 

37^ 

38.4 

39-4 

40.4 

41.4 

42.3 

43-3 

44-3 

45-3 

46.3 

47.2^ 

48.2 
49.2 
50.2 
51.2 
52.  2 
I 
I 
I 
I 
I 


Dep. 


53 
54 
55 
56 
57 
58.0 

59- o 

60.  o 

61.  o 
62.0 
63.0 

63-9 
64.9 
65.9 

66^9 
6779 

68:8 

69.8 
70.8 
71.8 
72.8 
73-7 
74-7 
75-7 
76.7 

Dep. 


23.1 

23-3 
23-5 
23-7 
23-9 
24.  o 

24.  2 
24.4 

24.  6 
24.8 

25.  o 
25.2 

25.4 

25.  6 
25.8 

26.  o 
26.  I 
26.  3 
26.  5 

26.  7 
26.9 

27.  I 

27-3 

27-5 
27.7 

27.9 
28.0 
28.2 
28.4 
j8^ 
2878 
29.  o 
29.  2 
29.4 
29.6 

29.  S 
30.0 

30.  I 
30-3 
30-5 


30 
30 
31 
31 
31 
31 
31 
32 
32.  2 

32^ 

32.6 

32.8 

33- o 

33 

33 

33 

33 

34.0 

34-2 

34-3 
Lat. 


Dist. 

181 

82 

83 
84 

85 
86 

87 
88 
89 

191 
92 
93 
94 

95 
96 

97 
98 

99 
200 


Lat. 


201 

02 

03 
04 

05 
06 
07 
08 
09 
10 


211 
12 

13 

14 

15 
16 

17 
18 

19 

20 

221 

22 

23 

24 

25 
26 

27 
28 
29 
30 


177.7 
178.7 

1 79.  6 
180.6 
181. 6 
182.6 
183.6 
184.5 

185.5 
186.5 

187.5 
188.5 

189.5 
190.4 

191-4 
192.4 

193-4 
194.4 

195-3 

197-3 
198.3 
199.3 

200.  3 

201.  2 

202.  2 

203.  2 

204.  2 
205.2 

206.  I 

207.  I 

208.  I 

209.  I 

210.  I 

211.  o 
212.0 
213.0 
214.  o 

215.0 

216.  o 
216.  9 
217.9 
218.9 
219.9 

220.  9 

221.  8 

222.  8 

223.  8 

224.  8 
225.8 


Dep. 

34-5 
34-7 
34-9 
35-1 
35-3 
35-5 
35-7 
35-9 
36.  I 

36.3 

36.4 
36.6 
36.8 
37- o 
37-2 
37-4 
37-6 
37-8 
38.0 
!  38.2 

i38-4 
38.5 

38-7 

!  38.9 

39-1 

39-3 

I  39-5 


39. 

39' 
40, 


40.3 
40.5 
40. 6 

I  40.  8 
i  41.0 

I  41 
I  41 
\  41 

!  41 

j  42.  o 

I    42.  2 

42.4 
42.6 
42.7 
42 

43 
43 
43 
43 
43 


231 
32 
33 
34 
35 
36 
37 
38 
39 
40 

Dist. 


226.8 
227.  7 
228.7 
229.  7 
230.7 

231-7 
232.6 

233-6 
234.6 

235-6 
Dep. 


44-  I 

44-3 

44-5 
44.6 

44-8 
45.0 

45-2 
45-4 
45-6 
45-8 

Lat. 


52  i 

53  ! 

54  1 

55  ! 

56  ^ 

57  ! 
58 

59 
60^ 

261 

62 

63 
64 

65 
66 
67 
68 
69 
70 
271 
72 
73 
74 

75 
76 

77 
78 

79 
80 


247-4 
248.  4 

249 
250 

251 
21:2 

253 

254-2 

255-2 


281 

82 

83  I 
84: 

85  I 
86 

87 
88 

89 
90 

291 
92 

93 
94 

95 
96 

97 
98 

99 
300 


256.  2 

257.2 
258.2 

259-1 

260.  I 

261.  I 

262.  I 
263.1 
264.  I 

^65^0 

266.  o 

267.0 

268.0 

269.  o 

269.  9 

270.9 
271.9 

272. 

273' 
274, 

2  75' 
276, 

277-8 
278.8 
279.8 
280.  7 
281.7 
282.  7 


Dist. 

Lat. 

241 

236.6 

42 

237-6 

43 

238.5 

44 

239-5 

45 

240.5 

46 

241.5 

47 

242.5   I 

48 

243-4 

49 

244.4 

50 

245-4  ■ 

251 

246.4 

Dep. 

46.0 
46.  2 
46.4 
46.6 
46.7 
46.9 

47-1 
47-3 
47-5 
47- 7_^ 

47-9 
48.  I 

48.3 
48.5 
48.7 
48.8 
49.0 
49-2 
49.4 

49^6 
49.8 
50.0 
50.2 

50.4 
50.6 

50.8 
50.9 
51- I 
51-3 

51.7 
5t-9 
52.1 

52-3 

52-5 

52-7 

52-9, 

53-0 


283 
^84, 

■785, 
286 
287 
288 
289 
290, 
291 
292.5 
293-5 
294-5 


53-2 
53-4 
53-6 
53.8 
54.0 
54-2 

54-4 
54-6 
54.  S 
55-0 
55-1 
55-3 
55-5 
55-7 

55-9 
56.1 

56. 

56. 

56, 

56. 

57-1 

57-2 


Dist.        Dep.      [     Lat. 
[For  79  Degrees. 


B 


1 

Page  226 

TABLE  2. 

1 

Difference  of  Latitude  and  Departure  for  12  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.2 

61 

59.7 

12.7 

121 

118.  4 

25.2 

181 

177.0 

37.6 

241 

235.7 

' — -^ 

50.  I  " 

2 

2.0 

0.4 

62 

60.6 

12.9 

22 

119.  3 

25.4 

82 

178.0 

37.8 

42 

236.7 

50.3 

3 

2.9 

0.6 

63 

61.6 

13.1 

23 

120.3 

25.6 

83 

179.0 

38.0 

43 

237.  7  I  50.  5 

4 

3-9 

0.8 

64 

62.6 

13.3 

24 

121. 3 

25.8 

84 

180.0 

38.3 

44 

238.  7  1  50.  7 

5 

4-9 

1.0 

65 

63.6 

13.5 

25 

122.3 

26.0 

85 

■    181. 0 

38.5 

45 

239.  6     50. 9 

6 

5-9 

1.2 

66 

64.6 

13.7 

26 

123.2 

26.  2 

86 

181. 9 

38.7 

46 

240.6 

51.  I 

7 

6.8 

1-5 

67 

65.5 

13.9 

27 

124.2 

26.4 

87 

182.9 

38.9 

47 

241.6 

51.4 

8 

7.8 

1-7 

68 

66.5 

14.  I 

28 

125.2 

26.6 

88 

183.9 

39.1 

48 

242.6 

51.6 

9 

8.8 

1-9 

69 

67.5 

14.3 

29 

126.2 

26.8 

89 

184.9 

39-3 

49 

243.6 

51.8 

lO 

9.8 

2.  I 

70 

68.5 

14.6 

30 

127.2 

27.0 

90 

185.8 
186.8 

39.5 

50 

244.5 

52.0 
52.2 

II 

10.8 

2.3 

71 

^6974" 

14.8 

131 

128.7^ 

27.  2 

191 

39.7 

251 

245-5 

12 

II. 7 

2.5 

72 

70.4 

15.0 

32 

129.  I 

27.4 

92 

187.8 

39.9 

52 

246.5 

52.4 

13 

12.7 

2.7 

73 

71.4 

15.2 

33 

130.  I 

27-7 

93 

188.8 

40.  I 

53 

247-5 

52.6 

14 

13-7 

2.9 

74 

72.4 

15.4 

34 

131.1 

27.9 

94 

189.8 

40.3 

54 

248.4 

52.8 

15 

14.7 

3-1 

75 

73-4 

15.6 

35 

132.0 

28.1 

95 

190.7 

40.5 

55 

249.4 

53-0 

16 

15-7 

3-3 

76 

74-3 

15.8 

36 

133-0 

28.3 

96 

191.  7 

40.8 

56 

250.4 

53-2 

17 

16.6 

3-5 

77 

75-3 

16.0 

37 

134.0 

28.5 

97 

192.7 

41.  0 

57 

251.4 

53-4 

18 

17.6 

3-7 

78 

76.3 

16.2 

38 

135.0 

28.7 

98 

193.7 

41.2 

58 

252.4  1  53-6 

19 

18.6 

4.0 

79 

77.3 

16.4 

39 

136.0 

28.9 

99 

194.7 

41.4 

59 

253-3     53-8 

20 

19.6 

4.2 

80 

78.3 

16.6 

40 

136.9 

29.1 

200 

195.6 

41.6 

60 

254-  3  1  54-  I 

21 

20.5 

4.4 

81 

79.2 

16.8 

141 

137.9 

29.3 

201 

196.6 

41.8 

261 

255-3 

54-3 

22 

21.5 

4.6 

82 

80.2 

17.0 

42 

138.9 

29.5 

02 

197.6 

42.0 

62 

256.3 

54.5 

23 

22.  5 

4.8 

83 

81.2 

17.3 

43 

139.9 

29.7 

03 

198.6 

42.  2 

63 

257.3 

54-7 

24 

23-5 

5-0 

84 

82.2 

17.5 

44 

140.9 

29.9 

04 

199.5 

42.4 

64 

258.2 

54-9 

25 

24.5 

5-2 

^^ 

83.1 

17.7 

45 

141.  8 

30.  I 

05 

200.  5 

42.6 

^A 

259.2 

55-1 

26 

25-4 

5-4 

86 

84.  I 

17.9 

46 

142.8 

30.4 

06 

201.  5 

42.8 

66 

260.2 

55-3 

27 

26.4 

5-6 

87 

85.1 

18.  I 

47 

143.8 

30.6 

07 

202.  5 

43.0 

67 

261.2  1  55.5    I 

28 

27.4 

5-8 

88 

86.1 

18.3 

48 

144.8 

30.8 

08 

203.5 

43-2 

68 

262. 1 

55-7 

29 

28.4 

6.0 

89 

87.1 

18.5 

49 

145.7 

31.0 

09 

204.4 

43.5 

69 

263.1 

55-9 

30 

29-3 

6.2 

90 

88.0 

18.7 

50 

146.7 

31.2 

10 

205.4 

43-7 

70 

264. 1 

56.1 

31 

30.3 

6.4 

91 

89.0 

18.9 

151 

147.7 

31-4 

211 

206.4 

43-9 

271 

265. 1 

56.3" 

32 

31-3 

6.7 

92 

90.0 

19.  I 

52 

148.7 

31-6 

12 

207.4 

44.1 

72 

266.  I 

56.6 

33 

32.3 

6.9 

93 

91.0 

19.3 

53 

149-7 

.31-8 

13 

208.3 

44-3 

73 

267.0 

56.8 

34 

33-3 

7.1 

94 

91.9 

19.5 

54 

150.6 

32.0 

14 

209.3 

44.5 

74 

268.0 

57.0 

35 

34.2 

7-3 

95 

92.9 

19.8 

55 

151. 6 

32-2 

15 

210.3 

44.7 

75 

269.0 

57.2 

36 

35-2 

7-5 

96 

93-9 

20.  0 

56 

152.6 

32.4 

16 

211. 3 

44.9 

76 

270.  0 

57-4 

37 

36.2 

7-7 

97 

94-9 

20.2 

57 

153.6 

32.6 

17 

212.3 

45-1 

77 

270.9 

57-6 

38 

37-2 

7-9 

98 

95-9 

20.4 

58 

154.5 

32.9 

18 

213.2 

45-3 

78 

271.9 

57-8 

39 

38.1 

8.1 

99 

96.8 

20.6 

59 

155.5 

33-1 

19 

214.  2 

45-5 

79 

272.9 

58.0 

40 

39-1 

8.3 

100 

97.8 

20.8 

60 

156.5 

33-3 

20 

215.2 

45-7 

80 

273-9 

58.2 

41 

40.  I 

8.5 

101 

98.8 

21.0 

161 

157.5 

33-5 

221 

216.2 

45.9 

281 

274-9     58.4 

42 

41.  I 

8.7 

02 

99.8 

21.2 

62 

158.5 

33-7 

22 

217. 1 

46.  2 

82 

275.8     58.6 

43 

42.1 

8.9 

03 

100.  7 

21.4 

63 

159.4 

33-9 

23 

218. 1 

46.4 

f^ 

276.  8     58.  8 

44 

43- 0 

9.1 

04 

101.  7 

21.6 

64 

160.4 

34-1 

24 

219.  I 

46.6 

84 

277-8  1  59-0 

45 

44- 0 

9-4 

05 

102.  7 

21.8 

65 

161. 4 

34.3 

25 

220. 1 

46.8 

^^ 

278.8  !  59.3 

46 

45- 0 

9.6 

06 

103.7 

22.0 

66 

162.4 

34.5 

26 

221. 1 

47.0 

86 

279.  8  ^  59.  5 

47 

46.0 

9.8 

07 

104.7 

22.2 

67 

163.4 

34.7 

27 

222.0 

47.2 

87 

280.  7  ,  59.  7 

48 

47.0 

10. 0 

08 

105.7 

22.  5 

68 

164.3 

34.9 

28 

223.0 

47-4 

88 

281.7 

59-9 

49 

47-9 

10.2 

09 

106.6 

22.  7 

69 

165-3 

35.1 

29 

224.0 

47-6 

89 

282.7 

60. 1 

50 

48.9 

10.4 

10 

107.6 

22.9 

70 

166.3 

35.3 

30 

225.0 

47-8 

90 

283.7 

60.3 

51 

49-9 

10.  6 

III 

To8."6~ 

23.1 

171 

167.3 

35.6 

231 

226.  0 

48.0 

291 

284.6 

60.5 

52 

50-9 

10.8 

12 

109.  6 

23.3 

72 

168.  2  . 

35.8 

32 

226.9 

48.2 

92 

285.6 

60.  7 

53 

51.8 

II. 0 

13 

no.  5 

23.5 

73 

169.  2 

36.0 

33 

227.9 

48.4 

93 

286.6 

60.  9 

54 

52.8 

II.  2 

14 

III. 5 

23.7 

74 

170.  2 

36.2 

34 

228.  9 

48.7 

94 

287.6 

61. 1 

55 

53-8 

II. 4 

IS 

112. 5 

23.9 

75 

171.  2 

36.4 

35 

229.9 

48.9 

95 

288.6 

61.3 

56 

54-8 

II. 6 

16 

113.5 

24.1 

76 

172.2 

36.6 

36 

230.8 

49.1 

96 

289.5 

61.5 

57 

55-8 

II. 9 

17 

114.4 

24-3 

77 

173.  I 

36.8 

37 

231.8 

49.3 

97 

290.5 

61.7 

58 

56.7 

12.  I 

18 

II5-4 

24.5 

78 

174.  I 

37-0 

38 

232.8 

49.5 

98 

291.5 

62.0 

59 

57.7 

12.3 

19 

116. 4 

24.7 

79 

175- I 

37-2 

39 

233.8 

49-7 

99 

292.5 

62.  2 

60 

58.7 

12.5 

20 

117.4 

24.9 

80 

176.  I 

37.4 

40 

234.8 

49-9 

300 

293.4 

62.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fo 

r  78  Degrees.         1 

TABLE  2. 

[Page  227  | 

,» 

Difference  of  Latitude  and  Departure  for  i 

3  Degrees. 

Dist. 

I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
176.4 

Dep. 

Dist. 

Lat. 

Dep. 

I.o 

0.2 

61 

59-4 

13-7 

121 

117.  9 

27.2 

181 

40.7 

241 

234.8 

54.2 

'i. 

1.9 

0.4 

62 

60.4 

13-9 

22 

1 18.  9 

27.4 

82 

177.3 

40.9 

42 

235-8 

54-4 

3 

2.9 

0.7 

63 

61.4 

14.2 

23 

1 19.  8 

27.7 

^3 

178-3 

41.2 

43 

236.8 

54-7 

4 

3-9 

0.9 

64 

62.4 

14.4 

24 

120.8 

27-9 

84 

179-3 

41.4 

44 

237-7 

54-9 

5 

4.9 

I.  I 

65 

63.3 

14.6 

25 

121,8 

28.1 

85 

180.3 

41.6 

45 

238.7 

55-1 

6 

5-8 

1-3 

66 

64-3 

14.8 

26 

122.8 

28.3 

86 

181. 2 

41.8 

46 

239.7 

55-3 

7 

6.8 

1.6 

67 

65-3 

15- I 

27 

123.7 

28.6 

87 

182.2 

42.1 

47 

240.7 

55-6 

8 

7.8 

1.8 

68 

66.3 

15-3 

28 

124.7 

28.8 

88 

183.2 

42.3 

48 

241.6 

55.8 

9 

8.8 

2.0 

69 

67.2 

15-5 

29 

125.7 

29.0 

89 

184.2 

42-5 

49 

242.6 

56.0 

lO 

9.7 

2.2 

70 

68.2 

15-7 

30 

126.  7 

29.  2 

90 

185.  I 

42.7 

50 

243.6 
244.6 

56.2 
56.5 

II 

10.7 

2.5 

71 

69.2 

16.0 

131 

127.6 

29-5^ 

191 

186.  I 

43-0 

251 

12 

II.  7 

2.7 

72 

70.2 

16.2 

32 

128.6 

29-7 

92 

187.  I 

43-2 

52 

245-5 

56.7 

13 

12.7 

2.9 

73 

71.  I 

16.4 

33 

129.6 

29-9 

93 

1 88.  I 

43-4 

53 

246.5 

56.9 

14 

13.6 

3-1 

74 

72.1 

16.6 

34 

130.6 

30.1 

94 

189.0 

43-6 

54 

247-5 

57-1 

15 

14.6 

3-4 

75 

73-1 

16.9 

35 

131- 5 

30-4 

95 

190.  0 

43-9 

55 

248.5 

57-4 

i6 

15.6 

^•^ 

76 

74.1 

17.  I 

36 

132-5 

30.6 

96 

191. 0 

44.1 

56 

249.4 

57-6 

17 

16.6 

3-S 

77 

75- 0 

17-3 

37 

133-5 

30.8 

97 

192.  0 

44-3 

57 

250.4 

57.8 

i8 

17.5 

4.0 

78 

76.0 

17-5 

38 

134-5 

31-0 

98 

192.9 

44-5 

58 

251-4 

58.0 

19 

18.5 

4-3 

79 

77.0 

17.8 

39 

135-4 

31.3 

99 

193-9 

44-8 

^9 

252.4 

58-3 

20 

19-5 

4.5 

80 

77.9 

18.0 

40 

136.4 

31-5 

200 

194.9 

45-0 

60 

253-  3 

58.5 

21 

20.5 

4-7 

81 

78.9 

18.2 

141 

137-4 

31.7 

201 

195.8 

45-2 

261 

254.3 

58.7 

22 

21.4 

4.9 

82 

79-9 

18.4 

42 

138.4 

31-9 

02 

196.8 

45-4 

62 

255.3 

58.9 

23 

22.4 

5-2 

83 

80.9 

18.7 

43 

139-3 

32.2 

03 

197.8 

45-7 

63 

256.3 

59.2 

24 

23-4 

5-4 

84 

Si. 8 

18.9 

44 

140.3 

32.4 

04 

198.8 

45-9 

64 

257.2 

59.4 

25 

24.4 

5-6 

85 

82.8 

19.  I 

45 

141.  3 

32.6 

05 

199.7 

46.  I 

65 

258.2 

59-6 

26 

25-3 

5-8 

86 

83.8 

19-3 

46 

142.3 

32.8 

06 

200.  7 

46.3 

66 

259.2 

59-8 

27 

26.3 

6.1 

87 

84.8 

19.6 

47 

143-2 

33- I 

07 

201.  7 

46.6 

67 

260.2 

60.  I 

28 

27-3 

6.3 

88 

85.7 

19.8 

48 

144.2 

33-3 

08 

202.  7 

46.8 

68 

261. 1 

60.3 

29 

28.3 

6.5 

89 

86.7 

20.0 

49 

145.2 

33-5 

09 

203.6 

47.0 

69 

262.  I 

60.5 

30 

29.2 

6.7 

90 

87.7 

20.  2 

50 

146.  2 

33-7 

10 

204.  6 

47-2 

70 

263. 1 

60.  7 

31 

30.2 

7.0 

91 

88.7 

20.5 

151 

~i47^r 

34-0 

211 

'20576 

47.  5 

271 

264. 1 

61.0 

32 

31.2 

7.2 

92 

89.6 

20.  7 

52 

148. 1 

34-2 

12 

206.6 

47-7 

72 

265.0 

61.2 

33 

32.2 

7-4 

93 

90.6 

20.9 

53 

149. 1 

34-4 

13 

207.5 

47-9 

73 

266.  0 

61.4 

34 

33-1 

7.6 

94 

91.6 

21.  I 

54 

150. 1 

34-6 

14 

208.5 

48.  I 

74 

267.0 

61.6 

35 

34.1 

7-9 

95 

92.6 

21.4 

55 

151. 0 

34-9 

15 

209.5 

48.4 

75 

268.0 

61.9 

36 

35-1 

8.1 

96 

93-5 

21.  6 

56 

152.0 

35-1 

16 

210.  5 

48.6 

76 

268.9 

62.1 

37 

36.1 

8.3 

97 

94-5 

21.8 

57 

153-0 

35-3 

17 

211. 4 

48.8 

77 

269.  9 

62.3 

38 

37- 0 

8.5 

98 

95-5 

22.0 

58 

154.0 

35-5 

18 

212.4 

49-0 

78 

270.9 

62.  5 

39 

38.0 

8.8 

99 

96.5 

22.3 

59 

154-9 

35-8 

19 

213-4 

49-3 

79 

271.8 

62.8 

40 

39- 0 

9.0 

100 

97-4 

22^5_ 

60 

155-9 

36.0 

20 

214.4 

49.5 

80 

272.8 

63.0 

41 

39-9 

9.2 

lOi 

98.4 

22.  7 

161 

156.9 

36.  2 

221 

215-3 

49-7 

281 

273.8 

63.2 

42 

40.9 

9-4 

02 

99.4 

22.  9 

62 

157-8 

36.4 

22 

216.3 

49-9 

82 

274-8 

63-4 

43 

41.9 

9-7 

03 

100.4 

23.  2 

63 

158.8 

36.7 

23 

217-3 

50.2 

l^ 

275-7 

63-7 

44 

42.9 

9-9 

04 

101.3 

23-4 

64 

159.8 

36.9 

24 

218.3 

50.4 

84 

276.7 

63-9 

45 

43.8 

10.  I 

05 

102.  3 

23.6 

65 

160.8 

37.1 

25 

219.2 

50.  6 

85 

277-7 

64.  I 

46 

44.8 

10.3 

06 

103-3 

23-8 

66 

161.  7 

37-3 

26 

220.  2 

50.8 

86 

278.7 

64-3 

47 

45.8 

10.  6 

07 

104.3 

24.1 

67 

162.  7 

37-6 

27 

221.2 

51- I 

87 

279.6 

64.6 

48 

46.8 

10.8 

08 

105.  2 

24-3 

68 

163-7 

37-8 

28 

222.  2 

51-3 

88 

280.6 

64.8 

49 

47-7 

II. 0 

09 

106.  2 

24-5 

69 

164-7 

38.  0 

29 

223.  I 

51-5 

89 

281.6 

65.0 

50 

48.7 

II. 2 

10 

107.2 

24-7 

70 

165.6 

38.2 

30 

224.  I 

51-7 

90 

282.6 

65.  2 

SI 

49-7 

"•5 

III 

108.2 

25.0 

171 

166.6 

38.5 

231 

225.  I 

52.0 

291 

283.5 

65.5 

52 

50-7 

II. 7 

12 

109.  I 

25.2 

72 

167.6 

38.7 

32 

226.  I 

52.2 

92 

284.5 

65-7 

53 

51.6 

II. 9 

13 

no.  I 

25-4 

73 

168.6 

38.9 

33 

227.0 

52.4 

93 

285-5 

65-9 

54 

52.6 

12. 1 

14 

III.  I 

25.6 

74 

169.5 

39-1 

34 

228.0 

52.6 

94 

286.5 

66.  I 

55 

53.6 

12.4 

15 

112.  I 

25-9 

75 

170.5 

39-4 

35 

229.0 

52.9 

95 

287.4 

66.  d. 

56 

54-6 

12.6 

16 

113-0 

26.  I 

76 

171. 5 

39-6 

36 

230.0 

53.1 

96 

288.4 

66.6 

57 

56-5 

12.8 

17 

114. 0 

26.3 

77 

172.5 

39-8 

37 

230.9 

53.3 

97 

289.4 

66.8 

58 

56.5 

13.0 

18 

115. 0 

26.5 

78 

173-4 

40.0 

38 

231.9 

53-5 

98 

290.4 

67.0 

59 

57-5 

13-3 

19 

116.0 

26.8 

79 

I7V-4 

40.3 

39 

232.9 

53-8 

99 

291.3 

67-3 

60 

58.5 

13-5 

20 

116. 9 

27.0 

80 

175.4 

40.5 

40 

233.8 

54- 0 

300 

292.3 

67-5 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

[Fo 

■  77  Degr 

ees. 

Pag 

e228] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  i 

4  Degree; 

>. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0,2 

61 

59-2 

14.8 

121 

I17.4 

29.3 

181 

175.6 

4.3-8 

241 

233.8 

58.3 

2 

1.9 

0-5 

62 

60.2 

15.0 

22 

118. 4      29.5 

82 

176.6 

44.0 

42 

234.8 

58.  5 

.3 

2.9 

0.7 

63 

61.  I 

15-2 

23 

1 19.  3      29.8 

83 

177.6 

44-3 

43 

235.8      58.8 

4 

3-9 

1.0 

64 

62.  I      15.  5 

24 

120.3      30-0 

84 

178.5 

44.5 

44 

236.8  1  59.0 

S 

4-9 

I.  2 

6S 

63.1  '  15-7 

25 

121.  3        30.2 

85 

179-5 

44.8 

45 

237.7      59.3 

6 

S.8 

1.5 

66 

64.0     16.0 

26 

122.3        30-5 

86 

180.5 

45.0 

46 

238. 7  ;  59. 5 

7 

6.8 

1.7 

67 

65.0  !  16.2 

27 

123.2        30.7 

87 

181. 4 

45.2 

47 

239.  7     59.  8 

8 

7.« 

1.9 

68 

66.0  i  16. 5 

28 

124.  2       31.  0 

88 

182.4 

45-5 

48 

240.  6     60.  0 

Q 

8.7 

2.2 

69 

67. 0  !  16.  7 

29 

125.2       31.2 

89 

183.4 

45-7 

49 

241.  6  i  60.  2 

lO 

II 

9-7 

2.4 

70 

67.9     16.9 

30 

126.  I        31.4 

90 

184.4 

46.0 

50 

242.6 

60.5     I 

10.7 

2.7 

71 

68. 9     1 7. 2 

131 

127.  I        31.7 

191 

185.3 

46.  2 

251 

243.5 

60.7 

12 

II. 6 

2.9 

72 

69.9     17.4 

32 

128.  I        31.9 

92 

186.3 

46.4 

52 

244.5     61.0    1 

13 

12.  6 

3-1 

73 

70.8  j  17.7 

33 

129.0       32.  2 

93 

187.3 

46.7 

53 

245.5 

61.2 

14 

13.6 

3-4 

74 

71.8     17.9 

34 

130.0        32.4 

94 

188.2 

46.9 

54 

246.5 

61.4 

IS 

14.6 

3.6 

75 

72.8 

18. 1 

35 

131-0     32-7 

95 

189.2 

47-2 

55 

247.4 

61.  7 

i6 

15-5 

3-9 

76 

73-7 

18.4 

3& 

132.0    32.9 

96 

190.2 

47-4 

56 

248.4 

61.9 

17 

16.  s 

4.1 

77 

74.7     18.6 

37 

132.9     33-  I 

97 

191.  I 

47-7 

57 

249.4 

62.  2 

18 

\7-5 

4.4 

78 

75-7 

18.9 

38 

133-9     33-4 

98 

192.  I 

47-9 

58 

250.3 

62.4 

19 

18.4 

4.b 

79 

76.7 

19. 1 

39 

134-9     33-(> 

99 

193.  I 

48.  I 

59 

251.3     62.7    1 

20 

19.4 

4.8 

80 
81 

77.6 

19.4 

40 

135-8     33-9 

200 

194.  I 

48.4 

60 

252.3 

62.9 

21 

20.4 

51 

78.6 

19.6 

141 

136.  8  i  34.  I 

201 

195.0 

48.6 

261 

253.2 

63.1 

22 

21.3 

5-3 

82 

79.6 

19.8 

42 

137.8  •  34.4 

02 

196.0 

48.9 

62 

254.2 

63.4 

2,1 

22.3 

5.6 

83 

80.5 

20.  I 

43 

138.8     34.6 

03 

197.0 

49-1 

63 

255.2 

63.6 

24 

23-3 

S.8 

84 

81.5 

20.3 

44 

139-7     34-8 

04 

197.9 

49-4 

64 

256.  2 

63.9 

2S 

24-3 

6.0 

8S 

82.  5      20.  6 

45 

140.  7     35-  I 

05 

198.9 

49.6 

65 

257.1 

64.  I 

26 

25.  2 

6.3 

86 

83.  4  1  20.  8 

46 

141- 7     35-3 

06 

199.9 

49-8 

66 

258.  I    ;  64.  4     1 

27 

26.  2 

6.S 

87 

84.4 

21.0 

47 

142.6     35.6 

07 

200.9 

50.  I 

67 

259- 1  !  64.  6    1 

28 

27.2 

6.8 

88 

85.4 

21.3 

48 

143-6     35-8 

08 

201.8 

50-3 

68 

260.0 

64.8 

29 

28.1 

7.0 

89 

86.4 

21.  5 

49 

144.  6     36.  0 

09 

202.  8 

50.6 

69 

261.0 

65.1 

30 

29.  I 

7-3 

90 

87.3 

21.8 

50 

145-  5     36-  3 

10 

203.8 

50.8 

70 

262.0 

65-3 

31 

30.1 

7-5 

91 

88.3 

22.0 

151 

146.5 

36.5 

211 

204.7 

51-0 

271 

263.0  j  65.6     1 

32 

31.0 

7-7 

92 

89.3 

22.3 

52 

147-5 

36.8 

12 

205.7 

51-3 

72 

263.9 

6q.8 

33 

32.0 

8.0 

93 

90.2 

22.  5 

53 

148.5 

37.0 

13 

206.  7 

5'-§ 

73 

264.9 

66.0 

34 

33- 0 

8.2 

94 

91.  2 

22.  7 

54 

149.4 

37.3 

14 

207.  6 

51.8 

74 

265.9 

66.3 

3S 

34- 0 

8.S 

95 

92.  2 

23.0 

55 

150.4 

37-5 

15 

208.6 

52.0 

75 

266.8 

66.5 

36 

34-9 

8.7 

96 

93-1 

23.2 

5^) 

151-4 

37.7 

16 

209.  6 

52-3 

76 

267.8 

66.8 

37 

35-9 

9.0 

97 

94- 1 :  23. 5 

57 

152.3 

38.0 

17 

210.6 

52-5 

77 

268.8 

67,0 

3^ 

36.9 

9.2 

98 

95.  I      23.  7 

58 

153-3 

38.2 

18 

211. 5 

52-7 

78 

269.7 

67.3 

39 

37.8 

9.4 

99 

96.  I      24.  0 

59 

154-3 

38.5 

19 

212.  5 

53-0 

79 

270.7 

67.5 

40 

38.8 

9-7 

100 

97.0 

24.2 

60 

155-2 

38.7 

20 

213.5 

53-2 

80 

271-7 

272.7 

67.7 

41 

39-8 

9-9 

lOI 

98.0 

24.4 

161 

156.2     38.9 

221 

214.4 

53-5 

281 

68.0 

42 

40.8 

10.  2 

02 

99.0 

24.7 

62 

157.2  1  39.2 

22 

215.4 

53-7 

82 

273.6 

68.2 

43 

41.7 

10.4 

03 

99.  9     24.  9 

^3 

158.2     39.4 

23 

216.4 

53-9 

T' 

274.6 

68.5 

44 

42.7 

10.  6 

04 

100.9  :  25.  2 

64 

159. 1     39.  7 

24 

217.3 

54-2 

84 

275.6 

68.  7 

4S 

43-7 

10.  9 

OS 

101.9     25.4 

65 

160.  I     39.9 

25 

218.3 

54-4 

^5 

276.5 

68.9 

46 

44.6 

II.  I 

06 

102.9     25. 6 

66 

161. 1     40.  2 

26 

219.3 

54-7 

86 

277.5 

69.  2 

47 

45-6 

II. 4 

07 

103.8  1  25,9 

67 

162. 0     40. 4 

27 

220.3 

54-9 

87 

278.5 

69.4 

48 

46.6 

II. 6 

08 

104.  8  1  26.  I 

68 

163.0     40.6 

28 

221.  2 

55-  2 

88 

279.4 

69.7 

49 

47-5 

II. 9 

09 

105.8 

26.4 

69 

164. 0     40. 9 

29 

222.  2 

55-4 

89 

280.4 

69.9 

50 

48.5 

12.  I 

10 

106.  7     26.  6 

70 

165.0     41. 1 

30 

223.  2 

55-6 

90 

281.4 

282.4 

70.2 

SI 

49-5 

12.3 

III 

107.7 

26.9 

171 

165.9  1  41.4 

231 

224.  I 

55-9 

291 

70.4 

52 

50-5 

12.6 

12 

108.7 

27.1 

72 

166.9     41.6 

32 

225.  I 

56. 1 

92 

283.3 

70.6 

53 

51-4 

12.8 

13 

109.  6 

27.3 

73 

167.9  '  41.9 

33 

226.  I 

56.4 

93 

284.3 

70-9 

54 

52.4 

13-1 

14 

no.  6 

27.6 

74 

168.  8     42.  I 

34 

227.0 

56.6 

94 

285.3 

71.  I 

SS 

53-4 

13-3 

15 

III. 6 

27.8 

75 

169.8  1  42.3 

35 

228.0 

56.9 

95 

286.2 

71.4 

S6 

54-3 

13-5 

16 

112. 6 

28.1 

76 

170.  8  i  42.6 

36 

229.0 

57.1 

96 

287.2 

71.6 

S7 

55-3 

13.8 

17 

"3-5 

28.3 

77 

171.  7  ,  42.8 

^ 

230.0 

57.3 

97 

288.2 

71.9 

S8 

S6.3 

14.0 

18 

114.  5 

28.5 

78 

172.7  1  43.1 

38 

230.9 

57.6 

98 

289.1 

72.1 

S9 

57-2 

14.3 

19 

115.  5  ,  28.8 

79 

173.7  ,  43.3 

39 

231.9 

57.8 

99 

290.  I 

72.3 

60 

58.2 

14.5 

20 

116. 4 

29.0 

80 

174.7 

43.5 

40 

232.9 

58.1 

300 

291.  I 

72.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fo 

r  76  Degr 

ees. 

TABLE  2. 

Page  229 

_A — 

Difference  of  Latitude  and  Departure  for  i 

5  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.3 

61 

58.9 

15-8 

121 

116.  9 

31.3 

181 

174.8 

46.8 

241 

232.8 

62.4 

2 

1-9 

0.5 

62 

59-9 

16.0 

22 

I17.8 

31.6 

82 

175-8 

47-1 

42 

233.  8  :  62.  6 

3 

2.9 

0.8 

^3 

60.9 

16.3 

23 

1 18.  8 

31-8 

83 

176.8 

47-4 

43 

234.  7  1  62.  9 

4 

3-9 

I.  0 

64 

61.8 

16.6 

24 

1 19.  8 

32.  I 

84 

177-7 

47-6 

44 

235.  7     63.  2 

5 

4.8 

1-3 

65 

62.8  i  16.8 

25 

120.  7 

32.4 

85 

178.7 

47-9 

45 

236.  7     63. 4 

6 

5-8 

1.6 

66 

63.8 

17. 1 

26 

121.  7 

32.6 

86 

179.7 

48.1 

46 

237.  6     63.  7 

7 

6.8 

1.8 

67 

64.7 

17-3 

27 

122.  7 

32.9 

87 

180.6 

48.4 

47 

238.  6     63.  9 

8 

7.7 

2. 1 

68 

65.7 

17.6 

28 

123.6 

33-1 

88 

181. 6 

48-7 

48 

239.  5     64.  2 

9 

8.7 

2.3 

69 

66.6 

17.9 

29 

124.6 

33-4 

89 

182.6 

48.9 

49 

240.5  ,  64.4 

10 

9-7 

2.6 

70 

67.6 

18. 1 

30 

125.6 

33-6 

90 

183.5 

49-2 

50 

241.5     64.7 

II 

10.6 

2.8 

71 

68.6 

18. 4 

131 

126.5 

33-9 

191 

184.5 

49-4 

251 

242. 4     65.  0 

12 

II. 6 

3-1 

72 

69-5 

18.6 

32 

127.5 

34-2 

92 

185.  5  !  49-  7 

52 

243.  4     65.  2 

13 

12.6 

-     3-4 

73 

70.5 

18.9 

2>2, 

128.5 

34-4 

93 

186.4 

50.0 

53 

244.4     65.5 

14 

13-5 

3-6 

74 

71.5 

19.  2 

34 

129.4 

34-7 

94 

187.4 

50.  2 

54 

245-  3  1  65.  7 

'5 

14.5 

3-9 

^ 

72.4 

19.4 

35 

130.4 

34-9 

95 

188.4 

50-5 

55 

246.  3     66.  0 

16 

'1-5 

4-1 

76 

73-4 

19.7 

36 

131-4 

35-2 

96 

189-3 

50.7 

56 

247.3  i  66.3 

17 

16.4 

4.4 

77 

74-4 

19.9 

37 

132.3 

35-5 

97 

190. 3      51.0 

57 

248.2 

66.5 

18 

17.4 

4-7 

78 

75.3  1  20.2 

38 

133-3 

35-7 

98 

191. 3      51.2 

58 

249.2 

66.8 

19 

18.4 

4.9 

79 

76.3 

20.4 

39 

134-3 

36.0 

99 

192.2  !  51.  5 

59 

250.2 

67.0 

20 

19-3 

5-2 

80 

77.3 

20.  7 

40 

135-2 

36-2 

200 

193-2 

51-8 

60 

251.  I 
252. 1 

67.3 

21 

20.3 

5-4 

8T 

78.2 

21.0 

141 

136.2 

36.5 

201 

194.2 

52.0 

261 

67.6 

22 

21.3 

5-7 

82 

79.2 

21.2 

42 

137-2 

36.8 

02 

195- I 

52-3 

62 

253-1 

67.8 

23 

22.2 

6.0 

f^ 

80.2 

21.5 

43 

138.  I 

37.0 

03 

196.  I 

52-5 

63 

254. 0     68.  I     1 

24 

23.  2 

6.2 

84 

81.  I 

21.7 

44 

139- I 

37.3 

04 

197.0     52.8 

64 

255.0     68.3     1 

25 

24.1 

6.5 

85 

82.1 

22.  0 

45 

140.  I 

37-5 

05 

198.0     53.1 

65 

256.0 

68.6 

26 

25.1 

6.7 

86 

83.1 

22.3 

46 

141. 0 

37-8 

06 

199-0  i  53-3 

66 

256.9 

68.8 

27 

26.1 

7.0 

87 

84.0 

22.5 

47 

142.0 

38-0 

07 

199.9 

53.6 

67 

257.9 

69.  I 

28 

27.0 

7.2 

88 

^5-° 

22.8 

48 

143.0 

38-3 

08 

200.9 

53-8 

68 

258.9 

69.4 

29 

28.0 

7-5 

89 

86.0 

23.0 

49 

143-9 

38.6 

09 

201.9 

54-1 

69 

259.8 

69.6 

30 

29.0 

7.8 

90 

86.9 

23-3 

50 

144.9 

38.8 

10 

202.8 

54-4 

70 

260.8 

_69_^_ 
70.  I 

31 

29.9 

8.0 

91 

87.9 

23.6 

151 

145-9 

39-1 

211 

203.8 

54-6 

271 

261.8 

32 

30-9 

f-3 

92 

88.9 

23.8 

52 

146.8 

39-3 

12 

204.8 

54-9 

72 

262.  7 

70.4 

33 

31-9 

^•5 

93 

89.8 

24.1 

53 

147.8 

39-6 

13 

205.7 

55-1 

73 

263.7 

70.7 

34 

32.8 

8.8 

94 

90.8 

24-3 

54 

148.8 

39-9 

14 

206.  7 

55-4 

74 

264.7 

70.9 

35 

33-8 

9-1 

95 

91.8 

24.6 

55 

149.7 

40.  I 

15 

207.7 

55-6 

75 

265.  6 

71.2 

36 

34-8 

9-3 

96 

92.7 

24.8 

56 

150-7 

40.4 

16 

208. 6155.9 

76 

266.6 

71.4 

37 

35-7 

9.6 

97 

93-7 

25.1 

57 

151- 7 

40.  6 

17 

209.  6     56.  2 

77 

267.6 

71.7 

38 

36.7 

9.8 

98 

94-7 

25.4 

58 

152.6 

40.9 

18 

210.6 

56-4 

78 

268.5 

72.0 

39 

H-t 

10.  I 

99 

95-6 

25.6 

59 

153-6 

41.2 

19 

211. 5      56.7 

79 

269.5 

72.2 

40 

38.6 

10.4 

100 

96.6 

25i^9_ 

60 

154.5 

41.4 

20 

212.5     56.9 

80 

270.5 

72.5 

41 

39-6 

10.6 

lOI 

97.6 

26.  I 

161 

155-5 

41.7 

221 

213-5     57-2 

281 

271.4 

72.7 

42 

40.6 

10.9 

02 

98.5 

26.4 

62 

156-5 

41.9 

22 

214.4 

57-5 

82 

272.4 

73.0 

43 

41.5 

II.  I 

03 

99-5 

26.  7 

^3 

157.4 

42.  2 

23 

215.4 

57-7 

^3 

273-4 

73-2 

44 

42. 5 

II. 4 

04 

100.5 

26.9 

64 

158.4 

42.4 

24 

216.4 

58.0 

84 

274.3 

73-5 

45 

43-5 

II. 6 

05 

101.4 

27.2 

65 

159-4 

42.7 

25 

217-3 

58.2 

85 

275-3 

73.8 

46 

44.4 

II. 9 

06 

102.4 

27.4 

66 

160.3 

43-0 

26 

218.3     58.5 

86 

276.3 

74.0 

47 

45-4 

12.  2 

07 

103.4 

27.7 

67 

161.  3 

43-2 

27 

219.3     58.8 

87 

277.2 

74-3 

48  j 

46.4 

12.4 

08 

104.3 

28.0 

68 

162.3 

43-5 

28  j 

220.  2     59.  0 

88 

278.2 

74-5 

49    ; 

47.3 

12.7 

09 

105.  3  i  28.  2 

69 

163.2 

43-7 

29 

221.2     59.3 

89 

279.2      74.8    1 

50  ! 

48.3 

12.9 

10 

106.  3     28.  5 

70 

164.2 

44.0 

30 

222. 2     59.  5 

90 

280.1 

75  I 

51  ! 

49-3 

13.2 

III 

107. 2     28.  7 

171 

165.2 

44-3 

231 

223.  I      59.  8 

291 

281.  I 

75-3    1 

52 

50.2 

13-5 

12 

108. 2     29. 0 

72 

166. 1 

44-5 

32 

224.  I      60.  p 

92 

282.  I      75.  6 

53 

5'.2  ' 

13-7 

13 

109.  I     29.  2 

73 

167.  I 

44-8 

33 

225.  I 

60.3 

93  ! 

283.0  :  75.8 

54 

52.  2 

14.0 

14 

no.  I      29.  5 

74 

168.  I 

45- 0 

34 

226.0 

60.6 

94 

284. 0     76.  1 

55 

53-1 

14.2 

15 

III.  I      29.8 

75 

169.0 

45-3 

35 

227.0  !  60.  8 

95 

284.9     76.4 

56 

54.1 

14.5 

16  i 

112. 0     30.0 

76 

170.0 

45.6 

36 

228.0     61.  I 

96 

285.  9      76.  6 

57 

55-1 

14.8 

17 

"3-0     30-3 

77 

171. 0 

45-8 

37 

228.  9     61.  3 

97 

286.9      76.9 

58 

56.0 

15.0 

18 

114.  0 

30-5 

78 

171-9 

46.  I 

38  j 

229.9  1 

61.6 

98 

287.  8  !  77.  I 

59 

57.0 

15-3 

19 

1 14.  9 

30.8 

79 

172.9 

46.3 

39 

230.9 

61.9 

99 

288.  8      77.  4 

60 

58.0, 

'5-5 

20 

"5-9 

31-1 

80 

173.9 

46.6 

40 

231.8 

62. 1 

300 

289.8 

77-6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For 

75  Degrees.         | 

Page  230 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  16  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

1.0 

0.3 

61 

58.6 

16.8 

121 

1x6.  3 

33-4 

181 

174.0 

49.9 

241 

231.7 

66.4 

2 

1.9 

0.6 

62 

59.6 

17.  I 

22 

117.3 

33-6 

82 

174.9 

50.2 

42 

232.6 

66.7 

3 

2.9 

0.8 

63 

60.6 

17.4 

23 

118.2 

33.9 

^3 

175.9 

50.4 

43 

233.6 

67.0 

4 

3-! 

1.  I 

64 

61.5 

17.6 

24 

119.  2 

34-2 

84 

176.9 

50.7 

44 

234.5 

67.3 

5 

4.8 

1.4 

65 

62.  5 

17.9 

25 

120.  2 

34.5 

85 

177.8 

51.0 

45 

235-5 

67.5 

6 

5.8 

1-7 

66 

63-4 

18.2 

26 

121.  I 

34.7 

86 

178.8 

51.3 

46 

236.5 

67.8 

7 

6.7 

1.9 

67 

64.4 

18.5 

27 

122.  I 

35.0 

87 

179.8 

51.5 

47 

237-4 

68.1 

8 

7-7 

2.2 

68 

65.4 

18.7 

28 

123.0 

35.3 

88 

180.  7 

51.8 

48 

238.4 

68.4 

9 

8.7 

2.  5 

69 

66.3 

19.  0 

29 

124.0 

35.6 

89 

181.7 

52.1 

49 

239.4 

68.6 

10 

9.6 

2.8 

70 

67.3 

19-3 

30 

125.0 

35.8 

90 

182.6 

52.4 

50 

240.3 

68.9 
69.2 

II 

10.  6 

3-0 

71 

68.2 

19.6 

131 

125^9^ 

36.1 

191 

183.6 

52.6 

251 

241.3 

12 

II. 5 

3-3 

72 

69.  2 

19.8 

32 

126.9 

36.4 

92 

184.6 

52.9 

52 

242.2 

69.5 

13 

12-5 

3-6 

7i 

70.  2 

20.  I 

?>?, 

127.8 

36.7 

93 

185.5 

53.2 

53 

243.2 

69.7 

14 

13-5 

3-9 

74 

71.  I 

20.4 

34 

128.8 

36.9 

94 

186.5 

53-5 

54 

244.2 

70.0 

15 

14.4 

4.1 

75 

72.1 

20,  7 

35 

129.8 

37.2 

95 

187.4 

53.7 

55 

245.1 

70.3 

i6 

15-4 

4.4 

76 

73-1 

20,9 

36 

130.7 

37.5 

96 

188.4 

54- 0 

56 

246.  I 

70.6 

17 

16.3 

4.7 

77 

74.0 

21.2 

37 

131-7 

37.8 

97 

189.4 

54.3 

57 

247.0 

70,8 

i8 

17.3 

5-0 

78 

75- 0 

21.5 

38 

132.7 

38.0 

98 

190.3 

54.6 

58 

248.0 

71.  I 

19 

18.3 

5-2 

79 

75-9 

21.8 

39 

133.6 

38.3 

99 

191. 3 

54-9 

59 

249.0 

71.4 

20 

19.2 

5-5 

80 

76.9 

22.  I 

40 

134.6 

38.6 

200 

192.3 

55-1 

60 

249.9 

71.7 

21 

20.2 

5.8 

81 

77-9 

22.3 

141 

135.5 

38.9 

201 

193.2 

55-4 

261 

250.9 

71.9 

22 

21.  I 

6.1 

82 

78.8 

22.6 

42 

136.  5 

39.1 

02 

194.2 

55-7 

62 

251.9 

72.  2 

23 

22. 1 

6.3 

^3 

79.8 

22.  9 

43 

137.5 

39.4 

03 

195.  I 

56.0 

63 

252.8 

72.5 

24 

23.1 

6.6 

84 

80.  7 

23.2 

44 

138.4 

39.7 

04 

196.  I 

56.2 

64 

253.8 

72.8 

25 

24.0 

6.9       85 

81.7 

23-4 

45 

139.4 

40.0 

05 

197.  I 

56.5 

65 

254.7 

73.0 

26 

25.0 

7.2       86 

82.7 

23-7 

46 

140.3 

40.2 

06 

198.0 

56.8 

66 

255.7 

73.3 

27 

26.0 

7.4       87 

f3-^ 

24.0 

47 

141.3 

40.5 

07 

199.0 

57.1 

67 

256.7 

73.6 

28 

26.9 

7-7 

88 

84.6 

24-3 

48 

142.3 

40.8 

08 

199.9 

57.3 

68 

257.6 

73.9 

29 

27.9 

8.0 

89 

85.6 

24-5 

49 

143.2 

41.  I 

09 

200.9 

57.6 

69 

258.6 

74.1 

30 

28.8 

8.3 

90 

86.5 

24.8 

50 

144.2 

41.3 

10 

201.9 

57-9 

70 

259.5 

74.4 

31 

29.8 

8.5       91 

87.5 

25-1 

151 

145.2 

41.6 

211 

202.8 

58.2 

271 

260.  5 

74.7 

32 

30.8 

8.8 

92 

88.4 

25-4 

52 

146.  I 

41.9 

12 

203.8 

58.4 

72 

261   5 

75.0 

33 

31-7 

9.1 

93 

89.4 

25.  6 

53 

147.  I 

42.2 

13 

204.7 

58.7 

73 

262.4 

75.2 

34 

32.7 

9-4 

94 

90.4 

25-9 

54 

148.0 

42.4 

14 

205.7 

59- 0 

74 

263.4 

75-5 

35 

33-6 

9.6 

95 

91-3 

26.  2 

55 

149.0 

42.7 

15 

206.  7 

59.3 

75 

264.3 

75.8 

36 

34-6 

9.9 

96 

92.3 

26.5 

56 

150.0 

43.0 

16 

207.6 

59.5 

76 

265.3 

76. 1 

3^ 

35.6 

10.2 

97 

93-2 

26.  7 

57 

150.9 

43.3 

17 

208.6 

59.8 

77 

266.3 

76.4 

38 

36.5 

10.5 

98 

94.2 

27.0 

58 

151.9 

43.6 

18 

209.  6 

60.  I 

78 

267.2 

76.6 

39 

37.5 

10.7 

99 

95-2 

27-3 

59 

152.8 

43.8 

19 

210.5 

60.4 

79 

268.2 

76.9 

40 

38.5 

II. 0 

100 

96,  I 

27.6 

60 

153.8 

44.1 

20 

211. 5 

60.6 

80 

269.2 

77.2 

41 

39-4 

"•3 

lOI 

97.1 

27.8 

161 

154.8 

44.4 

221 

212.4 

60.9 

281 

270.  I 

77.5 

42 

40.4 

II. 6 

02 

98.0 

28.1 

62 

155.7 

44.  7 

22 

213.4 

61.2 

82 

271.  I 

77.7 

43 

41-3 

II. 9 

03 

99.0 

28.4 

63 

156.7 

44.9 

23 

214.4 

61.5 

f3 

272.0 

78.0 

44 

42.3 

12.  I 

04 

100.  0 

28.7 

64 

157.6 

45.2 

24 

215.3 

61.7 

84 

273.0 

78.3 

45 

43-3 

12.4 

05 

100.9 

28.9 

65 

158.6 

45.5 

25 

216.3 

62.  0 

85 

274.0 

78.6 

46 

44.2 

12.7 

06 

loi.  9 

29.  2 

66 

159.6 

45.8 

26 

217.2 

62.3 

86 

274.9 

78.8 

47 

45-2 

13.0 

07 

102.9 

29.5 

67 

160.  5 

46.0 

27 

218.2 

62.6 

87 

275.9 

79.1 

48 

46.  I 

13.2 

08 

103.8 

29.8 

68 

161. 5 

46.3 

28 

219.  2 

62.8 

88 

276.8 

79.4 

49 

47.1 

'3-5 

09 

104.8 

30.0 

69 

162.  5 

46.6 

29 

220.  I 

63.1 

89 

277.8 

79.7 

50 
51 

48.1 

13.8 

10 

105.7 

30.3 

70 

163.4 

46.9 

30 

221.  I 

63.4 

90 

278.8 

79.9 

49.0 

14. 1 

III 

106.  7 

30.6 

171 

164.4 

47.1 

231 

222.  I 

63.7 

291 

279.7 

80.2 

52 

50.0 

14-3 

12 

107.7 

30-9 

72 

165.3 

47-4 

32 

223.0 

63.9 

92 

280.  7 

80.5 

53 

50.9 

14.6 

13 

108.6 

31-1 

73 

166.3 

47.7 

33 

224.0 

64.2 

93 

281.6 

80.8 

54 

51-9 

14.9 

14 

109.6 

31-4 

74 

167.3 

48.0 

34 

224.9 

64.5 

94 

282.6 

81.0 

55 

52.9 

15-2 

15 

no.  5 

31-7 

75 

168.2 

48.2 

35 

225.9 

64.8 

95 

283.6 

81.3 

56 

53.8 

H-A 

16 

III. 5 

32.0 

76 

169.2 

48.5 

36 

226.9 

65.1 

96 

284.5 

81.6 

57 

54.8 

15-7 

17 

112.5 

32.2 

77 

170.  I 

48.8 

37 

227.8 

65.3 

97 

285.5 

81.9 

58 

55.8 

16.0 

18 

II3-4 

32.5 

78 

171.  I 

49.1 

38 

228.8 

65.6 

98 

286.5 

82.1 

P 

56.7 

16.3 

19 

114.  4 

32.8 

79 

172.  I 

49.3 

39 

229.7 

65.9 

99 

287.4 

82.4 

60 

57-7 

16.5 

20 

115-4 

2,2,-'^ 

80 

173.0 

49.6 

40 

230.7 

66.2 

300 

288.4 

82.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Foi 

74  Degrt 

;es. 

TABLE  2. 

Page  231 

Difference  of  Latitude  and  Departure 

for  I 

7  Degrees 

• 

Dist. 
I 

LaU- 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

35-4 

Dist. 

Lat. 

Dep. 

52.9 

Dist. 
241 

Lat. 

Dep. 

I.O 

0-3 

61 

S8.3 

17.8 

121 

115- 7 

181 

173.  I 

230.5 

70.5 

2 

1-9 

0.6 

62 

59.3 

18.  I 

22 

116.  7 

35.7 

82 

174.0 

53-2 

42 

231.4  j   70.8 

3 

2.9 

0.9 

63 

60.2 

18.4 

23 

117.  6 

36.0 

83 

175-0 

53-5 

43 

232.4      71.0 

4 

^•f 

I.  2 

64 

61.2 

18.7 

24 

1 18.  6 

36.3 

84 

176.  0 

53.8 

44 

233-3   1   71.3 

5 

4.8 

1-5 

65 

62.2 

19.0 

25 

"9-5 

36.5 

85 

176.9 

54.1 

45 

234.3  ;  71.6 

6 

5-7 

I. 8 

66 

63.1 

19-3 

26 

120.  5 

36.8 

86 

177.9 

54-4 

46 

235.3  1  71.9 

7 

6.7 

2.0 

67 

64.  I 

19.6 

27 

121.  5 

37.1 

87 

178.8 

54-7 

47 

236.2  i  72.2 

8 

7-7 

2.3 

68 

65.0 

19.9 

28 

122.4 

37-4 

88 

179.8 

55- 0 

48 

237.2  I  72.5 

9 

8.6 

2.6 

69 

66.0 

20.2 

29 

123.4 

37.7 

89 

180.7 

55.3 

49 

238.1 

72-8 

10 

9.6 

2.9 

70 

66.9 

20.5 

30 

124.3 

38.0 

"38.3" 

90 

181.  7 

182.  7 

55-6 
55-8^ 

50 

239.1 

73.1     1 

^i 

10.5 

3-2 

71 

67.9 

20.8 

131 

125.3 

191 

251 

240.0  i  73.4    1 

12 

"•5 

3-5 

72 

68.9 

21.  I 

32 

126.  2 

38.6 

92 

183.6 

56.1 

52 

241-0  :  73.7    1 

13 

12.4 

3-8 

73 

69.8 

21.3 

32, 

127.2 

38.9 

93 

184.6 

56.4 

53 

241.9 

74-0     1 

14 

13-4 

4.1 

74 

70.8 

21.6 

34 

128. 1 

39-2 

94 

185.5 

56.7 

54 

242.9 

74-3    1 

'5- 

14-3 

4-4 

75 

71.7 

21.9 

35 

129. 1 

39-5 

95 

186.5 

57.0 

55 

243.9  1  74.6 

i6 

IS- 3 

4-7 

76 

72.7 

22.2 

36 

130. 1 

39.8 

96 

187.4 

57.3 

56 

244.  8  1  74.  8 

17 

16.3 

5-0 

77 

73.6 

22.  5 

37 

131.0 

40.  I 

97 

188.4 

57.6 

57 

245-  8  1  75- 1 

i8 

17.2 

5-3 

78 

74.6 

22.8 

38 

132.0 

40.3 

98 

189.3 

57.9 

58 

246.  7  1  75-  4 

19 

18.2 

5-^ 

79 

75-5 

23-1 

39 

132.9 

40.  6 

99 

190.3 

58.2 

59 

247.  7     75-  7 

20 

19. 1 

5-8 

80 

76.5 

23.4 

40 

133-9 

40.9 
41.2 

200 

191-3 

58.5 
58.8 

60 

248.  6     76.  0 

21 

20. 1 

6.1 

81 

77.5 

23.7 

141 

134.8 

201 

192.2 

261 

249.6     76.3 

22 

21.0 

6.4 

82 

78.4 

24.0 

42 

135.8 

41-5 

02 

193.2 

59.1 

62 

250.6     76.6 

23 

22.  0 

6.7 

l^ 

79-4 

24-3 

43 

136.8 

41.8 

03 

194.  I 

59-4 

63 

251.5  1  76.9 

24 

23.0 

7.0 

84 

80.3 

24.  6 

44 

137.7 

42.1 

04 

195.1 

59.6 

64 

252.5  ,  77.2 

-5 

23-9 

7-3 

85 

81.3 

24.9 

45 

138.7 

42.4 

05 

196.0 

59-9 

65 

253-4  1  77.5 

26 

24.9 

7.6 

86 

82.2 

25-1 

46 

139.6 

42.7 

06 

197.0 

60.  2 

66 

254.4  !  77-8 

27 

25.8 

7-9 

87 

83.2 

25-4 

47 

140.6 

43.0 

07 

198.0 

60.  5 

67 

255-3 

78.1 

28 

26.8 

8.2 

88 

84.2 

25-7 

48 

141.5 

43-3 

08 

198.9 

60.8 

68 

256.3 

78.4 

29 

27.7 

^•5 

89 

85.1 

26.  0 

49 

142.5 

43-6 

09 

199.9 

61. 1 

69 

257.2 

78.6 

30 

28.7 

8.8 

90 
91 

86.1 

26.3 

50 

143-4 

43-9 

10 

200.8 

61.4 

70 

258.2 

78.9 

31 

29.6 

9-1 

87.0 

26.6 

151 

144.4 

44-1 

211 

201.8 

"6177 

271 

259.2 

79-2 

32 

30.6 

9-4 

92 

88.0 

26.9 

52 

145.4 

44.4 

12 

202.  7 

62.0 

72 

260.  I 

79-5 

33 

31.6 

9.6 

93 

88.9 

27.2 

S3 

146.3 

44.7 

13 

203.7 

62.3 

73 

261. 1 

79.8 

34 

32.5 

9-9 

94 

89.9 

27-5 

54 

147.3 

45-0 

14 

204.6 

62.6 

74 

262.0 

80.  I 

35 

33.5 

10.  2 

95 

90.8 

27.8 

55 

148.2 

45-3 

15 

205.6 

62.9 

75 

263.0 

80.4 

36 

34.4 

10.5 

96 

91.8 

28.1 

56 

149.  2     45.  6 

16 

206.  6 

63.2 

76 

263.9 

80.7 

37 

35-4 

10.8 

97 

92.8 

28.4 

57 

150.  I  '  45.9 

17 

207.5 

63.4 

n 

264.9 

81.0 

38 

36.3 

II.  I 

98 

93-7 

28.7 

58 

151.  I 

46.  2 

18 

208.5 

63.7 

78 

265.9     81.3    1 

39 

37-3 

II. 4 

99 

94-7 

28.9 

59 

152.  I 

46.5 

19 

209.4 

64.0 

79 

266.  8 

81.6 

40 

38.3 

II. 7 

100 

95-6 

29.  2 

60 

153.0 

46.8 

20 

210.4 

64.3 

80 

267.8 

8). 9 

41 

39-2 

12.0 

lOI 

96.6 

"29.5 

161 

154.0 

47-1 

221 

211.3 

64.6 

268.7 

82.2 

42 

40.  2 

12.3 

02 

97.5 

29.8 

62 

154.9 

47-4 

22 

212.3 

64.9 

82 

269.  7  1  82. 4 

43 

41.  I 

12.6 

03 

98.5 

30.1 

63 

155.9 

47-7 

23 

213.3 

65.2 

l^ 

270.  6     82.  7 

44 

42.1 

12.9 

04 

99-5 

30.4 

64 

156.8 

47-9 

24 

214.2 

65-5 

84 

271.6     83.0 

45 

43- 0 

13.2 

OS 

100.4 

30.7 

65 

157.8 

48.2 

25 

215.  2 

65.8 

85 

272.5     83.3 

46 

44.0 

13-4 

06 

101.4 

31.0 

66 

158.7 

48.5 

26 

216.  I 

66.1 

86 

273.5  i  83.6 

47 

44-9 

^2,-: 

07 

102.3 

31-3 

67 

159.7 

48.8 

27 

217.  I 

66.4 

87 

274-5  1  83.9 

48 

45-9 

14.0 

08 

103-3 

31.6 

68 

160.  7 

49-1 

28 

218.0 

66.7 

88 

275.  4  ,  84.  2 

49 

46.9 

14-3 

09 

104.  2 

31-9 

69 

161. 6 

49.4 

29 

219.0 

67.0 

89 

276.4  '  84.  5 

50 
5' 

47.8 

14.  6 

10 

105.  2 

32.2 

70 

162.6 

49-7 

30 

220.0 

67.  2 

_90 

277.3  '  84.8 

48.8 

14.9 

III 

106. 1 

32.5 

171 

163.5 

50.  0 

231 

220.9 

"67:5" 

291 

278.3 

^' 

52 

49-7 

15.2 

12 

107. 1 

32.7 

72 

164.5 

50.3 

32 

221.9 

67.8 

92 

279.2 

85-4 

53 

50-7 

15-5 

13 

108. 1 

33- 0 

73 

165.4 

50.6 

33 

222.8 

68.1 

93 

280.  2     85.  7    1 

54 

51.6 

15.8 

14 

109.0 

33-3 

74 

166.4 

50.9 

34 

223.8 

68.4 

94 

281.2  '86.0    1 

55 

52.6 

16. 1 

15 

IIO.O 

33-6 

75 

167.4 

51.2 

35 

224.7 

68.7 

95 

282.  I 

86.2 

56 

53-6 

16.4 

16 

no.  9 

33  9 

76 

168.3 

51.5 

36 

225.7 

69.  0 

96 

283.1 

86.5 

57 

54.5 

16.7 

17 

III. 9 

34-2 

77 

169.3 

51.7 

37 

226.  6 

69-3 

97 

284.0 

86.8 

58 

55-5 

17.0 

18 

112.8 

34-5 

78 

170.2 

52.0 

38 

227.6 

69.6 

98 

285. 0     87.  I     1 

59 

56.4 

17.2 

19 

113.  8 

34-8 

79 

171.2 

52-3 

39 

228.6 

69.9 

99 

285.9 

87.4 

60 

57.4, 

17-5 

20 

114.8 

35-1 

80 

172.  I 

52.6 

40 

229.  5 

70.2 

300 

286.9 

87-7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For 

73  Degrees.        | 

Page  232 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  i 

8  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

55-9 

Dist. 

Lat. 

Dep. 

74.5 

I 

I.O 

0.3 

61 

58.0 

18.9 

121 

115.  I 

37-4 

181 

172.  I 

241 

229.  2 

2 

1.9 

0.6 

b2 

59- 0 

19.  2 

22 

116.  0 

37-7 

82 

173- I 

56.2 

42 

230.2 

74.8 

3 

2.9 

0.9 

63 

59-9 

19.5 

23 

117.  0 

38.0 

83 

174.0 

56.6 

43 

231.  I 

75.1 

4 

3-^ 

1.2 

64 

60.9 

19.8 

24 

117.  9  !  3^-3 

84 

175-0 

56.9 

44 

232.  I 

75-4 

5 

4.8 

1-5 

65 

61.8 

20.  I 

25 

1 18.  9  :  38.6 

85 

175.9 

57.2 

45 

233.0 

75-7 

6 

5-7 

1-9 

66 

62.8 

20.4 

26 

119-8  ;  38.9 

86 

176.9 

57.5 

46 

234.  0 

76.0 

7 

6.7 

2.2 

67 

63.7 

20.  7 

27 

120.8 

39-2 

87 

177.8 

S7.8 

47 

234.  9 

76.3 

8 

7.6 

2.  5 

68 

64.7 

21.0 

28 

121.  7 

39-6 

88 

178.8 

S8.i 

48 

235.9 

76.6 

9 

8.6 

2.  8 

69 

65.6 

21.3 

29 

122.  7 

39.9 

89 

179.7 

S8.4 

49 

;      236.8 

76.9 

10 

9-5 

31 

70 

66.6 

21.6 

30 

123.6 

40.2 

90 

180.7 

58.7 
59.0 

50 

237.8 

77-3 
77-6 

II 

10.5 

3-4 

71 

67.5 

21.9 

131 

124.  6 

40.5 

191 

181.  7 

251 

238.7 

12 

"•4  1     3-7  1 

72 

68.5 

22.  2 

32 

125.  5  !  40.  8 

92 

182.6 

59-3 

52 

239-7 

77-9 

13 

12.4 

4.0 

73 

69.4 

22.  6 

33 

126.  5 

41.  I 

93 

183.6 

59-6 

53 

240.  6 

78.2 

14 

13-3 

4-3 

74 

70.4 

22.  9 

34 

127.4 

41.4 

94 

184.5 

59-9 

54 

241.6 

78.5 

15 

14-3 

4.6 

75 

71-3 

23.2 

35 

128.4 

41.7 

95 

185.5 

60.3 

55 

242.5 

78.8 

16 

15-2 

4.9 

76 

72.3 

23-5 

3b 

129.3 

42.0 

96 

186.4 

60.6 

56 

243.5 

79.1 

17 

16.2 

5-3 

77 

73-2 

23.8 

37 

130.3 

42.3 

97 

187.4 

60.9 

57 

244.4 

79-4 

18 

17.  I 

5-b 

75^ 

74.2 

24.1 

3« 

131. 2     42.6 

98 

188.3 

61.  2 

58 

245.4 

79-7 

19 

18.  I 

5-9 

79 

75-1 

24.4 

39 

132.2 

43.0 

99 

189.3 

61.5 

59 

246.3 

80.0 

20 

19.0 
20.  0 

6.2 

80 

76. 1 

24.7 

40 

133- I 

43.3 

200 

190.2 

61.8 

60 

247.3 

80.3 

21 

6.5 

81 

77.0 

25.0 

141 

'34-1 

43-6 

201 

191. 2 

62. 1 

261 

248.2 

80.7 

22 

20.  9 

6.8 

82 

78.0 

25.3 

42 

135.1 

43-9 

02 

192.  I 

62.4 

62 

249.2 

81.0 

23 

21.9 

7-1 

«3 

78.9 

25.6 

43 

136.0 

44.2 

03 

193- I 

62.  7 

63 

250.  I 

81.3 

24 

22.8 

7-4 

84 

79-9 

26.  0 

44 

137- 0 

44.5 

04 

194.0 

63.0 

64 

251.  I 

81.6 

25 

23.8 

7-7 

«5 

80.8 

26.3 

45 

137.9 

44.8 

OS 

195.0 

63.3 

6S 

252.0 

81.9 

26 

24.7 

8.0 

86 

81.8 

26.6 

46 

138.9     45-1 

06 

195-9 

63.7 

66 

253-0 

82.2 

27 

25.7 

«.3 

«7 

82.7 

26.9 

47 

139.8 

45-4 

07 

196.9 

64.  0 

67 

253-9 

82.5 

28 

26.6 

8.7 

88 

«3.7 

27.  2 

48 

140.8 

45-7 

08 

197.8 

64.3 

68 

254.9 

82.8 

29 

27.6 

9.0 

89 

84.6 

27.5 

49 

141.  7 

46.0 

09 

198.8 

64.6 

69 

255.8 

83.1 

30 

28.5 

9-3 

90 

85.6 

27.8 

50 

142.7 

46-4 

10 

199.7 

64.9 

70 

256.8 

83.4 

31 

29-5 

9.6 

91 

86.5 

28.1 

151 

143.6 

46.7 

211 

200.  7 

65.2 

271 

257.7 

83.7 

32 

30.4 

9-9 

92 

87.5 

28.4 

52 

144.6    ;    47.0 

12 

201.6 

65-5 

72 

258.7 

84.1 

33 

31-4 

10.  2 

93 

88.4 

28.7 

53 

145.5     47-3 

13 

202.  6 

65.8 

73 

259.6 

84.4 

34 

32.3 

10.5 

94 

89.4 

29.0 

54 

146.5     47.6 

14 

203.5 

66.  I 

74 

260.6 

84.7 

35 

33-3 

10.8 

95 

90.4 

29.4 

55 

147.4  :  47.9 

15 

204.5 

66.4 

75 

261.5 

85.0 

3b 

34.2 

II.  I 

96 

91-3 

29.7 

56 

148. 4     48. 2 

16 

205.4 

66.7 

76 

262.  5 

85.3 

37 

35-2 

II. 4 

97 

92.3 

30.0 

57 

149.  3     48.  5 

17 

206.4 

67.1 

77 

263.4 

85.6 

3« 

36.1 

II. 7 

98 

93-2 

30.3 

5« 

150.  3     48.  8 

18 

207.  3 

67-4 

78 

264.4 

85.9 

39 

H-' 

12.  I 

99 

94.2 

30.6 

59 

151.2 

49.1 

19 

208.3 

67-7 

79 

265.  3 

86.2 

40 

38.0 

12.4 

100 

95-1 

30.9 

60 

152.2 

49.4 

20 

209.  2 

68.0 
68:3 

80 

266.3 

86.5 
86.8 

41 

39- 0 

12.7 

lOI 

96. 1 

31.2 

161 

153- I 

49.8 

221 

210.  2 

281 

267.2 

42 

39-9 

13.0 

02 

97- 0 

31.5 

62 

154.1 

SO.  I 

22 

211.  I 

68.6 

82 

268.  2 

87.1 

43 

40.9 

13-3 

03 

98.0 

3i.« 

63 

155.0 

50.4 

23 

212.  I 

68.9 

83 

269.  1 

87.5 

44 

41.8 

13.6 

04 

98.9 

32.1 

64 

156.0 

SO.  7 

24 

213.0 

69.2 

84 

270.  I 

87.8 

45 

42.8 

13-9 

05 

99.9 

32.4 

(^5 

156.9 

51.0 

2S 

214.  0 

69-5 

8S 

271.1 

88.1 

4b 

43-7 

14.2 

06 

100.8 

32.8 

66 

157.9 

51.3 

26 

214.9 

69.8 

86 

272.0 

88.4 

47 

44-7 

14-5 

07 

101.8 

33- i 

67 

158.8 

SI. 6 

27 

215- 9 

70.1 

87 

273.0 

88.7 

48 

45-7 

14.8 

08 

102.  7 

33-4 

68 

159.8 

51-9 

28 

216.8 

70.5 

88 

273-9 

89.0 

49 

46.6 

15-1 

09 

103.7 

33-7 

69 

160.  7 

52.2 

29 

217.8 

70.8 

89 

274.9 

89.3 

50 

47.6 

15-5 

10 

104.6 

34.0 

70 

161.  7 

52.5 

30 

218.7 

71.  I 

90 

275.8 

89.6 

51 

48.5 

15.8 

III 

105.6 

34-3 

171 

162.6     52.8 

231 

219.7 

71.4 

291 

276.8 

89.9 

52 

49-5 

16. 1 

12 

106.  5 

34-6 

72 

163.6     53.2 

32 

220.6 

71-7 

92 

277.7 

90.2 

53 

50-4 

16.4 

13 

107.5 

34-9 

73 

164-5  i  53-5 

33 

221.6 

72.0 

93 

278.7 

90.5 

54 

51-4 

16.  7 

14 

108.4 

35-2 

74 

165.5  '  53-8 

34 

222.  5 

72.3 

94 

279.6 

90.9 

55 

.  52.  3 

17.0 

15 

109.4 

35-5 

75 

1 66.  4     54.  I 

35 

223.5 

72.6 

95 

280.6 

91.2 

5t> 

53-3 

^7-3 

lb 

no.  3 

35- « 

76 

167.4  1  54.4 

36 

224.4 

72.9 

96 

281.5 

91.5 

57 

54-2 

17.  b 

17 

III. 3 

36.2 

77  : 

168.3  1  54.7 

37 

225.4 

73-2 

97 

282.5 

91.8 

5« 

55-2 

17.9 

18 

112. 2 

36-5 

7^ 

169.3  !  55-0 

38 

226.4 

73-5 

98 

283.4 

92. 1 

59 

56.1     18.2  1 

19 

113-2 

36.8 

79 

170.  2 

55-  3 

39 

227.3 

73-9 

99 

284.4 

92.4 

60 

57-1 

18.5 

Lat. 

20 

114. 1 

37.1 

80 

171. 2 

55.6 

40 

228.3 

74-2 

300 

285.3 

92.7 

Dist. 

Dep.     1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For 

72  Degrees.        1 

TABLE  2. 

Page  233 

•  Diflference  of  Latitude  and 

Depart 

ure  for  19  Degrees. 

Dist. 

Lat. 

Dep. 
0.3 

Dist. 
61 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 
181 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

H-I 

19.9 

121 

1 14.  4 

39.4 

171.  I 

58.9 

241 

227.9 

78.5 

2 

1-9 

0.  7 

62 

58.6 

20.  2 

22 

"5-4 

39-7 

82 

172.  I      59.3 

42 

228.  8     78.  8 

3 

2.8 

I.  0 

63 

59.6 

20.  5 

23 

1 16.  3 

40.0 

83 

173.0  1  59.6 

43 

229.  8     79.  I 

4 

3-8 

1-3 

64 

60.5 

20.8 

24 

117.  2 

40.4 

84 

174- 0     59.9 

44 

230.  7     79.  4 

5 

4-7 

1.6 

65 

61. 5 

21.  2 

25 

1 18.  2 

40.7 

85 

1 74.  9     60.  2 

45 

231.7  :  79.8 

6 

5-7 

2.  0 

66 

62.4 

21.5 

26 

119.  I 

41.0 

86 

175.9     60.6 

46 

232.  6     80.  I 

7 

6.6 

2.3 

67 

63.3 

21.8 

27 

120.  I 

41.3 

87 

1 76.  8  1  60.  9 

47 

233.  5     80.  4 

8 

7.6 

2.6 

68 

64.3 

22.  I 

28 

121. 0 

41.7 

88 

177.8     61. 2 

48 

234.  5     80.  7 

9 

8.5 

2.9 

69 

65.2 

22.  5 

29 

122.0 

42.  0 

89 

178.7     61.5 

49 

235.4     81.  I 

10 

II 

9-5 
10.4 

3-3 

70 

66.2 

22.8 
23:1 

30 

122.9 

_42.3_ 
42.6 

90 

179.6     61.9 

50 

236.4  ;  81.4 

3.6 

71 

67.1 

131 

123,  9 

191 

180.6  j  '62.2 

251 

237.3  i  81.7 

12 

"•3 

3-9 

72 

68.1 

23-4 

32 

124.8 

43- 0 

92 

181.  5  '  62.  5 

52 

238.  3     82.  0 

13 

12.3 

4.2 

73 

69.0 

23.8 

33 

125.8 

43-3 

93 

182.5     62.8 

53 

239.  2     82. 4 

14 

13.2 

4.6 

74 

70.0 

24.1 

34 

126.7 

43.6 

94 

183.4     63.2 

54 

240.  2  1  82.  7 

15 

14.2 

4.9 

75 

70.9 

24.4 

35 

127.6 

44.0 

95 

184.4     63.5 

55 

241.  I      83.  0 

i6 

15. 1 

5-2 

76 

71.9 

24.7 

3^' 

128.6 

44.3 

96 

185.3     63.8 

56 

242.  I      83.  3 

17 

16.  I 

5-5 

77 

72.8 

25-1 

37 

129.5 

44.6 

97 

186.3     64.  I 

57 

243.0 

83.7 

i8 

17.0 

5-9 

78 

73-8 

25-4 

38 

130.5 

44.9 

98 

187.  2     64.  5 

58 

243-9 

84.0 

19 

18.0 

6.2 

79 

74-7 

25-7 

39 

131.4 

45-3 

99 

188.2     64.8 

59 

244.9 

84.3 

20 
21 

18.9 
"19. 9 

6.5 

80 

75.6 

26.0 

40 

132.4 

45-6 

200 
201 

189.  I 

65.1 

60 

245.8 

84.6 

6.8 

81 

76.6 

26.4 

141 

133.3 

45-9 

190.0 

65.4 

261 

246.8 

85.0 

22 

20.8 

7.2 

82 

77.5 

26.  7 

42 

134.3 

46.  2 

02 

191.  0 

65.8 

62 

247.7 

85.3 

23 

21.7 

7.  5 

83 

78.5 

27.0 

43 

135.2 

46.6 

03 

191.  9 

66.  I 

63 

248.7 

85.6 

24 

22.  7 

7.8 

84 

79-4 

27-3 

44 

136.2 

46.9 

04 

192.9 

66.4 

64 

249.6 

86.0 

25 

23.6 

8.1 

85 

80.4 

27.7 

45 

137.1 

47.2 

05 

193.  8     66.  7 

65 

250.6 

86.3 

26 

24.6 

^•5 

86 

81.3 

28.0 

46 

138.0 

47-5 

06 

194.8     67.  I 

66 

251-5 

86.6 

27 

25-5 

8.8 

87 

82.3 

28.3 

47 

139.0 

47-9 

07 

195.7 

67.4 

67 

252.5 

86.9 

28 

26.5 

9-1 

88 

83.2 

28.7 

48 

139.9 

48.2 

08 

196.7 

67.7 

68 

253.4 

87.3 

29 

27.4 

9-4 

89 

84.2 

29.0 

49 

140.9 

48.5 

09 

197.  6 

68.0 

69 

254-3 

87.6 

30 

28.4 

9.8 

90 

85.1 

29-3 

50 

141.  8 

48.8 

10 

198.6 

68.4 

70 

__255.3 

87.9 

31 

29-3 

10.  I 

91 

86.0 

29.  6 

151 

142.8 

49.2 

211 

199.  5     68.  7 

271 

256.2 

88.2 

32 

30.3 

10.4 

92 

87.0 

30.0 

52 

143.7 

49.5 

12 

200. 4  !  69. 0 

72 

257.2 

88.6 

33 

31.2 

10.7 

93 

87.9 

30-3 

53 

144.7 

49.8 

13 

201.4    69.3 

73 

258.1 

88.9 

34 

32.1 

II.  I 

94 

88.9 

30.6 

54 

145.6 

50.1 

14 

202.  3   !  69.  7 

74 

259.1 

89.2 

35 

33-1 

II. 4 

95 

89.8 

30-9 

55 

146.6 

50.5 

15 

203.  3      70.  0 

75 

260. 0 

89.5 

36 

34-0 

II. 7 

96 

90.8 

31-3 

56 

147.5 

50.8 

16 

204.  2    1    70.  3 

76 

261.0 

89.9 

H 

35- 0 

12.0 

97 

91.7 

31-6 

57 

148.4 

51.1 

17 

205.  2      70.  6 

77 

261.9 

90.  2 

38 

35-9 

12.4 

98 

92.7 

31-9 

58 

149.4 

51.4 

18 

206. 1      71.0 

78 

262.9 

90.5 

39 

36.9 

12.7 

99 

93-6 

32.  2 

59 

150.3 

51.8 

19 

207.1   ,  7«.3 

79 

263.8 

90.8 

40 

37.8 

13.0 

100 

94.6 

32.6 
32.9 

60 
161 

J5I.3 
152.2 

52.1 

20 

208.0  !  71.  6 

80 

264.7 

91.  2 

41 

38.8 

13-3 

lOI 

95-5 

52.4 

221 

209.  0  '  72.  0 

281 

265.7 

91.5 

42 

39-7 

13-7 

02 

96.4 

33-2 

62 

153.2 

52.7 

22 

209.  9      72.  3 

82 

266.  6 

91.8 

43 

40.7 

14.0 

03 

97-4 

33-5 

63 

154.  I 

53.1 

23 

210.  9  !  72.  6 

83 

267.6 

92.  I 

44 

41.6 

14.3 

04 

98.3 

33-9 

64 

155-1 

53-4 

24 

211. 8      72.9 

84 

268.  5 

92.5 

45 

42.5 

14.7 

05 

99-3 

34-2 

65 

156.0 

53-7 

25 

212.7  !  73-3 

85 

269.5 

92.8 

46 

43-5 

15.0 

06 

100.2 

34-5 

66 

157.0 

54.0 

26 

213.7     73.6 

86 

270.4 

93-1 

47 

44.4 

15-3 

07 

101.2 

34.8 

67 

157.9 

54.4 

27 

214.6      73.9 

87 

271.4 

93-4 

48 

45-4 

15-6 

08 

102.  I 

35-2 

68 

158..8 

54.7 

28 

215.6     74.2 

88 

272.3 

93-8 

49 

46.3 

16.0 

09 

103.  I 

35-5 

69 

159-8 

55.0 

29 

2 lb.  5      74.6 

89 

273.3 

94.1 

50 

47-3 
48.2 

16.3 

ID 

104.0 

35-8 

70 

160.  7 

55.3 

30 

217.5 

74.9 

90 

274.2 

94.4 

51 

16.6 

III 

105.0 

36.1 

171 

161.  7 

55.7 

231 

218.4 

75.2 

291 

275.1 

94-7 

52 

49.2 

16.9 

12 

105.9 

36.5 

72 

162.6 

56.0 

32 

219.4 

75-5 

92 

276.  I 

95-1 

53 

50.1 

17.3 

13 

106.8 

36.8 

73 

163.6 

56.3 

33 

220.3      75.9 

93 

277.0 

95-4 

54 

51-1 

17.6 

14 

107.8 

37-1 

74 

164.5 

56.6 

34 

221.3    ]  ,76.  2 

94 

278.0 

95-7 

55 

52.0 

17.9 

15 

108.7  1  37.4 

75 

165-5 

57.0 

35 

222.  2    '    76.  5 

95 

278.9 

96.0 

56 

52.9 

18.2 

16 

109.7  i  37-8 

76 

166.4 

57.3 

36 

223.  I      76.  8 

96 

279.9 

96.4 

57 

53-9 

1S.6 

17 

no.  6     38.  I 

77 

167.4 

57.6 

37 

224.  I        77.  2 

97 

280.8 

96.7 

58 

54.8 

18.9 

18 

III.  6 

38.4 

78 

168.3 

58.0 

38 

225.  0 

77.5 

98 

281.8 

97.0 

59 

55-8 

19.2 

19 

112.  5 

38.7 

79 

169.  2 

58.3 

39 

226.0 

99 

282.  7 

97.3 

00 

56.7 

19-5 

20 

113-5 

39.1 
Lat. 

80 

170.2 

58.6 

40 

226,9 

78.1 

300 

283.7 

97-7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[For 

71  Degrees,         | 

Page  234 

TABLE  2. 

Difference  of  Latitude  and  " 

Departure  for 

20  Degrees. 

Dist. 

I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

0.9 



0-3 

61 

57-3 

20.9 

121 

"3-7 

41.4 

181 

170.  I 

61.  9 

241 

226.5 

82.4 

2 

1.9 

0.7 

62 

58-3 

21.2 

22 

114.  6 

41.7 

82 

171. 0 

62.  2 

42 

227-4 

82.8 

3 

2.8 

I.O 

63 

59-2 

21.5 

23 

115. 6 

42.1 

l^ 

172.0 

62.6 

43 

22S.3 

83.1 

4 

3-8 

1.4 

64 

60. 1 

21.9 

24 

116.  5 

42-4 

84 

172.9 

62.9 

44 

229-3 

83-5 

5 

4-7 

1-7 

65 

61.  I 

22.2 

25 

117.  5 

42.8 

85 

173-8 

63-3 

45 

230.2 

83.8 

6 

5-6 

2. 1 

66 

62.  0 

22.  6 

26 

1 18. 4 

43-1 

86 

174-8 

63.6 

46 

231.2 

84.  I 

7 

6.6 

2.4 

67 

63.0 

22.9 

27 

"9-3 

43-4 

87 

175-7 

64.0 

47 

232.1 

84-5 

8 

7-5 

2.7 

68 

63-9 

23-3 

28 

120.3 

43-8 

88 

176.7 

64-3 

48 

233-0 

84.  8 

9 

8.5 

3-1 

69 

64.8 

23.6 

29 

121.  2 

44-1 

89 

177.6 

64.6 

49 

234.0 

85.2 

lO 

9-4 

3-4 

70 

65.8 

23-9 

30 

122.2 

44-5 

90 

178.5 

65.0 

50 

234-9 

85.5 
85.  8 

II 

10.3 

3.8 

71 

66.7 

24-3 

131 

123. 1 

44-8 

191 

179-5 

65-y 

251 

^235.  9 

12 

"•3 

4.1 

72 

67.7 

24.6 

32 

124.0 

45-1 

92 

180.4 

65-7 

52 

236.8 

86.2 

13 

12.2 

4.4 

73 

68.6 

25.0 

33 

125.0 

45-5 

93 

181. 4 

66.0 

53 

237-7 

86.5 

14 

13.2 

4.8 

74 

69.5 

25-3 

34 

125-9 

45-8 

94 

182.3 

66.4 

54 

238-7 

86.9 

15 

14.  I 

5-1 

75 

70.5 

25-7 

35 

126.9 

46.  2 

95 

183.2 

66.7 

55 

239.6 

87.2 

i6 

15.0 

5-5 

76 

71.4 

26.0 

36 

127.8 

46-5 

96 

184.2 

67.0 

56 

240.  6 

87.6 

17 

16.  0 

5-8 

77 

72.4 

26.3 

37 

128.7 

46.9 

97 

185.  I 

67.4 

57 

241.5 

87.9 

i8 

16.9 

6.2 

78 

73-3 

26.  7 

38 

129.7 

47-2 

98 

186.  I 

^Z-7 

58 

242.4 

88.2 

19 

17.9 

6.5 

79 

74.2 

27.0 

39 

130.6 

47-5 

99 

187.0 

68.1 

59 

243-4 

88.6 

20 

18.8 

6.8 

80 

75-2 

27.4 

40 

131. 6 

47-9 

200 

187.9 

68.4 

60 

244-3 

88.9 
89.3 

21 

19.7 

7.2 

81 

76.1 

27.7 

141 

132.5 

48.  2 

201 

188.9 

68.  f 

261 

245-  3 

22 

20.  7 

7.5 

82 

77.1 

28.0 

42 

133-4 

48.6 

02 

189.8 

69.  I 

62 

246.  2 

89.0 

23 

21.6 

7-9 

83 

78.0 

28.4 

43 

134-4 

48-9 

03 

190.8 

69.4 

63 

247.1 

90.0 

24 

22.6 

8.2 

84 

78.9 

28.7 

44 

135-3 

49-3 

04 

191.  7 

69.8 

64 

248.  I 

90.3 

25 

23-5 

8.6 

85 

79-9 

29. 1 

45 

136.3 

49-6 

05 

192.6 

70. 1 

65 

249.0 

90.6 

26 

24.4 

8.9 

86 

80.8 

29.4 

46 

137-2 

49.9 

06 

193.6 

70-5 

66 

250.0 

91.0 

27 

25.4 

9.2 

87 

81.8 

29.8 

47 

138-  I 

50-3 

07 

194-5 

70.8 

67 

250.9 

91-3 

28 

26.3 

9.6 

88 

82.7 

30.1 

48 

139- I 

50.6 

08 

195-5 

71.  I 

68 

251.8 

91.7 

29 

27-3 

9.9 

89 

83.6 

30-4 

49 

140.0 

51.0 

09 

196.4 

7'- 5 

69 

252.  8 

92.0 

30 

28.2 

10^3 
10.6 

90 
91 

84.6 
85.5 

30.8 

50 

140.9 

51-3 

10 

197-3 

71.8 

70 

253-7 

92.3 

31 

29.  I 

31- 1 

151 

F41.9" 

51-6 

211 

198.3 

72.2 

271 

254-7 

92.7 

32 

30.1 

10.9 

92 

86.5 

31-5 

52 

142.8 

52.0 

12 

199.2 

72-5 

72 

255.6 

93- 0 

33 

31.0 

"•3 

93 

87.4 

31-8 

53 

143.8 

52-3 

13 

200.  2 

72-9 

73 

256- 5 

93-4 

34 

31-9 

II. 6 

94 

88.3 

32.1 

54 

144-7 

52-7 

14 

201.  I 

73-2 

74 

257-5 

93-7 

35 

32.9 

12.0 

95 

89-3 

32.5 

55 

145-7 

53-0 

15 

202.0 

73-5 

75 

258.4 

94-  I 

36 

33.8 

12.3 

96 

90.2 

32.8 

56 

146.  6 

53-4 

16 

203.  0 

73-9 

76 

259.4 

94-4 

37 

34.8 

12.7 

97 

91.2 

33-2 

57 

147-5 

53-7 

17 

203.9 

74.2 

77 

260.  3 

94-7 

3« 

35-7 

13.0 

98 

92.1 

33-5 

58 

148.5 

54- 0 

18 

204.9 

74-6 

78 

261.  2 

95-1 

39 

36.6 

13-3 

99 

93- 0 

33-9 

59 

149.4 

54-4 

19 

205.  8 

74-9 

79 

262.2 

95-4 

40 

37-6 

13-7 

100 

94.0 

34-2 
34.5 

60 

150.4 

54-7 

20 

206.  7 

75-2 

80 

_263.  I 

95-8^ 
96.  I 

41 

.38.5 

14.0 

lOI 

94.9 

161 

151-3 

55-1 

221 

207.7 

75-6 

~28r 

264. 1 

42 

39-5 

14.4 

02 

95-8 

34-9 

62 

152.  2 

55-4 

22 

208.6 

75-9 

82 

265.  0 

96.4 

43 

40.4 

14.7 

03 

96.8 

35-2 

63 

153-2 

55-7 

23 

209.6 

76.3 

83 

265.9 

96.8 

44 

41.3 

15.0 

04 

97-7 

35-6 

64 

154-1 

56-1 

24 

210.5 

76.6 

84 

266.  9 

97.1 

45 

42.3 

15-4 

05 

98.7 

35-9 

65 

155-0 

56-4 

25 

211. 4 

77.0 

85 

267.8 

97-5 

46 

43-2 

15-7 

06 

99.6 

36-3 

66 

156.0 

56.8 

26 

212.4 

77-3 

86 

268.8 

97-8 

47 

44.2 

16.  I 

07 

100.  5 

36.6 

67 

156.9 

57-1 

27 

213-3 

77-6 

87 

269.7 

98.2 

48 

45.1 

16.4 

08 

loi.  5 

36.9 

68 

157-9 

57-5 

28 

214.2 

78.0 

88 

270.6 

98.5 

49 

46.  0 

16.8 

09 

102.4 

37-3 

69 

158.8 

57-8 

29 

215.2 

78-3 

89 

271.6 

98.8 

50 
51 

47.0 
47-9 

17.  I 

10 

103.4 

37.6 
38.0 

70 

159-7 

58-1 

30 

216.  I 

78.7 

90 

272.5 

99.2 
99.5 

17.4 

III 

104.3 

171 

160.  7 

58-y 

231 

217.  I 

79.0 

291 

273-5 

52 

48.9 

17.8 

12 

105.2 

38.3 

72 

161. 6 

58.8 

32 

218.0 

79-3 

92 

274-4 

99.9 

53 

49.8 

18.  I 

13 

106.2 

38.6 

7?, 

162.6 

59-2 

2,2, 

218.9 

79-7 

93 

275-3 

100.  2 

54 

50.7 

18.5 

14 

107.  I 

39-0 

74 

163-5 

59-5 

34 

219.9 

80.0 

94 

276.3 

100.  6 

55 

51-7 

18.8 

15 

108.  I 

39-3 

75 

164.4 

59-9 

35 

220.  8 

80.4 

95 

277.2 

100.9 

56 

52.6 

19.2 

16 

109.0 

39-7 

76 

165.4 

60.  2 

36 

221.8 

80.7 

96 

278.  I 

lOI.  2 

57 

53-6 

19-5 

17 

109.9 

40.0 

77 

166.3 

•60.  5 

37 

222.  7 

81.  I 

97 

279.  I 

loi.  6 

58 

54-5 

19.  8 

18 

no.  9 

40.4 

78 

167-3 

60.9 

38 

223.6 

81.4 

98 

280.  0 

101.9 

59 

55-4 

20.  2 

19 

III. 8 

40.7 

79 

168.  2 

61.  2 

39 

224.6 

81.7 

99 

281.0 

102.3 

60 

56.4 

20.  5 

20 

1 12.  8 

41.0 

80 

169.  I 

61.6 

40 

225.5 

82.1 

300 

281.9 

102.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[F< 

Dr  70  Deg 

rees. 

TABLE  2. 

Page  235 

Difference  of  Latitude  and  Departure  for 

21  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 
61 

Lat. 

Dep. 

Dist. 

Lat. 
1 13.0 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.4 

56.9 

21.9 

121 

43  4 

181 

169.0 

64.9 

241 

225.0 

86.4 

2 

1-9 

0.7 

62 

57-9 

22.2 

22 

113-9 

43.7 

82 

169.9 

65.2 

42 

225.9 

86.7 

3 

2.8 

I.  I 

63 

58.8 

22.  6 

23 

1 14.  8 

44.  I 

83 

170.8 

65.6 

43 

226.  9 

87.1 

4 

3-7 

1.4 

64 

59-7 

22.  9 

24 

115.8 

44.4 

84 

171. 8 

65.9 

44 

227.8 

87-4 

5 

4-7 

I.  8 

65 

60.7 

23-3 

25 

116.  7 

44-8 

85 

172.  7 

66.3 

45 

228.7 

87.8 

6 

5-<' 

2    2 

66 

61.6 

23-7 

26 

117.  6 

45-2 

86 

173-6 

66.7 

46 

229.7 

88.2 

7 

6.5 

2-5 

67 

62.5 

24.0 

27 

1 18.  6 

45-5 

87 

174.6 

67.  0 

47 

230.  6 

88.  s 

8 

7-5 

2.9 

68 

63.5 

24.4 

28 

1 19- 5 

45-9 

88 

175-5 

67.4 

48 

231-5 

88.9 

9 

8.4 

3-2 

69 

64.4 

24.7 

29 

120.4 

46.  2 

89 

176.4 

67.7 

49 

232.5 

89.2 

lO 

II 

9-3 
10.3 

3-6 
3-9 

70 
71 

65-4 
66.3 

25.1 

25-  4 

30 

121. 4 

46.6 

90 

177-4 

68.  I 

50 

233-4 

89.6 
90.0 

131 

12273 

46.9 

191 

178.3 

68. 4 

251 

234-3 

12 

II.  2 

4-3 

72 

67.  2 

25.8 

32 

123.2 

47.3 

92 

179.2 

68.8 

52 

235-3 

90-3 

13 

12. 1 

4-7 

73 

68.2 

26.  2 

33 

124.  2 

47.7 

93 

180.2 

69.  2 

53 

236.2 

90.7 

14 

13- I 

5-0 

74 

69.  I 

26.  5 

34 

125.  I 

48.0 

94 

181.  I 

69.5 

54 

237.1 

91.  0 

IS 

14.0 

5-4 

'5 

70.0 

26.  9 

35 

126.  0 

48.4 

95 

182.0 

69.9 

55 

238.1 

91.4 

16 

14.9 

5-7 

76 

71.0 

27.2 

36 

127.0 

48.7 

96 

183.0 

70.  2 

56 

239.0 

91.7 

17 

15.9 

6.1 

77 

71.9 

27.  6 

37 

127.9 

49.  I 

97 

183-9 

70.  6 

57 

239.9 

92.1 

18 

16.8 

6.5 

78 

72.8 

28.0 

38 

128.8 

49-5 

98 

184.8 

71.0 

58 

240.9 

92-5 

19 

n-^ 

6.8 

79 

73-8 

28.3 

39 

129.8 

49.8 

99 

185.8 

71-3 

59 

241.8 

92.8 

20 

18.7 

7.2 

80 

74.7 

28.7 

40 

_i30i7_ 
131. 6 

50.  2 

200 

186.7 

J\-  7 

60 

242.7 

93-2 

21 

19.6 

7.5 

81 

75-^ 

29.0 

141 

50.5 

201 

187.6 

72.0 

261 

243.7 

93-5 

22 

20. 5 

7-9 

82 

76.6 

29.4 

42 

132.6 

50.9 

02 

188.6 

72.4 

62 

244.6 

93-9 

23 

21. 5 

8.2 

^3 

77.5 

29.7 

43 

133-5 

51.2 

03 

189-5 

72.7 

63 

245-5 

94-3 

24 

22.4 

8.6 

84 

78.4 

30.1 

44 

134-4 

51.6 

04 

190.5 

73-1 

64 

246.5 

94.6 

^5 

23-3 

9.0 

85 

79-4 

30-5 

45 

135-4 

52.0 

05 

191.4 

73-5 

65 

247-4 

95-0 

26 

24.3 

9-3 

86 

80.3 

30.8 

46 

136-3 

52.3 

06 

192.3 

73-8 

66 

248.3 

95-3 

27 

25.2 

9-7 

87 

81.2 

31.2 

47 

137.2 

52.7 

07 

193-3 

74-2 

67 

249-3 

95-7 

28 

26.1 

10. 0 

88 

82.2 

31-5 

48 

138.2 

53.0 

08 

194.2 

74-5 

68 

250.  2 

96.  0 

29 

27.1 

10.4 

89 

83.1 

31-9 

49 

139.1 

53-4 

09 

195-1 

74-9 

69 

251.  I 

96.4 

30 

28.0 

10.8 

90 

84.0 

_32^3_ 

50 

140.  0 

53-8 

10 

196.  I 

75-3 

70 

252.  I 

96.8 

31 

28.9 

II.  I 

91 

85.0 

32.6 

151 

141.  0 

54-1 

211 

197.0 

75-6 

271 

253-0 

97.1 

32 

29.9 

II.  5 

92 

85.9 

33- 0 

52 

141.9 

54-5 

12 

197.9 

76.0 

72 

253-9 

97-5 

33 

30.8 

II.  8 

93 

86.8 

33-3 

53 

142.8 

54-8 

13 

198.9 

76.3 

73 

254-9 

97.8 

34 

31-7 

12.  2 

94 

87.8 

33-7 

54 

143.8 

55-2 

14 

199.8 

76.7 

74 

255.8 

98.2 

35 

32.7 

12.5 

95 

88.7 

34- 0 

55 

144-7 

55-5 

15 

200.  7 

77.0 

75 

256.7 

98.6 

36 

33-6 

12.9 

96 

89.6 

34-4 

56 

145.6 

55-9 

16 

201.  7 

77.4 

76 

257-7 

98.9 

37 

34.5 

13-3 

97 

90.  6 

34.8 

57 

146.6 

56.3 

17 

202.6 

77-8 

77 

258.6 

99.3 

38 

35-5 

13.6 

98 

91-5 

35-1 

58 

147.5 

56.6 

18 

203-5 

7^  ' 

78 

2j9-5 

99.^ 

39 

36.4 

14.0 

99 

92.4 

35-5 

59 

148.4 

57.0 

19 

204.5 

78.5 

79 

260.5 

100.  0 

40 

37.3 

14-3 

100 

93-4 

35.8 

60 

149.4 

57-3 

20 

205.4 

78.8 

80 

261.4 

100.3 

41 

38.3 

14.7 

loi 

94-3 

36.2 

161 

150.3 

57-7 

221 

206.3 

79.2 

281 

262.3 

100.  7 

42 

39-2 

15-1 

02 

95.2 

36.6 

62 

151.2 

58.1 

22 

207.3 

79.6 

82 

263.3 

loi.  1 

43 

40.1 

15.4 

03 

96.2 

36.9 

63 

152.  2 

58.4 

23 

208.2 

79.9 

83 

264.  2 

101.4 

44 

41. 1 

15.8 

04 

97.1 

37-3 

64 

153.1 

58.8 

24 

209.  I 

80.3 

84 

265.  1 

101.8 

45 

42.0 

16.  I 

05 

98.0 

37-6 

65 

154.0 

59-1 

25 

210.  I 

80.6 

85 

266.  1 

102.  1 

46 

42.9 

16.5 

06 

99.0 

38.0 

66 

155-0 

59.5 

26 

211. 0 

81.0 

86 

267.0 

102.  5 

47 

43-9 

16.8 

07 

99.9 

38.3 

67 

155-9 

59.8 

27 

211. 9 

81.3 

87 

267.9 

102.9 

48 

44.8 

17.2 

08 

100.8 

38.7 

68 

156.8 

60.  2 

28 

212.  9 

81.7 

88 

268.9 

103.2 

49 

45-7 

17.6 

09 

101.8 

39-1 

69 

157-8 

60.6 

29 

213.8 

82.1 

89 

269.8 

103.6 

50 

46.7 

17.9 

10 

102.  7 

39.4 

70 

158.7 

60.  9 

30 

214.7 

82.4 
82.8 

90 
291 

270.7 
271.7 

103.9 

51 

47.6 

18.3 

III 

103.  6 

39.8" 

171 

159.6 

61.3 

231 

215-7 

104.3 

52 

48.5 

18.6 

12 

104.  6 

40.  I 

72 

160.6 

61.6 

32 

216.6 

83.1 

92 

272.6 

104.6 

53 

49-5 

19.0 

13 

•05-5 

40.5 

73 

161.  5 

62.0 

33 

217-5 

83.5 

93 

273-5 

105.  0 

54 

50.4 

19.4 

14 

106.4 

40.9 

74 

162.4 

62.  4 

34 

218.5 

83.9 

94 

274-5 

105.4 

55 

51-3 

19.7 

15 

107.4 

41.2 

75 

163.4 

62.  7 

35 

219.4 

84.2 

95 

275-4 

105-7 

56 

52.3 

20.  I 

16 

108.3 

41.  6 

76 

164.3 

63.1 

36 

220.  3 

84.6 

96 

276.3 

106.  I 

H 

53-2 

20.4 

17 

109.  2 

41.9 

77 

165.2 

63-4 

37 

221.3 

84.9 

97 

277-3 

106.4 

58 

54-1 

20.8 

18 

no.  2 

42.3 

78 

166.2 

63.8 

38 

222.  2 

85.3 

98 

278.  2 

106.8 

59 

55-1 

21.  I 

19 

III.  I 

42.6 

79 

167.  I 

64.  I 

39 

223.1 

85.6 

99 

279-1 

107.2 

60 
Dist. 

56.0 

21. 5 

20 

112.  0 

43- 0 

80 

168.0 

64.5 

40 

224. 1 

Dep. 

86.0 

300 

280.1 

107-5 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Lat. 

Dist. 

Dep. 

Lat. 

[F( 

3r  69  Deg 

rees. 

Page  236 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

22  Degrees. 

Dist. 

I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

0.9 

0.4 

61 

56.6 

22.9 

121 

II2.2 

45-3 

181 

167.8 

67.8 

241 

223.5 

90.3 

2 

1.9 

0.7 

62 

57.5 

23.2 

22 

113.  I 

45-7 

.82 

168.7 

68.2 

42 

224.4 

90.7 

3 

2.8 

I.  I 

63 

58.4 

23.6 

23 

114.  0 

46.  I 

^3 

169.  7  1  68.  6 

43 

225.3 

91.0 

4 

3-7 

1-5 

64 

59-3 

24.  0 

24 

115. 0 

46.5 

84 

170.6 

68.9 

44 

226.  2 

91.4 

5 

4.6 

1-9 

65 

60.3 

24-3 

25 

115.  9       46.8 

85 

171-5 

69-3 

45 

227.  2 

91.8 

6 

5-6 

2.  2 

66 

61.  2 

24.7 

26 

116. 8     47.2 

86 

172.5  1  69.7 

46 

228.1 

92.  2 

7 

6.5 

2.6 

67 

62.1 

25-1 

27 

117. 8     47.6 

87 

173.4     70.1 

47 

229.0 

92.5 

8 

7-4 

3-0 

68 

63.0 

25-5 

28 

118.  7     47-9 

88 

174.3      70.4 

48 

229.9 

92.9 

9 

8-3 

3-4 

69 

64.0 

25.8 

29 

1 19.  6  \  48.3 

89 

175.2   ;   70.8 

49 

230.9 

93.3 

lO 

9.3 

?,-7 

70 

64.9 

26.  2 

30 

120.  5 

48.7 

90 

176.2  1   71.2 

50 

231.8 

93.7 

II 

10.2 

4.1 

71 

65.8 

26.6 

131 

121.  5 

49.1 

191 

177.  I 

71-5 

251 

232.  7 

94.0 

12 

II.  I 

4-5 

72 

66.8 

27.  0 

32 

122.4  '  49.4 

92 

178.0  !  71.9 

52 

233.7 

94-4 

13 

12.  I 

4.9 

73 

67.7 

27-3 

ii 

123.3     49.8 

93 

178.9 

72.3 

53 

234.6 

94.8 

14 

13.0 

5-2 

74 

68.6 

27.7 

34 

124.  2  1  50.  2 

94 

179.9 

72.7 

54 

235-5 

95-2 

15 

13-9 

5-6 

75 

69-5 

28.1 

35 

125.  2  1  50.  6 

95 

180.8 

73- 0 

55 

236.4 

95-5 

16 

14.8 

6.0 

76 

70.5 

28.5 

36 

126.  I      50.  9 

96 

181.  7 

73-4 

56 

237.4 

95-9 

17 

"   15-8 

6.4 

77 

71.4 

28.8 

37 

127.0 

51.3 

97 

182.7 

73-8 

57 

238.3 

96.3 

18 

16.7 

6.7 

78 

72.3 

29.  2 

38 

128.0 

51-7 

98 

183.6 

74-2 

58 

239.2 

96.6 

19 

17.6 

7-1 

79 

73-2 

29.  6 

39 

128.9 

52.1 

99 

184.5 

74-5 

59 

240.  I 

97- 0 

20 

18.5 

7-5 

80 

74.2 

30.0 

40 

129.8 

52.4 

52.8 

200 

185.4  :  74.9 

60 

241.  I 

■97.4 

21 

19-5 

7-9 

81 

75.1 

30.3 

141 

~i3o.y 

201 

180.4  1  75-3 

261 

242.0 

97.8 

22 

20.4 

8.2 

82 

76.0 

30.7 

42 

131-7     53-2 

02 

187.3  '  75-7 

62 

242.9 

98.1 

23 

21.3 

8.6 

83 

77.0 

31- I 

43 

132.6     53.6 

03 

188.2  j  76.0 

^3 

243.8 

98.5 

24 

22.3 

9.0 

84 

77.9 

31-5 

44 

133-5     53-9 

04 

189.  I      76.4 

64 

244.8 

98.9 

25 

23.2 

9.4 

85 

78.8 

31.8 

45 

134-4     54-3 

05 

190.  I      76.  8 

65 

245-7 

99-3 

26 

24. 1 

9-7 

86 

79-7 

32.2 

46 

135-4     54-7 

06 

191. 0 

77-2 

66 

246.  6 

99.6 

27 

25.0 

10.  I 

87 

80.7 

32.6 

47 

136-3     55-1 

07 

191.  9 

77.5 

67 

247.6 

100.  0 

28 

26. 0 

10.5 

88 

81.6 

33- 0 

48 

137-2     55.4 

08 

192.9  1  77.9 

68 

248.5 

100.4 

29 

26.9 

10.  0 

89 

82.5 

33-3 

49 

138-2  .  55-8 

09 

193.8 

78.3 

69 

249.4 

100.8 

30 
31 

27.8 

II. 2 

90 

83.4 

33-7 

50 

J39- 1 

56.2 

10 

194.7 

78.7 

70 

250.3 

lOI.  I 

28.7 

II. 6 

91 

8474 

34-1 

151 

140.  0 

56.6 

211 

195-6 

79.0 

271 

251.3 

loi.  5 

32 

29  7 

12.0 

92 

85.3 

34-5 

52 

140.9  !   56.9 

12 

196.6 

79.4 

72 

252.  2 

101.9 

33 

30.6 

12.4 

93 

86.2 

34.8 

53 

141-9     57-3 

13 

197.5 

79.8 

73 

253.1 

102.3 

34 

31-5 

12.7 

94 

87.2 

35-2 

54 

142.8     57.7 

14 

198.4 

80.2 

74 

254.0 

102.6 

35 

32.5 

13-1 

95 

88.1 

35.6 

55 

143-  7     58-  I 

15 

199.3 

80.5 

75 

255.0 

103.0 

36 

33-4 

13-5 

96 

89.0 

36.0 

56 

144.6     58.4 

16 

200.  3 

80.9 

76 

255.9 

103.4 

2>1 

34-3 

13-9 

97 

89.9 

36.3 

57 

145.6  :  58.8 

17 

201. 2     81.3 

77 

256.8 

103.8 

38 

35-2 

14.2 

98 

90.9 

36.7 

58 

146.5  '  59.2 

18 

202.  I      81.  7 

78 

257.8 

104.  I 

39 

36.2 

14.6 

99 

91.8 

37-1 

59 

147.4  ,  59.6 

19 

203.  I      82.  0 

79 

258.7 

104.5 

40 
41 

37-1 

15.0 

100 

92.7 

37-5 
37.8 

60 

148.3  ]  59.9 

20 

204.  0     82.  4 

80 

259^6^ 

104.9 

38.0 

15-4 

loi' 

93-6 

161 

149.3  1  60.3 

221 

204.9  !  82.8 

■^81 

260.  5 

105.3 

42 

38.9 

15-7 

02 

94.6 

38.2 

62 

150.2 

60.  7 

22 

205.8  :  83.2 

82 

261.5 

105.6     1 

43 

39-9 

16.  I 

03 

95-5 

38.6 

63 

151-1 

61. 1 

23 

206. 8  1  83.  5 

l^ 

262.4 

X06. 0     1 

44 

40.8 

16.5 

04 

96.4 

39- 0 

64 

152.  I 

61.4 

24 

207.  7  1  83. 9 

84 

263  3 

106.4      . 

45 

41.7 

16.  9 

05 

97-4 

39-3 

65 

153-0 

61.8 

25 

208.6  !  84.3 

f^ 

264.2 

106.  8 

46 

42.7 

17.2 

06 

98.3 

39-7 

66 

153-9 

62.  2 

26 

209.  5  1  84.  7 

86 

265.2 

107.  I 

47 

43-6 

17.6 

07 

99.2 

40.  I 

67 

154.8 

62.6 

27 

210.  5  1  85.0 

87 

266.  I 

107. 5     : 

48 

44-5 

18.0 

08 

100.  I 

40.5 

68 

155-8 

62.9 

28 

211. 4  1  85.4 

88 

267.0 

107.9 

49 

45-4 

18.4 

09 

lOI.  I 

40.8 

69 

156.7     63.3 

29 

212.3 

P/^ 

89 

268.0 

108.3     1: 

50 

46.4 

18.7 

10 

102.0 

J^I.2 

70 

157.6  :  63.7 

30 

213.3 

86.2 

90 

268.9 

108. 6      [ 

51 

47.3 

19. 1 

III 

102.9 

41.  6 

171" 

158.  5    !   64.  I 

231 

214.2 

86.5 

291 

269.8 

109.0      i 

52 

48.2 

19-5 

12 

103.8 

42.0 

72 

159.5    '   64.4 

32 

215.  I 

86.9 

92 

270.7 

109.4 

53 

49.1 

19.9 

13 

104.  8 

42.3 

73 

160.4     64. 8 

?,i 

216.0  ;  87.3 

93 

271.7 

109.8      1 

54 

50.1 

20.  2 

14 

105.7 

42.7 

74 

161.  3     65.  2 

34 

217. 0  '  87.  7 

94 

272.  6 

no.  I 

55 

51.0 

20.  6 

15 

106.  6 

43-1 

75 

162.  3     65.  6 

35 

217.9    88.0 

95 

273-5 

no.  5 

56 

51-9 

21.0 

16 

107.6 

43-5 

76 

163.2     65.9 

36 

218.8     88.4 

96 

274-4 

no.  9 

57 

52.8 

21.4 

17 

108.5 

43-8 

77 

164.  I      66.  3 

37 

219.7     88.8 

97 

275-4 

III. 3 

58 

53.8 

21.7 

18 

109.4 

44.2 

78 

165.  0     66.  7 

38 

220.  7 

89.2 

98 

276.3 

III. 6 

59 

54-7 

22.  I 

19 

1 10.  3 

44.6 

79 

166.  0     67.  I 

39 

221.6 

89.5 

99 

277.2 

112. 0 

60 
Dist. 

55.6 
Dep. 

22.5 

20 

III. 3 

45- 0 

80 

166.9     67.4 

40 

222.  5 

89-9 

300 

278.2 

112. 4 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.    j    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

' 

[Fc 

r  68  Deg 

rees. 

TABLE 

,    2. 

Page  237 

»■ 

Difference  of  Latitude  and  Departure  for  23  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

2.3.8 

Dist. 

Lat. 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist. 
241 

Lat. 

Dep. 

I 

0.9 

0.4 

61 

56.2 

121 

III. 4 

47.3 

166.6 

70.7 

221.8 

94.  2 

o 

1.8 

0.8 

62 

57-1 

24.  2 

22 

112. 3 

47-7 

82 

167.5 

71.  I 

42 

222.  8 

94.6 

3 

2.8 

I.  2 

63 

58.0 

24.  6 

23 

113. 2 

48.  I 

83 

168.5 

71.5 

43 

223-7 

94.9 

4 

3-7 

1.6 

64 

58.9 

25.  0 

24 

114.  I 

48.5 

84 

169.4 

71.9 

44 

224.  6 

95-3 

s 

4.6 

2.  0 

65 

59-8 

25-4 

25 

115.  I 

48.8 

85 

170.3 

72.3 

45 

225-5 

95.7 

6 

5-5 

2-3 

66 

60.8 

25.8 

26 

116. 0 

49-  2 

80 

171.  2 

72.7 

46 

226.  4 

96.  I 

7 

6.4 

2.7 

67 

61.7 

26.  2 

27 

116.  9 

49-6 

87 

172.  I 

73-1 

47 

227.4 

96.5 

8 

7-4 

3-  I 

68 

62.6 

26.6 

28 

117. 8 

50.  0 

88 

173-1 

73.5 

48 

228.3 

96.9 

9 

8-3 

3-S 

69 

63.5 

27.  0 

29 

118.  7 

50.4 

89 

174.0 

73.8 

49 

229.  2 

97.3 

lO 

11 

9.2 

3-9 

70 
71 

64.4 

27.4 
27.7 

30 

"9-7 

50.8 

90 

174.9 

74.2 
74.6 

50 

230.  I 

97-7 

10.  I 

4-3 

65-4 

131 

120.  6 

51.2 

191 

175-8 

251 

231.0 

98.  I 

12 

II.  0 

4-7 

72 

66.3 

28.  I 

32 

121.  5 

51.6 

92 

176.7 

75.0 

52 

232.  0 

98-5 

13 

12.0 

51 

73 

67.2 

28.5 

?,Z 

122.  4 

52.0 

93 

177.7 

75.4 

53 

232.9 

98.9 

14 

12.9 

S-S 

74 

68.  I 

28.9 

34 

123-3 

52.4 

94 

178.6 

75.8 

54 

233-8 

99.2 

IS 

13-8 

5' 9 

75 

69.0 

29-3 

35 

124.3 

52.7 

95 

179.5 

76.  2 

55 

234-7 

99-6 

16 

14.7 

6.3 

76 

70.  0 

29.7 

36 

125.  2 

53-1 

96 

180.4 

76.6 

56 

235-6 

100.  0 

17 

15.6 

6.6 

77 

70.9 

30.  I 

37 

126.  I 

53.5 

97 

181.  3 

77.0 

57 

236.6 

100.4 

18 

16.6 

7.0 

78 

71.8 

30.5 

38 

127.  0 

53-9 

98 

182.3 

77.4 

58 

237.5 

100.  8 

19 

17-5 

7-4 

79 

72.7 

30-9 

39 

128.0 

54.3 

99 

183.2 

77.8 

59 

238.4 

101.  2 

20 

21 

18.4 

7.8 

80 
81 

73-6 

31-3 

40 
141 

128.9 

54-7 

200 

184.  I 

78.1 

60 

239.3 

loi.  6 

19-3 

8.2 

74.6 

31.6 

129.8 

55-1 

201 

185.0 

78.5 

261 

240.3 

102.  0 

22 

20.3 

8.6 

82 

75-5 

32.0 

42 

130.7 

55-5 

02 

185.9 

78.9 

62 

241.  2 

102.  4 

23 

21.  2 

9.0 

83 

76.4 

32-4 

43 

131. 6 

55.9 

03 

186.9 

79-3 

63 

242.  I 

102.8 

24 

22.  I 

9-4 

84 

77-3 

.32.8 

44 

132.6 

56.  3 

04 

187.8 

79.7 

64 

243.0 

103.2 

25 

23.  0 

9.8 

85 

78.2 

33-2 

45 

133.5 

.56.7 

05 

188.7 

80.  I 

65 

243.9 

103-5 

26 

23- 9 

10.  2 

86 

79.2 

2,3- (> 

46 

134-4 

57.0 

06 

189.  6 

80.5 

6b 

244.9 

103.9 

27 

24.9 

10.  s 

87 

80.1 

34- 0 

47 

135-3 

57.4 

07 

190.5 

80.9 

67 

245.  8 

104.3 

28 

25.8 

10.  9 

88 

81.0 

34-4 

48 

136.  2 

57-8 

08 

191.  5 

81.3 

68 

246.7 

104.7 

29 

26.7 

"•3 

89 

81.9 

.H-8 

49 

137.2 

58.2 

09 

192.4 

81.7 

69 

247.6 

105.  I 

30 
31 

27.  6 
28.5 

II. 7 

90 
91 

82.8 
83.8 

35-2 

50 
151 

138.  I 

58.6 

10 
211 

193.3 

82.  I 

70 

248.5 

105.5 

12.  I 

35-6 

139.0 

59-0 

194.2 

82.4 

271 

249.5 

105.  9 

32 

29-5 

12.  5 

92 

84.7 

35-9 

52 

139.9 

59-4 

12 

195.  I 

82.8 

72 

250.4 

106.3 

33 

30- 4 

12.9 

93 

85.6 

36-  3 

53 

140.  8 

59-8 

13 

196.  I 

83.2 

73 

251.3 

106.  7 

34 

Z^-2> 

13-3 

94 

86.5 

36.7 

54 

141.  8 

60.  2 

14 

197.0 

83.6 

74 

252.  2 

107.  I 

35 

32.2 

13-7 

95 

87.4 

37-1 

55 

142.7 

60.6 

15 

197.9 

84.0 

75 

253.1 

107.5 

36 

Zi-  I 

14.  I 

96 

88.4 

37-5 

56 

143.6 

61.  0 

16 

198.8 

84.4 

76 

254.  I 

107.  8 

37 

34-1 

14- S 

97 

89-3 

37-9 

57 

144.5 

61.3 

17 

199.7 

84.8 

77 

255.0 

108.2 

38 

35- 0 

14.8 

98 

90.  2 

38-3 

58 

145.4 

61.7 

18 

200.  7 

85.2 

78 

255.9 

108.6 

39 

35-9 

IS- 2 

99 

91.  I 

38-7 

59 

146.4 

62.1 

19 

201.  6 

85.6 

79 

256.8 

109.  0 

40 
41 

36.8 

15.6 

100 

92.  I 

39-1 
39-5 

60 

147-3 

62.  5 

20 

202.  5 

86.0 

80 

257-7 

109.  4 

37-7 

16.  0 

lOI 

93- 0 

161 

148.2 

62.  9 

221 

203.4 

86.4 

281 

258.7 

109.8 

42 

.38.  7 

16.  4 

02 

93-9 

39-9 

62 

149.  I 

63.3 

22 

204.4 

86.7 

82 

259.6 

no.  2 

43 

39-6 

16.8 

03 

94.8 

40.  2 

63 

150.0 

6.1.7 

23 

205.3 

87.1 

83 

260.  5 

no.  6 

44 

40.5 

17.2 

04 

95-7 

40.  6 

64 

151.  0 

64.  I 

24 

206.  2 

87.5 

84 

261.  4 

III.  0 

4'i 

41.4 

17.6 

05 

96.7 

41.  0 

65 

151-9 

64-5 

25 

207.  I 

87.9 

85 

262.3 

111.4 

46 

42.3 

18.0 

06 

97.6 

41.4 

66 

152.8 

64.9 

26 

208.0 

88.3 

86 

263.3 

III. 7 

47 

43^  3 

18.4 

07 

98.5 

41.8 

67 

153-7 

65-3 

27 

209.0 

88.7 

87 

264.  2 

112.  I 

48 

44.2 

18.8 

08 

99-4 

42.2 

68 

154-6 

65.6 

28 

209.  9 

89.  I 

88 

265.  I 

112.  5 

49 

45-1 

19.  I 

09 

100.3 

42.  6 

69 

155-6 

66.0 

29 

210.8 

89.5 

89 

266.  0 

112.  9 

50 
51 

46.  0 
46.9 

19- S 
19.9 

10 
III 

101.3 

43- 0 

70 
171 

156.5 

66.4 

30 

2n.  7 

89.9 

90 
291 

266.  9 

1 13- 3 

102.  2 

43-4 

157.4 

66.8 

231 

212.  6 

90.3 

267.9 

113.7 

52 

47-9 

20.  3 

12 

103.  I 

43-8 

72 

158.3 

67.2 

32 

213.6 

90.  6 

92 

268.8 

114.  I 

S3 

48.8 

20.  7 

13 

104.  0 

44-2 

73 

159.2 

67.6 

Zi 

214.5 

91.0 

93 

269.7 

114.5 

S4 

49-7 

21.  I 

14 

104.9 

44-5 

74 

160.  2 

68.0 

34 

215.4 

91.4 

94 

270.  6 

114.9 

5S 

50.  6 

21.5 

15 

105-9 

44-9 

75 

161.  I 

68.4 

35 

216.3 

91.8 

95 

271.5 

115. 3 

S6 

51-5 

21.  9 

16 

106.8 

45-3 

76 

162.0 

68.8 

36 

217.  2 

92.  2 

96 

272.5 

115. 7 

57 

52.5 

22.3 

17 

107.7 

45-7 

77 

162.9 

69.  2 

37 

218.2 

92.  6 

97 

273.  4 

116. 0 

58 

53-4 

22.7 

18 

108.6 

46.  I 

78 

163.8 

69.6 

38 

219.  I 

93- 0 

98 

274.  3 

1 16.4 

59 

S4-3 

23.1 

19 

109-5 

46.5 

79 

164.8 

69-9 

39 

220.  0 

93-4 

99 

275.2 

116.8 

60 

55-2 

23-4 

20 

no.  5 

46.9 

80 

165.7 

70.3 

40 

220.  9 

93-8 

300 

276.  2 

117.  2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fc 

)r  67  De 

^rees. 

Pag 

e238 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

24  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.4 

61 

55-7 

24.8 

121 

no.  5 

49-2 

181 

165.4 

73-6 

241 

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98.0 

2 

1.8 

0.8 

02 

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2 

22 

III.  5     49.  6 

82 

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3 

2.7 

1.2 

63 

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6 

23 

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4 

3-7 

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0 

24 

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4 

25 

1 14.  2  1  50.  8 

85 

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6 

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66 

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26 

8 

26 

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86 

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7 

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67 

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3 

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7 

28 

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9 

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I 

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5 

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9 

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3 

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7 

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5 

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9 

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3 

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7 

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I 

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20 

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5 

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9 

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4 

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8 

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2 

44 

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58.6 

04 

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85 

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6 

45 

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2& 

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86 

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0 

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87 

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4 

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8 

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2 

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6 

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0 

151 

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271 

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32 

29.  2 

13.0 

92 

84.0 

37 

4 

52 

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61.8 

12 

193-7 

86.2 

72 

248.5 

no.  6 

33 

30.1 

13-4 

93 

85.0 

37 

8 

53 

139.8 

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13 

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73 

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34 

31- I 

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94 

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2 

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in. 4 

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14.2 

95 

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6 

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0 

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5 

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50 
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4 

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122.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[F 

or  66  Deg 

rees. 

TAULE   2. 

Page  239  | 

V 

Difference  of  Latitude  and  Departure  for 

25  Degrees. 

Dist. 

I 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
loi.  9 

0.9 

0.4 

61 

55-3 

25.8 

121 

109.7 

51.  I 

181 

164.0 

76.5 

241 

218.4 

2 

1.8 

0.8 

62 

56.2 

26.  2 

22 

no.  6 

51.6 

82 

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76.9 

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3 

2.7 

1-3 

63 

57.1 

26.6 

23 

III. 5 

52.0 

83 

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43 

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4 

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77-8 

44 

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103.1 

5 

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2.  I 

65 

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25 

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52.8 

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7 

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68 

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28 

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10 

II 

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50 

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13 

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15 

1 3- 6 

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75 

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35 

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95 

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107.8 

16 

14.5 

6.8 

76 

68.9 

32.1 

36 

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82.8 

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232.0 

108.2 

17 

15-4 

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77 

69.8 

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37 

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18 

16.3 

7.6 

78 

70.7 

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19 

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59 

234.7 

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20 

18.  I 

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80 

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200 

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60 

235-6 

109.9 
1 10.  3 

21 

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81 

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201 

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84.9 

261 

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22 

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82 

74.3 

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42 

128.7 

60.  0 

02 

183-1 

85-4 

62 

237-5 

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23 

20.8 

9-7 

P 

75-2 

35-1 

43 

129.  6 

60.4 

03 

184.0 

85.8 

63 

238.4 

III.  I 

24 

21.8 

10.  I 

b 

76.1 

35-5 

44 

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04 

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64 

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25 

22.  7 

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77.0 

35-9 

45 

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26 

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77-9 

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66 

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113.4 

27 

24-5 

II. 4 

87 

78.8 

36.8 

47 

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07 

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67 

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112.8 

28 

25-4 

II. 8 

88 

79.8 

37-2 

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08 

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87.9 

68 

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113-3 

29 

26.3 

12.3 

89 

80.7 

37.6 

49 

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31 

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100.6 

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24.9 

19 

107.9 

50-3 

79 

162.  2 

75-6 

39 

216.6 

lOI.O 

99 

271.  0 

126.4 

60 

54-4 

25-4 

20 

108.8 

50.7 

80 

163.  I 

76.1 

40 

217-5 

loi.  4 

300 

271.9 

126.8 

Dist. 

Dep. 

Lat. 

Dist. 



Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fc 

)r  65  Deg 

rees. 

Page  240 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  26  Degr 

;es. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.4 

61 

54-8 

26.  7 

121 

108.8 

53-0 

181 

162.  7 

79-3 

241 

216.6 

105.6 

2 

1.8 

0.9 

62 

55-7 

27.  2 

22 

109.7 

53-5 

82 

163.6 

79-8 

42 

217-5 

106.  I 

3 

2.7 

1-3 

63 

1    56.6 

27.6 

23 

1 10.  6 

53-9 

83 

164.5 

80.2 

43 

218.4 

106.  5 

4 

3-6 

1.8 

64 

57-5 

28.1 

24 

III. 5 

54-4 

84 

165.4 

80.  7 

44 

219.3 

107.  0 

5 

4-5 

2.  2 

65 

58.4 

28.5 

25 

112.3 

54-8 

85 

166.3 

81.  I 

45 

220.2 

107.4 

6 

5-4 

2.6 

66 

59-3 

28.9 

26 

113-2 

55-2 

86 

167.  2 

81.5 

46 

221.  I 

107.8 

7 

6.3 

31 

67 

60.  2 

29.4 

27 

114.  I 

55-7 

87 

16S.  I 

82.0 

47 

222.0 

108.3 

8 

7.2 

3-5 

68 

61.  I 

29.8 

28 

115.  0 

56.1 

88 

169.  0 

82.4 

48 

222.  9 

108.  7 

9 

8.1 

3-9 

69 

62.0 

.  30.  2 

29 

115-9 

56-5 

89 

169.9 

82.9 

49 

223.8 

109.  2 

lO 

9.0 

4.4 

70 

62.  9 

30-7 

30 

116.  8 

57-0 

90 

170.8 
171.7 

83-3 
83-7 

50 

224.7 

109.  6 

II 

9.9 

4.8 

71 

63.8 

31- I 

131 

"7-7 

57-4 

191 

251 

225.6 

no.  0 

12 

10.8 

5-3 

72 

64.7 

31.6 

32 

118.  6 

57-9 

92 

172.  6 

84.2 

52 

226.  5 

1 10.  5 

13 

11.7 

5-7 

73 

65.6 

32.0 

33 

119- 5 

58.3 

93 

173-5 

84.6 

53 

227.4 

no.  9 

14 

12.6 

6.  I 

74 

66.5 

32-4 

34 

120.  4 

58-7 

94 

174-4 

85.0 

54 

228.3 

III. 3 

15 

13-5 

6.6 

75 

67.4 

32-9 

35 

121. 3 

59-2 

95 

175-3 

85-5 

55 

229.2 

III.  8 

16 

14.4 

7.0 

76 

68.3 

33-3 

36 

122.  2 

59-6 

96 

1 7().  2 

85-9 

56 

230.1 

112.  2 

17 

15-3 

7-5 

77 

69.  2 

33-8 

37 

123.  I 

60.  I 

97 

1/7-1 

86.4 

57 

231.0 

112.  7      ; 

18 

16.  2 

Z-9 

78 

70.1 

34-2 

38 

124.0 

60.  5 

98 

178.  0 

86.8 

58 

231.9 

113.  I       ' 

19 

17.  I 

8.3 

79 

71.0 

34-6 

39 

124.9 

60.9 

99 

178.9 

87.2 

59 

232.8 

113-5 

20 
21 

18.0 
18.9 

8.8 

80 

71.9 

35-1 

40 

125.8 

61.4 

200 

179.8 

87-7 

60 

233-7 

114.  0 

9.2 

81 

72.8 

35-5 

141 

126.  7 

61.8 

201 

180.  7 

88.1 

261 

234.6 

114.4 

22 

19.8 

9.6 

82 

73-7 

35-9 

42 

127.  6 

62.  2 

02 

181. 6 

88.6 

62 

235-5 

114-9 

23 

20.  7 

10.  I 

83 

74.6 

36-4 

43 

128.5 

62.7 

03 

182.5 

89.0 

63 

236.4 

115- 3 

24 

21.6 

10.5 

84 

75-5 

36.8 

44 

129.4 

63.1 

04 

183.4 

89-4 

64 

237-3 

115- 7 

-5 

22.5 

II.  0 

f5 

76.4 

37-3 

45 

130-3 

63.6 

05 

184.3 

89.9 

^A 

238.2 

116.  2 

26 

23-4 

II. 4 

86 

77-3 

37-7 

46 

131-  2 

64.  0 

06 

185.  2 

90.3 

66 

239.1 

1 16.  6 

27 

24-3 

II. 8 

87 

78.2 

38.1 

47 

132.  I 

64.4 

07 

186.  I 

90.7 

67 

240.0 

117.  0 

28 

25.2 

12.3 

88 

79.1 

38.6 

48 

133-0 

64.9 

08 

186.9 

91.  2 

68 

240.9 

117-5 

29 

26.  I 

12.7 

89 

80.0 

39- 0 

49 

133-9 

65-3 

09 

187.8 

91.  6 

69 

241.8 

1 1 7.  9 

30 
31 

27.0 

13.2 

90 

80.9 

39-5 

50 

134.8 

65.8 

10 

188.7 

92.  I 

70 

242.7 

118. 4 

13.6 

91 

81.8 

39-9 

151 

135-7 

66.2 

211 

189.6 

92.5 

271 

243.6 

1 18.  8 

32 

28.8 

14.  0 

92 

82.7 

40.3 
40.8 

52 

136.6 

66.6 

12 

190.5 

92.9 

72 

244-5 

119.  2 

33 

29.7 

14-5 

93 

83.6 

53 

137-5 

67.1 

13 

191. 4 

93-4 

73 

245.4 

119- 7 

34 

30.6 

14.9 

94 

84.5 

41.2 

54 

138.4 

67-5 

14 

192.3 

93-8 

74 

246.3 

120.  I       j 

35 

31-5 

15-3 

95 

85-4 

41.  6 

55 

139-3 

67.9 

15 

193-2 

94-2 

75 

247.2 

120.6 

36 

32-4 

IS- 8 

96 

86.3 

42.1 

56 

140.  2 

68.4 

16 

194.  I 

94-7 

76 

248.  I 

121. 0 

37 

33-3 

16.2 

97 

87.2 

42.5 

57 

141.  I 

68.8 

17 

195.0 

95-1 

77 

249.0 

121. 4      ' 

38 

34-2 

16.7 

98 

88.1 

43- 0 

58 

142.0 

69-3 

18 

195-9 

95-6 

78 

249.9 

121. 9 

39 

35-1 

17.1 

99 

89.0 

43-4 

59 

142.9 

69.7 

19 

196.8 

96.  0 

79 

250.8 

122.3 

40 

36.  0 

17-5 

100 

89.9 

43-8 

60 

143.8 

70.1 

20 

197.7 

96.4 

8ci. 

251-7 

122.  7 

41 

36-9 

18.0 

lOI 

90.8 

44-3 

161 

144.7 

70.6 

221 

198.6 

96.9 

281 

252. 6 

123.2 

42 

37-7 

18.4 

02 

91.7 

44-  7 

62 

145.6 

71.  0 

22 

199-5 

97-3 

82 

253-5 

123.6 

43 

38.6 

18.8 

03 

92.  6 

45-2 

63 

146.5 

71-5 

23 

200.  4 

97.8 

l^ 

254-4 

124.  I 

44 

39-5 

19-3 

04 

93-5 

45-6 

64 

147.4 

71.9 

24 

201.3 

98.  2 

84 

255-3 

124.5 

45 

40.4 

19.7 

OS 

94.4 

46.  0 

65 

148.3 

72.3 

25 

202.2 

98.6 

85 

256.2 

124.9 

46 

41-3 

20.  2 

06 

95-3 

46.5 

66 

149.2 

72.8 

26 

203.  I 

99-1 

86 

257-1 

125.4 

47 

42.2 

20.6 

07 

96.  2 

46.9 

67 

150.  I 

73-2 

27 

204.  0 

99-5 

87 

258.0 

125.8 

48 

43-1 

21.  0 

08 

97.1 

47-3 

68 

151.  0 

73-6 

28 

204.9 

99-9 

88 

258.9 

126.3 

49 

44.0 

21.5 

09 

98.0 

47.8 

69 

151-9 

74-  I 

29 

205.8 

100.4 

89 

259-  8 

126.  7 

50 

44.9 
45-8 

21.  9 

10 

98.9 

48.2 

70 

152.8 

74-5 

30 

206.  7 

100.8 
101.3 

90 
291 

260.  7 
^261.  5 

127. 1     ! 
127.6 

51 

22.4 

III 

99.8 

48.7 

171 

153-7 

75-0 

231 

207.6 

52 

46.7 

22.8 

12 

100.  7 

49.1 

72 

154.6 

75-4 

32 

208.5 

loi.  7 

92 

262.4 

128.0 

53 

47.6 

23.2 

13 

loi.  6 

49-5 

n 

155-5 

75-8 

33 

209.4 

102.  I 

93 

263-3 

128.4 

54 

48.5 

23-7 

14 

102.  5 

50.  0 

74 

156.4 

76.3 

34 

210.3 

102.  6 

94 

264.2 

128.9 

55 

49.4 

24.  I 

15 

103.4 

50.4 

75 

157-3 

76.7 

35 

211.  2 

103.0 

95 

265.  I 

129.3 

56 

50-3 

24-5 

16 

104.3 

50.9 

76 

158.2 

77-2 

36 

212.  I 

103.5 

96 

266.  0 

129.8 

57 

51.2 

25.  0 

17 

105.2 

51-3 

77 

159- I 

77-6 

H 

213.  0 

103.9 

97 

266.  9 

130.2 

58 

52.1 

25-4 

18 

106.  I 

51-7 

78 

160.  0 

78.0 

38 

213-9 

104.  3 

98 

267.8 

130.6 

59 

53- 0 

25-9 

19 

107.  0 

52.2 

79 

160.  9 

78.5 

39 

214.8 

104.  8 

99 

268.7 

131. 1 

60 

Dist. 

53-9 

26.3 

20 

107.9 

52.6 

80 

161.  8 

78.9 

40 

215-7 

105.2 

300 

269.6 

131- 5 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fc 

)r  64  Deg 

rees. 

• 

TABLE  2. 

Page  241 

Difference  of  Latitude  and  Departure  for 

27  Degrees. 

Dist. 

I 

Lat. 

Dep. 
0-5 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

0.9 

61 

54-4 

27.7 

121 

107.8 

54-9 

161.  3 

82.2 

241 

214.7 

109.4 

2 

1.8 

0.9 

62 

55.  2     28.  I 

22 

108.7 

55-4 

82 

162.2 

82.6 

42 ; 

215.6 

109.9 

3 

2.7 

1.4 

63 

56.  I      28.  6 

23 

109.  6     55.  8 

83 

163-1 

83.1 

43 

216.  5 

no.  3 

4 

3-6 

1.8 

64 

57.0     29.  I 

24 

I  lo-  5  .  56-  3 

84 

163.9 

83-5 

44 

217.4 

1 10.  8 

5 

4-5 

2-3 

65 

57-9 

29.5 

25 

III. 4 

56.7 

85 

164.8 

84.0 

45 

218.3 

III.  2 

6 

5-3 

2.7 

66 

58.8 

30.0 

26 

112.  3 

57-2 

86 

165-7 

84.4 

46 

219.  2 

III. 7 

7 

6.2 

3-2 

67 

59-7 

30-4 

27 

113. 2     57.7 

87 

166.6 

84.9 

47 

220.  I 

112.  I 

S 

7-  I 

3-6 

68 

60.6 

30-9 

28 

114.  0  i  58.  I 

88 

167.5 

^5-4 

48 

221.0 

112.  6 

9 

S.o 

4.  I 

69 

61.5 

313 

29 

1 14.  9  :  58.6 

89 

168.4 

f^-^ 

49 

221.  9 

113.  0 

lO 

8.9 

4-5 

70 

62.4 

31.8 

30 

115.  8  '  59.0 

90 

169.3 

86.3 

50 
251 

222.  8 

"3-5 

II 

9.8 

5-0 

71 

63-  3     32.  2  1 

131 

"6.7     59.5 

191 

170.  2 

86.7 

"22376" 

114. 0 

12 

10.  7 

5-4 

72 

64.  2 

32-7 

32 

117. 6     59.9 

92 

171.  I 

87.2 

52 

224.5 

1 14.  4 

13 

II. 6 

5-9 

73 

65.0 

33-1 

33 

118.  5  I  60.  4 

93 

172.0 

87.6 

5? 

225.4 

1 14.  9 

14 

12.5 

6.4 

74 

65-9 

33-6 

34 

119.  4     60.  8 

94 

172.9 

88.  1 

54 

226.3 

"5-3 

15 

13-4 

6.8 

75 

66.  8     34.  0 

35 

120.  3     61.  3 

95 

173-7 

88.5 

55 

227.  2 

115,8 

16 

14- 3 

7-3 

76 

67-  7  i  34-  5 

36 

121.  2     61.  7 

96 

174-6  1 

89.  0 

';6 

228.  I 

116.  2 

17 

15- I 

7-7 

77 

68.6     35.0 

37 

122.  I      62.  2 

97 

175-5 

89.4 

57 

229.  0 

116.  7 

18 

16.  0 

8.2 

78 

69-5 

35-4 

38 

123.0     62.7 

98 

176.4 

89-9 

58 

229.9 

117.  I 

19 

16.9 

8.6 

79 

70.4 

35-9 

39 

123.  8     63.  I 

99 

177-3 

90-3 

59 

230.8 

117.  6 

20 

17.8 

9.1 

80 

71-3 

36.3 

40 

124.  7 
125.6 

63.6 

200 

178.2 

90.8 

60 

231-7 

1 18.0 

21 

18.7 

9-5 

81 

72.2 

36.8 

141 

64.0 

201 

179.  I 

91-3 

261 

232.  6 

118.5 

22 

19.  6 

10. 0 

82 

73-1 

37-2 

42 

126.  5     64.  5 

02 

180.  0 

91.7 

62 

233-4 

1 18.  9 

23 

20.  5 

10. 4 

83 

74.0 

37-7 

43 

127.4     64.9 

03 

180.9 

92.  2 

63 

234-3 

"9-4 

24 

21.4 

10.9 

84 

74.8 

38.1 

44 

128.3     65.4 

04 

181.  8 

92.6 

64 

235-2 

"9-9 

25 

22.3 

II. 3 

85 

75-7 

38.6 

45 

129.  2  1  65.  8 

05 

182.7 

93-1 

^5 

236.1 

120.  3 

26 

23.  2 

II.  8 

86 

76.6 

39- 0 

46 

130.  I      66.  3 

06 

183-5 

93-5 

66 

237.0 

120.8 

27 

24.  I 

12.3 

87 

77-5 

39-5 

47 

131-0 

66.7 

07 

184.4 

94-0 

H 

.^^Z'  § 

121.  2 

28 

24.9 

12.7 

88 

78.4 

40.  0 

48 

131-9 

67.2 

08 

'!5-3 

94-4 

68 

238.8 

121.  7 

29 

25-8 

13.2 

89 

79-3 

40.4 

49 

132.8 

67.6 

09 

186.  2 

94-9 

69 

239-7 

122.  I 

30 
31 

26.7 
27.6 

13.6 

90 

80.2 

40.9 

50 

133-7 
134-5 

68.1 

10 

187. 1 

95-3 

70 

240.  6 

122.6 

14.  I 

91 

81.  I 

41-3 

151 

68.6 

211 

188.0 

95-8 

271 

241.5 

123.0 

32 

28.5 

14-5 

92 

82.0 

41.  8 

52 

135-4 

69.0 

12 

188.9 

96.  2 

72 

242.4 

123.5 

29.4 

15.0 

93 

82.9 

42.2 

53 

136-3 

69.5 

13 

189.8 

96.7 

73 

243-2 

123.9 

34 

30-3 

15-4 

94 

S3.  8 

42.7 

54 

137.2  1  69.9 

14 

190.7 

97-2 

74 

244.  I 

124.4 

35 

31.2 

15.9 

95 

84.6 

43-1 

55 

138.  I  1  70.  4 

15 

191.  6 

97-6 

75 

245-0 

124.8 

36 

32.  I 

16.3 

96 

85-5 

43-6 

56 

139.0  I  70.8 

16 

192-5 

98.  I 

76 

245-  9 

125-3 

37 

33- 0 

16.8 

97 

86.4 

44.0 

57 

139-9 

71-3 

17 

193-3 

98.5 

77 

246.8 

125.8 

38 

33-9 

17-3 

98 

U-^ 

44-5 

58 

140.8 

71.7 

18 

194.2 

99.0 

78 

247-7 

126.  2 

39 

34-7 

17.7 

99 

88.2 

44.9 

59 

141.  7 

72.  2 

19 

195- 1 

99.4 

79 

248.  6 

126.  7 

40 
41 

35-6 
36-5 

18.2 

100 

89.  I 
90.0 

4C4 

60 

142.  6 

72.6 

20 

196.0 

99-9 

80 

249-5 

127. 1 

18,6" 

lOI 

45-Y 

i6i 

~i43-5 

73-1 

221 

196.9 

100.  3 

281 

250.4  i   127.6    \ 

42 

37-4 

19.  I 

02 

90.9 

46.3 

62 

144-3 

73-5 

22 

197.8 

100.  8 

82 

251-3 

126.  0 

43 

38.3 

19-5 

03 

91.8 

46.8 

63 

145.2 

74.0 

23 

198.7 

loi.  2 

P 

252.  2 

1 28.  5 

44 

39-2 

20.0 

04 

92.7 

47.2 

64 

146.  I 

74-5 

24 

199.6 

loi.  7 

84 

253-0 

128.9 

45 

40.  I 

20.4 

05 

93-6 

47-7 

65 

147.0 

74-9 

«5 

200.  5 

102.  I 

85 

253-9 

129.4 

46 

41.0 

20.  9 

06 

94.4 

48.  I 

66 

147.9 

75-4 

26 

201.4 

102.  6 

86 

254.8 

129.8 

47 

41.9 

21.3 

07 

95-3 

48.  6 

67 

148.8 

75-8 

27 

202.3 

103.  I 

87 

255-  7 

130-3 

48 

42.8 

21.8 

08 

96.  2 

49.0 

68 

'149.  7 

76.3 

28 

203. 1 

103-5 

88 

256.  6 

130- 7 

49 

43-7 

22.  2 

09 

97.1 

49-5 

69 

150.6 

76.7 

29 

204.  0 

104.  0 

89 

257-5 

131-2 

50 

^^•A 

22.  7 

10 

98.0 
98-9 

49.9 

70 

151-5 

77.2 

30 

204.9 

104.4 

_90_ 

258.4 

131-7 

51 

45-4 

23.2 

III 

50.4 

171 

152.4 

77.6 

231 

205.8 

104.9 

291 

259-3 

132-1 

52 

46-3 

23.  6 

12 

99.8 

50.8 

72 

153-3 

78.. 

32 

206.7 

105-3 
105.8 

92 

2fc;0.  2   :    132.  6     1 

53 

47.2 

24.  I 

13 

100.  7 

513 

73 

154- I 

78.5 

33 

207.  6 

93 

261. 1  !  133.0   1 

54 

48.  I 

24.5 

14 

loi.  6 

51.8 

74 

155-0 

79.0 

34 

208.5 

106.  2 

94 

262.0 

133-5 

55 

49.0 

25.  0 

15 

102.  5 

52.2 

75 

155-9  '  79-4 

35 

209.4 

106.  7 

9| 

262.8 

133-9 

56 

49.9 

25-4 

16 

103.4 

52-7 

76 

156.8  i  79.9 

36 

210.3 

107.  I 

96 

263.7 

134-4 

57 

50.8 

25.9 

17 

104.  2 

53-  I 

77 

157.7  I  80.4 

37 

211.  2 

107.6 

97 

264.6 

134.  8 

58 

51-  7 

26.3 

i8 

105.  I 

53-6 

78 

158.6  [  80.8 

38 

212.  I 

108.0 

98 

265.5 

135-3 

59 

52.6 

26.8 

19 

106.  0 

54.0 

79 

159-5 

81.3 

39 

213.0 

108.5 

99 

266.4 

135-7 

60 

53-5 

27.  2 

20 

106.9 

54-5 

80 

160.4 

81.7 

40 

213.8 

109.0 

300 

267.3 

136.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[F 

Dr  63  Degrees.        | 

16    B 

Page  242 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  28  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0-5 

61 

53-9 

28.6 

121 

106.8 

56.8 

181 

159.8 

85.0 

241 

212.8 

113.  I 

2 

I 

8 

0.9 

62 

54-7 

29 

I 

22 

107.7 

57-3 

82 

160.  7 

85.4 

42 

213.7 

II3.6 

3 

2 

6 

1.4 

63 

55-6 

29 

6 

23 

108.6 

57-7 

83 

161. 6 

85.9 

43 

214.6 

114.  I 

4 

3 

5 

1.9 

64 

56.5 

30 

0 

24 

109.5 

58.2 

84 

162.  5 

86.4 

44       215.4 

I14.6 

5 

4 

4 

2.  3 

65 

57-4 

30 

5 

25 

1 10.  4 

58-7 

85 

163.3 

86.9 

45       216.3 

115.0 

6 

5 

3 

2.  8 

66 

58-3 

31 

0 

26 

III. 3 

59-2 

86 

164.  2 

87.3 

46       217.2 

"55 

7 

6 

2 

3-3 

67 

59-2 

31 

5 

27 

112.  I 

59-6 

87 

165.  I 

87.8 

47       218.  I 

116.  0 

8 

7 

I 

3-8 

68 

60.  0 

31 

9 

28 

II3.0 

60.  I 

88 

166.  0 

88.  3 

48       219.0 

116. 4 

9 

7 

9 

4.2 

69 

60.  9 

32 

4 

29 

113-9 

60.6 

89 

166.  9 

88.7 

49       219.9 

116. 9 

lO 

8 

8 

4-7 

70 

61.8 

32 

33 

9 

30 

114.  8 

61.  0 

90 

167.8 

89.2 

50       220.  7 

117.4 

II 

9 

7 

5-2 

71 

62.  7 

3 

131 

115- 7 

61.5 

191 

168.6 

89.7 

251 

221.6 

117.8 

12 

10 

6 

5.6 

72 

63.6 

33 

8 

32 

116.  5 

62.  0 

92 

169.5 

90.  I 

52 

222.  5 

118.  3 

13 

II 

5 

6.  I 

71, 

64-5 

34 

3 

ii 

II 7. 4 

62.  4 

93 

170.4 

90.  6 

53 

223.4 

118.  8 

14 

12 

4 

6.6 

74 

65.3 

34 

7 

34 

118.  3 

62.  9 

94 

171.3 

91.  I 

54       224. 3 

119.  2 

15 

13 

2 

7.0 

75 

66.2 

35 

2 

35 

119.  2 

63-4 

95 

172.2 

91.5 

55   ;     225.2 

119.  7 

16 

14 

I 

7-5 

76 

67.1 

35 

7 

36 

120.  I 

63.8 

96 

173.  I 

92.0 

56  ;   226. 0 

120.  2 

17 

15 

0 

8.0 

77 

68.0 

36 

I 

37 

121.  0 

64-3 

97 

173.9 

92-5 

57     226.9 

120.7 

18 

15 

9 

8.5 

78 

68.9 

36 

6 

38 

121. 8 

64.8 

98 

174.8 

93.0 

58  !   227.8 

121.  I 

19 

16 

8 

8.9 

79 

69.8 

37 

I 

39 

122.  7 

65-3 

99 

175-7 

93.4 

59  '   228. 7 

121. 6 

20 

17 

7 

9.4 

80 

70.  6 

37 

6 

40 

123.  6 

65-7 

200 

176.6 

93-9 

60       229. 6 

122.  I 

21 

18 

5 

9-9 

81 

71-5 

18 

0 

141 

124.5 

66.2 

201 

177-5 

94.4 

261        230. 4 

122.5 

22 

19 

4 

10.  3 

82 

72.4 

38 

5 

42 

125.4 

66.7 

02 

178.4 

94-8 

62       231.3 

123.0 

23 

20 

3 

10.8 

f3 

73-3 

39 

0 

43 

126.3 

67.1 

03 

179.2 

95-3 

63       232. 2 

123.5 

24 

21 

2 

"•3 

84 

74.2 

39 

4 

44 

127.  I 

67.6 

04 

180.  I 

95-8 

64       233.  I 

123.9 

25 

22 

I 

II. 7 

85 

75-1 

39 

9 

45 

128.0 

68.  I 

05 

i8i.o 

96.  2 

65        234. 0 

124.4 

26 

23 

0 

12.  2 

86 

75-9 

40 

4 

46 

128.9 

68.5 

06 

181. 9 

96.7 

66       234. 9 

124.9 

27 

23 

8 

12.7 

87 

76.8 

40 

8 

47 

129.8 

69.  0 

07 

182.8 

97-2 

67  :     235.  7 

125.3 

28 

24 

7 

13- I 

88 

77-7 

41 

3 

48 

130.7 

69-5 

08 

183.7 

97-7 

68       236. 6 

125.8 

29 

25 

6 

13-6 

89 

78.6 

41 

8 

49 

131. 6 

70.  0 

09 

184.5 

98.1 

69       237. 5 

126.3 

30 

26 

5 

J4J 

14.6 

90 

79-5 

42 

3 

50 

132.4 

70.4 

10 

185.4 

98.6 

70 

238.4 

126.8 

31 

27 

4 

91 

80.3 

42 

7 

151 

133-3 

70.9 

211 

186.3 

99-1 

271       239.3 

127.  2 

32 

28 

3 

15.0 

92 

81.2 

43 

2 

52 

134-2 

71.4 

12 

187.2 

99.5 

72  1     240.  2 

127.7 

33 

29 

I 

15-5 

93 

82.  I 

43 

7 

53 

135- I 

71.8 

13 

188.  I 

100.  0 

73       241.0 

128.2 

34 

30 

0 

16.  0 

94 

83.0 

44 

I 

54 

136.0 

72-3 

14 

189.0 

100.  5 

74       241.9 

128.6 

35 

30 

9 

16.4 

95 

83-9 

44 

6 

55 

136.9 

72.8 

15 

189.8 

100.  9 

75  !     242.8 

129.  I 

36 

31 

8 

16.9 

96 

84.8 

45 

I 

56 

137-7 

73-2 

16 

190.7 

101.4 

76  i     243.  7 

129.6 

37 

32 

7 

17.4 

97 

85.6 

45 

5 

57 

138.6 

73-7 

17 

191.  6 

lOI.  9 

77  1     244.6 

130.0 

38 

33 

6 

17.8 

98 

86.5 

46 

0 

58 

139-5 

74-2 

18 

192.5 

102.  3 

78  !    245. 5 

130.5 

39 

34 

4 

18.3 

99 

87.4 

46 

5 

59 

140.4 

74-6 

19 

193.4 

102.  8 

79       246.3 

131. 0 

40 

35 

3 

18.8 

100 

88.3 

46 

9 

60 

141-3 

75-1 

20 

194.2 

103.3 

80 

247.2 

131. 5 

41 

36 

2 

19.  2 

ioT~ 

89.2 

"47 

4 

161 

142.  2 

75-6 

221 

195.  I 

103.8 

281 

248.1 

131. 9 

42 

37 

I 

19.7 

02 

90.  I 

47 

9 

62 

143.0 

76.1 

22 

196.  0 

104.  2 

82 

249.0 

132.4      . 

43 

3^ 

0 

20.  2 

03 

90.9 

48 

4 

63 

143- 9 

76-5 

23 

196.9 

104.7 

83       249. 9 

132.9 

44 

38 

8 

20.  7 

04 

91.8 

48 

8 

64 

144.8 

77.0 

24 

197.8 

105.  2 

84  :     250.  8 

133.3 

45 

39 

7 

21.  I 

05 

92.7 

49 

3 

65 

145-7 

77-5 

25 

198.7 

105.  6 

85   ;     251.6 

133-8 

46 

40 

6 

21.  6 

06 

93-6 

49 

8 

66 

146.  6 

77-9 

26 

199.5 

106.  I 

86       252. 5 

134.3 

47 

41 

5 

22.  I 

07 

94-5 

50 

2 

67 

147-5 

78.4 

27 

200.  4 

106.  6 

87 

253.  4 

134.7 

48 

42 

4 

22.  5 

08 

95-4 

50 

7 

68 

148.3 

78.9 

28 

201.3 

107.  0 

88 

254.3 

135-2 

49 

43 

3 

23.0 

09 

96.  2 

51 

2 

69 

149.2 

79-3 

29 

202.  2 

107-5 

89 

255.2 

135-7 

50 

44 

I 

23-5 

lO 

97.1 

51 

6 

70 

150.  I 

79-8 

30 

^°3ii_ 

108.  0 
108.4 

90 
291 

256.  I 
256.  9 

136.1 
136.6 

51 

45 

0 

23-9 

III 

98.0 

52 

I 

171 

151.  0 

80.3 

231 

204.  0 

52 

45 

9 

24.4 

12 

98.9 

52 

6 

72 

151-9 

80.7 

32 

204.8 

108.  9 

92 

257.8 

137- I 

53 

46 

8 

24.9 

13 

99.8 

S3 

I 

73 

152.7 

81.2 

33 

205.7 

109.4 

93 

258.7 

137-6 

54 

47 

7 

25-4 

14 

100.  7 

53 

5 

74 

153-6 

81.7 

34 

206.  6 

109.9 

94 

259.6 

138.0 

55 

48 

6 

25.8 

15 

loi.  5 

54 

0 

75 

154-5 

82.  2 

35 

207.5 

no.  3 

95 

260.  5 

138-5 

56 

49 

4 

26.3 

16 

102.  4 

54 

5 

76 

IS5-4 

82.6 

36 

208.4 

1 10.  8 

96 

261.4 

139.0 

57 

50 

3 

26.8 

17 

103-3 

54 

9 

77 

156-3 

83.1 

37 

209.3 

III. 3 

97 

262.  2 

139-4 

58 

51 

2 

27.  2 

18 

104.  2 

55 

4 

78 

157-2 

83.6 

38 

210.  I 

III. 7 

98 

263.1 

139.9 

59 

52 

I 

27.7 

19 

105.  I 

55 

9 

79 

158.0 

84.0 

39 

211.  0 

112.  2 

99 

264.  0 

140.4 

60 
Dist. 

53- 0 

28.2 

20 

106.  0 

56-3 

80 

158.9 

84-5 

40 

211. 9 

112.  7 

300 

264.9 

140.8 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  62  Deg 

rees. 

f  r 

TABLE  2. 

Page  243 

Dist. 

_. 

Difference  of  Latitude  and  Depart! 

are  for 

29Deg 

rees. 

Lat. 

Dep. 

Dist. 

r.at. 
53-4 

1   Dep. 
29.  6 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

o-S 

61 

121 

105.8 

.58.7 

181 

158-3 

87.8 

241 

210.8 

116.  8 

2 

I.  7         I.O 

62 

i     54-2 

30-  I 

22 

106.  7 

59-1 

82 

159-2 

88.2 

42 

211.  7       117.  3 

3 

2.6        1. 5 

f>3 

1    55-1 

30.5 

23 

107.6 

59-6 

83 

160.  I 

88.  7 

43 

212.5      "7-8 

4 

3-5       1-9 

64 

56. 0 

31.0 

24 

108.5 

60.  I 

84 

160.9 

1     89.2 

.44 

213.4     "8.3 

5 

1       4-4        2. 4 

65 

5f'-9 

31-5 

25 

109.3 

60.6 

85 

i  161.  8 

89.7 

45 

214.3      "8.8 

6 

5.2        2.9 

66 

57-7 

32.0 

26 

110.  2 

61.  I 

86 

162.  7 

90.  2 

46 

215.2  i  119.  3 

7 

6.  I        3.  4 

67 

58.6 

32-5 

27 

III.  I 

61.6 

87 

163.  6 

90.7 

47 

216.  0 

"9-7    1 

8 

7-  0       3-9 

68 

59-5 

33- 0 

28 

112.  0 

62.1 

88 

'  164.4 

91.  I 

48 

216.  9 

120.2    1 

9 

7.  9       4.  4 

69 

60.3 

33-5 

29 

II2.8 

62.5 

89 

165-3 

91.  6 

49 

217.8      120.7    1 

lO 

8.7 
9.6 

4.8 

70 

61.2 

33-9 

30 

113- 7 

63.0 

90 

166.2 

92.  I 

50 

218.7      121. 2    1 

II 

5-3 

71 

62.  I 

34-4 

131 

114.  6 

63-5 

191 

167.  I 

92.6 

251 

219.5 

121.  7 

12 

10.5        5.8 

72 

93-° 

'  34-9 

32 

II5-4 

64.  0 

92 

167.9 

93-1 

52 

220.4 

122.2 

13 

11.4        5.  3 

73 

63.8 

35-4 

33 

1 16.  3 

64-5 

93 

168.8 

93-6 

53 

221.3 

122.  7 

H 

12.  2    ,       6.  8 

74 

64.7 

35-9 

34 

117.  2 

65.  0 

94 

169.7 

94-1 

54 

222.  2 

123.  I 

15 

13-  I        7-3 

75 

65.6 

36-4 

35 

118.  I 

65-4 

95 

170.  6 

94-5 

55 

223.0 

123.  6 

i6 

14.0       7.8 

76 

66.5 

i  36.8 

3^ 

1 18.  9 

65-9 

96 

171. 4 

95-0 

56 

223.9 

124.  I 

17 

14.9 

8.2 

77 

^7-3 

37-3 

37 

119.  8 

66.4 

97 

172.3 

95-5 

57 

224.  8 

124.  6 

i8 

15-7 

8.7 

78 

68.2 

37-8 

3« 

120.  7 

66.9 

98 

173.2 

96.  0 

58 

225-7 

125.  I 

19 

16.6 

9.2 

79 

69.  I 

3^-3 

39 

121.  6 

67-4 

99 

174.0 

96.5 

59 

226.  5 

125.6 

20 

17-5 

9-7 

80 

70.0 
70.8 

38.8 
39-3 

40 

122.4 

67.9 

200 

174.9 

97.0 

60 

227.4 

126.  I 

21 

18.4 

10.2 

81 

141 

123-3 

68.4 

201 

175-8 

97-4 

261 

228.3 

126.  5 

22 

19.  2 

10.7 

82 

71.7 

39- » 

42 

124.  2 

68.8 

02 

176.7 

97-9 

62 

229.  2 

127.0 

23 

20. 1 

II. 2 

«3 

72.6 

40.  2 

43 

125.  I 

69-3 

03 

177-5 

98-4 

63 

230.0 

127-5 

24 

21.0 

II. 6 

84 

73-5 

40.7 

44 

125.9 

69.8 

04 

178.4 

98.9 

64 

230.9 

128.0 

25 

21.  9 

12.  I 

«5 

74-3 

41.2 

45 

126.8 

70.3 

05 

179-3 

99-4 

65 

231.8 

128.5 

26 

22.7 

12.  6 

86 

75-2 

41.7 

46 

127.7 

70.8 

06 

180.2 

99-9 

66 

232.6 

129.  0 

27 

23.6 

13- I 

«7 

76.1 

42.  2 

47 

128.6 

71-3 

07 

181. 0 

100.  4 

67 

233-5 

129.4 

28 

24.5  1  13.6 

88 

77.0 

42.7 

48 

129.4 

71.8 

08 

181.  9 

100.  8 

68 

234-4 

129.9 

29 

25.4  1  14.  I 

89 

77.8 

43-1 

49 

130-3 

72.2 

09 

182.8 

lOI.  3 

69 

235-3 

130.4 

30 

26.  2     14.  5 

90 

78.7 

43-6 

50 

131-2 

72.7 

10 
211 

183.7 

101.8 

70 

236.  I 

130.9 

31 

27.1 

15.0 

91 

79.6 

44.1 

151 

132.  I 

73-2 

184.5 

102.3 

271 

237.0 

131-4 

32 

28.0 

155 

92 

80.5 

44.6 

52 

132-  9     73-  7 

12 

185.4 

102.  8 

72 

237-9 

131-9 

j3 

28.  9     16.  0 

93 

81.3 

45-1 

53 

133-8 

74-2 

13 

186.3 

103-3 

73 

238.8 

132.4 

34 

29.7     16.5 

94 

82.2 

45-6 

54 

J34-7 

74-7 

H 

187.2 

103-7 

74 

239-6 

132.8 

35 

30.6  1  17.0 

95 

83.1 

46.  I 

55 

135-6 

75-1 

15 

188.0 

104.  2 

75 

240-5 

^^33- 3 

3^' 

31-5  1  17-5 

96 

84.0 

46.5 

5& 

136.4 

75-6 

16 

188.9 

104.7 

76 

241.4 

133-8 

^Z 

32-4 

17.9 

97 

84.8 

47.0 

57 

137-  3     76-  I 

17 

189.8 

105.  2 

77 

242.3 

134-3 

3« 

33-2 

18.4 

98 

85.7 

47-5 

58 

138.  2      76.  6 

18 

190.7 

105-7 

78 

243-1 

134.8 

39 

34.1      18.9 

99  : 

86.6 

48.0 

59 

139- I 

77-1 

19 

191- 5 

106.  2 

79 

244-0 

•35-3 

40 

35.0  1  19.4 

100 

87-5 

48.5 

60 

139-9 

77-6 

20 

192.4 

106.  7 

80 

244.9 

135-7 

41 

35-9      19-9 

lOI 

88.3 

49.0 

161 

140.  8 

78.1 

221 

193-3 

107.  I 

281 

245.8 

136.2 

42 

36.  7  '  20.  4 

02 

89.2 

49-5 

62 

141.  7  , 

78.5 

22 

194.2 

107.6 

82 

246.6 

136-7 

43 

37.  6     20.  8 

03 

90.  I 

49.9 

^3 

142.  6 

79.0 

23 

195.0 

108.  I 

83 

247-5 

137-2 

44 

38-5  '  21.3 

04 

91.  0 

50.4 

64 

143-4 

79-5 

24 

195-9 

108.6 

84 

248.4 

137-7 

45 

39.4     21.8 

05 

91.8 

50.9 

b5 

144-3 

80.0 

25 

196.8 

109.  I 

85 

249-3 

138.2 

46 

40.2  1  22.3 

06 

92.7 

51-4 

66 

145-2 

80.5 

26 

197-7 

109.  6 

86 

250.  I 

138-7 

47 

41.  I      22.  8 

07  ' 

93-6 

51-9 

67 

146.  I 

81.0 

27 

198-5 

no.  I 

87 

251.0 

139-  I 

48 

42.  0 

23-3 

08 

94-5 

52-4 

68 

146.9 

81.4 

28 

199.4 

no.  5 

88 

251-9 

139.6 

49 

42.9 

23.8 

09 

95-3 

52.8 

b9 

147.8 

81.9 

29 

200.3 

III.  0 

89 

252.8 

140.  1 

50 
51 

43-7 

24.2 

10  } 

96.2 

53-3 
"53- S 

70  : 

148.7 

82.4 

30 

201.  2  ! 

III. 5 

90 

253-6 

140.6 

44.6 

24.7 

III 

97.1 

171 

149.6 

82.9 

231 

202.  0 

112.  0 

291 

254-  5 

141.  I 

52 

45-5     25.2 

12 

98.  0 

54-3 

72 

150.4 

83-4 

32 

202.  9 

112.  5 

92 

255-4 

141.  6 

53 

46. 4     25.  7 

13 

98.8 

54- « 

73 

151-3 

83-9 

33 

203-  8  i 

1 13.0 

93 

256-3 

142.  0 

54 

47.  2     26.  2 

14 

99-7 

55-3 

74 

152.  2 

84-4 

34 

204.7 

"3-4 

94 

257-1 

142.5 

55 

48.  I     26.  7 

15 

100.  6 

55- « 

75 

153- I 

84.8 

35 

205.5 

"3-9 

95 

258.0 

143.0 

S^ 

49.0     27.  I 

16 

loi.  5 

56.2 

76 

153-9 

^5-3 

36 

206.4 

114.4 

96 

258.9 

143-5 

57 

49.9 

27.  6 

17 

102.3 

5b.  7 

77 

154.8 

8i;.  8 

37 

207.3 

"4-9 

97 

259-8 

144.0 

5« 

50-7 

28.  I 

18 

103.2 

57-2 

7« 

155-7 

86.3 

38 

208.2 

"5-4 

98 

260.  6 

144-5 

59 

5i.b 

28.6 

19 

104.  I 

57-7 

79 

156.6 

86.8 

39 

209.  0 

"5-9 

99 

261.  5 

145.0 

60 

52-5 

29.  I 

20 

105.0 

58-2 

80 

157-4 

87-3 

40 

209.9 

116.  4 

300 

262.4 

145-4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  61  Degrees.        1 

Page  244 

TABLE  2. 

Difference  of  Latitude  and  Departi 

ire  for 

30  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0-5 

61 

52.8 

30-5 

121 

104.8 

60.  5 

181 

156.8 

90-5 

241 

208.  7 

120.  5 

2 

1-7 

I.  0 

62 

53-7 

31.0 

22 

105-7 

61.  0 

82 

157-6 

91.0 

42 

209.6 

121.  0 

3 

2.6 

1-5 

63 

54-6 

31-5 

23 

106.  5 

61.5 

P 

158-5 

91-5 

43 

210.4 

121.  5 

4 

3-5 

2.  0 

64 

55-4 

32.0 

24 

107.4 

62.  0 

84 

159-3 

92.0 

44 

211. 3 

122.  0 

5 

4-3 

2-5 

65 

56.3 

32-5 

25 

108.  3   1  62;  5 

85 

160.  2 

92-5 

45 

212.2 

122.  5 

6 

5-2 

3-0 

66 

57-2 

33- 0 

26 

109.  I 

63.0 

86 

161.  I 

93-0 

46 

213.0 

123.0 

7 

6.  I 

3-5 

67 

58.0 

33-5 

27 

1 10.  0 

63-5 

87 

161.  9 

93-5 

47 

213.9 

123-5 

8 

6.9 

4.0 

68 

58-9 

34- 0 

28 

no.  9 

64.  0 

88 

162.8 

94.0 

48 

214.8 

124.0 

9 

7.8 

4-5 

69 

59-8 

34-5 

29 

III.  7  ;  64.5 

89 

163-7 

94-5 

49 

215.6 

124.5 

lO 

8.7 

5-0 

70 

60.6 

35- 0 

30 

112.  6 
"3-4 

65.0 
"65:5" 

90 
191 

164.5 
165.4 

95-0 
95-5 

50 

216.  5 

125.0 
125-  5     1 

II 

9-5 

5-5 

71 

61.5 

35-5 

131 

251 

217.4 

12 

10.4 

6.0 

72 

62.4 

36.0 

32 

1 14- 3 

66.0 

92 

166.3 

96.  0 

52 

218.2 

126.  0 
126.  5 

13 

11-3 

6.5 

73 

63.2 

36.5 

33 

115-2  ;  66.5 

93 

167.  I 

96-5 

53 

219.  I 

H 

12.  I 

7.0 

74 

64.  I 

37- 0 

34 

116.  0 

67.  0 

94 

168.0 

97.0 

54 

220.  0 

127.  0 

IS 

13.0 

7-5 

75 

65.0 

37-5 

35 

116.  9 

67-5 

95 

168.9 

97-5 

55 

220.8 

127.5 

i6 

13-9 

8.0 

76 

65.8 

38.0 

36 

117.  8  1  68.0 

96 

169.7 

98.0 

56 

221.  7 

128.0 

17 

14.7 

8.5 

77 

66.7 

38.5 

37 

118.  6  1  68.5 

97 

1 70.  6 

98.5 

57 

222.  6 

128.5 

i8 

15.6 

9.0 

78 

^.7-5 

39-0 

38 

"9-5 

69.0 

98 

171- 5 

99-0 

58 

223.4 

129.  0 

19 

16.5 

9-5 

79 

68.4 

39-5 

39 

120.4 

69-5 

99 

172.3 

99-5 

59 

224.3 

129.5 

20 
21 

17-3 
18.2 

10.  0 

80 

69-3 

40.  0 

40 

121.  2 

70.  0 

200 
201 

173-2 

174.  I 

100.  0 
100.  5 

60 
261 

225.  2 

130.  0 

10.5 

81 

70.1 

~4or5" 

141 

122.  I      70.  5 

226.  0 

130-  5     ; 

22 

19.  I 

II. 0 

82 

71.0 

41.  0 

42 

123.0 

71.0 

02 

174.9 

lOI.O 

62 

226.  9 

131.0     i 

23 

19.9 

11-5 

P 

71.9 

41-5 

43 

123.8 

71-5 

03 

175-8 

loi.  5 

63 

227.8 

131-5 

24 

20.8 

12.  0 

84 

72.7 

42.  0 

44 

124.  71  72.  0 

04 

176.7 

102.  0 

64 

228.6 

132.0 

25 

21.7 

12.5 

^5 

73-6 

42.5 

45 

125.6 

72-5 

05 

177-5 

102.  5 

65 

229.5 

132.5 

26 

22.5 

13.0 

86 

74-5 

43- 0 

46 

126.  4 

73-0 

06 

178.4 

103.0 

66 

230.4 

133-0 

27 

23-4 

13-5 

87 

75-3 

43-5 

47 

127.3 

73-5 

07 

179-3 

103-5 

67 

231.  2 

133-5 

28 

24.  2 

14. 0 

88 

76.  2 

44.0 

48 

128.2 

74.0 

08 

180.  I 

104.  0 

68 

232.1 

134.0 

29 

25.1 

14-5 

89 

77.1 

44-5 

49 

129.0 

74-5 

09 

181. 0 

104.5 

69 

233-0 

134-5 

30 

26.0 

15.0 

90 

77-9 

45- 0 

50 

129.9 

75-0 

10 
211 

181. 9 

"182.  7 

105.0 
^05.5 

70 

233-8 

135-0 
135-  5 

31 

26.8 

15-5 

91 

78.8 

45-5 

151 

130.  8 

75-5 

271 

234-7 

32 

27.7 

16.0 

92 

79-7 

46.  0 

52 

131. 6 

76.0 

12 

183.6 

106.  0 

72 

235-6 

136.0 

33 

28.6 

16.5 

93 

80.5 

46.5 

53 

132.5 

76.5 

13 

184-5 

106.  5 

73 

236-  4 

136-5 

34 

29.4 

17.0 

94 

81.4 

47.0 

54 

133-4 

77.0 

14 

185-3 

107.  0 

74 

237-3 

137-0 

35 

30-3 

'Z-5 

95 

82.3 

47-5 

55 

134.2 

77-5 

15 

186.2 

107- 5 

75 

238.2 

137-5 

36 

31.2 

18.0 

96 

83.1 

48.0 

56 

135- I 

78.0 

16 

187.  I 

108.  0 

76 

239.0 

138-0 

37 

32.0 

18.5 

97 

84.0 

48.5 

57 

136.0 

78.5 

17 

187.9 

108.5 

77 

239-9 

138-5 

38 

32-9 

19.  0 

98 

84.9 

49.0 

58 

136.8 

79.0 

18 

188.8 

109.  0 

78 

240.8 

139.0 

39 

33-8 

19-5 

99 

85-7 

49-5 

P 

137-7 

79-5 

19 

189.  7 

109.5 

79 

241.  6 

139-5 

40 

34-6 

20.  0 
20.  5 

100 

86.6 

50.  0 

60 

138.6 

80.0 

20 

190-5 

no.  0 

80 

242.5 

140.  0 
140.5 

41 

35-5 

lOI 

S-5' 

lo-  5 

161 

139-4 

80.5 

22T 

191,4 

no.  5 

281 

243-4 

42 

36-4 

21.  0 

02 

88.3 

51.0 

62 

140.3 

81.0 

22 

192.3 

III.  0 

82 

244.2 

141.  0 

43 

37-2 

21.5 

03 

89.2 

515 

63 

141.  2 

81.5 

23 

193- I 

III. 5 

f^ 

245-  I- 

141-5 

44 

38.1 

22.  0 

04 

90.  I 

52.0 

64 

142.0 

82.0 

24 

194.0 

112.  0 

84 

246.  0 

142.0 

45 

39- 0 

22.5 

05 

90.9 

52-5 

65 

142.9 

82.5 

25 

194.9 

112.  5 

85 

246.8 

142.5 

46 

39-8 

23.0 

06 

91.8 

53-0 

66 

143-8 

83.0 

26 

195-7 

II V  0 

86 

247.7 

143.0 

47 

40.7 

23-5 

07 

92.7 

53-5 

67 

144.6 

83-5 

27 

196.  6 

"3-5 

87 

248.5 

143-5 

48 

41.  6 

24.  0 

08 

93-  5     54-  0 

68 

145-5 

84.0 

28 

197-5 

114.  0 

88 

249.4 

144.0 

49 

42.4 

24-5 

09 

94-  4     54-  5 

69 

146.4 

84.5 

29 

198.3 

"4-5 

89 

250-3 

144.5 

50 

43-3 

25.0 

10   ; 

95-3     55- 0 

70 

147.2 

85.0 

30 

.199.2 

115.  0 

_90 
291 

251.  I 

145.0 

51 

44.2 

25-5 

III 

96.  I 

55-5 

171 

148.  I 

f^-5 

231 

200.  I 

""5-  5 

252.0 

145-5 

52 

45- 0 

26.0 

12 

97.0 

56.0 

72 

149.0 

86.0 

32 

200.9 

116.  0 

92 

252-9 

146.  0 

53 

45-9 

26.  5 

13 

97-9 

56.5 

73 

149.8 

86.5 

33 

201.8 

116.  5 

93 

253-7 

146.5 

54 

46.8 

27.0 

14 

98.7 

57- 0 

74 

150-7 

87.0 

34 

202.  6 

117.  0 

94 

254.6 

147.0 

55 

47.6 

27-5 

15 

99.6 

57-5 

75 

151-6 

87-5 

35 

203-5 

"7-5 

95 

255-5 

147-  5      . 

56 

48.5 

28.0 

16 

100.  5 

58.0 

76 

152-4 

88.0 

36 

204.4 

118.0 

96 

256.3 

148.  0 

H 

49.4 

28.5 

17 

101.3 

58-5 

77 

153-3 

88.5 

37 

205.  2  1 

"8.5 

97 

257.  2 

148.5 

58 

50.2 

29.0 

18 

102.  2 

59- 0 

78 

154.2 

89.0 

38 

206.  I 

119. 0 

98 

258.1 

149.0 

59 

51- 1 

29-5 

19 

103.  I 

59-5 

79 

155- 0 

89-5 

39 

207.  0 

"9-5 

99 

258-9 

149-5 

60 

52.0 

30.0 

20 

103.9 

60.  0 

80 

15s- 9 

90.  0 

40 

207.8 

120.  0 

300 

259.8 

150.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fo 

r  60  Deg 

rees. 

TABLE  2. 

Page  245  | 

Difference  of  Latitude  and  Departure  for 

31  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0-5 

61 

52-3 

31-4 

121 

103.7 

62.3 

181 

155- I 

93-2 

241 

206.6 

124.  I 

2 

I-  7 

I.O 

62 

53-1      31-9 

22 

104.6 

62.8 

82 

156.0 

93-7 

42 

207.4 

124.6 

3 

2.6 

1-5 

63 

54.  0     32.  4 

23 

105.4 

63-3 

83 

156.9 

94-3 

43 

208.3 

125.2 

4 

3-4 

2. 1 

64 

54-  9     33-  0 

24 

106.3 

63-9 

84 

157-7 

94-8 

44 

209.  I 

125.7 

5 

4-3 

2.6 

65 

55-  7  ,  33-  5 

25 

107.  I 

64.4 

85 

158.6 

95-3 

45 

210.  0 

126.  2 

6 

5-  I 

3-  I 

66 

56.6  .  34.0 

26 

108.0 

64.9 

§6 

159-4 

95-8 

46 

210.9 

126.  7 

7 

6.0 

3-6 

67 

57-4     34-5 

27 

108.9 

65-4 

87 

160.3 

96-3 

47 

211. 7 

127.2 

8 

6.9 

4.  I 

68 

58-3  :  35- 0 

28 

109.7 

65-9 

88 

161.  I 

96.8 

48 

212.  6 

127.7 

9 

7-7 

4.6 

69 

59-1 

35-5 

29 

no.  6 

66.4 

89 

162.0 

97-3 

49 

213.4 

128.2 

lO 

1 1 

8.6 

5-2 

70 

60.0 

36.1 

30 

III. 4 

67.  0 
67.  5 

90 

162.  9 

97-9 

50 

214.3 

128.8 

9.4 

5-7 

71 

66.  9 

36.6 

131 

1 12.  3 

191 

163.7 

98.4 

251 

215.  I 

129.3 

12 

10.3 

6.2 

72 

6i-7  1  37-1  1 

32 

113.  I 

68.0 

92 

164.  6 

98-9 

52 

216.  0 

129.8 

•3 

II.  I 

6.7 

73 

62.6 

37-6 

33 

114.  0 

68.5 

93 

165.4 

99-4 

53 

216.  9 

130-3 

H 

12.  0 

7.2 

74 

63-4 

38.1 

34 

1 14.  9 

69.  0 

94 

166.3 

99-9 

54 

217.7 

130.8 

15 

12.  9 

7-7 

75 

64.  3     38-  6 

35 

115-7 

69-5 

95 

167.  I 

100.4 

55 

218.6 

13I-3 

16 

13-7 

8.2 

76 

65-  I  ;  39-  I 

36 

1 16.  6 

70.0 

96 

168.0 

100.9 

56 

219.4 

131. 8 

17 

14.  6 

8.8 

77 

66.  0  :  39.  7 

37 

117.4 

70.6 

97 

168.9 

loi.  5 

57 

220.3 

132-4 

iS 

15-4 

9-3 

78 

66.  9     40.  2 

38 

1 18.  3 

71.  I 

98 

169.7 

102.  0 

58 

221.  I 

132.9 

19 

16.3 

9.8 

79 

67.  7     40.  7 

39 

119.  I 

71.6 

99 

170.6 

102.  5 

P 

222.  0 

133-4 

20 
21 

17.  I 

10.3 

80 
81 

68.6  ;  41.2 

40 
141 

120.0 

72.1 

200 
201 

171. 4 

103.0 

60 

222.9 

133-9 

18.0 

10.8 

69.4 

41.7 

120.9 

72.6 

172.3 

103-5 

261 

223-7 

134-4 

22 

18.9 

II. 3 

82 

70.3 

42.2 

42 

121.  7 

73-1 

02 

173- I 

104.0 

62 

224.6 

134-9 

23 

19.7 

II.  8 

83 

71. 1 

42.7 

43 

122.6 

73-7 

03 

174.0 

104.  6 

63 

225-4 

135-5 

24 

20.  6 

12.4 

84 

72.0 

43-3 

44 

123.4 

74-2 

04 

174.9 

105.  I 

64 

226.3 

136.0 

25 

21.4 

12.9 

85 

■    72.9 

43-8 

45 

124.3 

74-7 

05 

175-7 

105.  6 

!5 

227.  I 

136-5 

20 

22.3 

13-4 

86 

73-7 

44-3 

46 

125.  I 

75-2 

06 

176.6 

106.  I 

66 

228.0 

137-0 

27 

23.  I 

13-9 

87 

74.6 

44.8 

47 

126.  0 

75-7 

07 

177-4 

106.  6 

67 

228.  9 

137-5 

28 

24.  0 

14.4 

88 

75-4 

45-3 

48 

126.9 

76.2 

08 

178-3 

107.  I 

68 

229.7 

138.0 

20. 

24.9 

14.9 

89 

76.3 

45-8 

49 

127.7 

76.7 

09 

179.  I 

107.6 

69 

230.6 

138.5 

30 
31 

25-7 
26.6 

15- 5_ 

90 

77.1 

46.4 
46.9 

50 

128.6 

77-3 

10 

180.  0 
180.  9 

108.  2 

70 

231.4 

139- I 

16.  0 

91 

78.0 

151 

129.4 

77-8" 

211 

108.7" 

271 

232-3 

139.6 

32 

27.4 

16.5 

92 

78.9 

47-4 

52 

130-3 

78-3 

12 

181.  7 

109.  2 

72 

233-1 

140.  I 

-1    "» 

28.3 

17.0 

93 

79-7 

47-9 

53 

131.  I 

78.8 

13 

182.6 

109.7 

73 

234.0 

140.  6 

34 

29.1 

17-5 

94 

80.6 

48.4 

54 

132.0 

79-3 

14 

183.4 

no.  2 

74 

234-9 

141.  I 

35 

30.0 

18.0 

95 

81.4 

48.9 

55 

132.9 

79-8 

15 

184-3 

no.  7 

75 

235-7 

141.  6 

36 

30- 9 

18.5 

96 

82.  3     49-  4 

56 

133-  7  :  80.  3 

16 

185.  I 

III. 2 

76 

236.6 

142.  2 

37 

31-  7 

19.  I 

97 

83.  I      50.  0 

57 

134.6  :  80.9 

17 

186.0 

III. 8 

77 

237-4 

142.7 

38 

32.6 

19.  6 

98 

84.  0  :  50.  5 

58 

135-4 

81.4 

18 

186.9 

112.  3 

78 

238-3 

143.2 

39 

33-4 

20.  I 

99 

84. 9     51.0 

59 

136.3 

81.9 

19 

187.7 

112.  8 

79 

239.1 

143-7 

40 
41 

34-3 

20.  6 

100 

85-7 

51-5 

■^2.0 

60 

137- 1 

82.4 

20 

188.6 

-"3-3 

80 

240.  0 

144.2 

35-  I 

21.  I 

lOI 

'  86.6 

161 

138.0 

82.9 

221 

189.4 

"3-8 

281 

240.9 

144.7 

42 

36.0 

21.6 

02 

87-4     52-5  1 

62 

138.9 

83-4 

22 

190.3 

"4-3 

82 

241.7 

145-2 

43 

36-9 

22.  I 

03 

88.3 

53- 0 

63 

139-7 

84.0 

23 

191.  I 

1 14.  9 

83 

242.  6 

145.8 

44 

37-7 

22.7 

04 

89.  I 

53-6 

64 

140.6 

84-5 

24 

192.  0 

"5-4 

84 

243-4 

146.  3 

45 

38.6 

23.2 

05 

90.0 

54-1 

65 

141. 4 

85.0 

25 

192.9 

"5-9 

85 

244-3 

146.  8 

46 

39-4 

23-7 

06 

90.9 

54-6 

66 

142.3 

85-5 

26 

193-7 

116. 4 

86 

245-1 

147-3 

47 

40-3 

24.2 

07 

91.7 

55-1 

67 

143- I 

86.0 

27 

194.6 

116.  9 

^ol 

246.  0 

147.8 

48 

41.  I 

24.7 

08 

92.  6 

55-6 

68 

144.0 

86..; 

28 

195-4 

"7-4 

88 

246.9 

148.3 

49 

42.0 

25.2 

09 

93-  4  1  56-  I 

69 

144.9 

87.0 

29 

196.3 

II7-9 

89 

247.7 

148.8 

50 
51 

42.9 
43-7 

25.8 
26.  3 

10 
III 

94-  3  I  56-  7 
95-1      57-2 

70 

145-7 

87.6 

30 

197.  I 

118.  5 

90 

248.6 

149.4 

171 

146.6 

88.1 

231 

198.0 

119. 0 

291 

249-4 

149.9 

52 

44.6 

26.8 

12 

96.0  1  57.7 

72 

147.4 

88.6 

32 

198.9 

"9-5 

92 

250.3 

150.4 

53 

45-4 

27-3 

13 

96.  9     58.  2 

73 

148.3 

89.  I 

33 

199.7 

120.0 

93 

251.  2 

150.9 

54 

46.3 

27.8 

14 

97-  7     58.  7 

74 

149.  I 

89.6 

34 

200.  6 

120.  5 

94 

252.0 

151-4 

'^S 

47.1 

28.3 

15 

98.  6      59.  2 

75 

150.  0 

90.  I 

35 

201.  4 

121.  0 

95 

252-9 

151-9 

56 

48.0 

28.8 

16 

99-  4  :  59-  7 

76 

150.9 

90.  6 

36 

202.3 

121.  5 

96 

253-7 

152-5 

57 

48.9 

29.4 

17 

100.3 

60.3 

77 

151-7 

91.  2 

37 

203.  I 

122.  I 

9| 

254.6 

153-0 

58 

49-7 

29.9 

18 

lOI.  I 

60.8 

78 

152.6 

91.7 

38 

204.0 

122.6 

98 

255-4 

153-5 

59 

50.  6 

30-4 

19 

102.  0 

61.3 

79 

153-4 

92.  2 

39 

204.9 

123.  I 

99 

256.3 

154.0 

60 

51-4 

30-9 

20 

102.  9 

61.8 

80 

154-3 

92.7 

40 

205-7 

123.6 

300 

257.1 

154-5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[F 

or  59  Deg 

;rees. 

• 

Page  246 

TABLE  2. 

" 

Difference  of  Latitude  and  Departure  for 

32  Degrees. 

1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.5 

61 

5'-l 

32.3 

121 

102.  6 

64.  I 

181 

153-5 

95-9 

241 

204.4 

127.7 

2 

1-7 

I.  I 

62 

52.6 

32-9 

22 

103-5 

64.7 

82 

154-3 

96.4 

42 

205.2 

128.2 

3 

2-5 

1.6 

63 

53-4 

33-4 

23 

104.3 

65.  2 

83 

155-2 

97-0 

43 

206.  1 

128.8 

4 

3-4 

2.  I 

64 

54-3 

33-9 

24 

105.  2 

65-7 

84 

156.0 

97-5 

44 

206.9 

129.3 

5 

4.2 

2.6 

65 

55-1 

34-4 

25 

106.  0 

66.2 

85 

156.9 

98.0 

45 

207.  8 

129.8 

6 

51 

3-2 

66 

56.0 

35- 0 

26 

106.  9 

66.8 

86 

157-7 

98.6 

46 

208.6 

130-4 

7 

5-9 

3-7 

67 

56.8 

35-5 

27 

107.7 

67-3 

87 

158.6 

99-1 

47 

209.5 

130.9 

8 

6.8 

4.2 

68 

57-7 

36.0 

28 

108.6 

67.8 

88 

159-4 

99.6 

48 

210.3 

131-4 

9 

7.6 

4.8 

69 

58.5 

36.6 

29 

109.4 

68.4 

89 

160.3 

100.  2 

49 

211.  2 

131-9 

lO 

8-5 

5-3 

70 

59-4 

37-1 

30 

no.  2 

68.9 

90 

161.  I 

100.  7 

50 

212.  0 

132-5 

II 

9-3 

5-"8" 

71 

60.  2 

'37.6 

131 

III.  I 

^9^4 

191 

162.  0 

101.  2 

251 

^212.  9 

133- 0 

12 

10.  2 

6.4 

72 

61.  I 

38.2 

32 

III. 9 

69.9 

92 

162.8 

101.  7 

52 

213-7 

133-5 

13 

II. 0 

6.9 

73 

61.9 

38.7 

33 

1 12.  8 

70-5 

93 

163-7 

102.  3 

53 

214.  6 

134- I 

14 

II. 9 

7-4 

74 

62.8 

39-2 

34 

113.6 

71.0 

94 

164.5 

102.  8 

54 

215.4 

134.6 

15 

12.  7 

7-9 

75 

63.6 

39-7 

35 

"4-5 

71-5 

95 

165.4 

103-3 

55 

216.  3 

135- I 

16 

13.6 

8-5 

76 

64.5 

40.3 

36 

115-3  !   72-1 

96 

166.  2 

103.9 

56 

217.  I 

135-7 

17 

14.4 

9.0 

77 

65-3 

40.8 

37 

116.  2 

72.6 

97 

167.  I 

104.4 

57 

217.9 

136.2 

18 

15-3 

9-5 

78 

66.1 

41-3 

38 

117.  0 

73-1 

98 

167.9 

104.9 

58 

218.8 

136-7 

19 

16.  I 

ID.  I 

79 

67.0 

41.9 

39 

1 1 7.  9 

73-7 

99 

168.8 

105-5 

59 

219.  6 

137-2 

20 
21 

17.0 

ID.  6 

80 

67.8 

42.4^ 
42.9 

40 
141 

118.  7 

74-2 

200 

201 

169.6 
^70.  5 

106.0 
106.  5 

60 

220.5 

137-8      ' 

17.8 

II.  I 

81 

68.7 

119^6     74.  7 

261 

221.3 

138-  3 

22 

18.7 

II. 7 

82 

69-5 

43-5 

42 

120.4     75.2 

02 

171-3 

107.  0 

62 

222.  2 

138.8 

23 

19- 5 

12.  2 

l^ 

70.4 

44.0 

43 

121. 3     75.8 

03 

172.2 

107.  6 

63 

223.  0 

139-4 

24 

20.4 

12.7 

!4 

71.2 

44-5 

44 

122.  I      76.  3 

04 

173.0 

108.  1 

64 

223-9 

139-9 

25 

21.2 

13.2 

85 

72.1 

45- 0 

45 

123.0     76.8 

05 

173.8     108.6 

65 

224.7 

140.4 

26 

22.  0 

13.8 

86 

72.9 

45-6 

46 

123-8  I  77.4 

06 

174. 7     109.2 

66 

225.  6 

141.  0 

27 

22.9 

14- 3 

87 

73-8 

46.  I 

47 

124-7     77-9 

07 

175-5  1  109.7 

67 

226.4 

141.5 

28 

23-7 

14.8 

88 

74.6 

46.6 

48 

125-5      78.4 

08 

1 76.  4 

no.  2 

68 

227.3 

142.  0 

29 

24.  6 

15-4 

89 

75-5 

47.2 

49 

126.4 

79-0 

09 

177.2 

no.  8 

69 

228.  I 

142-5 

30 

25-4 

J_5-9 

90 

76-3 

47-7 

50 

127.  2 

79-5 

10 

178. 1 

III. 3 

■70 
271 

229.  0 
"229.  8" 

143-'  1 
143.6 

31 

26.3 

16.4 

91 

77.2 

48.2 

151 

"128.  I 

80.0' 

211 

178-9 

111.  8 

32 

27.1 

17.0 

92 

78.0 

48.8 

52 

128.9     80.5 

12 

179-8 

112.3 

72 

230.7 

144.  I 

33 

28.0 

17-5 

93 

78.9 

49-3 

53 

129.  8  1  81.  I 

13 

180.6 

112.  9 

73 

231-5 

144-  7 

34 

28.8 

18.0 

94 

79-7 

49.8 

54 

130.6     81.6 

14 

181.5 

"3-4 

74 

232.4 

145.2 

35 

29.7 

18.  5 

95 

80.6 

50.3 

55 

131. 4     82.1 

15 

182.3  '  "3-9 

75 

233-2 

145-  7 

36 

30-5 

19.1 

96 

81.4 

50-9 

56 

132.3     82.7 

16 

1S3-2      114. 5 

76 

234.  1 

146.3 

37 

31-4 

19.6 

97 

82.3 

51.4 

57 

133- I      83.2 

17 

184.0     115.0 

77 

234-9 

146.8 

38 

32.2 

20. 1 

98 

83.1 

51-9 

58 

134.  0     83.  7 

18 

184-9     1 15- 5 

78 

235-8 

147-3 

39 

33-1 

20.  7 

99 

84.0 

52-5 

59 

134.8     84.3 

19 

185.  7  i  116. 1 

79 

236.6 

147.8 

40 

33-9 

21.  2 

100 

84.8 

53- 0 

60 

135-  7  i  84.  8 

20 

186.6 

1 16.  6 
II  7.1 

80 

237-5 

148.4 

41 

34-8 

21.7 

lOI 

85-7 

53-5 

161 

136.5     85.3 

221 

187.4 

281 

238-3 

148.  9 

42 

35-6 

22.3 

02 

86.5 

54-1 

62 

137.4     85.8 

22 

188.3  1  117,6 

82 

239-  I 

149-  4 

43 

36.5 

22.  8 

03 

87.3 

54-6 

63 

138.  2  !  86.  4 

23 

189.  1     118.  2 

83 

240.  0 

150.0 

44 

37-3 

23-3 

04 

88.2 

55-1 

64 

139- I 

86.9 

24 

190.  0  ,  118.  7 

84 

240.  8 

150.5 

45 

38.2 

23.8 

05 

89.0 

55-6 

65 

139-9 

87.4 

25 

190.  8    ;    119.  2 

85 

241.7 

151-  0 

46 

39- 0 

24.4 

06 

89.9 

56.2 

66 

140.  8 

88.0 

26 

191.7      119. 8 

86 

242.5 

151.6 

47 

39-9 

24.9 

07 

90.7 

56.7 

67 

141.  6 

88.5 

27 

192.5        120.3 

87 

243-4 

152.1 

48  . 

40.7 

25-4 

08 

91.  6 

57-2 

68 

142.5 

89.0 

28 

193.  4    1     120.  8 

88 

244.2 

152.6 

49 

41.6 

26.  0 

09 

92.4 

57.8 

69 

143-3 

89.6 

29 

194.2 

121.4 

89 

245-1 

153.1 

50 

_42-4 

26.  5 

10 

93-3 
94.1 

58.3 

70 

144.  2  1  90.  I  1 

30 

195- I 

121.  9 

90 

245-9 

153.7 

51 

43-3 

27.  0 

III 

58.8 

171 

145.0 

90.6 

231 

195-9 

122.4 

291 

246.8 

154.2 

52 

44.  I 

27.6 

12 

95- 0 

59-4 

72 

145-9 

91.  I 

32 

196.7 

122.  9 

92 

247.6 

154.7 

53 

44.9 

28.  I 

13 

95-8 

59-9 

73 

146.7 

91.7 

33 

197.6 

123-5 

93 

248.5 

155.3 

54 

45-8 

28.6 

14 

96.7 

60. 4 

74 

147.6 

92.  2 

34 

198.  4  !  124.  0 

94 

249-3 

155-8 

55 

46.6 

29.  I 

15 

97-5 

60.  9 

75 

148.4 

92.7 

35 

199-3  '  124-5 

95 

250.  2 

156-3 

56 

47-5 

29.7 

16 

98.4 

61.5 

76 

149-3 

93-3 

36 

200.  1  j  125.  1 

96 

251-0 

156.9 

57 

48.3 

30.2 

17 

99.2 

62.  0 

77 

150.  I      93.  8 

37 

201.0      125. 6 

97 

251-9 

157-4 

5« 

49.2 

30-7 

18 

100.  I 

62.5 

78 

151. 0     94.3 

38 

201.8     126.  1 

98 

252.7 

157-9 

59 

50.0 

31-3 

19 

100.9 

63.1 

79 

151.8 

94.9 

39 

202.  7 

126.  7 

99 

253.6 

158.4 

60 

50.9 

31.8 

20 

101.8 

63.6 

80 

152.  6 

95-4 

40 

203-5 

127.  2 

300 

254-4 

159.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[Fc 

)r  58  Deg 

rees. 

* 

• 

• 

TABLE  2. 

Page  247  | 

Difference  of  Latitude  and  Departm 

e  for 

33  Degrees. 

Dist. 

Lat^ 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0-5 

61 

51.2 

33-2 

121 

lOI.  5 

65-9 

181 

151-8 

98.6 

241 

202.  I 

13I-.3 

2 

1-7 

I.  I 

62 

52.  0 

33-8 

22 

102.3      66.4 

82 

152.6 

99-  I 

42 

203.  0 

131. 8 

3 

2.5 

1.6 

^3 

52.8 

34-3 

23 

103.  2      67.  0 

83 

153-5 

99-7 

43 

203.8 

132-3 

4 

3-4 

2.2 

64 

53-7 

34-9 

24 

104. 0  !  67. 5 

84 

154-3 

100.  2 

44 

204.  6 

132-9 

5  ' 

4.2 

2.7 

65 

54-5 

35-4 

25      104.  8  1  68.  I 

^^ 

155-2 

100.  8 

45 

205.5 

133-4 

6 

5.0 

3-3 

66 

55-4 

35-9 

26  ,   105.  7     68.  6 

86 

156.0 

loi.  3 

46 

206.3 

134.  0 

7 

5-9 

3-8 

67 

56.2 

36-5 

27      106.  5  ;  69.  2 

87 

156.8 

loi.  8 

47 

207.  2 

134-5 

8 

6.7 

4.4 

68 

57- 0 

37-0 

28  i  107.3 

69.7 

88 

157-7 

102.4 

48 

208.0 

135- I 

9 

7-5 

4-9 

69 

57-9 

37-6 

29 

108.2 

70-3 

89 

158-5 

102.  9 

49 

208.8 

135-6 

10 

8.4 

5-4 

70 

58.7 

38.1 

30 

109. 0 

70.8 

90 

159-3 

103-5 

50 

209.7 

136.2 

II 

9.2 

6.0 

71 

59-5 

38.7 

131 

109.9 

71-3 

191 

160.  2 

104.0 

251 

210.  5 

136.7 

12 

10.  I 

6.5 

72 

60.4 

39-2 

32 

no.  7 

71.9 

92 

161.  0 

104.  6 

52 

211.3 

137-2 

13 

10.  9 

7-5 

73 

61.  2 

39-8 

33 

III. 5 

72.4 

93 

161. 9 

105.  I 

53 

212.  2 

137-8 

14 

II. 7 

7.6 

74 

62.  I 

40-3 

34 

112.  4 

73-0 

94 

162.  7 

105.7 

54 

213.0 

138.3 

15 

12.6 

8.  2 

75 

62.9 

40.8 

35 

113-2 

73-5 

95 

163-5 

106.  2 

55 

213.9 

138.9 

16 

13' 4 

8.7 

76 

63.7 

41.4 

36 

114.  I 

74.1 

96 

164.4 

106.  7 

56 

214.7 

139-4 

17 

14-3 

9-3 

77 

64.6 

41.9 

37 

1 14.  9 

74-6 

97 

165.  2 

107.3 

57 

215-5 

140.  0 

18 

15- I 

9.8 

78 

65-4 

42.5 

38 

115.7 

75-2 

98 

166.  I 

107.8 

58 

216.4 

140.5 

19 

15-9 

10.3 

79 

66.3 

43-  0 

39 

116. 6     75.7 

99 

166.  9 

108.  4 

59 

217.  2 

141.  I 

20 

16.8 

10.  9 

80 

67.1 

43-6 

40 

117. 4  1  76.  2 

200 

167.7 

108.9 

60 

218.  I 

141.  6 

21 

17.6 

II. 4 

81 

67.9 

44.  I 

141 

118.  3 

76.8 

201 

168.  6 

109.5 

261 

218.9 

142.  2 

22 

18.5 

12.0 

82 

68.8 

44-  7 

42 

119.  1 

77-3 

02 

169.4 

no.  0 

62 

219.7 

142.7 

23 

19-3 

12.5 

l^ 

69.6 

45-2 

43 

1 19.  9 

77-9 

03 

170-3 

no.  6 

63 

220.  6 

143-2 

24 

20.  I 

13- I 

84 

70.4 

45-7 

44     120. 8 

78.4 

04 

171.  I 

in.  I 

64 

221.4 

143.8 

25 

21.  0 

13.6 

85 

71-3 

46.3 

45  I   121.  6 

79.0 

05 

171-9 

III. 7 

i5 

222.  2 

144-3 

26 

21.8 

14.2 

86 

72.1 

46.8 

46  \  122.4 

79-5 

06 

172.2 

112.  2 

66 

223.1 

144.9 

27 

22.  6 

14.7 

87 

73-0 

47-4 

47      123.3 

80.  I 

07 

173-6 

112.  7 

67 

223.9 

145.4 

28 

23-5 

15.2 

88 

73-8 

47-9 

48 

124.  I 

80.6 

08 

174.4 

1 13- 3 

68 

224.8 

146.  0 

29 

24-3 

15-8 

89 
90 

74.6 

48.5 

49 

125.  0 

81.2 

09 

175-3 

113.  8 

69 

225.6 

146.5 

30 

25.  2 

j6.3^ 

75-5 

49.0 

50 

125.8 

81.7 

10 

176.  I 

"4-4 

70 

226.4 

147-1 

31 

26.  0 

16.  9 

91 

76.3 

49.6 

151 

126.6 

82.2 

211 

177.0 

114.  9 

271 

~2'27r3~ 

147.6 

32 

26.8 

17.4 

92 

77.2 

50.1 

52 

127.5 

82.8 

12 

177.8 

115-5 

72 

228. 1 

148.  I 

33 

27.7 

18.0 

93 

78.0 

50-7 

53 

128.3 

83-3 

13 

178.6 

116.  0 

73 

229.  0 

148.7 

34 

28.  s 

18.5 

94 

78.8 

51.2 

54 

129.  2 

83-9 

14 

179-5 

116.6 

74 

229.  8 

149.2 

35 

29.4 

19.  I 

95 

79-7 

51-7 

55 

130.0 

84-4 

15 

180.3 

117.  I 

75 

230.6 

149.8 

36 

30.2 

19.  6 

96 

80.5 

52-3 

56  1  130.8  i  85.0  1 

16 

181.  2 

117.  6 

76 

231-5 

150-3 

37 

31.0 

20.  2 

97 

81.4 

52.8 

57 

131-7     85.5  1 

17 

182.0 

n8.2 

77 

232.3 

150.9 

38 

31-9 

20.  7 

98 

82.2 

53-4 

58 

132-5 

86.1 

18 

182.8 

118.  7 

78 

233-2 

151-4 

39 

32-7 

21.  2 

99 

83.0 

53-9 

59 

133-3 

86.6 

19 

183-7 

119- 3 

7"* 

234.0 

152.  0 

40 

33-5 

21.8 

100 

83-9 

54-5 

60 

134.2 

87.1 

20 

184.5 

119.  8 

80 

234.8 

152.5 

41 

34-4 

22.3 

lOI 

84.7 

55- 0 

161 

135-0  !  87.7 

221 

185-  3 

120.4 

281 

235-7 

153-0 

42 

35-2 

22.9 

02 

85-5 

55-6 

62 

135-9 

88.2 

22 

186.2 

120.  9 

82 

236-5 

153-6 

43 

36.1 

23-4 

03 

86.4 

56.1 

63 

136.7 

88.8 

23 

187.0 

121.  5 

83 

237-3 

154-  I 

44 

36-9 

24.  0 

04 

87.2 

56.6 

64 

137-5 

89-3 

24 

187.9 

122.0 

84 

238.2 

154-7 

45 

37-7 

24-5 

05 

88.1 

57-2 

65 

138.4 

89-9 

25 

188.7 

122.  5 

85 

239.0 

155- - 

46 

38.6 

25.1 

06 

88.9 

57-7 

66 

139.2 

90.4 

26 

189.5 

123.  I 

86 

239-9 

155-8 

47 

39-4 

25.6 

07 

89-  7  ;  58.  3 

67 

140.  I 

91.  0 

27 

190.4 

123.6 

87 

240.7 

156-3 

48 

40-3 

26.1 

08 

90.  6 

58.8 

68 

140.9 

91.5 

28 

191.  2 

124.  2 

88 

241.5 

156.9 

49 

41.  I 

26.7 

09 

91.4 

59-4 

69 

141-7 

92.0 

29 

192.  I 

124.7 

89 

242.4 

157-4 

50 

41.9 

27.  2 

10 

92-3 

59-9 

70 

142.6 

92.  6 

30 

192.9 

125-3 

90 

243-  2 
244.  I 

157-9 
158.5 

51 

42.8 

i  27.8 

III 

93-1 

60.5 

171 

143-4 

93-1 

231 

193-7 

125.8 

291 

52 

43-6 

28.3 

12 

93-9 

61.0 

72 

144-3 

93-7 

32 

194.6 

126.4 

92 

244.9 

159.0 

53 

44.4 

28.9 

13 

94.8 

61.5 

73 

145- I 

94-2 

33 

195-4 

126.9 

93 

245-7 

159.6 

54 

45-3 

29.4 

14 

95-6 

62.1 

74 

145.9 

94-8 

34 

196.  2 

127  ^.  jj    94 

246.  6 

160.  I 

55 

46.  I 

30.0 

15 

96.4 

62.6 

75 

146.8 

95-3 

35 

197.  I 

128.0 

95 

247.4 

160.  7 

56 

47.0 

30.5 

16 

97-3 

63.2 

76 

147.6 

95-9 

36 

197.9 

128.5 

96 

248.2 

161.  2 

57 

47.8 

31.0 

17 

98.1 

63.7 

77 

148.4 

96.4 

37 

198.8 

129.  I 

97 

249.  I 

161. 8 

58 

48.6 

31.6 

18 

99.0 

64-3 

78 

149-3 

96.9 

38 

199.6 

129.  6 

98 

249.9 

162.3 

59 

49-5 

32.1 

19 

99.8 

64.8 

79 

150.  I 

97-5 

39 

200.4 

130.2 

99 

250.  8 

162.8 

60 

50-3 

32-7 

20 

100.6 

65.4 

80 

151. 0 

98.0 

40 

201.  3 

130-7 

300 

251.  6 

163.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[F 

or  57  Deg 

rees. 

Page  248 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  34  Degrees. 

' 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

50.6 

34-1 

121 

100.3 

67.7 

181 

150.  I 

lOI.  2 

241 

199.8 

134-8 

2 

1-7 

I.  I 

62 

51-4 

34-7 

22 

lOI.  I 

68.2 

82 

150.9 

101.8 

42 

200.  6 

135-3 

3 

2.5 

1-7 

P 

52.2 

35-2 

23 

102.0 

68.8 

83 

151- 7 

102.3 

43 

201.  5 

135- 9 

4 

3-3 

2.  2 

64 

53-1 

35-8 

24 

102.8 

69-3 

84 

152-5 

102.  9 

44 

202.3 

136.4 

5 

4.1 

2.8 

^5 

53-9 

36.3 

25 

103.  6 

69.9 

85 

153-4 

103-5 

45 

203.1 

137-0 

6 

5-? 

3-4 

66 

54-7 

3^-9 

26 

104.5 

70.5 

86 

154.2 

104.0 

46 

203.9 

137.6 

7 

5-8 

3-9 

67 

55-5 

37-5 

27 

105- 3 

71.  0 

87 

155-0 

104.  6 

47 

204.  8 

138-1 

8 

6.6 

4-5 

68 

56-4 

38.0 

28 

106.  I 

71.6 

88 

155-9 

105.  I 

48 

205.6 

138-7 

9 

^•5 

5-0 

69 

57-2 

38.6 

29 

106.  9 

72.1 

89 

156-7 

105.7 

49 

206.4 

139.2 

lO 

8-3 

5-6 

70 

58.0 

39-1 

30 

107.8 

72.7 

90 

157-5 

106.  2 

50 

207.3 

139-8 

II 

9.1 

6.2 

71 

58-9 

39-7 

131 

108.6 

73-3 

191 

158-3 

106.8^ 

251 

208.1 

140.4 

12 

9.9 

6.7 

72 

59-7 

40-3 

32 

109.4 

73-8 

92 

159.2 

107.4 

52 

208.  9 

140.9 

13 

10.8 

7-3 

73 

60.5 

40.8 

33 

no.  3 

74-4 

93 

160.0 

107.9 

53 

209.7 

141-5 

14 

II. 6. 

7.8 

74 

61.3 

41.4 

34 

III.  I 

74-9 

94 

160.8 

108.5 

54 

210.  6 

142.  0 

15 

12.4 

8.4 

75 

62.  2 

41.9 

35 

III.  9 

75-5 

95 

161.  7 

109.0 

55 

211. 4 

142.  6 

i6 

13-3 

8.9 

76 

63.0 

42.5 

36 

112.  7 

76.1 

96 

162.  5 

109.6 

56 

212.  2 

143-2 

17 

14.  I 

9-5 

77 

63.8 

43-1 

37 

113.  6 

76.6 

97 

163-3 

no.  2 

57 

213-1 

143-7 

i8 

14.9 

10.  I 

78 

64.7 

43-6 

38 

1 14.  4 

77.2 

98 

164.  I 

no.  7 

58 

213-9 

144-3 

19 

15.8 

10.  6 

Z9 

^5-5 

44.2 

39 

115.  2 

77-7 

99 

165.  0 

III. 3 

59 

214.7 

144.8 

20 

16.6 

II. 2 

80 

66.3 

44-7 

40 
141 

116.  I 

78.3 

200 

165.8 

III. 8 

60 

215-5 

145-4 

21 

17.4 

II. 7 

81 

67.2 

45-3 

116.  9 

78.8 

201 

166.6 

112. 4 

261 

216.4 

145-9 

22 

18.2 

12.3 

82 

68.0 

45-9 

42 

117.  7 

79-4 

02 

167.5 

113.0 

62 

217.2 

146.5 

23 

19.  I 

12.9 

f3 

68.8 

46.4 

43 

1 18.  6 

80.0 

03 

168.3 

113-5 

63 

218.0 

147-1 

24 

19.9 

13-4 

84 

69.6 

47.0 

44 

1 19.  4 

80.5 

04 

169. 1 

114.  I 

64 

218.9 

147.6 

25 

20.  7 

14.  0 

85 

70.5 

47-5 

45 

120.  2 

81.  I 

05 

170.0 

114.  6 

65 

219.7 

148.  2 

26 

21.6 

14-5 

86 

71-3 

48.  I 

46 

121.  0 

81.6 

06 

170.8 

115. 2 

66 

220.  5 

148-  7 

27 

22.4 

15- 1 

87 

72.1 

48.  6 

47 

121.  9 

82.2 

07 

171. 6 

115-8 

67 

221.4 

149-3 

28 

23.2 

15-7 

88 

73- 0 

49.2 

48 

122.  7 

82.8 

08 

172.4 

116.  3 

68 

222.  2 

149-9 

29 

24.  0 

16.2 

89 

73-8 

49.8 

49 

123-5 

83-3 

09 

173-3 

116.  9 

69 

223.0 

150-4 

30 

24.9 

16.8 

90 

74.6 

50-3 

50 

124.  4_ 

83-9 

10 

174.  I 

117-4 

70 

223.8 

151-0 

31 

25-7 

17-3 

91 

75-4 

50-9 

151 

125.2 

84.4 

211 

174.9 

1 18.0 

271 

224.7 

151-5" 

32 

26.5 

17.9 

92 

76-3 

51-4 

52 

126.0 

85.0 

12 

175-8 

118.5 

72 

225-5 

152. 1 

33 

27.4 

18.5 

93 

77.1 

52.0 

53 

126.8 

85-6 

13 

176.6 

119.  I 

73 

226.3 

152-7       : 

34 

28.2 

19.0 

94 

77-9 

52.6 

54 

127.7 

86.  I 

14 

177-4 

119.  7 

74 

227.  2 

153-2      : 

35 

29.0 

19.  6 

95 

78.8 

53-1 

55 

128.5 

86.7 

15 

178.2 

120.2 

75 

228.0 

153-8 

36 

29.8 

20.  I 

96 

79.6 

53-7 

56 

129.3 

87.2 

16 

179.  I 

120.8 

76 

228.8 

154-3 

37 

30-7 

20.  7 

97 

80.4 

54-2 

57 

130.  2 

87.8 

17 

179.9 

121.  3 

77 

229.6 

154-9 

38 

31-5 

21.  2 

98 

81.2 

54-8 

58 

131. 0 

88.4 

18 

180.7 

121.  9 

78 

230.5 

155-5 

39 

32-3 

21.8 

99 

82.1 

55-4 

59 

131-8 

88.  9 

19 

181.  6 

122.5 

79 

231-3 

156.0 

40 

33-2 

22.4 

100 

82.9 

55-9 

60 

132.  6 

89-5 

20 

182.4 

123.0 

80 

232,  I 

156.6 

41 

34-0 

22.9 

lOI 

f3-7 

56.5 

161 

133-5 

90.0 

221 

183.2 

123.6 

28t 

233-0 

157- 1 

42 

34-8 

23-5 

02 

84.6 

57- 0 

62 

134-3 

90.  6 

22 

184.0 

124.  I 

82 

233-8 

157-7 

43 

35-6 

24.  0 

03 

85-4 

57-6 

63 

135- I 

91.  I 

23 

184.9 

124.7 

83 

234.6 

'5!^-§ 

44 

36-5 

24.  6 

04 

86.2 

58.2 

64 

136.0 

91.7 

24 

185-7 

125-3 

84 

235-4 

158.8 

^^ 

37-3 

25.2 

05 

87.0 

58.7 

65 

136.8 

92-3 

25 

186.5 

125.8 

85 

236-3 

159-4 

46 

38.1 

25.7 

06 

.87.9 

59-3 

66 

137-6 

92.8 

26 

187.4 

126.  4 

86 

237-1 

1599 

4Z 

39- 0 

^^3 

07 

88.7 

59-8 

67 

138.4 

93-4 

27 

188.2 

126.  9 

87 

237-9 

160.  5 

48 

39-8 

26.8 

08 

89-5 

60.4 

68 

139-3 

93-9 

28 

189.  0 

127-5 

88 

238.8 

161.  0 

49 

40.  6 

27.4 

09 

90.4 

61.0 

69 

140.  I 

94-5 

29 

189.8 

128.  I 

89 

239-6 

161. 6 

50 

41-5 

28.0 

10 

91.  2 

61.5 

70 

140.  9 

95-1 

30 

190.7 

128.6 

90 

240.4 

162.  2 

51 

42.3 

28.5 

III 

92.0 

62.  I 

171 

141- 8 

95-6 

231 

191-5 

129.  2 

291      241.2 

162.  7 

52 

43-1 

29.  I 

12 

92.9 

62.6 

72 

142.  6 

96.  2 

32 

192.3 

129-7 

92 

242.  I 

163-3 

53 

43-9 

29.6 

13 

93-7 

63.  2 

73 

143-4 

96.7 

33 

193-2 

130-3 

93 

242.9 

163.8 

54 

44.8 

30.2 

14 

94-5 

63-7 

74 

144-3 

97-3 

34 

194.0 

130.9 

94 

243-7 

164.4 

5| 

45-6 

30.8 

15 

95-3 

64-3 

75 

145- I 

97-9 

35 

194.8 

131-4 

95      244. 6 

165.0 

56 

46.4 

31-3 

16 

96.  2 

64.9 

76 

145.9 

98-4 

36 

195-7 

132.0 

96 

245-4 

165-5 

H 

47.3 

319 

17 

97.0 

65-4 

77 

146.7 

99.0 

37 

196.5 

132-5 

97 

246.  2 

166.  I 

58 

48.1 

32.4 

18 

97.8 

66.0 

78 

147.6 

99-5 

38 

197-3 

133-1 

98 

247.1 

166.6 

59 

48.9 

33- 0 

19 

98.7 

66.5 

79 

148.4 

IOC.  I 

39 

198.  I 

133-6 

99 

247.9 

167.2 

60 

49-7 

33-6 

20 

99-5 

67.1 

80 

149.2 

100.  7 

40 

199.0 

134.2 

300 

248.7 

167.  8 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

[For  56  Deg 

rees. 

TABLE  2. 

Page  249 

DiflFerence  of  Latitude  and  Departure  for  35  Degrees. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

35- 0 

Dist. 

121 

Lat. 

Dep. 

Dist. 

Lat. 
148.3 

Dep. 

Dist. 

Lat. 

Dep. 
138.2 

I 

0.8 

0.6 

61 

50.0 

99.1 

69.4 

181 

103.8 

241 

197.4 

2 

1.6 

I.I 

62 

50.8 

35 

6 

22 

99.9 

70.0 

82 

149.  1 

104.4 

42 

198.  2 

138.8 

3 

2-5 

1-7 

63 

51-6  '  36 

I 

23 

100.  8 

70.5 

f^ 

149.9 

105.0 

43 

199.  1 

139-4 

4 

3-3 

2-3 

64 

52.4      36 

7 

24 

loi.  6 

71.  I 

84 

150-7 

105-5 

44 

199.9 

140.0 

5 

4.1 

2.9 

65 

53-2     37 

3 

25 

102.4 

71-7 

!5 

15I-5 

106.  1 

45 

200.  7 

140-5 

6 

4.9 

3-4 

66 

54-  I  !  37 

9 

26 

103.2 

72.3 

86 

152.4 

106.  7 

46 

201.  5 

141.  1 

7 

5-7 

4.0 

67 

54-  9     38 

4 

27 

104.0 

72.8 

87 

153-2 

107.3 

47 

202.3 

141.  7 

8 

6.6 

4.6 

68 

55-  7  i  39 

0 

28 

104.9 

73-4 

88 

154.0 

107.8 

48 

203.  1 

142.  2 

9 

7-4 

5-2 

69 

56.5 

39 

6 

29 

105-7 

74.0 

89 

154.8 

108.4 

49 

204.0 

142.8 

10 

II 

8.2 

5-7 

70 

57-3 

40 

2 

30 
131 

106.  5 

74-6 

90 
191 

155-6 
156.5 

109.  0 

50 

204.8 

143.4 

9.0 

6-3 

71 

58.2 

40 

Y 

107.3 

75-1 

109.  6 

251 

205.6 

144.0 

12 

9.8 

6.9 

72 

59- 0 

41 

■^ 

0 

32 

108.  I 

75-7 

92 

157-3 

no.  1 

52 

206.4 

144-5 

13 

10.6 

7-5 

73 

59-8 

41 

9 

33 

108.  9 

76-3 

93 

158.  1 

■110.7 

53 

207.2 

145.1 

14 

"•5 

8.0 

74 

60.6 

42 

4 

34 

109.8 

76.9 

94 

158.9 

111.3 

54 

208.1 

145.7 

15 

12.3 

8.6 

75 

6i-4  i  43 

0 

35 

no.  6 

77-4 

95 

159-7 

111.8 

55 

208.9 

146.3 

16 

13- I 

9.2 

76 

62.3 

43 

6 

36 

III. 4 

78.0 

96 

160.6 

112.4 

56 

209.7 

146.8 

17 

13- 9 

9.8 

77 

63-1 

44 

2 

37 

112.2 

78.6 

97 

161.4 

113.0 

57 

210.  5 

147.4 

18 

14.7 

10.3 

78 

63- 9 

44 

7 

38 

113.0 

79-2 

98 

162.  2 

113.6 

58 

211.3 

14S.  0 

19 

156 

10.  9 

79 

64-  7  i  45 

T 

J 

39 

"3-9 

79-7 

99 

163.0 

114.1 

59 

212.  2 

148.6 

20 
21 

16.4 
17.2 

"•5 
12.  0 

80 
81 

65-5 
66.4 

45 
46 

9 

40 

114.  7 

80.3 

200 

163.8 

114.  7 

60 

213.  0 

149.  1 

5 

141 

II5-5 

80.9 

201 

164.6 

"5-3 

261 

213.8 

149-7 

22 

18.0 

12.6 

82 

67.2  ^  47 

0 

42 

116.  3 

81.4 

02 

165-5 

115-9 

62 

214.6 

150-3 

23 

18.8 

13.2 

83 

68.0  '  47 

6 

43 

117. 1 

82.0 

03 

166.3 

116.  4 

63 

215.4 

150.9 

24 

19.7 

13.8 

84 

68. 8     48 

2 

44 

118.  0 

82.6 

04 

167.  1 

117.0 

64 

216.3 

151-4 

25 

20.  5 

14-3 

85 

69. 6     48 

8 

45 

118.  8 

83.2 

05 

167.9 

117.6 

65 

217.  1 

152.  0 

26 

21.3 

14.9 

86 

70.4 

49 

1 

46 

119.  6 

83-7 

06 

168.7 

118.2 

66 

217.9 

152.  6 

27 

22.  I 

15-5 

87 

71-3 

49 

9 

47 

120.4 

84-3 

07 

169.  6 

118.7 

67 

218.  7 

153-  I  ■ 

28 

22.9 

16.  I 

88 

72.1 

50 

5 

48 

121.  2 

84.9 

08 

170.4 

"9-3 

68 

219.5 

153-7 

29 

23.8 

16.6 

89 

72.9 

51 

0 

49 

122.  I 

i|-5 

09 

171. 2 

1 19.  9 

69 

220.4 

154-3 

30 

24.6 

17.2 

90 

73-7 

51 

6 

50 
151 

122.9 

86.0 

10 

172.0 

120.  5 

70 
271 

221.  2 

222.  0 

154-9 
155-4 

31 

25-4 

lys" 

91 

74-5 

52 

2 

123.7 

86.6 

211 

172.8 

121.  0 

32 

26.  2 

18.4 

92 

75-4 

52 

8 

52 

124.5 

87.2 

12 

173-7 

121.6 

72 

222.8 

156.0 

33 

27.  0 

18.9 

93 

76.2 

53 

3 

53 

125-3 

87.8 

13 

174-5 

122.  2 

73 

223.6 

156.6 

34 

27.9 

19-5 

94 

77.0 

53 

9 

54 

126.  1 

11-^^ 

14 

175-3 

122.  7 

74 

224.4 

157.2 

35 

28.7 

20. 1 

95 

77.8 

54 

5 

55 

127.0 

88.9 

15 

176.  I 

123-3 

75 

225-3 

157-7 

3'^ 

29.5 

20.  6 

96 

78.  6    :    55 

I 

56 

127.8 

89-5 

16 

176.9 

123.9 

76 

226.  1 

158.3 

37 

30-3 

21.  2 

97 

79-  5  !  55 

6 

57 

128.6 

90.  1 

17 

177.8 

124-5 

77 

226.  9 

158.9 

3'S 

31- I 

21.8 

98 

80.  3  1  56 

2 

58 

129.4 

90.  6 

18 

178.6 

125.  0 

78 

227.  7 

159-5 

39 

31-9 

22.4 

99 

81.  I     56 

8 

59 

130.2 

91.  2 

19 

179.4 

125.6 

79 

228.5 

160.  0 

40 
41 

32.8 

22.9 

100 

81-9     57 

4 

60 

131.1 

91.8 

20 

180.2 

126.  2 

80 

229.4 

160.6 

33-6 

23-5 

lOl 

'82.7  !  57 

9 

161 

131-9 

92-3 

221 

181.0 

126.8 

281" 

230.2 

161.  2 

42 

34-4 

24.  I 

02 

83.  6  1  58 

5 

62 

132-7 

92.9 

22 

181.9 

127-3 

82 

231.0 

161.  7 

43 

35-2 

24.7 

03 

84.4  '  59 

I 

63 

133-5 

93-5 

23 

182.7 

127.9 

■  83 

231.8 

162.  3 

44 

36.0 

25.  2 

04 

85-2  :  59 

7 

64 

134-3 

94-  I 

24 

183-5 

128.5 

84 

232-6 

162.  9 

45 

36-9 

25.8 

05 

86. 0     60 

2 

65 

135-2 

94-6 

25 

184.3 

129.  1 

85 

233-5 

163-5 

46 

37-7 

26.  4 

06 

86,8 

60 

8 

66 

136.0 

95-2 

26 

185.1 

129.6 

86 

234-3 

164.0 

47 

38.5 

27.  0 

07 

87.6 

61 

4 

67 

136.8 

95-8 

27 

185.9 

130.2 

87 

235-1 

164.6 

48 

39-3 

27.5 

08 

88.  5  '■  61 

9 

68 

137-6 

96.4 

28 

186.8 

130.8 

88 

235-9 

165.  2 

49 

40.  I 

28.1 

09 

89-3 

62 

5 

69 

138.4 

96.9 

29 

187.6 

I3I-3 

89 

236.7 

165.8 

50 

41.0 

28.  7 
29-3 

10 
III 

90.  I 

63 

I 

70 

139-3 

97-5 

30 

188.4 

i3'-9 

90 

237-6 

166.3 

51 

41.8 

90  y 

63 

7 

171 

140.  I 

98.1 

231 

189.2 

132-5 

291 

238-4 

166.9 

52 

42.  6 

29.8 

12 

91.7 

64 

2 

72 

140.9 

98.7 

32 

190.0 

133- I 

92 

239-2 

167.5 

53 

43-4 

30-4 

13 

92.6 

64 

8 

n 

141.7 

99-2 

33 

190.9 

133-6 

93 

240.0 

168.  I 

54 

44.2 

31.0 

14 

93-4 

65 

4 

74 

142.5 

99-8 

34 

191.7 

134.2 

94 

240.8 

168.6 

55 

45-  ' 

31-5 

15 

94.2 

66 

0 

75 

143-4 

100.  4 

35 

192.5 

134.8 

95 

241.  6 

169.  2 

56 

45-9 

32.1 

16 

95.  0  ,  66 

5 

70 

144.2 

100.9 

36 

193-3 

135-4 

96 

242-5 

169.8 

57 

46.7 

32-7 

17 

95.8  1  67 

I 

77 

145.0 

loi.  5 

37 

194.  1 

135-9 

97 

243-3 

170.4 

58 

47-5 

18 

96.  7  1  67 

7 

78 

145-8 

102.  1 

38 

195.0 

136-5 

98 

244-1 

170.9 

59 

48.3 

33-^ 

19 

97. 5     68 

3 

79 

146.  6 

102.  7 

39 

195.8 

137-1 

99 

244.9 

171.5 

60 

49.1 

34-4 

20 

98.3 

68.8 

80 

147.4 

103.  2 

40 

196.6 

137-7 

300 

245-7 

172.  1 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

[Fo 

r  55  Deg 

rees. 

Page  250 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  36  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

49.4 

35-9 

121 

97-9 

71.  I 

181 

146.4 

106.4 

241 

195.0 

141-7 

2 

1.6 

I.  2 

62 

50.  2 

36-4 

22 

98.7 

71-7 

82 

147.2 

107.  0 

42 

195-8 

142.  2 

3 

2.4 

i.S 

63 

51.0 

37- 0 

23 

99-5 

72.3 

83 

148.  I 

107.6 

43 

196.  6 

142.8 

4 

3-2 

2.4 

64 

51-8 

37-6 

24 

100.3 

72.9 

84 

148.9 

108.2 

44 

197.4 

143-4 

5 

4.0 

2.9 

65 

52.6 

3^-? 

25 

lOI.  I 

73-5 

85 

149.7 

108.7 

45 

198.2 

144.0 

6 

4.9 

3-5 

66 

53-4 

38.8 

26 

lOI.  9 

74.1 

86 

150.5 

109.3 

46 

199.0 

144.6 

7 

5-7 

4.1 

67 

54-2 

39-4 

27 

102.  7 

74-6 

87 

15I-3 

109.9 

47 

199.8 

145.2 

8 

6.5 

4-7 

68 

55- 0 

40.  0 

28 

103.6 

75-2 

88 

152.  I 

110.5 

48 

200.  6 

145.8 

9 

^■^ 

5-3 

69 

55-8 

40.6 

29 

104.4 

75-8 

89 

152-9 

111.1 

49 

201.  4 

146.4 

lO 

8.  I 

5-9 

70 

56.6 

41.  I 

30 

105.  2 

76.4 

90 

153-7 

111.7 

50 

202.3 

146.9 

II 

8.9 

6.5 

71 

57-4 

41.7 

131 

106.0 

77.0 

191 

154-5 

112.3 

251 

203.1 

147-5 

12 

9-7 

7-1 

72 

58.2 

42.3 

32 

106.8 

77-6 

92 

155-3 

112.9 

52 

203.9 

148.  I 

13 

10.5 

7.6 

73 

59-1 

42.9 

33 

107.  6 

78.2 

93 

156.  I 

"3-4 

53 

204.7 

148.7 

14 

"•3 

8.2 

74 

59-9 

43-5 

34 

108.  4 

78.8 

94 

156.9 

114.  0 

54 

205.5 

149-3 

15 

12.  I 

8.8 

75 

60.  7 

44.  I 

35 

109.  2 

79-4 

95 

157.8 

114.  6 

55 

206.3 

149.9 

16 

12.  9 

9.4 

76 

61.  5 

44-7 

36 

no.  0 

79-9 

96 

158.6 

115.2 

56 

207.  I 

150.5 

17 

13.8 

10.  0 

77 

62.3 

45-3 

37 

no.  8 

80.5 

97 

159-4 

"5-8 

57 

207.9 

151.  I 

18 

14.  6 

10.  6 

78 

63.1 

45.8 

38 

III.  6 

81.  I 

98 

160.  2 

116.4 

58 

208.7 

151.  6 

19 

15-4 

II.  2 

79 

63-9 

46.4 

39 

112.  5 

81.7 

99 

161.  0 

117.0 

59 

209.5 

152.  2 

20 

16.  2 

II. 8 

80 

64.7 

47.0 

40 

113-3 

82.3 

200 

161. 8 

117.6 

60 

210.3 

152.8 

21 

17.0 

12.3 

81 

65-5 

47.6 

141 

114.  I 

82.9 

201 

162.6 

118.1 

261 

211.  2 

153-4 

22 

17.8 

12.  9 

82 

66.3 

48.  2 

42 

114.9 

83-5 

02 

163.4 

118.7 

62 

212.  0 

154.0 

23 

18.6 

13-5 

P 

67.1 

48.8 

43 

115.7 

84.1 

03 

164.  2 

"9-3 

63 

212.8 

154.6 

24 

19.4 

14.  I 

84 

68.0 

49-4 

44 

116.  5 

84.6 

04 

165.  0 

119.9 

64 

213.6 

15s- 2 

25 

20.  2 

14.7 

85 

68.8 

50.  0 

45 

II7-3 

85.2 

05 

165.8 

120.5 

65 

214.4 

155.8 

26 

21.0 

15-3 

86 

69.6 

50-5 

46 

118.  I 

85.8 

06 

166.7 

121.  I 

66 

215.  2 

156.4 

27 

21.8 

15-9 

87 

70.4 

51- I 

47 

118.  9 

86.4 

07 

167.5 

121.7 

67 

216.  0 

156.9 

28 

22.7 

16.5 

88 

71.2 

51-7 

48 

119.  7 

87.0 

08 

168.3 

122.  3 

68 

216.8 

157-5 

29 

23-5 

17.0 

89 

72.  0 

52.3 

49 

120.  5 

87.6 

09 

169.  I 

122.  8 

69 

217.  6 

158.1 

30 

24-3 

17.6 

90 

72.8 

52-9 

50 

121. 4 

88.2 

10 

169.9 

123.4 

70 

218.4 

158.7 

31 

25-1 

18.2 

91 

73-6 

53-5 

■151 

122.  2 

88.8 

211 

170.7 

124.  0 

271 

219.  2 

159-3 

32 

25-9 

18.8 

92 

74-4 

54-1 

52 

123.0 

89-3 

12 

I7I-5 

124.  6 

72 

220.  1 

159.9 

33 

26.  7 

19.4 

93 

75-2 

54-7 

53 

123.8 

89-9 

13 

172.3 

125.2 

73 

22  \  9 

160.  5 

34 

27-5 

20.  0 

94 

76.0 

55-3 

54 

124.6 

90-5 

14 

173-  I 

125.8 

74 

221.  7 

161.  1 

35 

.28.3 

20.  6 

95 

76.9 

55-8 

55 

125.4 

91.  I 

15 

173-9 

126.4 

75 

222.  5 

161.6 

36 

29.  I 

21.  2 

96 

77-7 

56.4 

56 

126.  2 

91.7 

16 

174-7 

127.  0 

76 

223.3 

162.  2 

37 

29.9 

21.7 

97 

78-5 

57- 0 

57 

127.  0 

92.3 

17 

175-6 

127.5 

77 

224.  I 

162.8 

38 

30-7 

22.3 

98 

79-3 

57.6 

58 

127.8 

92.9 

18 

176.4 

128.1 

78 

224.9 

163.4 

39 

31.6 

22.  9 

99 

80.  I 

58.2 

59 

128.6 

93-5 

19 

177.2 

128.7 

79 

225.7 

164.0 

40 

32-4 

23-5 
24.1 

100 

80.9 

58.8 

60 

129.4 

94.0 

20 
221 

178.0 

129.3 

80 

226.  5 

164.6 

41 

33-2 

lOI 

81.7 

59-4 

161 

130-3 

94-6 

178.8 

129.9 

281 

227.3 

165.  2 

42 

34- 0 

24.7 

02 

82.5 

60.  0 

62 

131-1 

95-2 

22 

179.6 

130.5 

82 

228.  I 

165.8 

43 

34-8 

25-3 

03 

83-3 

60.  5 

63 

131-9 

95-8 

23 

180.4 

131.1 

83 

229.  0 

160.3 

44 

35-6 

25-9 

04 

84.1 

61.  I 

64 

132-7 

96.4 

24 

181.  2 

131- 7 

84 

229.8 

166.9 

45 

36-4 

26.  5 

05 

84.9 

61.  7 

65 

133-5 

97.0 

25 

182.0 

132-3 

85 

230.  6 

167.5 

46 

37-2 

27.0 

06 

85.8 

62.3 

66 

134-3 

97-6 

26 

182.8. 

132.8 

86 

231.4 

168.  I 

47 

38.0 

27.  6 

07 

86.6 

62.9 

67 

135- I 

98.2 

27 

183.6 

133-4 

87 

232.2 

168.7 

48 

38.8 

28.2 

08 

87.4 

63-5 

68 

135-9 

98-7 

28 

184.5 

134.0 

88 

233-0 

169.3 

49 

39-6 

28.8 

09 

88.2 

64.  I 

69 

136-7 

99-3 

29 

185-3 

134.6 

89 

233-8 

169.9 

50 

40.5 

29.4 

10 

89.0 

64.7 

70 

137-5 

99-9 

30 

186.  I 

135-2 

90 

234.6 

170-5 

SI 

41-3 

30.0 

III 

89.8 

65.2 

171 

138-3 

100.  5 

231 

186.9 

135-8 

291 

235-4 

171.0 

52 

42.  I 

30.6 

12 

90.  6 

65.8 

72 

139.2 

lOI.  I 

32 

187.7 

136.4 

92 

236.2 

171.6 

53 

42.9 

31.2 

13 

91.4 

66.4 

73 

140.  0 

loi.  7 

33 

188.5 

137-0 

93 

237.0 

172.  2 

54 

43-7 

31-7 

14 

92.  2 

67.  0 

74 

140.  8 

102.3 

34 

189.3 

137-  5 

94 

237-9 

172.8 

55 

44-5 

32-3 

15 

93- 0 

67.6 

75 

141.  6 

102.  9 

35 

190.  I 

138.  I 

95 

238-7 

173-4 

56 

45-3 

32-9 

16 

93-8 

68.2 

76 

142.4 

103-5 

36 

190.9 

138-7 

96 

239-5 

174.0 

57 

46.  I 

33-5 

17 

94-7 

68.8 

77 

143.2 

104.  0 

H 

191.  7 

139-3 

97 

240.3 

174.6 

58 

46.9 

34-1 

18 

95-5 

69.4 

78 

144.0 

104.  6 

38 

192.5 

139-9 

98 

241.  I 

175-2 

59 

47-7 

34-7 

19 

96.3 

69.9 

79 

144.8 

105.  2 

39 

193-4 

140.5 

99 

241.9 

175-7 

60 

48.5 

35-3 

20 

97.1 

70-5 

80 

145.6 

105.8 

40 

194.2 

141.1 

300 

242.7 

176.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  54  Deg 

rees. 

TABLE  2. 

Page  251  | 

% 

Difference  of  Latitude  and  Departure  for  37  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
144.6 

Dep. 

Dist. 
241 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

48.7 

36.7 

121 

96.6 

72.8 

181 

108.9 

192.5 

145.0 

2 

1.6 

1.2 

62 

49-5 

37-3 

22 

97-4 

73-4 

82 

145-4 

109.5 

42 

193-3 

145 

.6 

3 

2.4 

1.8 

63 

50.3 

37-9 

23 

98.2 

74.0 

83 

146.  2 

no.  I 

43 

194-  1 

146 

2 

4 

3-2 

2.4 

64 

51- I 

38.5 

24 

99.0 

74-6 

84 

146.9 

no.  7 

44 

194.9 

146 

'.s 

5 

4.0 

3-0 

65 

51-9 

39- I 

25 

99.8 

75-2 

85 

147-7 

III. 3 

45 

195-7 

147 

4 

6 

4-8 

3-6 

66 

52-7 

39-7 

26 

100.  6 

75-8 

86 

148.5 

III. 9 

46 

196.5 

148 

0 

7 

5-6 

I     4.2 

67 

53-5 

40- 3 

27 

101.4 

76.4 

87 

•49- 3 

1 12.  5 

47 

197.3 

148 

.6 

8 

6.4 

4.8 

68 

54-3 

40.9 

28 

102.  2 

77.0 

88 

150.  I 

113.  I 

48 

198.  I 

149 

3 

9 

7.2 

5-4 

69 

55-1 

41-5 

29 

103.0 

77.6 

89 

150.9 

113- 7 

49 

198.9 

149 

9 

lO 

8.0 

6.0 

70 

55-9 

42.  I 

30 

103.8 

78.2 

90 

151-7 

114.3 

50 

199.7 

150 
151 

5 

II 

8.8 

6:6 

71 

56.7 

42.7 

131 

104.6 

78:8 

191 

152-5 

"4-9 

251 

200.  5 

I 

12 

9.6 

7.2 

72 

57-5 

43-3 

32 

105.4 

79-4 

92 

153-3 

115-5 

52 

201.3 

151 

7 

13 

10.  4 

7.8 

73 

58.3 

43-9 

33 

106.  2 

80.0 

93 

154-1 

116.  2 

53 

202.  I 

152 

3 

14 

II. 2 

8.4 

74 

59-1 

44-5 

34 

107.0 

80.6 

94 

154-9 

116.  8 

54 

202.9 

152 

9 

15 

12.  0 

9.0 

75 

59-9 

45-1 

35 

107.8 

81.2 

95 

155-7 

117.4 

55 

203.7 

153 

5 

16 

12.8 

9.6 

76 

60.  7 

45-7 

36 

108.  6 

81.8 

96 

156-5 

118.  0 

56 

204.5 

154 

I 

17 

13.6 

10.  2 

77 

61.5 

46.3 

37 

109.4 

82.4 

97 

157-3 

118.  6 

57 

205.  2 

154 

7 

18 

14.4 

10.8 

78 

62.3 

46.9 

38 

no.  2 

83.1 

98 

158.  I 

119.  2 

58 

206.  0 

155 

3 

19 

15.2 

II. 4 

79 

63.1 

47-5 

39 

III.O 

83-7 

99 

158.9 

119.  8 

59 

206.8 

155 

9 

20 

16.  0 

12.  0 

80 

63-9 

48.  I 

40 

III. 8 

84-3 

200 

159-7 

120.  4 

60 

207.  6 

156 

5 

21 

16.8 

12.  6 

81 

64.7 

48.7 

141 

112.  6 

84.9 

201 

160.  5 

121. 0 

261 

208.  47 

157 

I 

22 

17.6 

13.2 

82 

65-5 

49-3 

42 

II3-4 

85.5 

02 

161. 3 

121.  6 

62 

209.  2 

157 

7 

23 

18.4 

13.8 

83 

66.3 

50.0 

43 

114.  2 

86.  I 

03 

162.  I 

122.  2 

63 

210.0 

158 

3 

24 

19.2 

14.4 

84 

67.1 

50.6 

44 

115. 0 

86.7 

04 

162.  9 

122.8 

64 

210.8 

158 

9 

25 

20.0 

15.0 

85 

67.9 

51.2 

45 

115-8 

87-3 

05 

163-7 

123.4 

65 

211. 6 

159 

5 

26 

20.8 

,5.6 

86 

68.7 

51.8 

46 

116.  6 

87.9 

06 

164.5 

124.  0 

66 

212.  4 

160 

I 

27 

21.  6 

16.2 

87 

69.5 

52-4 

47 

117.4 

88.5 

07 

165-3 

124.  6 

67 

213-2 

160 

7 

28 

22.4 

16.  9 

88 

70-3 

53- 0 

48 

1 18.  2 

89.  I 

08 

166.  I 

125.  2 

68 

214.  0 

161 

3 

29 

23.2 

'Z-5 

89 

71.  I 

53-6 

49 

119.  0 

89.7 

09 

166.9 

125.8 

69 

214.8 

161 

9 

30 

24.0 

18. 1 

90 

71.9 

72.7 

54-2 

50 

1 19.  8 

90.3 

10 

167.7 

126.4 

70 

215.6 

162 

5 

31 

24.8 

18.7 

91 

54-8 

J55 

120.  6 

90.9 

211 

168.5 

127.  0 

271 

216.4 

163 

I 

32 

25.  6 

19-3 

92 

73-5 

55-4 

52 

121. 4 

91-5 

12 

169.3 

127.6 

72 

217.  2 

163 

7 

33 

26.4 

19.9 

93 

74-3 

56.0 

53 

122.  2 

92.1 

13 

170.  I 

128.2 

73 

218.0 

164 

3 

34 

27.  2 

20.  5 

94 

75-1 

56.6 

54 

123.0 

92.7 

14 

170.9 

128.8 

74 

218.  8 

164 

9 

35 

28.0 

21.  I 

95 

75-9 

57-2 

55 

123.8 

93-3 

15 

171-7 

129.4 

75 

219.6 

165 

5 

36 

28.8 

21.7 

96 

76.7 

57.8 

56 

124.6 

93-9 

16 

172.5 

130.0 

76 

220.4 

166 

I 

H 

29-5 

22.3 

97 

77-5 

58.4 

57 

125.4 

94-5 

17 

173-3 

130.  6 

77 

221.  2 

166 

7 

38 

30-3 

22.9 

98 

78.3 

59- 0 

58 

126.2 

95-1 

18 

174.  I 

131.2 

78 

222.  0 

167 

3 

39 

31-1 

23-5 

99 

79.1 

59-6 

59 

127.0 

95-7 

19 

174.9 

131. 8 

79 

222.  8 

167 

9 

40 

31-9 

24.1 

100 

79-9 

60.2 

60 

127.8 

96-3 

20 

175-7 

132.4 

80 

223.  6 

168 

5 

41 

32-7 

24.7 

lOI 

80.7 

■60:"  r 

161 

128.6 

96.9 

221 

176.5 

133-0 

281 

224.4 

169 

I 

42 

33-5 

25-3 

02 

81.5 

61. 4 

62 

129.4 

97-5 

22 

177.3 

133.6 

82 

225.  2 

169 

7 

43 

34-3 

25.9 

03 

82.3 

62.0 

63 

130.2 

98.  I 

23 

178.  I 

134.2 

83 

226.  0 

170 

3 

44 

35-1 

26.  5 

04 

83.1 

62.6 

64 

131. 0 

98.7 

24 

178.9 

134.8 

84 

226.8 

170 

9 

45 

35-9 

27.1 

05 

83-9 

63.2 

65 

131-8 

99-3 

25 

179.7 

135.4 

85 

227.  6 

171 

5 

46 

36.7 

27.7 

06 

84.7 

63.8 

66 

132.6 

99-9 

26 

180.  5 

136.0 

86 

228.4 

172 

I 

47 

37-5 

28.3 

07 

85-5 

64.4 

67 

133-4 

100.  5 

27 

181.3 

136-6 

87 

229.  2 

172 

7 

48 

38-3 

28.9 

08 

86.3 

65.0 

68 

134.2 

lOI.  I 

28 

182.  I 

137-2 

88 

230.0 

173 

3 

49 

39-1 

29-5 

09 

87.1 

65.6 

69 

135-0 

loi.  7 

29  , 

182.  9 

137-8 

89 

230.8 

173 

9 

50 
51 

39-9 

30.1 

10 

87.8 

66.2 

70 

135-8 

102.  3 

30  i 

183.  7 

138.4 

90 

231.6 

174 

5 

40.7 

30-7 

III 

88.6 

66.8 

171 

136.6 

102.9 

231 

184.5 

139.0 

291 

232.4 

175- 

I 

52 

41.5 

3^-3 

12 

89.4 

67.4 

72 

137-4 

103-5 

32 

'!5-3 

139.6 

92 

233.2 

175- 

7 

53 

42.3 

31-9 

13 

90.  2 

68.0 

73 

138.2 

104.  I 

33 

186.  I 

140.  2 

93 

234.0 

176. 

3 

54 

43-1 

32- 5 

14    : 

91.  0 

68.6 

74 

139.0 

104.7 

34 

186.9 

140.8 

94 

234.8 

176. 

9 

55 

43-9 

33-  • 

15 

91.8 

69.  2 

75 

139.8 

105-3 

35 

187.7 

141.4 

95 

235.6 

177. 

5 

56 

44-7 

33-7 

16 

92.  6 

69.8 

76 

140.  6 

105.9 

36 

188.5 

142.  0 

96 

236.4 

178. 

I 

57 

45-5 

34-3 

17 

93-4 

70.4 

77 

141-4 

106.  5 

37 

189.3 

142.  6 

97 

237.2 

178. 

7 

58 

46.3 

34-9 

18 

94.2 

71.0 

78 

142.  2 

107.  I 

38 

190.  I    ! 

143-2 

98 

^3^-2 

179- 

3 

P 

47.1 

35-5 

19 

95- 0 

71.6 

79 

143.0 

107.7 

39 

190.9 

143.8 

99 

238.8 

179- 

9 

60 

47-9 

36.1 

20 

95.8 

72.2 

80 

143.8 

108.3 

40 

191.  7 

144.4 

300 

239.6 

180.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  53  Degrees.         | 

Pag 

e252] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  38  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

48.  I 

37-6 

121 

95-3 

74-5 

181 

142.  6" 

III. 4 

241 

189.9 

148.4 

2 

1.6 

I.  2 

62 

48.9 

38.2 

22 

96.  I 

75-1 

82 

143-4 

112.  I 

42 

190.7 

149.  0 

3 

2.4 

1.8 

63 

49.6 

38.8 

23 

96.9 

75-7 

83 

144.2 

112.  7 

43 

191-5 

149.6 

4 

3-2 

2-5 

64 

50.4 

39-4 

24 

97-7 

7b.  3 

84 

145.0 

113.3 

44 

192.3 

150.2 

5 

3-9 

31 

65 

51.2 

40.  0 

25 

98.5 

77.0 

85 

145.8 

113.9 

45 

193-1 

150.8 

6 

4-7 

3-7 

66 

52.  0 

40.  6 

26 

99-3 

77.6 

86 

146.  6 

114-5 

46 

193-9 

151.5 

7 

5-5 

4-3 

67 

52.8 

41.2 

27 

100.  I 

78.2 

87 

147.4 

115.1 

47 

194.6 

152.  I 

8 

6-3 

4.9 

68 

53- (^ 

41.9 

28 

100.  9 

78.8 

88 

148.  I 

115- 7 

48 

195-4 

152.7 

9 

7-1 

5-5 

69 

54-4 

42.5 

29 

loi.  7 

79-4 

89 

148.9 

116.  4 

49 

196.  2 

153-3 

lO 

7-9 

6.2 

70 

55-2 

43-1 

30 

102.  4 

80.0 

90 

149.7 

117.  0 

50 

197.0  ' 

153-9 

II 

8.7 

6.8 

71 

55-9 

43-7 

131 

103.2 

80.7 

191 

150-5 

117.  6 

251 

197-8 

154-5 

12 

9-5 

7-4 

72 

5t>-7 

44-3 

32 

104.  0 

81.3 

92 

151-3 

118.  2 

52 

198.6 

155- I 

13 

10.2 

8.0 

73 

5Z-5 

44.9 

33 

104.  8 

81.9 

93 

152.  I 

118.  8 

53 

199.4 

155-8 

14 

II. 0 

8.6 

74 

5^-3 

45-6 

34 

105.6 

82.5 

94 

152.9 

"9-4 

54 

200.  2 

156.4 

i.S 

II. 8 

9.2 

75 

59-1 

46.  2 

35 

106.4 

83.1 

95 

153-7 

120.  I 

55 

200.  9 

157-0 

i6 

12.6 

9.9 

76 

59-9 

46.8 

3^^ 

107.  2 

83-7 

96 

154-5 

120.  7 

56 

201.  7 

157-6 

17 

13-4 

10.5 

77 

60.  7 

47-4 

37 

108.  0 

84-3 

97 

155-2 

121. 3 

57 

202.  5 

158.2 

i8 

14.2 

U.  I 

7« 

61.5 

48.0 

38 

108.7 

85.0 

98 

156.0 

121.  9 

58 

203.3 

158.8 

19 

15.0 

II. 7 

79 

62.  3 

48.6 

39 

109.5 

85.6 

99 

156.8 

122.  5 

59 

204.  I 

159.5 

20 

15-8 

12.3 

80 

63.0 

49-3 

40 

1 10.  3 

86.2 

200 

157.6 

123.1 

60 

204.9 

160.  I 

21 

16.5 

12.9 

81 

63.8 

49.9 

141 

III.  I 

86.8 

201 

158.4 

123.7 

261 

205.7 

160.  7 

22 

17-3 

13-  5 

82 

64.6 

50-5 

42 

III.  9 

87-4 

02 

159.2 

124.4 

62 

206.  5 

161. 3 

23 

18.  I 

14.2 

«3 

65-4 

51- I 

43 

112.  7 

88.0 

03 

160.  0 

125.  0 

63 

207.  2 

161.  9 

24 

18.9 

14.8 

84 

66.2 

51-7 

44 

"3-5 

88.7 

04 

160.8 

125.  6 

64 

208.  0 

162.  5 

25 

19.7 

15-4 

«5 

67.0 

52.  3 

45 

1 14- 3 

89-3 

05 

161.  5 

126.  2 

65 

208.8 

163.2 

26 

20.  5 

16.0 

86 

67.8 

52-9 

46 

115. 0 

89-9 

06 

162.3 

126.8 

66 

209.6 

163.8 

27 

21.3 

16.6 

«7 

68.6 

53-6 

47 

1 15.  8 

90-5 

07 

163.1 

127.4 

67 

210.4 

164.4 

28 

22. 1 

17.2 

88 

69-3 

.54-2 

48 

116.  6 

91.  I 

08 

163.9 

128.  I 

68 

211.  2 

165.  0 

29 

22.  9 

17.9 

89 

70.  I 

54.8 

49 

117.4 

91.7 

00 

164.7 

128.7 

69 

212.0 

165.6 

30 

23.6 

18-5 

90 

70.9 

55-4 
56.  0 

SO 
151 

118.  2 

119.  0 

92.3 
93-0 

10 
211 

165-5 

129.3 

70 

212.8 

166.  2 

31 

24.4 

19. 1 

91 

71.7 

166.3 

129.9 

271 

213.  6 

166.8 

32 

25.2 

19.7 

92 

72-5 

56.6 

52 

1 19.  8 

93-6 

12 

167.  I 

130-5 

72 

214.3 

167.5 

33 

25.  0 

20.3 

93 

73-3 

57-3 

53 

120.  6 

94-2 

13 

167.8 

131-1 

73 

215.  I 

168.  I 

34 

26.8 

20.9 

94 

74.1 

57-9 

54 

121. 4 

94.8 

14 

168.6 

131-8 

74 

215-9 

168.7 

35 

27.6 

21-5 

95 

74-9 

58.  5 

55 

122.  I 

95-4 

15 

169.4 

132.4 

75 

216.  7 

169.3 

36 

28.4 

22.  2 

96 

75.6 

.59-1 

5& 

122.  9 

96.  0 

16 

170.  2 

133-0 

76 

217.5 

169.9 

^7 

29.  2 

22.8 

97 

76.4 

.59-7 

57 

123.7 

96.7 

17 

171.  0 

133-6 

77 

218.3 

170-5 

3« 

29.9 

23-4 

98 

77.2 

60.  3 

58 

124-5 

97-3 

18 

171. 8 

134-2 

78 

219.  I 

171.  2 

39 

30-7 

24.0 

99 

7^-o 

61.  0 

59 

125-3 

97-9 

19 

172.  6 

134.8 

79 

219.9 

171. 8 

40 

31-5 

24.  6 

25.  2 

100 
ToT 

78.8 
79.6 

61.6 

60 

126.  I 

98.5 

20 
221 

173-4 

135-4 

80 

220.  6 

172-4 

41 

32-3 

62.  2 

161 

126.  9 

99-1 

174.2 

136.  I 

281 

221.4 

173.0 

42 

33-1 

25-9 

02 

80.4 

62.8 

62 

127.7 

99-7 

22 

174.9 

136-7 

82 

222.  2 

173-6 

43 

33-9 

26.5 

03 

81.2 

63-4 

^3 

128.4 

100.  4 

23 

175-7 

137- 3 

P 

223.0 

174-2 

44 

34-7 

27.1 

04 

82.0 

64.  0 

64 

129.  2 

lOI.O 

24 

176.5 

137-9 

84 

223.8 

174.8 

45 

35-5 

27.7 

05 

82.7 

64.6 

65 

130.0 

loi.  6 

25 

177.3 

138.  5 

85 

224.  6 

175-5 

46 

36.2 

28.3 

06 

83-5 

65-3 

66 

130.8 

102.  2 

26 

178.  I 

139.1 

86 

225.4 

176.  I 

47 

37- 0 

28.9 

07 

«4-3 

65-9 

67 

131-6 

102.8 

27 

178.9 

139.8 

87 

226.  2 

176.7 

48 

.37-8 

29.  6 

08 

85.1 

66.5 

68 

132.4 

103.4 

28 

179-7 

140.4 

88 

226.9 

1 77-  3 

49 

38.6 

30.2 

09 

85-9 

67.1 

69 

133-2 

104.  0 

29 

180.5 

141.  0 

89 

227.7 

177-9 

50 

39-4 

.30.  S 

10 

86.  7 

67.7 

70 

134.0 

104.7 

30 

181.  2 

1   141.  6 

90 

228.5 

178.5 

SI 

40.2 

31-4 

III 

87.5 

68.3 

171 

134-7 

105-3 

231 

182.0 

142.  2 

291 

229.3 

179-2 

52 

41.  0 

32.0 

12 

88.3 

69.0 

72 

135- 5 

105.9 

32 

182.8 

142.8 

92 

230.  I 

179-8 

53 

41.8 

32.  6 

13 

89.0 

69.6 

73 

136-3 

106.  5 

33 

183.6 

143-4 

93 

230.9 

180.4 

54 

42.  6 

33-2 

14 

89.8 

70.  2 

74 

137- 1 

107.  I 

34 

184.4 

144.  I 

94 

231-7 

181. 0 

55 

43-3 

33-9 

15 

90.  6 

70.8 

75 

137-9 

107.7 

35 

185.2 

144-  7 

95 

232-5 

181. 6 

5^^ 

44.  I 

34-  5 

16 

91.4 

71.4 

76 

138-7 

108.4 

36 

186.0 

145-3 

96 

233.  3 

182.2 

57 

44.9 

35-1 

17 

92.  2 

72.  0 

77 

139-5 

109.  0 

37 

186.8 

145-9 

97 

234.0 

182.9 

5« 

45-7 

35-  7 

18 

93- 0 

72.6 

78 

140.3 

109.  b 

38 

187.5 

146.5 

98 

234-8 

183-5 

59 

46-5 

3b-  3 

19 

93-8 

73-3 

79 

141.  I 

no.  2 

39 

188.3 

147-  1 

99 

235-6 

184.  I 

60 

47-3 

36-9 

20 

94.6 

73-9 

80 

141.  8 

no.  8 

40 

189.  I 

147-8 

300 

236.4 

184.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.   - 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  52  Deg 

rees. 

TABLE  2. 

[Page  253  | 

^%. 

Difference  of  Latitude  and  Departure  for  39  Degrees, 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

47-4 

38-4 

121 

94.0 

76.1 

181 

140.7 

"3-9 

241 

187-3 

151.7 

2 

1.6 

1-3 

62 

48.2 

39- 0 

22 

94.8 

76.8 

82 

141.  4 

114.5 

42 

188.  I 

152.3 

1 

2-3 

1.9 

63 

49.0 

39-6 

23 

95-6 

77-4 

83 

142.  2 

"5-2 

43 

188.8 

152.9 

4 

31 

2-5 

64 

49-7 

40-3 

24 

96.4 

78.0 

84 

143.0 

"5-8 

44 

189.6 

153-6 

5 

3-9 

^l 

^5 

50-5 

40.9 

25 

97.1 

78.7 

85 

143-8 

116. 4 

45 

190.4 

154.2 

6 

4-7 

3-8 

66 

51-3 

41-5 

26 

97-9 

79-3 

86 

144-5 

117.1 

46 

191.  2 

154.8 

7 

5-4 

4.4 

67 

52.1 

42.  2 

27 

98.7 

79-9 

87 

H5-3 

"7-7 

47 

192.0 

155-4 

8 

6.2 

5-0 

68 

52.8 

42.8 

28 

99-5 

80.6 

88 

146.  I 

"8.3 

48 

192.7 

156.  I 

9 

7-2 

5-7 

69 

53-6 

43-4 

29 

100.3 

81.2 

89 

146.9 

118.9 

49 

193-5 

156-7 

lO 

7.8 

6-3 

70 

54-4 

44.1 

30 

lOI.O 

81.8 

90 

147-7 

119.  6 

50 

194-3 

157-3 

II 

8-5 

6.9 

71 

55-2 

44-7 

131 

101.8 

82.  4 

191 

148.  4 

120.  2 

251 

195- I 

158.0 

12 

9-3 

7.6 

72 

56.0 

45-3 

32 

102.  6 

83.1 

92 

149.2 

120.8 

52 

195.8 

158.6 

13 

10.  I 

8.2 

7Z 

56-7 

45-9 

2,:^ 

103.4 

83.7 

93 

150.  0 

121.  5 

53 

196.  6 

159.2 

14 

10.  9 

8.8 

74 

57-5 

46.6 

34 

104.  I 

84-3 

94 

150.8 

122.  I 

54 

197.4 

159.8 

15 

II. 7 

9.4 

75 

58.3 

47.2 

35 

104.9 

85.0 

95 

151-5 

122.  7 

55 

198.2 

160.  5 

i6 

12.4 

10.  I 

76 

59-1 

47.8 

36 

105-7 

85.6 

96 

152-3 

123-3 

56 

198.9 

161.  I 

17 

13.2 

10.  7 

77 

59-8 

48.5 

37 

106.  5 

86.2 

97 

1^3-1 

124.0 

57 

199.7 

161.  7 

i8 

14.0 

II. 8 

78 

60.6 

49.1 

38 

107.  2 

86.8 

98 

153-9 

124.  6 

58 

200.  5 

162.  4 

19 

14.8 

12.0 

79 

61.4 

49-7 

39 

108.0 

87.5 

99 

154-7 

125.2 

59 

201.3 

163.  0 

20 

15-5 

12.6 

80 

62.  2 

50-3 

40 

108.8 

88.1 

.  200 

155-4 

125.9 

60 

202.  I 

163.6 

21 

16.3 

13.2 

81 

62.9" 

51.0 

141 

109.  6 

'  88.  7 

201 

156.  2 

126.  5 

261 

"202.8 

164.3 

22 

17. 1 

13.8 

82 

63-7 

51.6 

42 

no.  4 

89.4 

02 

157-0 

127.  I 

62 

203.6 

164.9 

23 

17.9 

14.5 

83 

64-5 

52.  2 

43 

III.  I 

90.  0 

03 

157-8 

127.8 

63 

204.  4 

165-5 

24 

18.7 

15- 1 

84 

65-3 

52-9 

44 

III.  9 

90.  6 

04 

158-5 

128.4 

64 

205.  2 

166.  I 

25 

19.4 

15-7 

85 

66.1 

53-5 

45 

112.  7 

91-3 

05 

159-3 

129.  0 

65 

205.  9 

166.8 

26 

20.  2 

16.4 

86 

66.8 

54-1 

46 

"3-5 

91.9 

06 

160.  I 

129.6 

66 

206.  7 

167.4 

27 

21.  0 

17.0 

87 

67.6 

54-8 

47 

114.  2 

92.5 

07 

160.  9 

130.3 

67 

207.5 

168.0 

28 

21.8 

17.6 

88 

68.4 

55-4 

48 

115.  0 

93-  I 

08 

161. 6 

130.9 

68 

208.3 

168.7 

29 

22.5 

18.3 

89 

69.  2 

56.  0 

49 

115-8 

93-8 

09 

162.  4 

131-5 

69 

209.  I 

169.3 

30 

23-3 

18.9 

90 

69.9 

56.6 

50 

116.  6 

94-4 

10 
211 

163.2 

132.2 

70 

209.  8 

169.9 

31 

24.1 

19-5 

91 

70.7 

57-3 

151 

"7-3 

95- 0 

164.  0 

132:8^ 

271 

210.6 

170.5 

32 

24.9 

20.  I 

92 

71-5 

57-9 

52 

118.  I 

95-7 

12 

164.8 

133-4 

72 

211. 4 

171.  2 

33 

25.6 

20.8 

93 

72-3 

58-5 

53 

1 18.  9 

96-3 

13 

165-5 

134.0 

73 

212.  2 

171. 8 

34 

26.4 

21.4 

94 

73- 0 

59-2 

54 

119.  7 

96.9 

14 

166.3 

134-7 

74 

212.9 

172.4 

35 

27.  2 

22.0 

95 

73-8 

59.8 

55 

120.  5 

97-5 

15 

167.  I 

135-3 

75 

213-7 

173- I 

36  1 

28.0 

22.  7 

96 

74.6 

60.4 

56 

121.  2 

98.2 

16 

167.9 

135-  9 

76 

214.5 

173-7 

Z7 

28.8 

23- 3 

97 

75-4 

61.0 

57 

122.  0 

98.8 

17 

168.6 

136.6 

77 

215-3 

174.3 

38 

29-5 

23- 9 

98 

76.2 

61.7 

58 

122.8 

99.4 

18 

169.4 

137-2 

78 

216.0 

175.0 

39 

Z"^--, 

24-5 

99 

76.9 

62.3 

59 

123.6 

100.  I 

19 

170.  2 

137-8 

79     216.8 

175.6 

40 

31- I 

25.2 

100 

77-7 

62.9 

60 

124.3 

100.  7 

20 

171. 0 

138.5 

80 

217.6 

176.2 

41 

319 

25.8^ 

lOI 

78.5 

63.6 

161 

125.  I 

107.3" 

221 

171.  7 

139-1 

281" 

218.4 

176.8 

42 

32.6 

26.4 

02 

79-3 

64.  2 

62 

125.9 

101.9 

22 

172-5 

139.7 

82 

219.2 

177-5 

43 

33-4 

27.1 

03 

80.0 

64.8 

P 

126.  7 

102.  6 

23 

173-3 

140.3 

^3 

219.9 

178. 1 

44 

34-2 

27.7 

04 

80.8 

65-4 

64 

127-5 

103.  2 

24 

174.  I 

141. 0 

84 

220.  7 

178.7 

45 

35- 0. 

28.3 

05 

81.6 

66.1 

65 

128.2 

103.8 

25 

174.9 

141.  6 

85  1  221.  5 

179.4 

46 

35-7 

28.9 

06 

82.4 

66.7 

66 

129.0 

104.5 

26 

175-6 

142.  2 

86     222. 3 

180.0 

47 

36.5 

29.  6 

°7 

83.2 

67-3 

67 

129.8 

105.  I 

27 

176.4 

142.9 

87  I  223.0 

180.6 

48: 

37-3  ; 

30.2 

08 

83-9 

68.0 

68 

130.  6 

105.7 

28 

177.2 

143-5 

88  '  223.8 

181. 2 

49 

38.1  ! 

30.8 

09 

84.7 

68.6 

69 

131-3 

106.  4 

29 

17S.0 

144.  I 

89     224. 6 

181. 9 

50 

38-9 

31- 5 

10 

85.5 

69.2 

70 

132-1 

107.  0 

30 

178.7 

144.7 

145.4 

90     225. 4 

182.5 

51 

39. 6     32.  I 

III 

86.3 

69.9 

171 

132.9" 

107.  6 

231 

179-5 

291      226.  I 

183.  I 

52 

40.  4     32.  7 

12 

87.0 

70.5 

72 

133-7 

108.2 

32 

180.3 

146.  0 

92     226. 9 

183.8 

53 

41-2     33-4 

13 

87.8 

71.  I 

73 

134-4 

108.9 

i?, 

181.  I 

146.6 

93 

227.7 

184.4 

54 

42.  0     34.  0 

14 

88.6 

71-7 

74 

135-2 

109.5 

34 

i8i.  9 

147.3 

94 

228.5 

185.0 

55 

42.  7     34.  6 

15 

89.4 

72.4 

75 

136.0 

no.  I 

35 

182.6 

147.9 

95 

229.3 

185.6 

56 

43-  5     35-  2 

16 

90.  I 

73- 0 

76 

136.8 

no.  8 

36 

183.4 

148.5 

96  ;  230. 0 

186.3 

57 

44-  3     35-  9 

17 

90.9 

73-6 

77 

137.6 

III.  4 

37 

184.2 

149.  I 

97  i  230.  8 

186.9 

5^  I 

45.1 

36.5 

18 

91.7 

74-3 

78 

138-3 

112. 0 

38 

185.0 

149.8 

98     231.6 

187.  5 

P 

45-9 

37-1 

19 

92.5 

74-9 

79 

139- I 

112.  6 

39 

185.7 

150.4 

99 

232.4 

1S8.  2 

60 

1 

46.  6     37.  8  1 

20 

93-3 

75-5 

80  , 

139-9 

"3-3 

40 

186.5 

151. 0 

300 

233-1 

188.8 

Dist. 

Dep. 

Lat.    1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  51  Deg 

rees. 

Pag 

•e  254] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  40  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

46.7 

39-2 

121 

92.7 

77.8 

181 

138-  7 

116.3 

241 

184.6 

154-9 

2 

1-5 

1-3 

62 

47-5 

39-9 

22 

93-5 

78.4 

82 

139-4 

117.  0 

42 

185.4 

155-6 

3 

2.3 

1.9 

^3 

48.3 

40-5 

23 

94.2 

79.1 

83 

1 40.  2  I   "7-6 

43 

186.1 

156.2 

4 

3-1 

2.6 

64 

49.0 

41.  I 

24 

95-0 

79-7 

84 

14^.0 

118.3 

44 

186.9 

156.8 

S 

S.8 

3-2 

65 

49-8 

41.8 

25 

95-8 

80.3 

85 

141.  7 

118.9 

45 

187.7 

157-5 

6 

4.6 

3-9 

66 

50.6 

42.4 

26 

96.5 

81.0 

86 

142.5 

119.  6 

46 

188.4 

158.  I 

7 

5-4 

4-5 

67 

51-3 

43-1 

27 

97-3 

81.6 

87 

143-3 

120.  2 

47 

189.2 

158.8 

8 

6.1 

5-1 

68 

52-1 

43-7 

28 

98.  I 

82.3 

88 

144.0 

120.8 

48 

190.0 

159-4 

9 

6.9 

5-8 

69 

52-9 

44.4 

29 

98.8 

82.9 

.89 

144.8 

121.  5 

49 

190.7 

160. 1 

lO 

7-7 

6.4 
7-1 

-   70 

53-6 

45- 0 

30 

99.6 

83-6 

90 

145-5 

122.  I 

50 

191-5 

160.  7 

II 

8.4 

71 

54-4 

45-6 

131 

100.4 

84.2 

191 

146.3 

122.8 

251 

192.3 

161.3 

12 

9.2 

7-7 

72 

55-2 

46-3 

32 

lOI.  I 

84.8 

92 

147.  I 

123.4 

52 

193.0 

162.0 

1.3 

10. 0 

8.4 

73 

55-9 

46.9 

33 

lOI.  9 

85-5 

93 

147.8 

124.  1 

53 

193.8 

162.6 

14 

10.7 

9.0 

74 

.50.7 

47.6 

34 

102.  6 

86.  I 

94 

148.6  1  124.  7 

54 

194.6 

163-3 

IS 

"•5 

9.b 

75 

57-5 

48.  :i 

35 

103.4 

86.8 

95 

149.4 

125-3 

55 

195-3 

163.9 

i6 

12.3 

10.3 

76 

58.2 

48.9 

36 

104.  2 

87.4 

96 

150.  I 

126.  0 

56 

196.  I 

164.6 

17 

13.0 

10.  9 

77 

59-0 

49-5 

37 

104.9 

88.  I 

97 

150.  9      126.  6 

57 

196.9 

165.  2 

i8 

13.8 

II. 6 

78 

59-8 

50.1 

38 

105-7 

88.7 

98 

151-7 

127-3 

58 

197.6 

165.8 

19 

14.6 

12.2 

79 

60.  5 

50.8 

39 

106.  5 

89-3 

99 

152.4 

127-9 

59 

198.4 

166.5 

20 

15-3 

12.9 

80 

61.3 

51-4 

40 

107.  2 

90.  0 

200 

153-2 
154.0 

128.6 
129.  2 

60 

199.2 

167.  I 

21 

16. 1 

13-5 

81 

62.0 

52.1 

141 

108.0 

90.6 

201 

261 

199.9 

167.8 

22 

16.9 

14.  I 

82 

62.8 

52-7 

42 

108.8 

91-3 

02 

154.7  '   129.8 

62 

200.  7 

168.  4 

23 

17.6 

14.8 

83 

63.6 

53-4 

43 

109.5 

91.9 

03 

155-5  :  130-5 

63 

201.  5 

169. 1 

24 

18.4 

15-4 

84 

64-3 

54- 0 

44 

1 10.  3 

92.6 

04 

i5b-3  ,  131-1 

64 

202.  2 

169.7 

25 

19.  2 

16.  I 

85 

6s.  I 

54-6 

45 

III.  I 

93-2 

05 

157.0  1  131.  8 

65 

203.0 

170-3 

26 

19.9 

16.7 

86 

65-9 

55-3 

46 

III. 8 

93-8 

06 

157.8  !  132.4 

66 

203.8 

171. 0 

27 

20.  7 

17.4 

«7 

66.6 

55-9 

47 

112.6 

94-5 

07 

158.6  1  133. 1 

67 

204.5 

171.6 

2b 

21.4 

18.  0 

88 

67.4 

56.6 

48 

113-4 

95-1 

08 

159-3  :  133-7 

68 

205-3 

172.3 

29 

22.  2 

18.6 

89 

68.2 

57-2 

49 

114.  I 

95-8 

09 

160.  I  ,  134.3 

69 

206.  1 

172.9 

30 

23.0 

19-3 

90 
91 

68.9 

57-9 

SO 

"4-9 

9b.  4 

10 

160.  9 
167.6 

135-0 

70 

206.  8 

173.6 
174.2 

31 

23-7 

19.9 

■    69.7 

.58.5 

151 

115- 7 

97-1 

211 

135-6 

271 

207.  6 

32 

24-5 

20.  6 

92 

70.5 

59.1 

52 

116.4 

97-7 

12 

162.4  !  136.3 

72 

208.4 

174.8 

33 

25-3 

21.  2 

93 

71.2 

59-8 

53 

117.2 

98.3 

13 

163.2  1  136.9 

73 

209.  1 

175-5 

34 

26.  0 

21.  9 

94 

72.0 

60.  4 

54 

1 18.0 

99.0 

14 

163.9     137.6 

74 

209.  9 

176. 1 

3S 

26.8 

22.  5 

95 

72.8 

61.  I 

55 

118.  7 

99-6 

15 

164.  7     138.  2 

75 

210.  7 

176.8 

36 

27.6 

23.1 

96 

73-5 

61.  7 

5^ 

"9-5 

100.3 

16 

163.5     138.8 

76 

211. 4 

177-4 

37 

28.3 

23.8 

97 

74-3 

62.4 

57 

120.3 

100.9 

17 

166.2  i  139.5 

77 

212.  2 

178. 1 

3« 

29.  I 

24.4 

98 

75-1 

63.0 

58 

121.  0 

loi.  6 

18 

167.  0 

140.  1 

78 

213.0 

178.7 

39 

29.9 

25.1 

99 

75.8 

63.6 

59 

121. 8 

102.  2 

19 

167.8 

140.  8 

79 

213.7 

179-3 

40 

30.6 

25.7 

100 

76.6 

64-3 

60 

122.  6 

102.8 

20 

168.5 
169.3 

141.4 

80 

214.5 
215-3 

180.0 

41 

31-4 

26.  4 

lOI 

77-4 

64.9 

161 

123-3 

103-5 

221 

142.  1 

281 

180.6 

42 

32.2 

27.  0 

02 

78.1 

65.6 

62 

124.  I 

104.  I 

22 

170.  I  i  142.7 

82 

216.0 

181.3 

43 

32-9 

27.6 

0^ 

78.9 

66.2 

63 

124.9 

104.8 

23 

170.8  1  143.3 

83 

216.8 

181.9 

44 

33-7 

28.3 

04 

79-7 

66.8 

64 

125.6 

105.4 

24 

171. 6      144.0 

84 

217.  6 

182.6 

4S 

34-5 

28.9 

05 

80.4 

67-5 

65 

126.4 

106.  I 

25 

172.4  1  144.  6 

85 

218.3 

183.2 

46 

35-2 

29.  6 

06 

81.2 

68.1 

66 

127.  2 

106.  7 

26 

173- I   1  145-3 

86 

219.  I 

1S3.8 

47 

36.0 

30.2 

07 

82.0 

68.8 

67 

127.9 

107-3 

27 

173-9  ;   145-9 

87 

219.9 

184.5 

48 

36.8 

30-9 

08 

82.7 

69.4 

68 

128.7 

108.0 

28 

174-7 

146.  6 

88 

220.  6 

185.  I 

49 

37-5 

31-5 

09 

83-5 

70.  I 

69 

129- 5 

108.  6 

29 

175-4 

147.2 

89 

221.4 

185.8 

50 

=;i 

3«-3 

32.1 

10 

84-3 
85.0 

70.7 

70 

130.2 

109.3 

30 
231 

176.2 

147-8 

90 

222.2 

186.4 

39-1 

32.8 

III 

71-3 

171 

131-0 

109.9 

177.0 

148.5 

291 

222.  9 

187.  I 

52 

39-8 

33-4 

12 

85.8 

72.  0 

72 

131.  8 

no.  6 

32 

177.7  i  149- I 

92 

223.7 

187.7 

■^3 

40.  6 

34-1 

13 

86.6 

72.6 

73 

132.  5 

III.  2 

33 

178.5      149.8 

93 

224.5 

188.3 

S4 

41.4 

34-7 

14 

87-3 

73-3 

74 

133-3 

III. 8 

34 

179-3      150-4 

94 

225.  2 

189.0 

55 

42.  I 

35-4 

15 

88.1 

73-9 

75 

134-1 

112.  5 

35 

i8c.  0      151.  I 

95 

226.0 

189.6 

56 

42.9 

36.0 

16 

88.9 

74.6 

76 

134.8 

113.  I 

36 

180.8      151.  7 

9b 

226.  7 

190.3 

57 

43-7 

36.6 

17 

89.6 

75-2 

77 

1.35- C 

113.8 

37 

181. 6      152.3 

97 

227.5 

190.9 

5« 

44.4 

37-3 

18 

90.4 

75-8 

78 

136.4 

1 14.  4 

38 

182.3      153.0 

98 

228.3 

191.  6 

59 

45-2 

37-9 

19 

91.  2 

76.  s 

79 

137-1 

115.  I 

39 

183.  I 

153-6 

99 

229.0 

192.2 

60 

46.0 

38.6 

20 

91.9 

77-1 

80 

137-9 

"5-7 

40 

183.9 

154-3 

300 

229.8 

192.8 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

. 

[For 

50  Deg 

rees. 

' 

TABLE  2. 

Page  255  1 

» 

Difference  of  Latitude  and  Departure  for  41  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
91-3 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     ! 
181.  9 

Dep. 
158.1 

, 

0.8 

0.7 

61 

46.0 

40.0 

121 

79-4 

181 

136.6 

118.  7 

241 

2 

1-5 

1-3 

62 

46.8 

40.7 

22 

92.  I 

80.0 

82 

137-4 

"9-4 

42 

182.6 

158.8 

3 

2.3 

2.  0 

63 

47-5 

41-3 

'    23 

92.8 

80.7 

83 

138-1 

120.  I 

43 

183.4 

159.4 

4 

3-0 

2.  6 

64 

48.3 

42.0 

24 

93-6 

81.4 

84 

138.9 

120.  7 

44 

184.  I 

160.  I 

5 

3-8 

3-3 

65 

49.1 

42.6 

25 

94-3 

82.0 

85 

139.6 

121. 4 

45 

184.9 

160.  7 

6 

4-5 

3-9 

66 

49.8 

43-3 

26 

95-1 

82.7 

86 

140.4 

122.0 

46 

185-  7 

161. 4 

7 

5-3 

4.6 

67. 

50.6 

44.0 

27 

95-8 

83-3 

87 

141.  I 

122.  7 

47 

186.4 

162.  0 

8 

6.0 

5-2 

68 

51-3 

44.6 

28 

96.6 

84.0 

88 

141. 9 

123-3 

48 

187.2 

162.7 

9 

6.8 

5-9 

69 

5--i 

45-3 

29 

97-4 

84.6 

89 

142.6 

124.  0 

49 

187.9 

163.4 

lO 

7-5 

6.6 

70 

52.8 

45-9 

30 

98.  I 

85-3 

90 

143-4 

124.7 

50 

188.  7  '. 

164.  0 
164-7 

II 

8.3 

7.2 

71 

53-6 

46.  6' 

J3I 

98.9 

85-9 

191 

144.  I 

125-3 

251 

189.4 

12 

9.1 

7-9 

72 

54-3 

47.2 

32 

99.6 

86.6 

92 

144.9 

126.  0 

52 

190.  2 

165-3 

13 

9.8 

8.5 

73 

55-' 

47-9 

100.  4 

87-3 

93 

145-7 

126.6 

53      190. 9 

166.0 

14 

10.  6 

9.2 

74 

55-8 

48.5 

34 

lOI.  I 

87.9 

94 

146.4 

127.3 

54 

191-7 

160.6 

15 

"•3 

9.8 

75 

56.6 

49.2 

35 

loi.  9 

88.6 

95 

147.2 

127.9 

55 

192.5 

167.3 

16 

12.  1 

10.  5 

76 

57-4 

49.9 

36 

102.6 

89.2 

96 

147.9 

128.6 

56 

193-2 

168.0 

17 

12.8 

II. 2 

77 

58.1 

50-5 

37 

103.4 

89.9 

97 

148.7 

129.  2 

57 

194.0 

168.6 

18 

13.6 

II. 8 

78 

58.9 

51.2 

38 

104.  I 

90-5 

98 

149.4 

129.9 

58 

194.7 

169-3 

19 

14-3 

12.5 

79 

59-6 

51.8 

39 

104.9 

91.  2 

99 

150.  2 

130.  6 

59 

195-5  i 

169.9 

20 

15- I 

13- I 

80 

60.  4 

52-5 

_40 

105.7 

91.8, 

200 
201 

150.9 
151- 7 

131-2 

60 

196.  2 

170.6 

21 

'5-f 

13.-8 

81 

61.  I 

53-1 

141 

106.  4 

92-  5 

'  131-9 

261 

197.0 

171.  2 

22 

16.6 

14.4 

82 

61.  9 

53-8 

42 

107.  2 

93-2 

02 

152-5 

132-5 

62 

197-7 

171.9 

23 

17.4 

15- I 

^3 

62.6 

54-5 

43 

107.9 

93-8 

03 

153-2 

133-2 

63 

198.5 

'72-5 

24 

iS.  I 

15-7 

84 

63-4 

55-1 

44 

108.7 

94-5 

04 

154.0 

133-8 

64 

199.2 

173-2 

25 

18.9 

16.4 

85 

64.  2 

55-8 

45 

109.4 

95-1 

05 

154-7 

134-5 

65 

200.  0 

1 73-  9 

26 

19.  6 

17.  I 

86 

64.9 

56-4 

46 

no.  2 

95-8 

06 

155-5 

135- I 

66 

200.  8 

174-5 

27 

20.  4 

17.7 

87 

65-7 

57-1 

47 

no.  9 

96.4 

07 

156.  2 

135-8 

67 

201 .  5 

175-2 

28 

21.  I 

18.4 

88 

66.4 

57-7 

48 

III.  7 

97-  I 

08 

157.0 

136-5 

68 

202.3 

1 75- 8 

29 

21.  9 

19.  0 

89 

67.  2 

58-4 

49 

112.  5 

97-8 

09 

157-  7 

137- I 

69 

203.0 

176.5 

30 
31 

22.6 

19.7 

90 

67.9 

59- 0 

50 

113-2 

98-4 

10 
211 

158-5 

137-8 

70 

203.8 

177-1 

177-8 

23-4 

20.3 

91 

68.7 

59-7 

151 

114.  0 

99.1 

159.2 

138.4 

271 

204.5 

32 

24.  2 

21.0 

92 

69.4 

60.  4 

52 

114.  7 

99-  7 

12 

160.  0 

139-  I 

72 

205-3 

178.4 

33 

24.9 

21.  6 

93 

70.  2 

61. Q 

53 

"5-5 

100.  4 

13 

160.8 

139-7 

73 

206.  0 

179-1 

34 

25-7 

22.  1, 

94 

70.9 

61.7 

54 

116.  2 

lOI.O 

14 

161.  5 

140.4 

74 

206.  8 

179.8 

35 

26.  4 

23-0 

95 

71.7 

62.3 

55 

117.  0 

loi.  7 

15 

162.3 

141.  I 

75 

207.5 

1 80. 4 

36 

27.  2 

23.6 

96 

72.5 

63.0 

56 

117.  7 

102.  3 

16 

163.0 

141.  7 

76 

208.3 

181.  I 

37 

27.9 

24-3 

97 

73-2 

63.6 

57 

118.  5 

103.0 

17 

163.8 

142.4 

77  1  209.  I 

181.  7 

38 

28.7 

24.9 

98 

•74.0 

64-3 

58 

119.  2 

103.7 

18 

164.5 

143.0 

78 

209.  8 

182.  4 

39 

29.4 

25.6 

99 

74-7 

64.9 

59 

120.  0 

104.3 

19 

165-3 

143-7 

79 

210.  6 

183.0 

40 

30.2 

26.  2 

100 

75-5 

65.6 

60 

120.8 

105.  0 

20 

166.  0 

144-3 
145.0 

80 

211.  3 

183-  7 

41 

30-9 

26.  9 

lOI 

76.2 

66.3 

161 

121.  5 

105.  6 

221 

166.8 

^8r 

212.  I 

184.4 

42 

31-7 

27.6 

02 

77.0 

66.9 

62 

122.  3 

106.  3 

22 

167-5 

145.6 

82 

212.8 

185.  0 

43 

32-5 

28.2 

03 

77-7 

67.6 

63 

123.  0 

106.  9 

23 

168.3 

146.3 

83 

213.6 

185-7 

44 

33-2 

28.9 

04 

78.5 

68.2 

64 

123.8 

107.6 

24 

169.  I 

147.0 

84 

214.  3 

186.3 

45 

34- 0 

29-5 

05 

79.2 

68.9 

65 

124.5 

108.2 

25 

169.8 

147.6 

85 

215.  I 

1S7.0 

46 

34-7 

30.2 

06 

80.  0 

69-5 

66 

125-3 

108.  9 

26 

170.  6 

148.3 

86 

215.  8 

187.6 

47 

35-5 

30.8 

07 

80.8 

70.  2 

67 

126.  0 

109.  6 

27 

171-3 

148.9 

87 

216.  6 

188.3 

48 

36.2 

31-5 

08 

81.5 

70.9 

68 

126.8 

1 10.  2 

28 

172.  I 

149.6 

88 

217.4 

188.9 

49 

37- 0 

32.1 

09 

82.3 

7'- 5 

69 

127-5 

110.9 

29 

172.8 

150.  2 

89 

218.  I 

189.  6 

50 
5' 

37-7 

38.5 

32.8 

10 

83.0 

72.  2 

70 

i28^3_ 

ni^S 
112.  2 

30 
231 

173.6 
174-3 

150.9 
151-5 

90 

218.9 

19^  3  _ 

1 90.  9 

33-5 

III 

83.8 

^278^ 

171 

129.  I 

291 

219.  6 

52 

39-2 

34-1 

12 

84-5 

73-5 

72 

129.8 

112.8 

32 

175- I 

152.  2 

92 

220.  4 

1 9 1 .  6 

53 

40.  0 

34-8 

13 

85-3 

74.1 

73 

130.  6 

II3-S 

33 

175-8 

152-9 

93 

221.  I 

192.  2 

54 

40.8 

35-4 

14 

86.0 

74.8 

74 

131- 3 

114.  2 

34 

176.6 

153-5 

94 

221.  9 

192.  9 

55 

41-5 

36.1 

15 

86.8 

75-4 

75 

132-1 

114.  8 

35 

177-4 

154.2 

95 

222.  6 

193-5 

56 

42-3 

36.7 

16 

87.5 

76.1 

76 

132.8 

115-5 

36 

178.  I 

154.8 

96 

223.4 

194.2 

57 

43- 0 

37-4 

17 

88.3 

76.8 

77 

133-6 

116.  I 

37 

178.9 

155-5 

97 

224.  I 

194-8 

58 

43-8 

38.1 

18 

89.  I 

77-4 

78 

'34-3 

116.  8 

38 

179.6 

156.  I 

98 

224.  9 

105-5 

59 

44-5 

38-7 

19 

89.8 

78.1 

79 

135-1 

117.4 

39 

180.  4 

i=;6.  8 

99 

225.7 

1 90.  2 

60 

45-3 

39-4 

20 

90.  6 

78.7 

80 

135-8 

118.  I 

40 

181.  I 

157-5 

300 

226.4 
Dep. 

196.8 
Lat. 
;es. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

[For  49  Degn 

Page  256 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  42  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
89.9 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.7 

0.7 

61 

45-3 

40.8 

121 

81.0 

181 

134-5 

121.  I 

241 

179-1 

161. 3 

2 

1-5 

I 

•3 

62 

46.  I 

41-5 

22 

90.7 

81 

6 

82 

135-  3 

121. 8 

42 

179.8 

161.  9 

"» 
J 

2.2 

2 

0 

63 

46.  8     42.  2 

23 

91.4 

82 

3 

53 

130.0 

122.5 

43 

180.6 

162.6 

4 

3-0 

2 

7 

64 

47.  6  i  42.  8 

24 

92.1 

!3 

0 

84 

136-7 

123-1 

44 

181.3 

163-3 

5 

3-7 

3 

3 

65 

48.  3  1  43-  5 

25 

92.9 

83 

6 

85 

137-5 

123-8 

45 

182.  I 

163-9 

6 

4-5 

4 

0 

66 

49.0 

44.2 

26 

93-6 

84 

3 

86 

138.2 

124-5 

46 

182.8 

164.6 

7 

5-2 

4 

7 

67 

49.8 

44.8 

27 

94.4 

85 

0 

87 

139.0 

125-1 

47 

183.6 

165-3 

8 

5-9 

5 

4 

68 

50-5 

45-5 

28 

95-1 

85 

6 

88 

139-7 

125.8 

48 

184.3 

165.9 

9 

6.7 

6 

0 

69 

51-3 

46.2 

29 

95-9 

86 

■^ 

J 

89 

140.5 

126.  5 

49 

185.0 

166.6 

lO 

7-4 

6 

J_ 

70 

52.0  !  46.8 

30 

96.  6 

87 

0 

7 

90 

141.  2 

127.  I 

50 

185.8 

167-3 

II 

8.2 

7 

4 

71 

"52.8  ^^7.5 

131 

~97^4 

87 

191 

141.  9 

127.8- 

251 

186.5 

168.0 

12 

8.9 

8 

0 

72 

53-  5     48.  2 

32 

98.1 

88 

92 

142.7 

128.5 

52 

^^7-3 

168.  6 

13 

9-7 

8 

7 

73 

54.  2     48.  8 

2>2, 

98.8 

89 

0 

93 

143-  4 

129.  I 

53 

188.0 

169-3 

14 

10.4 

9 

4 

74 

55-  0     49-  5 

34' 

99.6 

89 

7 

94 

144.2 

129.8 

54 

188.8 

170.  0 

15 

II.  I 

10 

0 

75 

55-7 

50.2 

35 

100.3 

90 

3 

95 

144.9 

130-5 

55 

189.5 

170.  6 

10 

II. 9 

10 

7 

76 

56.5 

50-9 

36 

lOI.  I 

91 

0 

96 

145-7 

131.  I 

56 

190.  2 

171-3 

17 

12.6 

II 

4 

77 

57-2     51-5 

37 

loi.  8 

91 

7 

97 

146.4 

131-8 

57 

191.  0 

172.0 

18 

13-4 

12 

0 

78 

58.  0  1  52.  2 

38 

102.  6 

92 

^ 

J 

98 

147-1 

132-5 

58 

191-7 

172.6 

19 

14.  I 

12 

7 

79 

58.  7  1  52.  9 

39 

103-3 

93 

0 

99 

147.9 

133-2 

59 

192.5 

173-3 

20 

14.9 

13 

A 

80 

59-  5  i  53-  5 

40 

104.  0 

93 

7 
3 

200 

148.6 

133-8 

60 

193-2 

174-0 

21 

IS- 6 

14 

I 

81 

60.  2     54.  2 

141 

104.  8 

94 

201 

149.4 

134-5 

26F 

194.0 

174.6 

22 

16.3 

14 

7 

82 

60.  9     54.  9 

42 

105-5 

95 

0 

02 

150.  I 

135-2 

62 

194-7 

175-3 

23 

17.  I 

15 

4 

83 

6i-7  •  55-5 

43 

106.  3 

95 

7 

03 

150.9 

135-8 

63 

195-4 

176.  0 

24 

17.8 

16 

I 

84 

62. 4  1  56.  2 

44 

107.  0 

96 

4 

04 

151.  6 

136-5 

64 

196.  2 

176-7 

25 

18.6 

16 

7 

^5. 

63.2 

56-9 

45 

107.8 

97 

0 

05 

152-3 

137-2 

65 

196.9 

177-3 

26 

19-3 

17 

4 

86 

63-9 

57-5 

46 

108.5 

97 

7 

06 

153-1 

137-8 

66 

197-7 

1 78.  0 

27 

20.  I 

18 

I 

87 

64.7 

58.2 

47 

109.  2 

98 

4 

07 

153-8 

138-5 

67 

198.4 

178.7 

28 

20.8 

18 

7 

88 

65-4 

58.9 

48 

no.  0 

99 

0 

08 

154.6 

139-2 

68 

199.2 

179-3 

29 

21.6 

19 

4 

89 

66.1 

59-6 

49 

no.  7 

99 

7 

09 

155-3 

139-8 

69 

199-9 

180.0 

30 

22.3 

20 

I 

90 

66.9 

60.  2 

50 

III. 5 

100 

lOI 

4_ 
0 

10 

156.  I 

140.5 

70 

200.  6 

180.  7 

i8i.y^ 

31 

23.0 

20 

7 

91 

67.6 

60.  9 

151 

112.  2 

211 

156.8 

141.  2 

271 

201.4 

32 

23.8 

21 

4 

92 

68.4 

61.6 

52 

113.0 

lOI 

7 

12 

157-5 

141-9 

72 

202.  I 

182.0 

2,i 

24-5 

22 

I 

93 

69.  I 

62.  2 

53 

113- 7 

102 

4 

13 

158-3 

142-5 

73 

202.  9 

182. 7 

34 

25-3 

22 

8 

94 

69.  9     62.  9 

54 

1 14.  4 

103 

0 

14 

159.0 

143-2 

74 

203.6 

183-3 

35 

26.  0 

23 

4 

95 

70.  6     63.  6 

55 

115.  2 

103 

7 

15 

159.8 

143-9 

75 

204.4 

184. 0 

3^ 

26.8 

24 

I 

96 

71.3     64.2 

56 

"5-9 

104 

4 

16 

160.  5 

144.5 

76 

205.  I 

184.7 

37 

27-5 

24 

8 

97 

72.  I  1  64.  9 

57 

116.  7 

105 

I 

17 

161. 3 

145.2 

77 

205.9 

185-3 

38 

28.2 

25 

4 

98 

72.8     65.6 

58 

117.4 

105 

7 

18 

162.  0 

145-9 

78 

206.  6 

186.0 

39 

29.  0 

26 

I 

99 

73-6 

66.2 

59 

118.  2 

106 

4 

19 

162.  7 

146-5 

79 

207.3 

186.7 

40 

29.7 

26 
'27 

8 
4 

100 

74-3 

66.9 

60 

118.  9 

107 

I 

20 

_i63-  5_ 

147-  2 

"2^81" 

»i208.  I 

208.  8 

187-4 

41 

30-5 

lOI 

75-1 

67.  6 

161 

119.  6 

107 

T 

221 

164.  2 

147-9 

188.0 

42 

31.2 

28 

I 

02 

75.8     68.3 

62 

120.4 

108 

4 

22 

165.  0 

148.5 

82 

209.  6 

188.7 

43 

32.0 

28. 

8 

03 

76.  5     68.  9 

^J> 

121.  I 

109 

I 

23 

165-7 

149.2 

^3 

210.3 

189-4 

44 

32-7 

29 

4 

04 

77.3     69.6 

64 

121.  9 

109 

7 

24 

166.5 

149-9 

84 

211.  I 

190. 0 

45 

33-4 

30 

I 

05 

78.  0  1  70.  3 

^5 

122.6 

no 

4 

25 

167.  2 

150.  6 

^5 

211. 8 

190.7 

46 

34-2 

30 

8 

06 

78.8     70.9 

66 

123.4 

III 

I 

26 

16S.0 

151. 2 

86 

212.  5 

191-4 

47 

34-9 

31 

4 

07 

79-5     71-6 

67 

124.  I 

III 

7 

27 

168.7 

151-9 

87 

213-3 

192. 0 

48 

35-7 

32 

I 

08 

80.3  !  72.3 

68 

124.8 

112 

4 

28 

169.4 

152.6 

88 

214.0 

192.7 

49 

3^-4 

32. 

8 

09 

81.0 

72.9 

69 

125.6 

"3 

I 

29 

170.2 

153-2 

89 

214.8 

193-4 

50 

37-2 

33 

5 

10 

81.7 

73-6 

70 

126.3 

"3 

8 

30 

170.9 

153-9 
154.6 

90_ 
291 

215-5 

194.0 

51 

37-5 

34 

I 

III 

82.-5^ 

74-3 

171 

127.  I 

114 

4 

231 

171-7 

216.3 

194-7 

52 

38-6 

34 

8 

12 

83.  2     74.  9 

72 

127.8 

"5 

I 

32 

172.4 

155-2 

92 

217.0 

195-4 

53 

39-4 

35 

5 

13 

84.  01  75.  6 

73 

128.6 

"5 

8 

Z2, 

173-2 

155-9 

93 

217-7 

196. 1 

54 

40.  I 

36 

I 

14 

84.  7     76.  3 

74 

129.3 

116 

4 

34 

173-9 

156.6 

94 

218.5 

196.7 

55 

40.9 

36 

8 

15 

85.5      77.0 

75 

130.  I 

117 

I 

35 

174-6 

157-2 

95 

219.  2 

197-4 

56 

41.  6 

37 

5 

16 

86.  2      77.  6 

76 

130.8 

117 

8 

36 

175-4 

157-9 

96 

220.  0 

198. 1 

5? 

42.4 

^l 

I 

H 

86.  9     78.  3 

77 

131-5 

118 

4 

H 

176.  I 

158.6 

H 

220.  7 

198-7 

58 

43-1 

38 

8 

18 

87.  7     79.  0 

78 

132-3 

119 

I 

38 

176.9 

159-3 

98 

221.  5 

199.4 

59 

43-8 

39 

5 

19 

88.  4     79.  6 

79 

133-0 

119 

8 

39 

177-6 

159-9 

99 

222.  2 

200. 1 

60 
Dist. 

44.6 

40.  I 

20 

89.2 

80.3 

80 

133-8 

120.4 

40 

178.4 

160.6 

300 

222.9 

200. 7 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For 

48Deg 

rees. 

TABLE  2. 

[Page  257 

% 

Difiference  of  Latitude  and  Departure  for  43  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.7 

0.7 

61 

44.6 

41.  6 

121 

88.5 

82.5 

181 

132.4 

123.4 

241 

176-3 

164.4 

2 

1-5 

1.4 

62 

45-3 

42.3 

22 

89.2 

83.2 

82 

1    133-  I 

124.  I 

42 

177.0 

165.  0 

3             2.2 

2.  0 

63 

46.  I 

43-0 

23 

90.  0 

83-9 

83 

133-8 

124.8 

43 

^77-7 

165-7 

4 

2.9 

2.7 

64 

46.  8 

43-6 

24 

90.7 

84.6 

84 

134.6 

125-5 

44 

178.5 

166.4 

5 

3-7 

3-4 

^1 

47-5 

44-3 

25 

91.4        85.2 

85 

135-3 

126.  2 

45 

179.2 

167.  I 

6         4.4 

4.1 

66 

48.3 

45- 0 

26 

92.2        85.9 

86 

136.0 

126.  9 

46 

179.9 

167.8 

I        5-' 

4.8 

67 

49.0 

45-7 

27 

92.  9  ,     86.  6 

87 

136.8 

127-5 

47 

180.6 

168.5 

8  '      5-9 

5-5 

68 

49-7 

46.4 

28 

93-  6  ;     87.  3 

88 

137-5 

128.2 

48 

181.  4 

169.  I 

9         6.6 

6.  I 

69 

50-5 

47.1 

29 

94-3 

88.0 

89 

138.2 

I     128.9 

49 

182.  I 

169.8 

10         7-3 

!     6.8 

70 

51.2 

47-7 

30 

95-1 

88.7 

90 

139.0 
139-7 

1     129.6 

50 

182.8 
183-6 

1 70.5 

II          8.0 

7-1" 

71 

519 

48.4 

131 

95-8 

'89.3" 

191 

1     130-3" 

251 

171. 2 

12         8.8 

8.2 

72 

52.7 

49.  I 

32 

96-5 

90.  0 

92 

i  140.4 

130-9 

52 

184-3 

171. 9 

13         9-5 

8.9 

73 

53-4 

49.8 

Z^ 

97-3 

'     90-7 

93 

141.  2 

131-6 

53 

185.0 

172-5 

14       10. 2 

9-5 

74 

54- I 

50-5 

34 

.98.0 

91.4 

94 

141-9 

132-3 

54 

185.8 

173-2 

15        ii-o 

10.  2 

75 

54-9 

i  5I-I 

35 

98  7 

92.  I 

95 

142.6 

133-0 

55 

186.5 

173-9 

16        II.  7 

1  10.  9 

76 

55-6 

SI. 8 

36 

99-5 

92.8 

96 

143-3  '  133-7 

56 

187.2 

174-6 

17        12.4 

II. 6 

77 

56.3 

52-5 

H 

100.  2 

93-4 

97 

144.  I   1  134.  4 

57 

188.0 

175-3 

18        13.2 

12.3 

78 

57- 0 

53-2 

38 

100.  9 

94.  I 

98 

144.8      135.0 

58 

188.7 

176.0 

19        13-9 

13.0 

79 

57.8 

53-9 

39 

loi.  7 

i     94.8 

99 

145-5  !  135-7 

59 

189.4 

176.6 

20        14. 6 

13.6 

80 

58-5 

t  54-6 

40 

102.4       95-5 

200 

146.3  1  136.4 

60 

190.  2 

^77- 2, 

21        15.4 

H-3 

81 

59-2 

55-2 

141 

103.  I 

96.  2 

20  ( 

147.0  !  137.  I 

261 

r9o.~9^ 

178.0 

22        16.  I 

15.0 

82 

60.  0 

55-9 

42 

103.9 

96.8 

02 

147-7     137-8 

62 

191. 6 

178.7 

23        16.8 

15-7 

l^ 

60.  7 

56.6 

43 

104.  6       97.  5 

03 

148.5      138.4 

63 

192.3 

179-4 

24        17.6 

16.4 

84 

61.4 

57-3 

44 

105-3 

98.2 

04 

149.  2      139.  I 

64 

193-1 

180.  0 

25        18.3 

17.0 

85 

62.2 

58.0 

45 

106.  0 

98.9 

05 

149.  9      139.  8 

65 

193-8 

180.7 

26        19.0 

17.7 

86 

62.  9 

58.7 

46 

io5.  8       99.  6 

06 

150.7     140.5 

66 

194-5 

181.4 

27        19.  7 

18.4 

87 

63.6 

59-3 

47 

107.5 

100.3 

07 

131. 4     141.  2 

67 

195-3 

182.  I 

28       20. 5 

19.  I 

88 

64.4 

60.  0 

48 

108.2 

100.  9 

08 

152.  I      141.  9 

68 

196.  0 

182.8 

•29       21. 2 

19.8 

89 

65.1 

60.  7 

49 

109.  0 

loi.  6 

09 

152.9  !  142.5 

69 

196-7 

183-5 

30  21.9 

31  22.  7 

20.  5 

21.  I 

90 

65.8 

61.4 

50 

109.7 

102.3 

10 

153-6  ,  143-2 

70 

197-5 

184.  I 

91 

66.6 

62.  I 

151 

no.  4 

103.0 

211 

154.  3     143.  9 

271 

198.  2 

184.8 

32       23.4 

21.8 

92 

H-^ 

62.  7 

52 

III.  2 

103-7 

12 

155.0     144.6 

72 

198-9 

185-5 

3i       24.  I 

22.5 

93 

68.0 

63-4 

53 

III.  9 

104.3 

13 

155-8     145-3 

72, 

199-7 

186.2 

34       24. 9 

23.  2 

94 

68.7 

64.  I 

54 

112.  6 

105.  0 

14 

156-5 

145.9 

74 

200. 4 

186.9 

35       25.6 

23-9 

95 

69-5 

64.8 

55 

113-4 

105-7 

15 

157-2 

146.  6 

75 

201.  I 

187-5 

36       26. 3 

24.  6 

96 

70.2 

65-5 

56 

114.  I 

106.  4 

16 

158.0 

147-3 

76 

201.  9 

188.2 

37       27.  I 

25.  2 

97  t 

70.9 

66.2 

57 

II  .8 

107.  I 

17 

158-  7 

148.  0 

77 

202.  6 

188.9 

38       27. 8 

25-9 

98  1 

71.7 

66.8 

58 

115.  6 

107.8 

i8 

159-4 

148.7 

78 

203-3 

189.6 

39        28.  5      26.  6  1 

99 

72.4 

67.5 

59 

1 16.  3 

108.4 

19 

160.  2 

149-4 

79 

204.  0 

190.3 

40        29. 3 

27-3 

100 

73-1 
73-9 

68.2 

60 

117.  0 

109.  I 

_20^ 

160.  9 

150.0 

80 

204.  8 

191.  0 

41   i     30.0 

28.0 

lOI 

68.  9 

i6T\ 

117.  7~ 

109.  8 

221 

161.^ 

150.  f 

281 

205-5 

191.  6 

42  '     30-  7 

28.6 

02 

74.6 

69.6 

62  i 

118.  5 

no.  5 

22 

162.4  • 

151-4 

82 

206.  2 

192-3 

43       31-4 

29-3 

03 

75-3 

70.  2 

63 

119.  2 

III.  2 

23    j 

163-  I 

152.  I 

83 

207.0 

193- 0 

44        32-2 

30.0 

04 

76.1 

70.9 

64 

119.9 

III. 8 

24    ' 

163-8 

152.  8 

84 

207-7 

193-7 

45        32-9 

2,°- 7 

05 

76.  S 

71.6 

65 

120.  7 

112.  5 

25 

164.6 

153-4 

85 

208.4 

194-4 

46       33-6 

31-4 

06  1 

77-5 

72-3 

66 

121. 4 

113.  2 

26 

165-3  i 

154.  I 

86 

209.  2 

195.  I 

47       34-4  , 

32.1 

07 

78-3  i 

73- 0 

67 

122.  I 

113-9 

27 

166.  0  i 

154.8 

87 

209.  9 

195-  7 

48        35-1   t 

32-7 

08 

79.0  1 

73-7 

68 

122.9 

114.  6 

28 

166.  7 

155-5 

88 

210.6 

196.4 

49       35-8  ' 

33-4 

09 

79.7  ! 

74-3 

69 

123.6 

"5-3 

29 

167-5 

156.  2 

89 

211. 4 

197-1 

50 

5^1"'" 

36.6 

34-  L 

10 
III 

80.4 
81.2 

75-  0 
75-7 

70 
171 

I24.3_ 

Li5_9_ 

30 

168.2 

156-9 

90^ 

212.  I 

197-8 

'  37-  3 

34-8 

125.  I      116.  6 

231 

16S.9     157.5 

291 

I2T278" 

19S-5 

52       38-  0 . 

35-5 

12 

81.9 

76.4 

72  ; 

125.  S      1 1 7.  3 

32 

169.  7     158.  2 

92 

213.6 

199-  I 

53       38. 8 

36., 

'3 

82.6 

77.1 

72, 

126.  5 

118.  0 

Z?,  1 

170.4     1 58.  9 

93 

214-3 

199.8 

54       39-  5 

36.8 

14 

83-4  ; 

77-7 

74 

127.3 

118.  7 

34  1 

171- I 

159.6 

94  1 

215.  0 

200.  5 

55       40-  2 

37-5 

15 

84. 1  j 

78.4 

75  i 

128.0 

1 19- 3 

35 

171-9 

160.3 

95 

215-7 

201.  2 

56       41. 0 

38.2 

16 

84.8 

79.1 

76  1 

128.7 

120.  0 

36  ' 

172.6 

161.  0 

96 

216.  5 

201.9 

57  i    41-7  1 

38-9 

17 

85.6  ; 

79.8 

77 

129.4      120.71 

37 

173-3 

161. 6 

97 

217-2  i 

202.  6 

58  1    42.4 

39-6 

18  { 

86.3  i 

80.5 

78, 

130.2      121.  4  1 

38 

174. 1 

162.3 

98 

217.9 

203.2 

59  :     43-  I 

40.  2 

19 

87.0 

81.2 

79 

130.9 

122.  I 

39 

174.8 

163.0 

99 

218.7  : 

203-9 

60       43.9  j 

40.9 

20 

87.8  i 

81.8 

80 

131-6  : 

Dep. 

122.8 

40 

175-5 

163-7 

300 

219.4 

204.  6 

Dist.       Dep. 

Lat. 

Dist.  j 

Dep.     '     Lat.    1 

Dist. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

f  T? 

...    T^ 

1 

[For  47  Degrees. 


17   B 


Pag 

•e  258] 

TABLE  2. 

Difference  of 

Latitude  and  Departure  for  44  Degrees. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

1 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.7 

0.7 

61 

43-9 

42.4 

121 

87.0 

84.  I 

181 

130.2 

125.7 

241 

173.4 

167.4 

2 

1.4 

1.4 

62 

44.6 

43-1 

22 

87.8 

84.7 

82 

130.9 

126.4 

42 

174.  I 

168.  I 

3 

2.2 

2.  1 

63 

45-3 

43-8 

23 

88.5 

85.4 

83 

131. 6 

127.  I 

43 

174.8 

168.8 

4 

2.9 

2.8 

64 

46.0 

44-5 

24 

89.2 

86.1 

84 

132.4 

127.8 

44 

175.5 

169.5 

5 

3-6 

3-5 

65 

46.8 

45-2 

25 

89.9 

86.8 

85 

133.  I 

128.5 

45 

176.  2 

170.  2 

6 

4-3 

4.2 

66 

47-5 

45-8 

26 

90.6 

87.5 

86 

133.8 

129.  2 

46 

177.0 

170.9 

7 

5.0 

4.9 

67 

48.2 

46.5 

27 

91.4 

88.2 

87 

134.5 

129.9 

47 

177.7 

171. 6 

8 

5-8 

5.6 

68 

48.9 

47.2 

28 

92.1 

88.9 

88 

135.2 

130.6 

48 

178.4 

172.3 

9 

6.5 

f-3 

69 

49.6 

47-9 

29 

92.8 

89.6 

89 

136.0 

131-3 

49 

179.  I 

173.0 

lO 

7.2 

6.9 

70 

50.4 

48.6 

30 

93-5 
94.2 

90.3 

90 

136.7 
137.4 

132.0 
132^7 

50 
251 

179.8 
180.6 

J  73^7 

174.4 

II 

7.9 

7.6 

71 

5^-' 

49-3 

131 

91.0 

191 

12 

8.6 

8.3 

72 

51.8 

50.0 

32 

95- 0 

91.7 

92 

138.  I 

133.4 

52 

181.  3 

175.1 

13 

9-4 

9.0 

73 

52.5 

50.7 

33 

95-7 

92.4 

93 

138.  8 

134.  I 

53 

182.0 

175-7 

14 

10.  I 

9-7 

74 

53-2 

51-4 

34 

96.4 

93.1 

94 

139-6 

134.8 

54 

182.7 

176.4 

15 

10.8 

10.4 

75 

54.0 

5^-  • 

35 

97.1 

93-8 

95 

140.3 

135-5 

55 

183.4 

177- I 

16 

II. 5 

II.  I 

76 

54-7 

52.8 

36 

97.8 

94-5 

96 

141. 0 

136.2 

56 

184.2 

177.8 

17 

12.  2 

II. 8 

77 

55-4 

53-5 

37 

98.5 

95.2 

97 

141.  7 

136.8 

57 

184.9 

178.5 

18 

12.9 

12.5 

78 

56.1 

54-2 

38 

99-3 

95-9 

98 

142.4 

137.5 

58 

.85.6 

179.2 

19 

13-7 

13.2 

79 

56.8 

54-9 

39 

100.  0 

96.6 

99 

143.  I 

138.2 

59 

186.3 

179.9 

20 

14.4 

13-9 

80 

57-5 

55-6 

40 

100.  7 

97-3 
97-9 

200 
201 

J43.,9_ 
144.6 

138.9 

60 

187.0 

180.6 

21 

15- 1 

14.6 

81 

58.3 

56.3" 

141 

101.4 

139.6 

261 

187.7 

181. 3 

22 

15-8 

15-3 

82 

59- 0 

57- 0 

42 

102.  I 

98.6 

02 

145.3 

140.3 

62 

188.5 

182.0 

23 

16.5 

16.0 

83 

59-7 

57-7 

43 

102.9 

99-3 

03 

146.0 

141. 0 

63 

189.2 

182.7 

24 

17-3 

16.7 

84 

60.4 

58-4 

44 

103.6 

100.  0 

04 

146.7 

141.7 

64 

189.9 

183.4 

25 

18.0 

17.4 

85 

61. 1 

59-0 

45 

104.3 

100.  7 

05 

147.5 

142.4 

65 

190.6 

184.  I 

26 

18.7 

18.  I 

86 

61.9 

59-7 

46 

105.0 

101.4 

Ob 

148.2 

143. 1 

66 

191. 3 

184.8 

27 

19.4 

18.8 

87 

62.6 

60. 4 

47 

105- 7 

102.  I 

07 

148.9 

143.8 

67 

192.  I 

185.5 

28 

20.  I 

19-5 

88 

63.3 

61.  I 

48 

106.  5 

102.8 

08 

149.6 

144.5 

68 

192.8 

186.2 

29 

20. 9 

20.  I 

89 

64.  0 

61.8 

49 

107.  2 

103-5 

09 

150.3 

145.2 

69 

193.5 

186.9 

30 

21.6 

20.8 

90 

64.7 

62.  5 

50 

107.9 

104.2 
104.9" 

10 

151.  I 
151. 8 

I45i9_ 
146.  6 

70 

194.2 

187.6 

31 

22.3 

21.5 

91 

65.5" 

63.2 

151 

108.6 

211 

271 

194.9 

188.  3"" 

32 

23.0 

22.  2 

92 

66.2 

63.9 

52 

109.3 

105.6 

12 

152.5 

147.3 

72 

195.7 

188.9 

33 

23-7 

22.9 

93 

66.9 

64.6 

53 

no.  I 

106.3 

13 

153.2 

148.0 

73 

196.4 

189.6 

34 

24.5 

23.6 

94 

67.6 

65-3 

54 

no.  8 

107.0 

14 

153.9 

148.7 

74 

197.1 

190.3 

35 

2;.  2 

24.3 

95 

68.3 

66.0 

55 

III. 5 

107.7 

15 

154.7 

149.4 

75 

197.8 

191. 0 

36 

25.9 

25.0 

96 

69.  I 

66.7 

56 

112.  2 

108.4 

16 

155.4 

150.0 

76 

198.5 

191.7 

37 

26.6 

25-7 

97 

69.8 

67.4 

57 

112. 9 

109.  I 

17 

156.  I 

150.7 

77 

199.3 

192.4 

38 

27-3 

26.  4 

98 

70-5 

68.1 

58 

113-7 

109.8 

iS 

156.8 

151. 4 

78 

200.0 

193- I 

39 

28.1 

27.1 

99 

71.2 

68.8 

59 

1 14. 4 

no.  5 

19 

157.5 

152.  I 

79 

200.  7 

193.8 

40 
41 

28.8 
29-5 

27.8 

100 

71.9 

_^9iL 

60 

115.1 

III.  I 

20 

158.3 
159.0 

152.8 

80 

201.4 

194.5 

28.-5 

lOI 

72.7 

70.  2 

161 

115. 8 

III. 8 

221 

153.5 

281 

202.  I 

195.2 

42 

30.  2 

29.2 

02 

73-4 

70.9 

62 

116.  5 

112.  5 

22 

159.7 

154-2 

82 

202.9    i    195.9      1 

43 

30-9 

29.9 

03 

74.1 

71-5 

63 

117.3 

113.  2 

23 

160.4 

154.9 

P 

203.6 

190.6 

4 

31-7 

30.6 

04 

74.8 

72.2 

64 

118.0 

113.9 

24 

161.  I 

155-6 

84 

204.3 

197.3 

45 

32.4 

31-3 

05 

75-5 

72.9 

65 

118.  7 

114.  6 

25 

161. 9 

156-3 

^5 

205.0 

198.0 

46 

33-1 

32.0 

06 

76.3 

73-6 

66 

119. 4 

115.3 

26 

162.6 

157.0 

86 

205.7 

198.7 

47 

33.8 

32.6 

07 

77.0 

74-3 

67 

120.  I 

116.  0 

27 

163.3 

157.7 

^7 

206.  5 

199.4 

48 

34.5 

33-3 

08 

77-7 

75- 0 

68 

120.8 

116.  7 

28 

164.0 

158.4 

88 

207.2 

200.  I 

49 

35-2 

34-0 

09 

78.4 

75-7 

69 

121. 6 

117.4 

29 

164.7 

159.  I 

89 

207.  9 

200.8 

50 

36.0 

34-7 

10 

79.1 

76.4 

70 

122.3 

118.  I 

30 

165.4 
166.2 

159.8 

90 

208.6 

201.  5 

51 

36.7 

35-4 

III 

79.8 

77-1 

171 

123.0 

118.8 

231 

160.  5 

291 

209.3 

202.  I 

52 

37-4 

36.1 

12 

80.6  1  77.8 

72 

123.7 

119.  5 

32 

166.9 

161.  2 

92 

210.0 

202.8 

53 

38.1 

36.8 

13 

81.3  :  78.5 

73 

124.4 

120.2 

33 

167.6 

161. 9 

93 

210.8 

203.5 

54 

38.8 

37-5 

14 

82. 0     79.  2 

74 

125.2 

120.9 

34 

168.3 

162.6 

94 

211.  5 

204.2 

55 

39-6 

38.2 

15 

82.  7  i   79-  9 

75 

125.9 

121. 6 

35 

169.0 

163.2 

95 

212.2 

204.9 

56 

40.3 

38.9 

16 

83. 4  1  80.  6 

76 

126.  6 

122.3 

36 

169.8 

163.9 

96 

212.9 

205.6 

57 

41.  0 

39-6 

17 

84.2     81.3 

77 

127.3 

123.0 

37 

170.5 

164.  6 

97 

213.6 

206.3 

58 

41.7 

40.3 

18 

84.  9     82.  0 

78 

128.0 

123.6 

38 

171. 2 

165.3 

98 

214.4 

207.0 

59 

42.4 

41.0 

19 

85.6 

82.7 

79 

128.8 

124.3 

39 

171. 9 

166.0 

99 

215.  I 

207.7 

60 

43-2 

41.7 

20 

86.3 

83.4 

80 

129.5 

125.0 

40 

172.6 

166.7 

300 

215.8 

208.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

i 

[Foi 

"  46  Degrees.        1 

TABLE  2. 

Page  269  | 

% 

Difference  of  Latitude  and  Departure  for  45  Degre 

es. 

Dist. 
I 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

128.0 

Dep. 

Dist. 

Lat. 

Dep. 

0.  7        0.  7 

61 

43-1 

43-1 

121 

85.6 

85.6 

181 

128.0 

241 

170.4 

170.4 

2 

1.4        1.4 

62 

43-8 

43-8 

22 

86.3 

86.3 

82 

1 28.  7 

128.7 

42 

171.  I 

171.  I 

3 

2.  I 

2.  I 

63 

44-5 

44-5 

23 

87.0 

87.0 

f^ 

129.4 

129.4 

43 

171. 8 

171.8 

4 

2.8    '      2.8 

64 

45-3 

45-3 

24 

87.7 

87.7 

84 

130.1 

130.  I 

44 

172.5 

172.5 

5 

3-5  j    3-5 

65 

46.0 

46.  0 

25 

88.4 

88.4 

85 

130.8 

130.8 

45 

'73.2 

173-2 

6 

4. 2  1    4.2 

66 

46.7 

46.7 

26 

89.1 

89.1 

86 

131. 5 

131-5 

46 

173.9 

173-9 

7 

4. 9       4. 9 

67 

47-4 

47-4 

27 

89.8 

89.8 

87 

132.2 

132.2 

47 

174.7 

174-7 

8 

5-7  !     5-7 

68 

48.  I 

48.  I 

28 

:  90.5 

90.5 

88 

132.9 

132.9 

48 

175-4 

175-4 

9 

6.4 

6.4 

69 

48.8 

48.  8 

29 

91. 2 

91.2 

89 

133-6 

133-6 

49 

176.  I 

176,  1 

lO 

7-1 

7-1 

70 

_49-S 

49-5 

30 

91.9 

91.9 

90 

134-4 

134.4 

50 

176.8 

176.8 

II 

7.  8  1     7.  8 

71 

50.  2 

50.2 

131 

92.  6 

92.6 

191 

135- I 

135- I 

251 

177.5 

177-5 

12 

8.5  ,     8.5 

72 

50.9 

50.9 

32 

93-3 

93.3 

92 

135-8 

135-8 

52 

178.2 

178.2 

13 

9.2  1    9.2 

73 

51.6 

51.6 

33 

94.0 

94.0 

93 

136.5 

136.5 

53 

178.9 

178.9 

14 

9.9       9.9 

74 

52.3 

52.3 

34 

94.8 

94.8 

94 

137-2 

137.2 

54 

179.6 

179.6 

15 

10.6      10. 6 

75 

53- 0 

53- 0 

55 

95-5 

95-5 

95 

137.9 

137.9 

55 

180.3 

180.3 

16 

II. 3      II. 3 

76 

53-7 

53-7 

36 

96.  2 

96.2 

96 

138.6 

138.6 

56 

181. 0 

181. 0 

17 

12.  0 

12.0 

77 

54-4 

54-4 

37 

96.9 

96.9 

97 

139-3 

139.3 

57 

181.  7 

181.  7 

iS 

12.7 

12.7 

78 

55-2 

55-2 

38 

97.6 

97.6 

98 

140.0 

140.0 

58 

182.4 

182.  4 

19 

13-4 

13-4 

79 

55-9 

55-9 

39 

98.3 

98.3 

99 

140.7 

140.7 

59 

183.  I 

183.1 

20 
21 

14.  I 

14.  I 

80 

56.6 

56.6 

40 

99.0 

99.0 

200 

141-4 
142.  I 

141. 4 

60 

183.8 

183.8 

14.8      14.8 

81 

57-3 

57.3 

141 

99-7 

99-7 

201 

142.  I 

261 

184.6 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185.3 

185.3 

23 

16.3 

16.3 

l^ 

58.7 

58.7 

43 

lOI.  I 

lOI.  I 

03 

143-5 

H3-5 

63 

186.0 

186.0 

24 

17.0 

17.0 

84 

59-4 

59-4 

44 

101.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186.7 

25 

17.7      17-7 

85 

60.  I 

60.  I 

45 

102.  5 

102.  5 

05 

145.0 

145.0 

65 

187.4 

187.4 

26 

18.4      18.4 

86 

60.8 

60.8 

46 

103.2 

103.  2 

06 

145.7 

145.  7 

66 

188.  I 

188.  I 

27 

19.  I      19.  I 

87 

61.5 

61.5 

47 

103.9 

103.9 

07 

146.4 

146.4 

67 

188.8 

188.8 

28 

19.8  ,  19.8 

88 

62.  2  j  62.  2 

48 

104.7 

104.7 

08 

147.  I 

147.  I 

68 

189.5 

189.5 

29 

20.  5     20.  5 

89 

62.9 

62.9 

49 

105.4 

105.4 

09 

147.8 

147.8 

69 

190.  2 

190.  2 

30 
31 

21.2     21. 2 

90 

63.6 

63.6 

50 

106. 1 

106.  I 

10 

148.5 

148.5 

70 

190.9 

190.9 

21.9     21.9 

91 

64.3 

64-3 

151 

lo6.8^ 

106.8 

211 

149.2 

149.2 

271 

191.6 

191. 6 

32 

22.6     22.6 

92 

65.1 

65.1 

52 

107.5 

107.5 

12 

149.9 

149.9 

72 

192.3 

192.3 

33 

23-3     23.3 

93 

^A-^ 

65.8 

53 

108.2 

108.2 

13 

150.6 

150.  6 

73 

193.0 

193.0 

34 

24.  0     24.  0 

94 

66.5 

66.5 

54 

108.9 

108.9 

14 

151.3 

151- 3 

74 

193-7 

193-7 

35 

24  7     24.  7 

95 

67.2 

67.2 

55 

109.  6 

109.  6 

15 

152.0 

152.0 

75 

194-5 

194.5 

36 

25-  5     25.  5 

96 

67.9 

67.9 

56 

no.  3 

no.  3 

16 

152.7 

152.7 

76 

195-2 

195.2 

37 

2^.  2     26.  2 

97 

68.6 

68.6 

57 

III.O 

in.  0 

17 

153.4 

153.4 

77 

195-9 

195.9 

38 

26.  9     26.  9 

98 

69-3  '  69-3 

58 

III. 7 

III. 7 

18 

154.  I 

154.  I 

78 

196.6 

196.6 

39 

27.6     27.6 

99 

70.  01  70.  0 

59 

112. 4 

112. 4 

19 

154.9 

154.9 

79 

197-3 

197-3 

_4o  , 

28.3     28.3 

100 

70.7 

70.7 

60 

113.  I 

113.1 

20 

155-6 

155.6 

80 

198.0 

198.0 

4r 

29.0     29.0 

lOI 

71.4 

71.4 

161 

113.  8 

113.8 

221 

156.3 

156.3 

'281 

198.7 

198.  7  ~ 

42 

29.  7     29.  7 

02 

"^^•l 

72.1 

62 

114.  6 

114.6 

22 

157.0 

157.0 

82 

199.4 

199.4 

-^^ 

30-  4      30-  4 

03 

72.8 

72.8 

63 

"5-3 

115.3 

23 

157.7 

157.7 

S3 

200.  I 

200.  I 

44 

31- I      31- I 

04 

73-5 

73-5 

64 

116.  0 

116.  0 

24 

158.4 

158.4 

84 

200.  8 

200.8 

45 

31.8     31.8 

05 

74.2 

74.2 

65 

116.  7 

116.  7 

25 

159.  I 

159.1 

85 

201.5 

201.  5 

46 

32.  5     32.  5 

06 

75.0     75.0 

66 

117.4 

117.4 

26 

159-8 

159.8 

86 

202.  2 

202.  2 

47 

33-2     33-2 

07 

75-  7  i  75-  7 

67 

118.  I 

118.1 

27 

160.5 

160.  5 

87 

202.9 

202.  9 

48 

33-  9     33-  9 

08 

76.4  '■  76.4 

68 

1 18.  8 

1 18.  8 

28 

161.  2 

161.  2 

88 

203.6 

203.6 

49 

34.  6     34.  6 

09 

77.1  I  77.1 

69 

119.5 

"9.5 

29 

161. 9 

161.9 

89 

204.4 

204.4 

50 

35-4     35-4 

10 

77.8  i  77.8 

70 

120.2 

120.  2 

30 

162.6 

162.6 

90 

205.  I 

205.  I 

51 

36.  I      36.  I 

I  n    ' 

78.5      78.5 

171 

120.  9 

120.  9 

231 

163.  3 

163.3 

291 

"20578" 

205.8  " 

52  , 

36.  8     36.  8 

12 

79-'2      79.2 

72 

121. 6 

121.  6 

32 

164.0 

164.  0 

92 

206.  5 

206.  5 

53 

37-  5     37-  5 

13 

79-  9      79-  9 

73 

122.3 

122.3 

33 

164.8 

164.8 

93 

207.  2 

207.2 

54 

38.2     38. 2 

14 

80.  6     80.  6 

74 

123.0 

123.0 

34 

165.5 

165.5 

94 

207.9 

207.9 

55 

38.9     38.9 

1=; 

81.3     81.3 

75 

123.7 

123.7 

35 

166.2 

166.2 

95 

208.6 

208.6 

56 

39.  6     39.  6 

16 

82.0     82.0 

76 

124.5 

124.5 

36 

166.9 

166.9 

96 

209.3 

209.3 

5Z 

40.3     40.3 

17 

82.  7     82.  7 

77 

125.2 

125.2 

37 

167.6 

167.6 

97 

210.0 

210. 0 

58 

41.0     41.0 

18 

83-4     83.4 

78 

125.9 

125.9 

38 

168.3 

168.3 

98 

210.  7 

210.  7 

59 

41.7     41.7 

19 

84. 1  :  84. 1 

79 

126.6 

126.6 

39 

169.0 

169.  0 

99 

211. 4 

211.4 

60 

42.  4     42.  4 

20 

84.9   84.9 

80 

127-3 

127-3 

40 
Dist. 

169.7 

169.7 

300 

212.  I 

212.  I 

Dist. 

Dep. 

Lat.^ 

Dist. 

Dep. 

Lat.    1 

Dist. 

Dep. 

Lat. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

[For 

45  Deg 

rees. 

Page  260 

TABLE 

3- 

Meridional  Parts,  or  Increased  Latitudes. 

C 

] 

°i^^P-  299- 

1528 

M. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

1° 

8° 

9° 

10° 

M. 
0 

o 

0.0 

59.6 

1 
119.  2 

178.9 

/ 
238.6 

298.4 

358.3 

f 

418.3 

/ 

478.4 

538.6 

599.1 

I 

I 

0 

60.6 

120.2 

179.9 

239.6 

299.4 

359-3 

419-3 

479.4 

539-7 

600. 1 

I 

2 

2 

0 

61.6 

121.  2 

180.9 

240.6 

300.4 

360.3 

420.3 

480. 4 

540-7 

601. 1 

2 

3 

3 

0 

62.6 

122.  2 

181. 9 

241.6 

301.4 

361.3 

421.3 

481.4 

541.7 

602.  I 

3 

4 

4 

0 

63.6 

123.2 

182.9 
183.9 

242.6 

■302. 4 

362.3 
363-  3 

422.3 

482.4 

542.7 

603.1 
604. 1 

4 
f 

5 

5 

0 

64.6 

124.2 

243.6 

303.4 

423-3 

483-4 

543-7 

6 

6 

0 

65.6 

125.  2 

184.9 

244.6 

304.4 

364-3 

424-3 

484.4 

544-7 

605. 1 

6 

7 

7 

0 

66.6 

126.2 

185.8 

245.6 

305-4 

365.3 

425.3 

485.4 

545-7 

606.  2 

7 

8 

8 

0 

67.6 

127.  2 

186.8 

246.6 

306.  4 

366.3 

426.3 

486.4 

546.7 

607.  2 

8 

9 

10 

8 

9 

68.5 

128.2 

187.8 

247.6 

307.  4 

367-3 
368.3 

427-3 

487-4 

547-  7 
548.7 

608.2 
609.  2 

9 
10 

9 

9 

69-5 

129.2 

188.8 

248.6 

308.4 

428.3 

488.4 

II 

10 

9 

70.5 

130.2 

189.8 

249.6 

309.4 

369.3 

429-3 

489-4 

549-7 

610.  2 

II 

12 

II. 

9 

71-5 

131. 2 

190.8 

250.6 

310.4 

370-3 

430-3 

490.4 

550.7 

611. 2 

12 

13 

12. 

9 

72.5 

132.  2 

191.  8 

251.5 

311.4 

371-3 

431- 3 

491.4 

551-7 

612.  2 

13 

15 

13- 

9 

73-5 
74-5 

133.1 
134.1 

192.8 

252.5 

312.3 

372.3 

432.3 

492-4 
493-4 

552.7 
553-7 

613-2 

14 
15 

14. 

9 

193.  8 

253.5 

313-3 

373.3 

433-3 

614.  2 

lb 

15 

9 

75-5 

135.1 

194.8 

254-5 

314-3 

374.3 

434.3 

494.4 

554.8 

615.2 

10 

17 

16 

9 

76.5 

136.1 

195.8 

255.5 

315.3 

375-3 

435.3 

495.4 

555-8 

616.2 

17 

i8 

17 

9 

77-5 

137.1 

196.8 

256.5 

316.3 

376.3 

436-3 

496.4 

556.8 

617-3 

18 

19 

20 

18 

9 

78.5 

138.1 

197.8 

257.5 

317.3 

377-3 

437.3 

497.4 

557.8 

618.3 

J9- 
20 

19 

9 

79-5 

139.1 

198.8 

258.5 

318.3 

378.3 

438.3 

498.5 

558.8 

619.3 

21 

20 

9 

80.5 

140. 1 

199.8 

259.5 

319.3 

379.2 

439.3 

499.5 

559.8 

620.3 

21 

22 

21 

9 

81.5 

141. 1 

200.8 

260.5 

320.3 

380.2 

440.3 

500.5 

560.8 

621.3 

22 

23 

22 

9 

82.5 

142. 1 

201.8 

261.5 

321.3 

381.2 

441.3 

501.5 

561.8 

622.  3 

23 

24 

2S 

23 

8 

83.5 

143.1 

202.  8 

262. 5 

322.  3 

382.2 

442-3 

502.5 

562.8 

623.3 

24 

25 

24 

8 

84.4 

144.1 

203.8 

263.5 

323-3 

383-2 

443-3 

503-5 

563-8 

624.3 

26 

25 

8 

85.4 

145.1 

204.  8 

264.5 

324.3 

384.2 

444-3 

504-5 

564.8 

625.3 

2b 

27 

26 

8 

86.4 

146. 1 

205.7 

265.5 

325-3 

385-2 

445-3 

505-5 

565.8 

626.3 

27 

28 

27 

8 

87.4 

147.1 

206.  7 

266.  5 

326.3 

386.2 

446-3 

506.5 

566.8 

627.4 

28 

29 

28 

8 

88.4 

148. 1 

207.7 

267.5 

327.3 

387-2 
388.2 

447-3 

507.5 

567.8 

628.4 

29 
30 

30 

29 

8 

89.4 

149. 1 

208.  7 

268.5 

328-  3 

448-3 

508.5 

568.8 

629.4 

31 

30 

8 

90.4 

150.0 

209.7 

269.5 

329.3 

389.2 

449-3 

509.5 

569.9 

630.4 

31 

32 

31 

8 

91.4 

151.0 

210.  7 

270.5 

330.3 

390.2 

450.3 

510.5 

570.9 

631.4 

32 

33 

32 

8 

92.4 

152.0 

211.  7 

271.5 

331.3 

391.2 

451-3 

5II-5 

571.9 

632.4 

33 

34 
35 

33 

8 

93-4 

153-0 

212.  7 

272.5 

332.3 
333.3 

392-2 
393-2 

452-3 
453-3 

512-5 
513-5 

572.9 
573-9 

633-4 

34 
35 

34 

8 

94.4 

154-0 

213.7 

273.5 

634-4 

3b 

35 

8 

95-4 

155.0 

214.7 

274.5 

334-3 

394-2 

454.3 

514-5 

574-9 

Pt"^ 

36 

37 

3^ 

8 

96.4 

156.0 

215.7 

275-5 

335.3 

395-2 

455.3 

515-5 

575-9 

636-5 

37 

3« 

37 

8 

97-4 

157.0 

216.  7 

276.5 

336.3 

396.2 

456-3 

516-5 

576-9 

637-5 

38 

39 

3« 

7 

98.4 

158.0 

217.7 

277.5 

337.3 

397-2 

457-3 
458-3 

517-5 
518-5 

577-9 
578.9 

638.5 
639.5 

39 
40 

40 

39 

7 

99.4 

159.0 

218.  7 

278.4 

338.3 

398.2 

41 

40 

7 

100.3 

i5o.  0 

219.7 

279.4 

339.3 

399-2 

459.3 

519.5 

579.9 

640.5 

41 

42 

41 

7 

101.3 

161. 0 

220.  7 

280.4 

340.3 

400.2 

460.3 

520.6 

580.9 

641.5 

42 

43 

42 

7 

102.3 

162.0 

221.  7 

281.4 

341.3 

401.2 

461.3 

521.6 

581.9 

642.5 

43 

44 

■  43 

7 

103.3 

163.0 

222.  7 

282.4 

342.3 

402.  2 

462.3 

522.6 

583.0 

643.  5  1  44 
644. 5     45 

45 

44 

7 

104.3 

164.  0 

223.7 

283.4 

243.3 

403.2 

463.3 

523.6 

584.0 

46 

45 

7 

105.3 

165.0 

224.7 

284.4 

344-3 

404.2 

464-3 

524.6 

585-0 

645. 6     46 

47 

46 

7 

106.3 

166.0 

225.7 

285.4 

345-3 

405-3 

465-3 

525.6 

586.0 

646.  6  ,  47 

48 

47 

7 

107.3 

167.0 

226.  7 

286.4 

346-3 

406.3 

466.3 

526.6 

587.0 

647.6  1  48 

49 

48 

7 

108.3 

167.9 

227,6 

287.4 

347.3 

407.3 

467-3 

527.6 

588.0 

648.6     49 

50 

49 

7 

109.3 

168.9 

228.6 

288.4 

348.3 

408.3 

468.3 

528.6 

589.0 

649.6 

50 

51 

50 

•7 

110.3 

169.9 

229.6 

289.4 

349.3 

409-3 

469-4 

529.6 

590.0 

650.6 

51 

52 

51 

7 

III. 3 

170.9 

230.6 

290.4 

350.3 

410-3 

470.4 

530-6 

591.0 

651.6 

52 

53 

52 

7 

112.  3 

171.9 

231.6 

291.4 

351.3 

411-3 

471.4 

531.6 

592.0 

652.6 

53 

54 

53 

.b 

113.3 

172.9 

232.6 

292.4 

352.3 

412.3 

472.4 

532.6 

593.0 

653.6 

54 

55 

55 

54 

.6 

114.  3 

173.9 

233.6 

293.4 

353.3 

413.3 

473-4 

533-6 

594.0 

654.7 

56 

55 

.b 

115-3 

174.9 

234.6 

294.4 

354.3 

414.3 

474-4 

534-6 

595-1 

^55-7 

56 

57 

5(' 

.b 

116.  2 

175.9 

235.6 

295-4 

355.3 

415.3 

475-4 

535-6 

596.1 

656.7 

57 

5« 

57 

.b 

117. 2 

176.9 

236.6 

296.4 

356.3 

416.3 

476.4 

536.6 

597.1 

657.7 

58 

59 

58.6 

118.  2 

177.9 

237.6 

297.4 

357.3 

417-3 

477.4 

537.6 

598.1 

658.7 

59     ; 

M. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

M. 

TABLE 

3- 

Page  261 

.* 

Meridional  Parts,  or  Increased  Latitudes. 

M. 

COmp.      3gg.,528 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

M. 
.  0 

o 

1 
659-7 

720.  6 

781.6 

842.9 

/ 
904-5 

966.4 

1028.  6 

1091. 1 

1154.0 

1 
1217.3 

1281.0 

I 

660.  7 

721.  6 

782.6 

844.0 

905.6 

967.4 

29.6 

92. 2 

55-1 

18.4 

82.0 

1 

■-> 

661.7 

722.  6 

783-7 

845.0 

906.  6 

968.  5 

30.7 

93-2 

56.1 

19.4 

83.1 

2 

662.8 

723.6 

784.7 

846.0 

907.6 

969-5 

31-7 

94.3 

57-2 

20.  5 

84.2 

3 

4 

663.8 

724.6 

785.7 

847.0 

908.6 

970.5 

32.8 

95-3 

58.2 

21.5 

85.2 

4 

5 

664.8 

725-6 

786.7 

848.1 

909.7 

971.6 

1033.8 

1096. 4 

1159.3 

1222.6 

1286. 3 

5 

6 

665.8 

726.7 

787.7 

849.1 

910.7 

972.6 

34-8 

97-4 

60.3 

23.6 

87.4 

6 

7 

666.8 

727.7 

788.8 

850.1 

911. 7 

973-6 

35-9 

98.4 

61.4 

24-7 

88.4 

7 

S 

667.8 

728.7 

789.8 

851. 1 

912.8 

974-7 

36.9 

99.5 

62.4 

^^A 

89-5 

8 

_9 

10 

668.8 
669.8 

729.7 

730.7 

790.8 

852.2 

913-8 

975-7 

38.0 

iioo.  5 
iioi.  6 

63-5 
1 164.  5 

26.8 

90.6 

9 

791.8 

853.2 

914.8 

976.7 

1039.  0 

1227.9 

1291.  6 

10 

II 

670.9 

731-7 

792.8 

S54.2 

915.8 

977-8 

40.0 

02.6 

65.6 

28.9 

92.7 

11 

12 

671.9 

732-7 

793-9 

855.2 

916.9 

978.8 

41.  I 

03-7 

66.6 

30.0 

93-8 

12 

I? 

672.9 

733-8 

794-9 

856.3 

917.9 

979.9 

42.1 

04.7 

67.7 

31- 1 

94-8 

13 

14 

673-9 

734.8 

795-9 
796.9 

857.3 

918.9 

980.9 

43-2 

05.8 

68.7 

32.1 

95-9 

14 
15 

15 

674.9 

735-8 

858.3 

920.0 

981.9 

1044.  2 

1106.8 

1169.8 

1233. 2 

1297.0 

I6 

675-9 

736.8 

797-9 

859-3 

921.0 

983.0 

45-2 

07.9 

70.9 

34.2 

98.0 

16 

17 

676.9 

737-8 

799-0 

860.4 

922.  0 

984.0 

46.3 

08.9 

71.9 

35-3 

99-1 

17 

i8 

677-9 

738.9 

800. 0 

861.4 

923.1 

985.0 

47-3 

10.  0 

73- 0 

36-4 

1300.  2 

18 

_'9 

20 

679.0 

739-9 

801.  0 

862.4 
863. 4 

924.1 

986.1 

48.4 

II. 0 

74.0 

37-4 

01.2 

19 

680.  0 

740.9 

802.0 

925-1 

987.1 

1049.4. 

1 1 12.  I 

1175.1 

1238.  5 

1302.  3 

20 

21 

681.0 

741.9 

803.1 

864.5 

926.  I 

988.1 

50.4 

13- I 

76.1 

39.5 

03.4 

21 

22 

682.0 

742.9 

804.  I 

865.5 

•  927.  2 

989.2 

51-5 

14.  I 

77.2 

40.  6 

04.4 

22 

2^ 

683.0 

743-9 

805.1 

866.5 

928.2 

990.2 

52.5 

15.2 

78.2 

41.7 

°^-^ 

23 

24 

684.0 

745-0 

806.1 

867.  5 

929.  2 

991.2 
992-3 

53.6 

16.2 

79-3 

42.7 

06.6 

24 
25 

25 

685.0 

746.0 

807.  I 

868.6 

930-3 

1054.  6 

1117.3 

1180.3 

1243.8 

1307.6 

26 

686.1 

747-0 

808.  2 

869.6 

931-3 

993-3 

55-7 

18.3 

81.4 

44.8 

08.7 

2b 

27 

687.1 

748.0 

809.2 

870.6 

932.3 

994-4 

56-7 

19.4 

82.4 

45-9 

09.8 

27 

28 

688.1 

749-0 

810.2 

871  6 

933-4 

995-4 

57-7 

20.4 

83-5 

47.0 

10.8 

28 

29 

689.1 

750.0 

811. 2 

872.7 
873:7" 

934.4 

996.4 

58.8 

21.5 

84.6 

48.0 

11.9 

29 
30 

30 

690.  I 

751.  I 

812.2 

935-  4 

997.5 

1059. 8 

"22.  5 

1185.6 

1249.  1 

1313.0 

31 

691.  I 

752.1 

813-3 

874-7 

936.5 

998.5 

60.9 

23.6 

86.7 

50.1 

14.0 

31 

32 

692.  I 

753-1 

814-3 

875.7 

937-5 

999.5 

61.9 

24.  6 

87.7 

51-2 

'!•' 

32 

3j 

693.2 

754-1 

815-3 

876.8 

938-5 

1000.6 

62.9 

25.7 

88.8 

52-3 

16.2 

33 

34 

694.2 

755-1 

816.3 

877.8 

939-6 

01.  6 

64.0 
1065.0 

26.7 

89.8 

53-3 

17.3 

34 

35 

695.2 

756.1 

817.4 

878.8 

940.6 

1002.6 

1 127.  8 

1190.9 

1254.4 

1318.3 

35 

36 

696.  2 

757.2 

818.4 

879.9 

941.6 

03.7 

66.1 

28.8 

91.9 

55.5 

19.4 

36 

37 

697.2 

758.2 

819.4 

880.9 

942.6 

04.7 

67.1 

29.9 

93-0 

56.5 

20.5 

H 

35^ 

698.2 

759-2 

820.4 

881.9 

943-7 

05.8 

68.2 

30.9 

94.0 

n-^. 

21.5 

38 

39 

699.2 

760.2 

821.4 

882.9 

944-7 

06.8 

69.  2 

32.0 

95-1 

58.6 

22.6 

39 

40 

700.3 

761.2 

822.5 

884.0 

945-7 

1007.  8 

1070.  2 

1133.0 

1196. 2 

1259. 7 

1323. 7 

40 

41 

701-3 

762.3 

823.5 

885.0 

946.8 

08.9 

71-3 

34-1 

97-2 

60.8 

24.7 

41 

42 

702.3 

763.3 

824.5 

886.0 

947.8 

09.9 

72.3 

35-1 

98.3 

61.8 

25.8 

42 

43 

703-3 

764.3 

825.5 

887.0 

948.8 

10.  9 

73-4 

36.  2 

99.3 

62. 9 

26. 9 

43 

44 
45 

704-3 
705-3 

765-3 

826.6 

888.1 

949-9 

12.0 

74.4 

37-2 

1200.4 

64.0 

27.9 
1329.0 

44 
45 

766.3 

827.6 

889.1 

950.9 

1013.0 

I075-  5 

"38.3 

1201.4 

1265. 0 

46 

706.3 

767.4 

828.6 

890.  I 

951.9 

14.  I 

76.5 

39-3 

02.  5 

66.  I 

30.1 

46 

47 

707.4 

768.4 

829.6 

891.2 

953-0 

15.  I 

77.6 

40.4 

03-6 

67.  1 

31.2 

47 

48 

708.4 

769-4 

830.7 

892.2 

954- 0 

16.  I 

78.6 

41.4 

04.  6 

68.2 

32.2 

48 

49 

709.4 

770.4 

831.7 

893.2 

955.0 

17.2 

79.6 

42.5 

05-7 

69.3 

33-3 

49 
50 

50 

710.4 

771.4 

832-7 

894.2 

956-1 

1018.  2 

1080.  7 

1 143- 5 

1206.  7 

1270.3 

1334-4 

51 

711. 4 

772.4 

833-7 

895.3 

957-1 

19.  2 

81.7 

44.6 

07.8 

71.4 

35-4 

51 

52 

712.4 

773.5 

834.7 

896.3 

958.1 

20.3 

82.8 

45.6 

08.8 

72.5 

36.5 

52 

53 

713-4 

774.5 

835-8 

897.3 

959.2 

21.3 

83.8 

46.7 

09.9 

73-5 

37-6 

53 

54 

55 

714.5 

775-5 

836.8 

898.4 

960.2 

22.4 

84.9 
1085.  9 

47-7 
1148.8 

10.9 

74.6 

38.7 

54 

715-5 

776-5 

837.8 

899.4 

961.2 

1023.  4 

1212.0 

1275-7 

1339-  7 

55 

5^^ 

716.  5 

777-5 

838.8 

900.4 

962.3 

24-4 

87.0 

49-8 

13.1 

76.7 

40.8 

56 

57 

717-5 

778-6 

839.9 

901.4 

963-3 

25.5 

88.0 

•  50-9 

14.1 

77-^ 

41.9 

57 

5H 

718-5 

779-6 

840.9 

902.5 

964.3 

26.5 

89.0 

51.9 

15.2 

78.8 

42.9 

58 

59 

719-5 

780.6 

841.9 

903-5 

965-4 

27.6 

90. 1 

53-0 

16.2 

79-9 

44.0 

59 

M. 

11° 

12° 

13° 

14° 

15° 

16° 

n° 

18° 

19° 

20° 

21° 

M. 

Page  262] 

TABLE  . 

3- 

1 

Meridional  Parts 

,  or  Increased  Latitudes. 

Co 

I 

""P-  299.1528 

M. 
o 

22° 

23° 

24° 

25° 

26° 

2r 

28° 

29° 

30° 

31° 

32° 

M. 
0    , 

1345- 1 

1409.  7 

1474-  7 

1540.  3 

1606.4 

1673. 1 

/ 

1740.4 

1808.3 

1876.9 

/ 
1946. 2 

2016. 2 

I 

46.2 

10.7 

75-8 

41.4 

07.5 

74.2 

41.5 

09.5 

78.0 

47.4 

17-4 

I 

2 

47.2 

II. 8 

76.9 

42.5 

08.6 

75-3 

42.6 

10.6 

79.2 

48.5 

18.6 

2 

3 

48.3 

12,9 

78.0 

43-6 

09.7 

76.5 

43.8 

II. 7 

80.3 

49.7 

19.7 

3 

4 

49.4 

14.0 

79.1 

44-7 

10.8 

77-6 

44-9 

12.9 

81.5 

50.8 

20.  9 

4 
5" 

5 

1350.  5 

1415. 1 

1480. 2 

1545-  8 

1611.9 

1678. 7 

1 746.  0 

1814. 0 

1882.  6 

1952.0 

2022. 1 

6 

51-5 

16,2 

81.3 

46.9 

13- 1 

79-8 

47-2 

15. 1 

83-8 

53-2 

23-3 

6 

7 

52.6 

17.2 

82.3 

48.0 

14.2 

80.9 

48.3 

16.3 

84.9 

54.3 

24.4 

7 

8 

53-7 

18.3 

83.4 

49.1 

15-3 

82.0 

49-4 

17.4 

86.1 

55.5 

25.6 

8 

9 

54-7 

19.4 

84-5 

50.  2 

16.4 

83.2 

50-5 

18.6 

.S7.2 

56.6 
1957-8 

26.8 

9 

lO 

1355-8 

1420.  5 

1485.  6 

1551-3 

1617.5 

1684.3 

1751-7 

1819.  7 

1888.  4 

2028. 0 

10 

II 

56.9 

21.6 

86.7 

52.4 

18.6 

85.4 

52.8 

20.8 

89.6 

59-0 

29. 1 

II 

12 

58.0 

22.6 

87.8 

53-5 

19.7 

86.5 

53-9 

22.  0 

90.  7        60.  I 

30-3 

12 

1.3 

59-0 

23-7 

88.9 

54-6 

20.8 

87.6 

55.1 

23.1 

91.9 

61.3 

31-5 

13 

14 

60. 1 

24.8 

90.0 

55-7 

21.9 

88.7 

56.2 

24-3 

93.0 

62.5 

32-7 

14 
15 

i.S 

1361.2 

1425. 9 

1491.  I 

1556.8 

1623.0 

1689. 9 

1757.3 

1825.4 

1894.  2 

1963.  6 

2033. 9 

i6 

62.3 

27.  0 

52.2 

57-9 

24.1 

91. 0 

58.4 

26.  5 

95.3 

64.8 

35.0 

16 

17 

63-3 

28.0 

93-3 

59- 0 

25.2 

92. 1 

59-6 

27.7 

96.5 

66.0 

36.2 

17 

18 

64.4 

29, 1 

94-3 

60.  I 

26.4 

93-2 

60.  7 

28.8 

97.6 

67.1 

37.4 

18 

19 

65.5 

30.2 

95-4 

61.  2 

27-5 

94-3 

61.8 

30.0 

98.8 

68.3 

38.6 

19 

20 

1366. 6 

H3I-3 

1496.  5 

1562.3 

1628.  6 

1695-  5 

1763.0 

1831.1 

1899.9 

1969-  5 

2039.  7 

20 

21 

67.6 

32.4 

97.6 

63.4 

29.7 

96.6 

64.  I 

32.2 

1 901.  I 

70.  6 

40.9 

21 

22 

68.7 

33-5 

98.7 

64.5 

30.8 

97.7 

65.2 

33-4 

02.2 

71.8 

42.1 

22 

23 

69.8 

34-5 

99-8 

65.6 

31.9 

98.8 

66.3 

34.5 

03.4 

72.9 

43-3 

23 

24 

70.9 

35.6 

1500.9 

66.7 
1567.8 

33- 0 
1634.  I 

99.9 
1701.  I 

67.5 

35.7 

04.5 

74.1 

44.4 

24 

2S 

1371.9 

1436-  7 

1502.0 

1768.6 

1836.  8 

.  1905.  7 

1975-3 

2045. 6 

25 

26 

73- 0 

37-8 

03.1 

68.9 

35-2 

02.  2 

69.7 

38.0 

06.8 

76-4 

46.8 

2b 

27 

74.1 

38.9 

04.  2 

70.0 

36.4 

03.3 

70.9 

39-1 

08.0 

77-6 

48.0 

27 

28 

75-2 

40.0 

05-3 

71. 1 

37-5 

04.4 

72.0 

40.2 

09.  I 

78.8 

49.2 

28 

29 

76.2 

41.0 

06.4 

72.2 

38.6 

05-5 

73-1 

41.4 

10.3 

79^_9. 
1981.  I 

50.3 
2051.5 

29 
30 

30 

1377-3 

1442. 1 

1507.4 

1573.3 

1639.  7 

1 706.  7 

1774-3 

1842.  5 

1911.5 

31 

78.4 

43-2 

08.5 

74-4 

40.8 

07.8 

75-4 

43.7 

12.6 

82.3 

52-7 

31 

32 

79-5 

44.3 

09.6 

75.5 

41.9 

08.9 

76.5 

44.8 

13-8 

l^-i 

53  9 

32 

33 

80,5 

45-4 

10.7 

76.6 

43-0 

10.  0 

77.7 

46.0 

14.9 

84.6 

55.1 

33 

34 

81.6 

46.5 

II. 8 

77-7 

44.  I 

II. 2 

78.8 

47.1 

16. 1 

85.8 

56.2 
2057.4 

34 
35 

3S 

1382.  7 

1447.6 

1512.9 

1578.8 

1645.  2 

1712.3 

1779.9 

1848.  2 

1917.2 

1987.0 

36 

83.8 

48.6 

14.0 

79.9 

46.4 

13-4 

81.  I 

49-4 

18.4 

88.1 

58.6 

36 

37 

84.9 

49-7 

15.  I 

81.0 

47.5 

14-5 

82.2 

50.5 

19-5 

89.3 

59.8 

^ 

38 

85-9 

50.8 

16.2 

82.1 

48.6 

15.6 

83.3 

51.7 

20.  7  j     90.  5 

61.0 

38 

39 

87.0 

51-9 

17.3 

83.2 

49.7 

16.8 

84.5 

52.8 

21.9 

91.6 

62.  2 

39 
40 

40 

1388. 1 

1453-  0 

1518.4 

1584-3 

1650.  8 

1717.9 

1785.6 

1854.0 

1923.0 

1992.  8 

3063.  3 

41 

89.2 

54-1 

19.5 

85-4 

51-9 

19.0 

86.7 

55-1 

24.  2 

94.0 

64-5 

41 

42 

90.2 

55-2 

20.  6 

86.5 

53.0 

20.  I 

87.9 

56.3 

25.3 

95-1 

65-7 

42 

43 

91.3 

S6.2 

21.7 

87.6 

54.1 

21.3 

89.0 

57.4 

26.5 

96.3 

66.9 

43 

44 

92.4 

57-3 

22.8 

88.7 

55.3 

22.4 

90.  I 

58.5 

27.6 

97.5 

68. 1' 

44 

45 

1393-  5 

1458. 4 

1523-9 

1589.8 

1656.4 

1723.5 

1791.3 

1859.  7 

1928.  8 

1998.  6 

2069.  3 

45 

46 

94.6 

59-5 

25.0 

90.9 

57.5 

24.6 

92.4 

60.8 

30.0 

99-8 

70.4 

4b 

47 

95-6 

60.6 

26.0 

92.0 

58.6 

25.8 

93-5 

62.0 

31.1 

2001.  0 

71.6 

47 

48 

96.7 

61.7 

27.1 

93-1 

59-7 

26.9 

94-7 

63.1 

32.3 

02.2 

72.8 

48 

49 

97.8 

62.8 

28.2 

94.3 

60.8 

28.0 

95-8 

64.3 

33-4 

03-3 

74.0 

49 

50 

1398. 9 

1463.8 

1529-3 

1595.4 

1661.9 

1729.  I 

1796.9 

1865.4 

1934-  6 

2004.  5 

2075.  2 

50 

51 

99.9 

64.9 

30.4 

96.5 

63.1 

30-3 

98. 1 

66.6 

35-8 

05-7 

76.4 

51 

S2 

1401.0 

66.0 

31-5 

97-6 

64.2 

31-4 

99-2 

67.7 

36.9 

06.8 

77.5 

52 

S3 

02. 1 

67.1 

32.6 

98.7 

65-3 

32-5 

1800. 4 

68.9 

38.1 

08.0 

78.7 

53 

54 

03.2 

68.2 

33-7 

99-8 

66.4 

33-6 

01.5 

70.0 

39.2 

09.2 

79-9 

54 

55 

1404. 3 

1469. 3 

1534.8 

1600.  9 

1667.  5 

1734-8 

1802.  6 

1871.2 

1940. 4 

2010.4 

2081. 1 

55 

56 

05-3 

70.4 

35-9 

02.0 

68.6 

35-9 

03  8 

72.3 

41.6 

II. 5 

82.3 

5'> 

57 

06.4 

71.5 

37- 0 

03.1 

69.8 

37-0 

04.9 

73-5 

42.7 

12.7 

83-5 

57 

5« 

07.5 

72.5 

38.1 

04.  2 

70.9 

38.1 

06.0 

74.6 

43.9 

13-9 

84-7 

58 

59 

08.6 

73-6 

39-2 

05.3 

72.0 

39-3 

07.2 

75-8 

45-0 

15.0 

85.8 

59 

M. 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

M. 

I 


TABLE  3. 

Page  263 

Meridional  Parts,  or 

Increased  Latitudes. 

% 

Con 

t 

8 

^P"  299.152 

M. 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

M. 

r 
O 

2087. 0 

2158.6 

2231. 1 

2304.  5 

2378.8 

/ 
2454. 1 

1 
2530. 5 

2607. 9 

2686. 5 

2766.3 

2847.  4 

0 

I 

88.2 

59.8 

32.3 

05.7 

80.1 

55-4 

31.8 

09.  2 

87.9 

67.7 

48.8 

I 

2 

89.4 

61.0 

33-6         07.0 

81.3 

56.7 

33- 0 

10.5 

89.2 

69.0 

50.  2 

2 

3 

90.6 

62.3 

34.8 

08.2 

82.6 

57-9 

34=3 

II. 8 

90-5 

70.4 

51.5 

3 

4 

91.8 

63.5 

36.0 

09.4 

83.8 

59-2 

35.6 

13.1 

91.8 

71.7 

52.9 

4 

■; 

2093. 0 

2164.  7 

2237.  2 

2310.  7 

2385. 1 

2460.  4 

2536. 9 

2614. 4 

2693. 1 

2773. 1 

2854. 3 

5 

6 

94.2 

65-9 

38.4 

II. 9 

86.3 

61.7 

38.2 

15-7 

94-5 

74-4 

55-6 

6 

7 

95-3 

67.1 

39-6 

13-1 

87.6 

63.0 

39-5 

17.0 

95-8 

75-7 

57-0 

7 

8 

96.5 

68.3 

40.9 

14.4 

88.8 

64.2 

40.7 

18.3 

97.1 

77-1 

58.3 

8 

9 

97-7 

69.5 

42.1 

15.6 

90.0 

65-5 

42.0 

19.6 

98.4 

78.4 

59-7 

9 
10 

lO 

2098. 9 

2170.  7 

2243- 3 

2316.8 

2391-3 

2466.  8 

2543. 3 

2621.0 

2699. 8 

2779.8 

2861. 1 

II 

2100.  I 

71.9 

44.  5         18.  I 

92.5 

68.0 

44-6 

22.3 

2701.  I 

81. 1 

62.4 

II 

12 

01.3 

73-1 

45-7  1       19-3 

93-8 

69-3 

45.9 

23.6 

02.4 

82.5 

63.8 

12 

n 

02.  5 

74-3 

46.9 

20.  5 

95- 0 

70.6 

47.2 

24.9 

03-7 

83.8 

65-2 

13 

14 

I"; 

03-7 
2104.9 

75-5 

48.2 

21.8 

96-3 

71.8 

48.5 

26.  2 

05.0 

85.2 

66.5 

14 
15 

2176.7 

2249. 4 

2323. 0 

2397-  5 

2473-  I 

2549.  7 

2627.  5 

2706. 4 

2786.  5 

2867. 9 

i6 

06.0 

77-9 

50.  6 

24.  2 

98.8 

74-4 

51.0 

28.8 

07.7 

87.8 

69.3 

16 

17 

07.2 

79.1 

51-8  1       25.5 

2400.  I 

75-7 

52.3 

30.1 

09.0 

89.2 

70.7 

17 

i8 

08.4 

80.3 

53.  0         26.  7 

01.3 

76.9 

53.6 

31-4 

10.4 

90.5 

72.0 

18 

19 

09.6 

81.5 

54-3 

27.9 

02.6 

78.2 

54-9 

32-7 

II. 7 

91.9 

73-4 

19 
20 

20 

21 10.  8 

2182.  7 

2255-  5 

2329.  2 

2403. 8 

2479- 5 

2556.  2 

2634. 0 

2713.0 

2793.  2 

2874.  8 

21 

12.0 

83.9 

56.7 

30.4 

05.1 

80.7 

57-5 

35-3 

14.3 

94.6 

76.1 

21 

22 

13.2 

85.1 

57-9 

31.6 

06.3 

82.0 

58.8 

36.6 

15-7 

95-9 

77.5 

22 

2^ 

14.4 

86.3 

59-1 

32-9 

07.  6 

83-3 

60.0 

37-9 

17.0 

97-3 

78.9 

23 

24 

15.6 

87.5 

60.4 

34-1 

08.8 

84-5 

61.3 

39-2 

18.3 

98.6 

80.  2 

24 

a-; 

2116.8 

2188.7 

2261.6 

2335-3 

2410.  I 

2485.  8 

2562. 6 

2640.  5 

2719.6 

2800. 0 

2881.6 

.25 

26 

18.0 

89.9 

62.8 

36.6 

"-3 

87.1 

63-9 

41.8 

21.0 

01.3 

83.0 

26 

27 

19.2 

91.2 

64.  0 

37.8 

12.6 

88.4 

65.2 

43-2 

22.  3 

02.  7 

84.4 

27 

28 

20.  3 

92.4 

65. 2        39.  r 

13.8 

89.6 

66.5 

44-5 

23.6 

04.0 

85-7 

28 

29 
30 

21-5 

93-6 

66.5  ,      40.3 

15- I 

90.9  1       67.8 

45-8 

25.0 

05.4 

87.1 

29 

2122.  7 

2194.8 

2267.  7 

2341.  5 

2416.  3 

2492.  2 

2569.  I 

2647.  I 

2726.  3 

2806.  7 

2888.  5 

30 

31 

23-9 

96.0 

68.9 

42.8 

17.6 

93-4 

70.4 

48-4 

27.6 

08. 1 

89.9 

31 

32 

25-1 

97.2 

70.1 

44.0 

18.9 

94-7 

71.6 

49-7 

28.9 

09.4 

91.2 

32 

.S3 

26.3 

98.4 

71.4 

45-3 

20.  I 

96.0 

72.9 

51.0 

30.3 

10.8 

92.6 

33 

34 

27-5 

99.6 

72.6 

46.5 

21.4 

97-3 

74.2 

52.3 

31.6 

12. 1 

94.0 

34 

3S 

2128.  7 

2200.  8 

2273.  8 

2347-  7 

2422.  6 

2498.5 

2575.5 

2653.  6 

2732.  9 

2813.5 

2895.  4 

35 

36 

29.9 

02.0 

75- 0 

49- 0 

23-9 

99.8 

76.8 

55.0 

34-3 

14.8 

96.7 

36 

37 

31-1 

03.2 

76.3 

50.2 

25-1 

2501. 1 

78.1 

56.3 

35-6 

16.2 

98.  I 

H 

38 

32-3 

04.4 

77-5 

51-5 

26.4 

02.4 

79.4 

57.6 

36-9 

17.6 

99-5 

38 

39 

33.5 

05.7 

78.7 

52.7 

27.7 

03.6 

80.7 
2582.  0 

58.9 

38.3 

18. 9  !  2900.  9 

39 

40 

2134-  7 

2206.  9 

2279.  9 

2353-  9 

2428. 9 

2504.  9 

2660.  2 

2739.  6 

2820. 3 

2902.  2 

40 

41 

35-9 

08.1 

81.2 

55-2 

30.2 

06.2 

83.3 

61.5 

40.9 

21.6 

03.6 

41 

42 

37-1 

09-3 

82.4 

56.4 

31.4 

07.5 

84.6 

62.8 

42.3 

23.0 

05.0 

42 

43 

38.3 

10.5 

83.6 

57-7 

32-7 

08.7 

85-9 

64.  I 

43-6 

24.3 

06.4 

43 

44 

39.5 

II. 7 

84.8 

58-9 

33-9 

10.  0 

87.2 

65.5 

44-9 

25-7 

07.7 

44 
45 

4S 

2140.  7 

2212.9 

2286.  I 

2360. 1 

2435-  2 

25"-3 

2588.  5 

2666.  8 

2746.  3 

2827.0 

2909.  I 

46 

41.9 

14.  I 

87.3 

61.4 

36-5 

12.6 

89.8 

68.1 

47-6 

28.4 

10.5 

46 

47 

43-1 

15-3 

88.5 

62.6 

37-7 

13.8 

91.  I 

69.4 

48.9 

29.8 

II. 9 

47 

48 

44-3 

16.6 

89.7 

63-9 

39-0 

15.1 

92.4 

70.7 

50-3 

31- 1 

'3-3 

48 

49 

45.5 

17.8 

91.0 

65.1 

40.  2 

16.4 

93-6 

72.0 

51.6 

32.5 

14.6 

49 

50 

2146.  7 

2219.0 

2292. 2 

2366.  4 

2441.5 

2517.7 

2594.  9 

2673. 4 

2753-0 

2833.  8 

2916.0 

50 

^i 

47.8 

20.  2 

93-4 

67.6 

42.8 

19.0 

96.2 

74.7 

54-3 

35-2 

17.4 

51 

52 

49.0 

21.4 

94-7 

68.9 

44.0 

20.  2 

97-5 

76.0 

55-6 

36.5 

18.8 

52 

S3 

50.2 

22.  6 

95-9 

70.1 

45-3 

21.5 

98.8 

77.3 

57- 0 

37.9 

20.  2 

53 

54 

51.4 

23.8 

97.1 

71-3 

46.6 

22.8 

2600.  I 

78.6 

58.3 

39.3 

21.  6 

54 

.S5 

2152.6 

2225.0 

2298.  3 

2372.6 

2447.8 

2524. 1 

2601.4 

2679.  9 

2759-  6 

2840. 6  i  2922. 9 

55 

.S6 

53.8 

26.3 

99.6 

73-8 

49.1 

25.4 

02.  7 

81.3 

61.  0 

42.0 

24-3 

56 

S7 

55- 0 

27.5 

2300.8 

75-1 

50-3 

26.6 

04.0 

82.6 

62.3 

43-3 

25-7 

57 

S« 

56.2 

28.7 

02.0 

76.3 

51.6 

27.9 

05-3 

83.9 

63.7 

44.7 

27.1 

58 

59 

57-4 

29.9 

1 

03-3 

77.6 

52.9 

29.2 

06.6 

85.2 

65.0 

46.  I 

28.5 

59 
M. 

M. 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

Page  264] 

TABLE  3. 

Meridional  Parts,  or  Increased  Latitudes. 

C( 

I 

^'i^P-  299.1528 

M. 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

M. 

o 

2929. 9 

/ 
3013-7 

3099. 0 

/ 

3185-9 

3274-  5 

/ 
3364-  7 

3456. 9 

3551-0 

/ 
3647- 1 

3745-  4 

3846. 1 

0 

I 

31.2 

15. 1 

3100.5 

87.4 

76.0 

66.3 

58.4 

52-5 

48.7 

47-1 

47-7 

I 

2 

32.6 

16.5 

01.9 

88.8 

77.4 

67.  B 

60.  0 

54-1 

50-3 

48.7 

49.4 

2 

3 

34- 0 

17.9 

03-3 

90.3 

78-9 

69-3 

61.5 

55-7 

52.0 

50.4 

^'•l 

3 

4 

35-4 

19.3 

04.8 

91.8 

80.4 

70.8 

63.1 

57.3 

53-6 

52-1 

52-8 

4 
5 

5 

2936.  8 

3020. 8 

3106,2 

3193-2 

3281.9 

3372-4 

3464. 6 

3558-  9 

3655-  2 

3753-  7 

3854-  5 

b 

38.2 

22.2 

07.6 

94-7 

83.4 

73-9 

66.2 

60.5 

56.8 

55-4 

56.2 

6 

7 

39-6 

23.6 

09. 1 

96.  2 

84.9 

75-4  1      67.8 

62. 1 

58.4 

57-0 

58.0 

7 

8 

41.0 

25.0 

10.5 

97-6 

86.4 

76.9 

69.3 

63-7 

60.  I 

58.7 

59.7 

8 

9 

lO 

42.3 
2943-  7 

26.4 

12.0 

99-1 

87.9 

78.4 

70.9 

65.2 

61.  7 

60.4 
3762.  0 

61.4 
3863-1 

9 
10 

3027.  8 

3113-4 

3200.  6 

3289. 4 

3380. 0 

3472. 4 

3566.8 

3633-  3 

II 

45.1 

29.  2 

14.8 

02.  0 

90.9 

81.5 

74-0 

68.4 

65.0 

63.7 

64.8 

II 

12 

46.5 

30.6 

16.3 

03.5 

92.4 

^^•9 

75-5 

69.0 

66.6 

65-4 

66.5 

12 

13 

47-9 

32.1 

17.7 

05.0 

93.9 

84.6 

77-1 

71.6 

68.2 

67.0 

68.2 

13 

14 

49.3 

33-5 

19.2 

06.4 

95-4 

86.1 

78.7 

73.2 

69.8 

68.7 
3770.4 

69-9 
3871.6 

14 
15 

15 

2950.  7 

3034. 9 

3120.6 

3207.  9 

3296.  9 

3387-6 

3480. 2 

3574-8 

3671.5 

16 

52.1 

36.3 

22.0 

09.4 

98-4 

89.1 

81.8 

76.4 

73-1 

72.0 

73-3 

16 

17 

53-5 

37-7 

23-5 

10.8 

99-9 

90.7 

83.3 

78.0 

74.7 

73-7 

75.0 

17 

18 

54.9 

39-1 

24-9 

12.3 

3301.4 

92.2 

84.9 

79-6 

76.4 

75-4 

76.7 

18 

19 

56.3 

40.6 

26.4 

13.8 

02.9 

93-7 

86.5 

81.2 
3582.8 

78.0 
T679-  6 

77-0 
3778.  7 

78.4 
3880. 1 

J9^ 
20 

20 

2957.6 

3042. 0 

3127.8 

3215-2 

3304-  4 

3395-  2 

3488.0 

21 

59- 0 

43-4 

29-3 

16.  7 

05-9 

96.8 

89.6 

84.4 

81.3 

80.4 

81.8 

21 

22 

60.4 

44.8 

30-7 

18.2 

07.4 

98.3  i      91.  I 

86.0 

82.9 

82.0 

83.6 

22 

23 

61.8 

46.2 

32-1 

19.7 

08.9 

99-  8  i      92.  7 

87.6 

84-5 

83.7 

85.3 

23 

24 

63.2 

47.6 

33.6 

21.  I 

10.4 

3401.4 

94-3 

89.2 

86.2 

85-4 

87.0 
'3888.-7 

24 
25 

25. 

2964. 6 

3049.  I 

3135-0 

3222.  6 

3311-9 

3402. 9 

3495-  8 

3590. 8 

3687.8 

37^7- 1 

26 

66.0 

50-5 

36-5 

24.1 

13-4 

04-4 

97-4 

92.4 

89-4 

88.7 

90.4 

26 

27 

67.4 

51.9 

37-9 

25.6 

14.9 

06.0 

99.0 

94.0 

91.  I 

90.4 

92. 1 

27 

28 

68.8 

53-3 

39-4 

27.0 

16.4 

07-  5  i  3500.  5 

95.6 

92.7 

92. 1 

93-8 

28 

29 
30 

70.2 

54.8 

40.8 

28.5 

17.9 

09. 0        02. 1 

97.2 

94.3 

93.8 

95-6 
3897-  3 

29 
30 

2971.6 

3056.  2 

3142.3 

3230-  0 

3319-4 

3410.6 

3503-  7 

3598.8 

3696. 0 

3795.  4 

31 

73- 0 

57-6 

43-7 

31-5 

20.9 

12. 1 

05.  2 

3600. 4 

97.6 

97-' 

99.0 

31 

32 

74-4 

59- 0 

45-2 

32.9 

22.4 

13.6 

06.8 

02.0 

99-3 

98.8 

3900.  7 

32 

33 

75.x 

60.4 

46.6 

34-4 

23-9 

15-2 

08.4 

03.6 

3700.  9 

3800. 5 

02.4 

33 

34 

77.2 

61.  9 

48.1 

35-9 

25-4 

16.  7 

09.9 

05.2 

02.  5 

02.  I 

04.2 

34 
35 

3S 

2978.  6 

30(33-  3 

3149-  5 

3237-  4 

3326.9  !  3418.3 

3511-5 

3606.  8 

3704.  2 

3803.  8 

3905.  9 

36 

80.0 

■  64.7 

51.0 

38.8 

28.4 

19.8 

13- 1 

08.4 

05.8 

05-5 

07.6 

36 

37 

81.4 

66.  I 

52.4 

40.3 

29-9 

21.3 

14.7 

10.0 

07.5 

07.  2 

09-3 

37 

3« 

82.8 

67.6 

53-9 

41.8 

31-4 

22.9 

16.2 

II. 6 

09.  I 

08.9 

II.  I 

38 

39 

84.2 

69.0 

55.3 

43-3 

32-9 

24.4 

17.8 

13.2 

10.7 

10.6 

12.8 

39 

40 

2985.  6 

3070.  4 

3156.8 

3244.8 

3334-  5 

3426. 0 

3519-4 

3614.  8 

3712.4 

3812.2 

3914.  5 

40 

41 

87.0 

71.8 

58-2 

46.  2 

36.0 

27-5 

20.9 

16.4 

14.0 

13-9 

16.  2 

41 

42 

88.4 

73-3 

59.7 

47-7 

37-5 

29.0 

22.  5 

18.0 

15-7 

15-6 

18.0 

42 

43 

89.8 

74-7 

61. 1 

49.2 

39-0 

30.6 

24.1 

19.6 

17-3 

17.3 

19.7 

43 

44 

91.2 

76.1 

62.6 

50.7 

40.5 

32. 1 

25-7 

21.2 

19.0 

19.0 

21.4 
3923- 1 

44 
45 

45 

2992.  6 

3077. 6 

3164.0 

3252.2 

3342-  0 

3433-  7  ■  3527-  2 

3622.  9 

3720.  6 

3820.  7 

46 

94.0 

79-0 

65-5 

53.6 

43-5 

35-2  :      28.8 

24.5 

22.3 

22.4 

24.9 

46 

47 

95-4 

80.4 

67.0 

55-1 

45.0 

36-8 

30-4 

26.1 

23.9 

24.0 

26.6 

47 

48 

96.8 

81.8 

68.4 

56.6 

46-5 

38.3 

32.0 

27-7 

25-6 

25.7 

28.3 

48 

49 

50 

98.2 

83.3 

69.9 

58.1 

48.1 

39-8 

33-6 

29-3 

27.  2 

27.4 

30. 1 

49 

2999. 6 

3084.  7 

3171-3 

3259-  6 

3349-  6 

3441-4  !  3535-1 

3630.  9 

3728.  9 

3829. 1 

3931.8 

50 

51 

3001.0 

86.1 

72.8 

61.  I 

51.  I   1      42.9         36.7 

32.5 

30.5 

30.8 

33-5 

51 

52 

02.4 

87.6 

74.2 

62.6 

52.6         44.5         38. 3 

34.2 

32.2 

32-5 

35.3 

52 

53 

03.8 

89.0 

75-7 

64.0 

54-1 

46.0        39.9 

35.8 

33.8 

34-2 

37.0 

53 

54 

05-3 

90.4 

77-2 

65-5 

55-6 

47-6  I      41.5 

37-4 

35-5 

35-9 

38.7 

54 

55 

3006.  7 

3091.9 

3178.6 

3267.  0 

3357-2 

3449. 1  1  3543-  0 

3639.  0 

3737- 1 

3837-  6 

3940.  5 

55 

56 

08. 1 

93-3 

80.1 

68.5 

58.7 

50.  7  \      44-6 

40.6 

38.8 

39-3 

42.2 

56 

57 

09-5 

94-7 

81.5 

70.0 

60.2 

52.  2         46.  2 

42.  2 

40-4 

41.0 

43.9 

57 

5« 

10.9 

96.2 

83.0 

71-5 

6i.7 

53-8        47-8 

43.9 

42.1 

42-7 

45-7 

58 

59 

12.3 

97.6 

84-5 

73- 0 

63.2 

55-3  '      49-4 

45.5 

43-8 

44.4 

47-4 

59 

M. 

44° 

45° 

46° 

47° 

48° 

49°          50° 

51° 

52° 

53° 

54° 

M. 

TABLE  3. 

Page  265 

Meridional  Parts,  or  Increased  Latitudes. 

Cor 

I 

8 

"P-  299.152 

M. 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

M. 

o 

3949-  I 

1 
4054. 9 

4163. 4 

4274-  8 

/     j 
4389-  4     4507-  5     4629. 1 

1 
4754.  7 

4884.  5 

5018.  8 

5158.0 

0 

I 

50.9 

56.6 

65.2 

76.7 

91.4  i      09.5 

31.2 

56.8 

86.  7        21.  5  ^     60.3 

I 

2 

52.6 

5^-4 

67.0 

78.6 

93-3  [      II.  5 

33.2 

58.9 

88.  9        23.  3        62.  7 

2 

3 

54.4 

60.2 

68.9 

80.5 

95.3 

13.5 

35-3 

61. 1 

91. 1        25.6        65.1 

3 

4 

56.1 

62.0 

70.7 

82.4 

97.2 

15.5 

37.4 

63.2 

93.  3  t      27. 9  !      67. 4 

4 

5 

3957.9 

4063. 8 

4172.5 

4284.  2 

4399. 1 

4517.5 

4639. 4 

4765. 3 

4895-5  15030-2    5169-8 

6 

59.6 

65.6 

74.4 

86.  I 

4401. 1 

19.5 

41.5 

67.5 

97-7 :    32.5     72.2 

b 

7 

61.3 

67.4 

76.2 

88.0 

03.0 

21.5 

43.6 

69.6 

99.9 

34-7 

74.6 

7 

8 

63.1 

69.  2 

78.0 

89-9 

05.0 

23.5 

45.6 

71-7 

4902.  I 

37.0 

76-9 

8 

9 

64.8 

70.9 

79.9 

91.8 

06.9 

25.5         47.7  1      73-9 

04-3 

39.3 

79-3 

9, 
10 

lO 

3966.  6 

4072.  7 

4181. 7 

4293-  7 

4408. 9     4527.  5     4649. 8 

4776. 0 

4906.  5 

5041.6    5181.7 

II 

68.3 

74-5 

83.6 

95-6 

10.8        29.5        51.8 

78.2 

08.7 

43-  9        84.  I 

II 

12 

70.1 

.  76.3 

85.4 

97-5 

12.8        31.5        53.9 

80.3 

10.9 

46.  21      86.  4 

12 

13 

71.8 

78.1 

87.2 

99-4 

14-  7  i      33-5  !      56.  0 

82.4 

13.2 

48.  5        88.  8 

13 

14 
15 

73-6 

79-9 

89. 1 

4301-  3 

16-  7  1      35.  5  1      58. 1 

84.6 

15.4 

50.8        91.2 

14 

3975-  3 

4081. 7 

4190.9 

4303.  2 

4418.6  j  4537.5     4660.1 

4786.  7 

4917.6 

5053.1     5193.6 

15 

16 

■  77-1 

83.5 

92.8 

05.1 

20.  6         39.  5         62.  2 

88.9 

19.8        55-4        96.0 

16 

17 

78.8 

85-3 

94.6 

07.0 

22.5         41.6         64.3 

91.0 

22.0  1     57.7  1     98.4 

17 

18 

80.6 

87.1 

96-5 

08.9 

24.5  ••      43-6  1      66.4 

93-2 

24.  3        60.  0  ,  5200.  8 

18 

19 
20 

82.3 
3984.  I 

88.9 

98.3 

10.8 

26.  4         45.  6         68.  5 

95-3 
4797-  5 

26.  6        62.  3        03.  2 

19 

4090.  7 

4200. 2 

4312.7 

4428. 4     4547.  6     4670.  5 

.4928.  7 

5064.  6    5205. 5 

20 

21 

85.8 

92.5 

02.0 

14.6 

30.4         49.6         72.6 

99-6 

30.9 

66.  9        07.  9 

21 

22 

87.6 

94.3 

03-9 

16.5 

32.3  !       51.6         74.7 

4801.8 

33.2        69.2        10.3 

22 

23 

89.4 

96.  I 

05.7 

18.4 

34-3         53-7         76-8 

03-9 

35-4        71.5         12-7 

23 

24 
25 

3992. 9 

97-9 

07.6 

20.3 

36.  2         55.  7         78.  9 

06.  I 

37.6  ;      73-8        15- I 

24 
25 

4099.  7 

4209. 4 

4322.  2 

4438.2     4557-7     4681.0 

4808.  2 

4939. 8 

5076.  2 

5217.5 

26 

94.6 

4101.5 

II. 3 

24.1 

40. 2  !      59.  7  !      83. 0 

10.4 

42.1 

78.5 

19.9 

26 

27 

96.4 

03-3 

13- I 

26.0 

42. 1         61.8        85. 1 

12.5 

44-3 

80.8 

22.3 

27 

28 

98.  I 

05.1 

15.0 

27.9 

44.  I         63.  8  '      87. 2 

14-7 

46.6 

83-1 

24-7 

28 

29 
30 

99-9 
4001  7 

06.9 

16.8 

29.8 

46.  I 

65.8 

89.3 

16.9 

48.8 

85-4 

27.1 

29 

4108.  7 

4218.7 

4331.  7 

44^8,  0 

4567.8 

4691.4 

4819.0 

4951  0 

5087.  7 

5229.  6 

30 

31 

03-4 

10.6 

20.6 

33-6 

50.0 

69-9        93.5 

21.2 

53-3 

90.  I 

32-0 

31 

32 

01;.  2 

12.4 

22.4 

35-5 

52.0  1      71.9        95.6 

23-4 

55-5  !     92-4 

34-4 

32 

33 

07.0 

14.2 

24-3 

37-5 

53. 9         73-  9        97-  7 

25-5 

57-  7        94-  7 

36,8 

-t  -> 

34 
35 

08.7 

16.0 

26.  I 

39.4 

55-9         75-9         99-8 

27.7 

60.0       97.0 
4962. 2  ■  5099. 4 

39-2 

34 

4010.  5 

4117.8 

4228.0 

4341.  3 

4457-9  !  4578.0     4701.9 

4829.  9 

5241-6     35  1 

3b 

12.3 

19.6 

.29.9 

43.2 

59.  8         80.  0         04.  0 

32.0 

64.5  '5101.  7 

44.  0     36  I 

V 

14.0 

21.4 

31.7 

45. 1 

61.  8         82.  0         06.  I 

34-2 

66.  7        04.  0 

46  5 

37 

3« 

15.S 

23.2 

33-6 

47.0 

63.  8         84.  I         08.  2 

36.4 

69.  0        06  3 

48.9 

38 

39 

17.6 

25.1 

35-5 

48.9 

65. 8         86.  I          10. 3 

38.5 

71.2 

08.7        51-3 

39 

40 

4019.3 

4126.9 

4237-  3 

4350.  9 

4467.  7     4588.  2  ;  4712. 4 

4840.  7 

4973-  5 

5111.0 

5253-  7 

40 

41 

21.  I 

28.7 

39.2 

52.8 

69.7         90.2         14.5 

42.9 

75-7 

13.3 

^t-l 

41 

42 

22.  9 

30.5 

41.  I 

54.7 

71. 7         92.2         16.6 

45-1 

78.0 

15.7 

58.6 

42 

43 

24.  6 

32.3 

42.9 

56.6 

73-  7  1      94-3         18. 7  ;      47-  2 

80.2        18.0        61.0 

43 

44 

26.4 

34-1 

44.8 

58.6 

75.  7         96.  3         20.  8  1      49.  4 

82.  51         20.  4    !         63.  4 

44 

45 

4028. 2 

4136.0 

4246. 7 

4360.  5 

4477-  6     4598-  4     4722.  9 

4851.6 

4984.  7 

5122. 7 

5265.  9 

45 

46 

30.0 

37.8 

48.5 

62.4 

79.  6     4600. 4         25.  0 

53.8 

87.0 

25.0 

68.3 

46 

47 

31-7 

39-6 

50.4 

64-3 

81.6         02.4         27.  I 

56.0 

89.3 

27.4 

70.7 

47 

48 

33-5 

41.4 

52.3 

66.3 

83.6  :       04.5           29.3 

58.2 

91-5 

29.7 

73-2 

48 

49 
50 

35-3 
4037-  I 

43-2 

54-1 

68.2 

85.6          06.5   ,       31.4 

60.3 

93-8 

32-1  !      75-6 

49 

4145-  I 

4256.  0 

4370.  I 

4487.  6     4608.  6  1  4733.  5 

4862.  5 

4996- 1 

5134.4 

5278. 0 

so 

51 

38.8 

46.9 

57.9 

72.0 

89.5          10.6 

35-6 

64.7 

98.3 

36.8 

80.5 

51 

52 

40.6 

48.7 

59-8 

74.0 

91.5 

12.7 

37.7 

66.9 

5000. 6 

39.1 

82.9 

52 

53 

42.4 

50-5 

61.6 

75.9 

93-5 

14.7 

39.8 

69.  I 

02.9 

41.5 

!5-4 

53 

54 

44.2 

52.4 

63.5 

77.8 

95.5 

16.8 

42.0 

71.3 

05.1 

43.8 

87.8 

54 

55 

4045-9 

4154-2 

4265. 4 

4379.  8 

4497-5     4618.8 

4744.  I     4873.  5 

5007. 4 

5146.2    5290.3 

55 

5b 

47-7 

56.0 

67-3 

81.7 

99-5         20.9 

46.  2 

75-7 

09.7 

48.  5        92.  7 

56 

H 

49-5 

57-9 

69.  2 

f3-^ 

4501.5  1      23.0 

48.3 

77.9 

II. 9 

50.9        95-1 

57 

5X 

51-3 

59-7 

71.0 

85.6 

03.5  j      25.0 

50.4 

80.1 

14.2 

53.3        97-6 

58 

59 

M. 

53-1 

61.5 

72.9 

87.5 

05.  5         27.  I 

1 

52.6 

82.3 

16.5 

55-6    5300.1 

59 
M. 

55° 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

Page  266 

TABLE  3. 

Meridional  Parts,  or  Increased  Latitudes 

• 

Comp 

I 

299.1528 

M. 

66° 

6^° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

M. 

o 

5302.  5 

5452.  8 

5609. 5 

=1773. 1 

5944.3 

6124.0 

6313.0 

6512.4 

6723.  6 

6948, 1 

0 

I 

05.0 

55.4 

12.2 

75-9 

47.2 

27.0 

16.2 

15.9 

27.3 

52.0 

I 

2 

07.4 

58.0 

14.8 

78.7 

50.2 

30.1 

19.5 

19.3 

30.9 

55.9 

2 

3 

09.9 

60.5 

17.5 

81.5 

53.1 

33.2 

22.7 

22. 7 

34.5 

'  59.7 

3 

4 

12.4 

63.1 

20. 2 

84-3 

56.0 

36.3 

25.9 

26.1 

38.2 

63.6 

4 

5 

5314.8 

5465.  7 

5622. 9 

5787. 1 

5959. 0 

6139.  3 

6329. 2 

6529.  6 

6741.8 

6967. 5 

5 

b 

17-3 

68.2 

25.5 

89.9 

61.9 

42.4 

32.4 

33.0 

45-5 

71.4 

b 

7 

19.7 

70.8 

28.2 

92.7 

64.8 

45.5 

35.7 

36.4 

49.1 

75.3 

7 

8 

22.2 

73-4 

30.9 

95-5 

67.8 

48.6 

38.9 

39-9 

52.8 

79.2 

8 

9 

24.7 

75.9 

33.6 

98.3 

70.7 

51.7 

42.2 

43.3 

56.4 

83.1 

9 

10 

5327-2 

5478.  5 

5636. 3 

5801. 1 

5973-  7 

6154.8 

6345.  5 

6546.  8 

6760. 1 

6987. 0 

10 

II 

29.  6 

81. 1 

39.0 

03.9 

76.6 

57.9 

48.7 

50.2 

63.8 

90.9 

II 

12 

32.1 

83.7 

41.7 

06.  7 

79.5 

61.0 

52.0 

53.7 

67.4 

94.8 

12 

13 

34-6 

86.2 

44.3 

09.5 

82.5 

64.  I 

55-3 

57.2 

7^-i 

98.7 

13 

14 
15 

37-1 

88.8 

47.0 

12.3 

85.  5 

67.2 

58.5 

60.6 

6564.  I 

74.8 

7002.  6 

14 

5339-  4 

5491.4 

5649.  7 

5815.2 

5988.4 

6170.3 

6361.8 

6778.  5 

7006.  5 

15 

lb 

42.0 

94.0 

52.4 

18.0 

91.4 

73.4 

65.1 

67.6 

82.1 

10.5 

lb 

17 

44-5 

96.6 

55-1 

20.8 

94.3 

76.5 

68.4 

71.0 

85.8 

14.4 

17 

18 

47.0 

99.2 

57.8 

23.6 

97.3 

79.6 

71.7 

74.5 

89.5 

18.3 

18 

19 

49-5 

5501.7 

60.5 

26.5 

6000. 3 

82.8 

75.0 

78.0 

93.2 

22.3 

19 

20 

5352.  0 

5504.  3 

5663. 2 

5829.  3 

6003.  2 

6185.9 

6378.2 

6581.5 

6796. 9 

7026.  2 

20 

21 

54-4 

06.9 

^§•9 

32.1 

06.  2 

89.0 

81.5 

^^•° 

6800.  6 

30.  2 

21 

22 

56.9 

09.5 

68.7 

35.0 

09.  2 

92.  I 

84.8 

88.4 

04.3 

34.1 

22 

23 

59-4 

12.  I 

71.4 

37.8 

12. 1 

95.3 

88.1 

91.9 

08.0 

38.1 

23 

24 

25 

61.9 

14.7 

74.1 

40.6 

15.1 

98.4 

91.4 

95.4 

II. 7 

42.1 

24 

5364.  4 

5517.3 

5676.  8 

5843.  5 

6018.  I 

6201.  5 

6394.  7 

6598.  9 

6815.6 

7046.  0 

25 

2b 

66.9 

19.9 

79-5 

46.3 

21. 1 

04.7 

98.  I 

6602.  4 

19.  2 

50.0 

26 

27 

69.4 

22.  5 

82.2 

49.2 

24.1 

07.8 

6401. 4 

05.9 

22.9 

54.0 

27 

28 

71.9 

25.1 

84.9 

52.0 

27.1 

10  9 

04.  7 

09-5 

26.6 

57-9 

28 

29 

74-4 

27.7* 

87.7 

54.9 

30.0 

14.  I 

08.0 

13.0 

30.4 

61.9 

29 

30 

5376.9 

5530.4 

5690. 4 

5857.  7 

6033.  0 

62 1 7.  2 

6411.3 

6616.  5 

6834.  I 

7065.  9 

30 

31 

79-4 

33.0 

93-1 

60.6 

36.0 

20.4 

14.7 

20.  0 

37.9 

69.9 

31 

32 

81.9 

35.6 

95.9 

63.4 

39.0 

23-5 

18.0 

23-5 

41.  b 

73-9 

32 

33 

84.5 

38.2 

98.6 

66.3 

42.0 

26.  7 

21.3 

27.1 

45.4 

77-9 

33 

34 

87.0 

40.8 

5701.3 
5704.  I 

69.1 

.     45.0 

29.9 

24.6 

30.6 

49-1 

81.9 

34 

35 

5389.  5 

5543.  4 

5872.0 

6048. 0 

6233. 0 

6428. 0 

6634.  I 

6852. 9 

7085.  9 

35 

3b 

92.0 

46.0 

06.8 

74-9 

51.0 

36.2 

31.3 

37-7 

56.6 

90.  0 

36 

37 

94-5 

48.7 

09  5 

77.7 

54-1 

39-4 

34-7 

41.2 

60.  4 

94.0 

37 

3^ 

97.0 

51.3 

12.3 

80.6 

57.1 

42.5 

38.0 

44-7 

64.  2 

98.0 

38 

39 

99-5 

53-9 

15.0 

83.5 

60.  I 

45.7 

41.4 

48.3 

67.9 

7102.  0 

39 

40 

5402.  I 

5556.  6 

5717.8 

5886. 4 

6063. 1 

6248.  9 

6444.7 

6651.9 

6871.  7 

7106.  I 

40 

41 

04.  6 

59-2 

20.  5 

89.2 

66.1 

52.1 

48.1 

55-4 

75.5 

10.  I 

41 

42 

07.1 

61.8 

23.3 

92.  I 

69.  I 

55-2 

51.4 

59.0 

79-3 

14.2 

42 

43 

09.  6 

64.4 

2b.  0 

95.0 

72.2 

58-4 

54.8 

62.5 

83.1 

18.2 

43 

44 
45 

12.2 

67.1 

28.8 

97.9 

75-2 

61.6 

58.2 

66.1 

86.9 

22.3 

44 

5414.  7 

5569. 7 

5731.5 

5900.  8 

6078. 2 

6264.  8 

6461.  5 

6669.  7 

6890.  7 

7126.3 

45 

4b 

17.2 

72.4 

34.3 

03.6 

81.2 

68.0 

64.9 

73.2 

94-5 

30.4 

46 

47 

19.8 

75. 0 

37.0 

06.5 

84.3 

71.2 

68.3 

76.8 

98.3 

34-5 

47 

48 

22.3 

77.6 

39.8 

09.4 

87.3 

74.4 

71.7 

80.4 

6902.  I 

38.5 

48 

49 

24.8 

80.3 

42.  6 

12.3 

90.4 

77.6 

75.0 

84.0 

05.9 

42.  6 

49 

.50 

5427.4 

5582.9 

5745.  3 

5915.2 

6093. 4 

6280.  8 

6478. 4 

6687.  6 

6909.  7 

7146.  7 

50 

51 

29.9 

ll-^ 

48.1 

18.  I 

96.4 

84.0 

81.8 

91.  2 

13.5 

50.8 

51 

52 

32.5 

88.2 

50.9 

21.0 

99-5 

87.2 

85.2 

94.8 

17.4 

54.9 

52 

53 

35.0 

90.9 

53.6 

23.9 

6102.5 

90.4 

88.6 

98.4 

21.  2 

59-0 

S^ 

54 

37.5 

93.5 

56.4 

26.8 

05.6 

93-6 

92.0 

6702.  0 

25.0 

63.1 

54 

55 

55 

5440.1 

5596. 2 

5759.2 

5929.  7 

6108.  7 

6296.  8 

6495. 4 

6705.  6 

6928. 9 

7167.2 

5fa 

42.6 

98.9 

62.0 

32.7 

II. 7 

6300.  I 

98.8 

09.2 

32.7 

71.3 

56 

57 

45.2 

5601.  5 

64.7 

35.6 

14.8 

03.3 

6502.  2 

12.8 

36.6 

75.4 

57 

5« 

47-7 

04. 2 

67.5 

38.  5 

17.8 

06.  5 

05.6 

16.4 

40.4 

79.5 

58 

59 

50.3 

06.8 

70.3 

41.4 

20.9 

09.7 

09.0 

20.0 

44.3 

83.6 

59 

M. 

66° 

67° 

68° 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

M. 

TABLE  3. 

[Page  267 

Meridional  Parts,  or  Increased  Latitudes. 

»»• 

Comp 

I 

•  299.1528 

M. 

0 

76° 

71° 

78° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

M. 

0 

/ 
7187.8 

7444.8 

7722. 1 

8023, 1 

8352.6 

/ 
8716.4 

9122.  7 

9583. 0 

10114. 0 

/ 
10741.7 

I 

91.9 

49-3 

26.9 

28.4 

58.3 

22.8 

29.9 

91.2 

23.6 

53.2 

I 

2 

96. 0 

53-7 

31-7 

33.6 

64.  I 

29. 2 

37.1 

99.4 

33.2 

64.7 

2 

7200. 2 

58.2 

36.5 

38.9 

69.9 

35.6 

44.3 

9607.  7 

42.8 

76.3 

3 

4 
5 

04-3 
7208.  5 

62.6 
7467.  I 

41.4 
7746. 2 

44.2 

75-7 

42.0 

51.5 

16.0 
9624. 3 

52.5 
10162. 2 

_    87.9^ 
10799. 6 

4 
5 

8049. 4 

8381.  S 

8748.5 

9158.8 

6 

12.6 

71.6 

51.0 

54-7 

87.3 

54.9 

66.1 

32.6 

71.9 

10811.3 

6 

7 

16.8 

76.1 

55-9 

60.0 

93.1 

61.4 

73.3 

40.9 

81.6 

23.0 

7 

S 

21.0 

So.  5 

60.8 

65.3 

67.9 

80.6 

49-3 

91.4 

34.7 

8 

9 

lO 

25-1 

85.0 

65.6 

70.6 

8404. 8 

74.4 

88.0 

57.6 

10201. 2 

46.6 

9 

7229.  3 

7489.  5 

7770.  5 

8075.  9 

8410.  6 

8780. 9 

9195.3 

9666.  0 

10211.0 

10858. 4     10  1 

II 

jj-  5 

94.0 

75-4 

81.3 

16.5 

87.4 

9202.  6 

74.5 

20.9 

70.3 

II 

12 

37-7 

98.  5 

80.3 

86.6 

22.3 

n  93-9 

10. 0 

82.9 

30.8 

82.2 

12 

13 

41.9 

7503-  I 

85.1 

91.9 

28.2 

8800.  5 

17.4 

91.3 

40.7 

94.2 

13 

14 
15 

46. 1 
7250. 3 

07.  6 
7512.  I 

90.0 
7795-  0 

97-3 

34.1 

07.0 

24.8 

99.8 

50.6 

1 0906. 2 

14 

8102.  6 

8440.0 

8813.6 

9232.  2 

9708. 3 

10260. 6 

10918. 3 

15 

i6 

54.5 

16.6 

99-9 

08.0 

45-9 

20.2 

39.6 

16.8 

70.6 

30.4 

16 

'l 

58.7 

21.2 

7804. 8 

13.4 

51.8 

26.  7 

47.0 

25.4 

80.6 

42.5 

17 

i8 

62.9 

25:7 

09.7 

18.7 

57.8 

33-3 

54.5 

33-9 

90.6 

54.7 

18 

19 

20 

67.2 

30.3 

14.  6 

24.1 

63.7 

40.0 

62.0 

42.5 

10300.  7 
10310.  8 

66.9 

19 

7271.4 

7534.  8 

7819.6 

8129.  5 

8469.  7 

8846.  6 

9269. 4 

9751- I 

10979. 2     20 

21 

75.6 

39-4 

24-5 

34.9 

75-6 

53-2 

76.9 

^i-7 

21.  0 

91.5     21 

22 

79-9 

44.0 

29-5 

40.4 

81.6 

59.9 

84.5 

68.4 

31.2 

1 1003.  8     22 

23 

84.1 

48.5 

34-4 

45. « 

87.6 

66.6 

92.0 

77.0 

41.4 

16.2  ,  23 

24 

25 

88.3 

53.1 

39-4 
7844.  4 

51.2 

93.6 

73-2 

99.5 

85.7 

51.6 

28.  7  1  24 
II041.2   !  25 

7292. 6 

7557-  7 

8156.6 

8499. 6 

8879.9 

9307. 1 

9794.  4 

10361.8 

26 

96.9 

62.3 

49.4 

62. 1 

8505. 6 

86.6 

14.7 

9803.  2 

72.  I 

53.7 

26 

27 

7301.  I 

66.9 

54-4 

67.6 

II. 6 

93-4 

22.3 

II. 9 

82.5 

66.3 

27 

28 

05-4 

71.5 

59.4 

73.0 

17.6 

8900.  I 

29.9 

20.  7 

92.8 

78.9 

28 

29 
30 

09.7 

76.1 

64.4 

78.5 

23.7 

06.8 
8913.6 

37.6 
9345. 2 

29.5 

10403.  2 

91.6 

29 

7313.9 

7580.  7 

7869.  4 

8184. 0 

8529.  7 

9838.3 

10413.6 

1 1 104.  3   '  30 

31 

18.  2 

85.3 

74.4 

89.5 

35.8 

20.4 

52.9 

47.2 

24.  I 

17.  I      31 

32 

22.5 

QO.  0 

79-4 

95.0 

41.8 

27.1 

60.6 

56.0 

34-6 

29.9      32 

33 

26.8 

94.6 

84.5 

8200.  5 

47.9 

33.9 

68.3 

64.9 

45-1 

42.8    :   S5 

34 

31- I 

99.2 

89.5 

06.0 

54.0 

40.8 

76.0 

73.8 

55-6 

55-  7  '  34 
1 1 168.  6  1  35 

35 

7335-4 

7603.  9 

7894-  5 

8211.5 

8560, 1 

8947.  6 

9383.  7 

9882.  8 

10466.  2 

3b 

39-7 

08.5 

99.6 

17.0 

66.2 

54.4 

91.5 

91.7 

76.8 

81.7     36 

37 

44.1 

13.2 

7904.  7 

22.6 

72.4 

61.3 

99.3 

9900.  7 

87.4 

94-  7     37 

3« 

48.4 

17.9 

09.7 

28.1 

78.5 

68.1 

9407. 0 

09.7 

98. 1 

1 1207.  8     38 

39 

40 

52.7 

22.5 

14.8. 

33.7 

84.7 

75.0 

14.8 

18.8 

10508.  8 

21.0     39 

1 1234. 2     40 

7357- 0 

7627.  2 

7919.9 

8239. 3 

8590.  8 

8981.9 

9422.  7 

9927.  8 

10519. 0 

41 

61.4 

31-9 

25.0 

44.8 

97.0 

88.8 

30.5 

36.9 

30.3 

47-4     41 

42 

65.7 

36.6 

30. 1 

50-4 

8603. 2 

95-7 

38.4 

46.0 

41.  I 

60. 8     42 

43 

70.1 

41-3 

35.2 

56.0 

09.4 

9002.  7 

46.3 

55.1 

52.0 

74.  I      43 

44 

74-4 

46.0 

40.3 

61.6 

15.6 

09.6 

54.2 

64.3 

62.9 

87.5 

44  1 

45 

7378.  8 

7650.  7 

7945-  4 

8267.  2 

8621.8 

9016.6 

9462.  I 

9973-  4 

10573.8 

11301.0 

45 

4b 

83., 

55-4 

50.5 

72.9 

28.0 

23-5 

70.0 

82.6 

84.7 

14. 5  ,  46 

47 

87.5 

60.  I 

55-7 

78.5 

34.2 

30.5 

77.9 

91.8 

95.7 

28.1     47 

48 

91.9 

65.8 

60.8 

84.1 

40.5 

37.5 

85.9 

lOOOI.  I 

10606.  7 

41. 7     48 

49 
50 

96.3 
7400.  6 

69.6 

66.0 

89.8 

46.8 

44.6 

93.9 

10.4 
10019. 7 

17.8 

10628.  9 

55.4  i  49 
1 1369.  I     50 

7674.  3 

7971.  I 

8295.4 

8653.0 

905 1 . 6 

9501.9 

51 

05.0 

79.1 

76.3 

8301.  I 

59-3 

58.6 

09.9 

29.0 

40.  0 

82.9     51 

52 

09.4 

83.  8 

81.5 

06.8 

65.6 

65.7 

18.0 

38.3 

51.  I 

96. 8     52 

53 

13.8 

88.6 

86.7 

12.5 

71.9 

72.8 

26.0 

47.7 

62.3 

11410. 7     53 

54 

18.  2 
"7422.7 

93-4 

91.8 

18.2 

78.2 

79.9 

34.1 

57.1 

73.6 

24. 6     54 

55 

7698.  I 

7997.  0 

8323.  9 

8684.  5 

9087.  0 

9542.  2 

10066. 5 

10684.  8 

1 1438.  6     55 

5^^ 

27.1 

7702.  9 

8002.  2 

29.6 

90.9 

94.1 

50.3 

76.0 

96.1 

52. 7     56 

57 

31-5 

07.7 

07.5 

35.3 

97.2 

9101.2 

58.5 

85.4 

10707.  5 

66.8  ;  57 

5« 

35-9 

12.5 

12.7 

41. 1 

8703.  6 

08.4 

66.6 

94.9 

18.8 

81.0  j  58 

59 
M. 

40.4 

17-3 

17.9 

78° 

46.8 

10.  0 

15.5 

74.8 

10104.  5 

30.3 

95-3  1  59 

76° 

77° 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

M.I 

Page  268] 

TABLE  4. 

Length  of  a 

Degree  in 

Latitude  and  Longitude. 

Lat. 

Deg.  of  Long. 

Deg.  of  Lat. 

Lat. 

Deg.  0 

'  Long. 

Deg.  ( 

)f  Lat. 

o 

Stat,  miles. 

Naut.  miles. 

Stat,  miles. 

Naut.  miles. 

0 

Stat,  miles. 

Naut.  miles. 

Stat,  miles. 

Naut.  miles. 

0 

69.  160 

60.  000 

68.  698 

59.  600 

45 

48.  986 

42.  498 

69.  044 

59- 899 

I 

.150 

59-  991 

.698 

.600 

46 

.  126 

41-  752 

.056 

.910 

2 

.119 

.964 

.699 

.601 

47 

47-251 

40-  993 

.068 

.920 

3 

.066 

.919 

.  700 

.602 

48 

46.  362 

.  222 

.080 

•931 

4 

68.  992 

•855 

.  702 

.603 

49 

45-  459 

39-439 

.092 

.941 

5 

68.  898 

59-773 

68.  704 

59-  605 

50 

44-  542 

38-643 

69.  104 

59^951 

6 

.783 

.673 

.  706 

.607 

51 

43.611 

37-  835 

.116 

.962 

7 

.647 

-555 

-709 

.609 

52 

42.  667 

.016 

.128 

•  972 

8 

.491 

.419 

.712 

.612 

53 

41-710 

36. 186 

.  140 

.982 

9 

.314 

.265 

•715 

-615 

54 

40.  740 

35-344 

-151 

-992 

lO 

68.116 

59-  093 

68.  719 

59-618 

55 

39-  758 

34.491 

69.  162 

60. 002 

II 

67.  898 

58- 904 

•723 

.621 

56 

3^-  763 

33-628 

•173 

.012 

12 

•659 

.697 

.728 

.625 

H 

37-  756 

32.  755 

.  184 

.022 

13 

.400 

-472 

-733 

.  629 

58 

36.  737 

31.872 

-195 

.032 

14 

.  120 

.229 

.738 

-634 

59 

35-  707 

30-  979 

.206 

.041 

15 

66. 820 

57.968 

68.  744 

59-  639 

60 

34. 666 

30.  076 

69.217 

60.  050 

16 

•  499 

.690 

.750 

-645 

61 

33-615 

29. 164 

.228 

.059 

17 

.158 

-394 

-757 

.651 

62 

32.553 

28.  242 

-238 

.068 

18 

65-  797 

.081 

.764 

-657 

63 

31.481 

27.311 

.248 

.077 

19 

.416 

56-751 

.771 

-663 

64 

30. 399 

26.  372 

.258 

.086 

20 

65.015 

56.404 

68.  779 

59.  669 

65 

29.  308 

25.425 

69. 268 

60. 094 

21 

64. 594 

-039 

-787 

.676 

66 

28.  208 

24. 471 

.277 

.  102 

22 

•  154 

55-657 

-795 

-683 

67 

27.  100 

23-  509 

.286 

.  no 

23 

63.  695 

.258 

.804 

.691 

68 

25.  983 

22. 540 

.294 

.117 

24 

.216 

54-  843 

-813 

.699 

69 

24.857 

21.  564 

-302 

.124 

25 

62.  718 

54-4" 

68.  822 

59-  707 

70 

23.  723 

20.582 

69.310 

60. 131 

26 

.  201 

53-  962 

.831 

•715 

71 

22.582 

19-593 

.318 

-137 

27 

61.665 

-497 

.840 

•723 

72 

21.435 

18.598 

.326 

-143 

28 

.  no 

.016 

•f5o 

.731 

73 

20.  282 

17-597 

-333 

- 149 

29 

60.  536 

52-518 

.860 

•  740 

74 

19.  122 

16.  590 

•339 

-155 

30 

59-  944 

52.  005 

68.  870 

59^  749 

75 

17-956 

15-578 

69-  345 

60.  161 

31 

•334 

51-476 

.881 

•758 

76 

16.  784 

14.561 

-351 

.166 

32 

58.  706 

50-931 

.892 

.767 

77 

15.607 

13-  539 

-357 

.171 

33 

.060 

-370 

•903 

.776 

78 

14.  425 

12.513 

.362 

-175 

34 

57-396 

49-  794 

.914 

.786 

79 

13-238 

1 1 . 484 

•  367 

.179 

35 

56-715 

49.  203 

68.  925 

59.  796 

80 

12.047 

10.452 

69.371 

60.  183 

3b 

.016 

48.  597 

-936 

.806 

81 

10.  853 

9-417 

•375 

.186 

37 

55-  300 

47.  976 

-947 

.816 

82 

9-656    . 

8-379 

•378 

.  189 

3« 

54.  568 

-340 

•959 

.826 

83 

8.456 

7-338 

.381 

.  192 

39 

53-819 

46.  690 

.971 

.836 

84 

7-253 

6.294 

•  384 

.194 

40 

53-  053 

46.  026 

68.  983 

59.  846 

85 

6.048 

5.248 

69^  387 

60. 196 

41 

52.271 

45-  348 

-995 

-856 

86 

4.841 

4.  200 

.389 

.198 

42 

51-473 

44-  656 

69. 007 

.866 

87 

3-632 

3- 151 

-390 

.199 

43 

50.  659 

43-  950 

.019 

.877 

88 

2.422 

2.  lOI 

•391 

.200 

44 

49.830 

.231 

.031 

.888 

89 

I.  211 

1.050 

•392 

.201 

TABLE  5A. 

Page  269 

V 

Distance  of  an  Object  by 

Two  Bearings 

Difference 

between 

DiCerence  between  the  course  and  first  bearing— Points. 

tlie  course 

<i  ri I'l  c  t» r'l^ n H 

bearing- 
Points. 

■» 

2 

2X 

VA 

2X 

3 

3X 

^%         1 

1.96 

1.09 

3'4' 

1-57 

0.94 

2. 19 

I-3I 

3'-^ 

1.32 

0.84 

1.76 

I.  12 

2.42 

1-53 

3f4 

1.14 

0.  76 

1.47 

0.99 

1.94 

1.30 

2.64 

1-77 

4 

1. 00 

0.71 

1.27 

0.90 

1.62 

I- 15 

2. 12 

1.50 

2.85 

2.01 

A% 

0.  90 

0.66 

1. 12 

0.83 

1.40 

1.04 

1-77 

'•^0 

2.29 

1.69 

3- OS 

2.  26 

4 '4 

0.81 

0.63 

I.  00 

0.77 

1.23 

0.95 

1-53 

I.  18 

1. 91 

1.48 

2.45 

1.90 

3-25 

2-51 

aH 

0.74 

0.  60 

0.91 

0.73 

1. 10 

0.89 

1-34 

1.08 

1.65 

1.32 

2.05 

1.65 

2.61 

2.  10 

5 

0.  69 

0.57 

0.83" 

0.  69 

1. 00 

0.83 

I.  20 

1. 00 

1-45 

I.  21 

1-77 

1.47 

2. 19 

1.82 

5. '4 

0.  64 

0.55 

0.77 

0.66 

0. 92 

0.79 

1.09 

0.94 

1.30 

I.  II 

1.56 

1-34 

1.88 

1.62 

5,'^ 

0. 60 

0.53 

0.  72 

0.63 

0.85 

0.75 

1. 00 

0.88 

1. 18 

I.  04 

1-39 

1.23 

1.66 

1.46 

5^/ 

0.57 

0.52 

0.68 

0.61 

0.79 

0.  72 

0.93 

0.84 

1.08 

0.98 

I.  26 

I.  14 

1.48 

1-34 

6 

0.54 

0.  50 

0.  64 

0.59 

0.74 

0.  69 

0.86 

0.  80 

1. 00 

0.92 

I.  16 

1.07 

1-35 

1.24 

6'^ 

0.  52 

0.49 

0.  60 

0.57 

0. 70 

0.66 

0.  Si 

0.  76 

0.93 

0.88 

1.07 

I.  01 

1.23 

I.  16 

6K 

0.  50 

0.47 

0.58 

0-55 

0.67 

0.  64 

0.77 

0.73 

0.88 

0.84 

I.  00 

0.96 

1. 14 

1.09 

634 

0.48 

0.46 

0.55 

0.54 

0.64 

0.  62 

0.73 

0.71 

0.83 

0.80 

0.94 

0.  91 

1.06 

1.03 

7 

0. 46 

0.45 

0.53 

0.52 

0. 61 

0.  60 

0.69 

0.68 

0.79 

0.77 

0.89 

0.87 

1. 00 

0.98 

7'^ 

0.45 

0.44 

0-51 

0.51 

0-59 

0.58 

0.  67 

0.66 

0.75 

0.74 

0.84 

0.83 

0.94 

0-93 

-T    I    / 

/    '2 

0.43 

0.43 

0.  50 

0.  50 

0.57 

0.  56 

0.  64 

0.64 

0.  72 

0.72 

0.80 

0.80 

0.  90 

0.  89 

iH 

0.42 

0.  42 

0.48 

0.48 

0-55 

0-55 

0.  62 

0.62 

0.  69 

0.69 

0.77 

0.77 

0.86 

0.86 

8 

0.41 

0.41 

0.47 

0.47 

0-53 

0.53 

0.60 

0.60 

0.67 

0.67 

0.74 

0.74 

0.82 

0.82 

«X 

0.41 

0.  41 

0.46 

0.46 

0.  52 

0.  52 

0  58 

0.58 

0.65 

0.65 

0.  72 

0.  72 

0.79 

0.79 

8"/ 

0.40 

0.40 

0-45 

0.45 

0.51 

0.51 

0.57 

0.57 

0.63 

0.63 

°-^g 

0.69 

0.  76 

0.  76 

834: 

0.39 

0.39 

0.45 

0.44 

0.  50 

0.  50 

0.  56 

0.55 

0.  61 

0.61 

0.68 

0.67 

0.74 

0.73 

9 

0.39 

0.38 

0.44 

0.43 

0.49 

0.48 

0.55 

0.54 

0.  60 

0.59 

0.66 

0.65 

0.  72 

0.71 

9 '4 

0.39 

0.38 

0.44 

0.42 

0.49 

0.47 

0.54 

0.  52 

0.59 

0.57 

0.64 

0.63 

0.  70 

0.68 

9'< 

0.38 

0-37 

0.43 

0,  41 

0.48 

0.46 

0-53 

0.51 

0.58 

0.56 

0.63 

0.  61 

0.  69 

0.66 

9V 

0.38 

0.36 

0.43 

0.  40 

0.48 

0.45 

0.  52 

0.49 

0.57 

0.54 

0.  62 

0.59 

0.  67 

0.63 

10 

0.3S 

0-35 

0.43 

0.40 

0.47 

0.44 

0.  52 

0.48 

0.57 

0.  52 

0.61 

0.57 

0.66 

0.61 

lo'i 

0.38 

0-35 

0.43 

0.39 

0.47 

0.43 

0.  52 

0.47 

0.  56 

0.51 

0.  61 

0.55 

0.65 

0-59 

10 14 

0.38 

0.34 

0.43 

0.38 

0.47 

0.42 

0.51 

0.45 

0.  56 

0.49 

0.  60 

0-53 

0.65 

0.57 

10  V 

0-39 

0.33 

0.43 

0.37 

0.47 

0.  40 

0.51 

0.44 

0.  56 

0.48 

0.  60 

0.51 

0.64 

0.55 

II 

0.39 

0.32 

0-43 

0.36 

0.47 

0.39 

0.51 

0.43 

0.  56 

0.46 

0.60 

0.  50 

0.  64 

0.53 

1 1 '4 

0.39 

0.31 

0.44 

0.35 

0.48 

0.38 

0.  52 

0.  41 

0.  56 

0.45 

0.  60 

0.48 

0.64 

0.51 

II  '2 

0.40 

0.31 

0.44 

0.34 

0.48 

0.37 

0.  52 

0.40 

0.  56 

0.43 

0.60 

0.46 

0.63 

0.49 

1 1 '4 

0.41 

0.30 

0.45 

0-33 

0.49 

0.36 

0.  52 

0.39 

0.56 

0.42 

0.  60 

0.44 

0.64 

0.47 

12 

0.41 

0.  29 

0.45 

0.32 

0.49 

0.3s 

0.53 

0.37 

0-57 

0.40 

0.  60 

0.43 

0.64 

0.45 

•2  ■4' 

0.42 

0.28 

0.46 

0.31 

0.50 

0.34 

0.54 

0.36 

0.57 

0.38 

0.61 

0.41 

0.  64 

0.42 

12  >< 

0.  43 

0.  28 

0.47 

0.30 

0.51 

0.32 

0-55 

0-35 

0.  58 

0.37 

0.  61 

0.39 

0.65 

0.41 

I2X 

0.45 

0.  27 

0.48 

0.29 

0.  52 

0.31 

0.  56 

0.33 

0.59 

0.35 

0.  62 

0.37 

0.65 

0.39 

13 

0.  46 

0.  26 

0.  50 

0.28 

0.53 

0.  ^0 

0.57 

0.32 

0,  60 

0.33 

0.63 

0.35 

0  66 

0.37 

i3>4; 

0.48 

0.  24 

0.51 

0.  26 

0-55 

0.28 

0.58 

0.  30 

0.  61 

0.32 

0.64 

0.33 

0.67 

0-35 

1 3 '^2 

0.  50 

0.23 

0.53 

0.25 

0.57 

0.  27 

0.60 

0.28 

0.63 

0.30 

0.66 

0.31 

0.69 

0.  32 

i3,¥ 

0.  52 

0.  22 

0-55 

0.  24 

0.59 

0.  25 

0.62 

0.  26 

0.65 

0.2S 

0.68 

0.  29 

0.  70 

0.  30 

14 

0.54 

0.  21 

0.58 

0.22 

0.61 

0.23 

0.64 

0.24 

0.67 

0.  26 

0.  69 

0.27 

0.  72 

0.28 

Page  270 

TABLE   5A. 

Distance  of  an  Object  by 

Two  Bearings. 

Difference 

between 

Difference  between  the  course  and  first  bearing— Points. 

the  course 

and  second 

bearing — 

Points. 

3J< 

4 

4X        1 

4>^ 

41^        1 

5 

5X         1 

4^ 



3-44 

2.  76 

5 

2.76 

2.  30 

3.62 

3.01 

5X 

2.31 

1.98 

2.91 

2.50 

3.80 

3.26 

S'A 

1.99 

1.76 

2.44 

2.15 

3-05 

2.69 

3.96  1 

^■il 

sH 

1-75 

1-59 

2. 10 

I.  90 

2.55 

2.31 

3.18 

2.88 

4.12 

3-72 

6 

1-57 

1-45 

1.85 

I.  71 

2. 20 

2.03 

2.66 

2.46 

3-31 

3-05 

4.26 

3-94 

6X 

1.42 

1-34 

1.65 

1.56 

1.94 

1.82 

2.29 

2.  16 

2.77 

2.61 

3-42 

3.22 

4.40 

4.  14 

(^Vz 

1-31 

1-25 

1.50 

1.44 

1-73 

1.66 

2.02 

1-93 

2.38 

2.28 

2.86 

2.74 

3-53 

3-38 

6U 

I.  21 

I.  17 

1.38 

^■V:, 

1-57 

1.52 

1. 81 

1-75 

2.  10 

2. 04 

2.47 

2.39 

2.95 

2.87 

7 

I-  13 

I.  II 

1.27 

1-25 

1.44 

1. 41 

1.64 

I. 61 

1.88 

1.84 

2.17 

2.13 

2-55 

2.  50 

T4 

1.06 

1.05 

1. 19 

I.  17 

^■i-, 

1.32 

1.50 

1.49 

1.70 

1.69 

1.94 

1.92 

2.  24 

2.22 

714 

1. 00 

I.  00 

I.  II 

I.  II 

1.24 

1.24 

1-39 

1.38 

1.56 

1-55 

1.76 

1.76 

2.  01 

2.  00 

IYa 

0.95 

0-95 

1.05 

1.05 

I. 17 

1. 17 

1.30 

1.30 

1-45 

1.44 

1.62 

1.62 

1.82 

1.82 

8 

0.  91 

0.  gi 

1. 00 

I.  00 

I.  10 

1. 10 

I.  22 

I.  22 

1-35 

1-35 

1.50 

1.50 

1.67 

1.67 

8X 

0.87 

0.87 

0.95 

0.95 

I.  OS 

1.05 

I- 15 

I- 15 

1.27 

1.26 

1.40 

1-39 

1-54 

1-54 

8^ 

0.84 

0.83 

0.91 

0.91 

1. 00 

1. 00 

1.09 

I.  09 

I.  20 

1. 19 

1-31 

1.30 

1.44 

1-43 

8^ 

0.81 

0.80 

0.88 

0.87 

0.  96 

0.95 

1.04 

1.03 

I.  14 

1. 12 

1.24 

I.  22 

^•^, 

1-34 

9 

0.  78 

0.77 

0.85 

0.83 

0.92 

0. 90 

1. 00 

0.98 

1.08 

1.06 

1. 18 

I- 15 

1.28 

I.  25 

9J4^ 

0.  76 

0.  74 

0.82 

0.80 

0.89 

0.86 

0.96 

0.93 

1.04 

1. 01 

I.  12 

1.09 

I.  21 

I.  18 

9'/^ 

0.  74 

0.  71 

0.80 

0.77 

0.86 

0.83 

0.93 

0.89 

1. 00 

0.96 

1.08 

1.03 

L.  16 

I.  II 

9^ 

o-  73 

0.68 

0.78 

0  74 

0.84 

0.79 

0.90 

0.85 

0.97 

0.91 

I.  04 

0.97 

I.  II 

1.04 

lO 

0.  71 

0.66 

0.  77 

0.71 

0.82 

0. 76 

0.88 

0.81 

0.94 

0.87 

I.  00 

0.92 

1.07 

0.99 

10^ 

0.  70 

0.63 

0-75 

0.68 

0.80 

0.72 

0.86 

0.77 

0. 91 

0.82 

0.97 

0.8S 

1.03 

0.93 

lo;^ 

0.  69 

0.61 

0.74 

0.65 

0.79 

0.69 

0.84 

0.74 

0.89 

0.78 

0.94 

0.83 

I.  00 

0.88 

lO^ 

0.68 

0-59 

0.73 

0.63 

0.77 

0.66 

0.82 

0.  70 

0.87 

0.75 

0.92 

0.79 

0.97 

0.83 

II 

0.68 

0.56 

0.  72 

0.  60 

0.  76 

0.64 

0.81 

0.67 

0.85 

0.71 

°-gS 

0.75 

0.95 

0.79 

"X 

0.67 

0.54 

0.71 

0.57 

0.  76 

0.61 

0.80 

0.64 

0.84 

0.67 

0.88 

0.71 

0.93 

0.75 

iiK 

0.67 

0.  52 

0.  71 

0-55 

0.75 

0.58 

0.79 

0.61 

0.83 

0.64 

0.87 

0.67 

0.91 

0.  70 

II 34: 

0.67 

0.  50 

0.  71 

0.52 

0.74 

0.55 

0.78 

0.58 

0.82 

0. 61 

0.86 

0.  64 

0.90 

0.66 

12 

0.67 

0.48 

0.  71 

0.  50 

0.74 

0.52 

0.78 

0.55 

0.81 

0.57 

0.85 

0.60 

0.88 

0.63 

12X 

0.67 

0.45 

0.71 

0.48 

0.74 

0. 50 

0.77 

0.52 

0.81 

0.54 

0.84 

0.  56 

0.87 

0.59 

12^ 

0.68 

0-43 

0.71 

0-45 

0.74 

0.47 

0.77 

0.49 

0.80 

0.51 

0.  84 

0.53 

0.87 

0.55 

12^ 

0.68 

0.41 

0.  71 

0.43 

0.74 

0.44 

0.77 

0.46 

0.80 

0.48 

0.83 

0. 50 

0.86 

0.51 

13 

0. 69 

0.38 

0.72 

0.  40 

0.75 

0. 42 

0.78 

0.43 

0.80 

0.45 

0.83 

0.46 

0.86 

0.48 

13X 

0.  70 

0.36 

0.73 

0-37 

0.  76 

0.39 

0.78 

0.  40 

0.  81 

0.41 

0.83 

0.43 

0.86 

0.44 

13K 

0.71 

0.34 

0.  74 

0-35 

0.  76 

0. 36 

0.79 

0.37 

0.81 

0.38 

0.84 

0.39 

0.86 

0.41 

13X 

0.73 

0.31 

0-75 

0.32 

0.77 

0.33 

0.80 

0.34 

0.82 

0.35 

0.84 

0.36 

0.86 

0.37 

14 

0.74 

0.28 

0.77 

0.  29 

0.79 

0. 30 

0.81 

0.  31 

0.83 

0.32 

0.85 

0.32 

0.87 

0.33 

5. 

/2 

5, 

'4 

( 

i 

6. 

4 

6. 

/< 

6K 

'      1 

6>^ 

4-52 

4-33 

6^ 

3-63 

3-52 

4.63 

4-49 

7 

3-04 

2.98 

3-72 

3.65 

4-74 

4.64 

7;^ 

2.62 

2.59 

3- 1 1 

3.08 

3.80 

3-76 

4.83 

4-77 

2.  30 

2.  29 

2.68 

2.67 

3.18 

3-17 

3-87 

3.86 

4.91 

4.88 

7X 

2.06 

2.  06 

2.36 

2.36 

2.74 

2.74 

3-24 

3  24 

3-94 

3-93 

4-97 

4-97 

8 

1.87 

1.87 

2.  II 

2.  II 

2.41 

2.41 

2.79 

2.79 

3.30 

3-30 

3-99 

3-99 

5-03 

5-03 

8^ 

1.72 

I.  71 

1.92 

1.92 

2.  16 

2.  16 

2.46 

2.46 

2.84 

2.84 

^■li 

3-34 

4.04 

4-03 

^A 

1-59 

1.58 

1.76 

1-75 

1.96 

1-95 

2.  20 

2.19 

2.50 

2.49 

2.88 

2.87 

3-38 

3-36 

m 

1.48 

1.46 

1.63 

1. 61 

1.80 

1.78 

2.00 

1.98 

2.24 

2.21 

2-53 

2.51 

2.91 

2.88 

9 

1-39 

1.36 

1-52 

1.49 

1.66 

1.63 

1.83 

1.80 

2.03 

1.99 

2.  27 

2.23 

2.56 

2.51 

-  9X 

I-3I 

1.27 

1.42 

1.38 

1.55 

1.50 

1.69 

1.64 

1.86 

I. 81 

2.06 

2.00 

2.  29 

2.23 

9K 

1.25 

I.  19 

1-35 

1.29 

1.46 

1-39 

1.58 

I-5I 

1.72 

1.65 

1.89 

1. 81 

2.08 

1.99 

9^ 

I.  19 

I.  12 

1.28 

I.  20 

1.38 

1.30 

1.48 

1.40 

I. 61 

I-5I 

1-75 

1.64 

I. 91 

1.80 

10 

I.  14 

1.05 

I.  22 

1-13 

I-3I 

I.  21 

1.40 

1.30 

I-5I 

1-39 

1.62 

1.50 

1.77 

1.63 

I0>( 

I.  10 

0.99 

I.  17 

I.  06 

1-25 

I-  13 

1-33 

1.20 

1.42 

I.  29 

1-53 

1.38 

1.65 

1.49 

io>^ 

1.06 

0.94 

I-  13 

0.99 

I.  20 

1.05 

1.27 

1. 12 

1-35 

I.  19 

1.44 

1.27 

'•55 

1.36 

10^ 

1.03 

0.88 

1.09 

0-93 

I- 15 

0.99 

I.  22 

1.04 

1.29 

I.  II 

1-37 

I.  iS 

1.46 

I.  25 

II 

1. 00 

0.83 

1.05 

0.88 

I.  II 

0.  92 

I.  17 

0.97 

1.24 

1.03 

I-3I 

1.09 

1-39 

1-15 

iiX 

0.98 

0.78 

1.03 

0.82 

1.08 

0.87 

I- 13 

0.91 

I.  19 

0.96 

1.25 

I. 01 

1.32 

1.06 

IIK 

0.95 

0.73 

1. 00 

0.77 

1.05 

0.81 

1. 10 

0.85 

I.  15 

0.89 

1. 21 

0.93 

1.27 

0.98 

1 1 34: 

0.94 

0.  69 

0.98 

0.  72 

1.02 

0.  76 

1.07 

0.  79 

I.  12 

0.83 

I. 17 

0.86 

I.  22 

0.  90 

12 

0.92 

0.65 

0. 96 

0.68 

I.  00 

0.71 

1.04 

0.73 

1.09 

0.77 

I- 13 

0.80 

I.  18 

0.83 

I2X 

0.91 

0.61 

0.94 

0.63 

0.98 

0.66 

1.02 

0.68 

1.06 

0.71 

1. 10 

0.  74 

I.  14 

0.77 

I2>^ 

0.90 

0.57 

0.93 

0.59 

0.97 

0.  61 

1. 00 

0.63 

1.04 

0.66 

1.07 

0.68 

I.  II 

0.  71 

12^ 

0.89 

0.53 

0. 92 

0.55 

0-95 

0.57 

0.98 

0.59 

1.02 

0.61 

1.05 

0.63 

1.08 

0.65 

13 

0.89 

0.49 

0.91 

0.51 

0.94 

0.52 

0.97 

0.54 

1. 00 

0.  56 

1.03 

0.57 

1.06 

0.59 

i3^( 

0.88 

0.45 

0.91 

0.47 

0.93 

0.48 

0.96 

0.49 

0.99 

0.51 

1. 01 

0.  52 

1.04 

0.54 

0 

13K 

0.88 

0.42 

0.91 

0.43 

0.93 

0.44 

0.95 

0.45 

0.98 

0.46 

1. 00 

0.47 

1.02 

0.48 

13X 

0.88 

0.38 

0.90 

0.39 

0. 92 

0.40 

0.95 

0.41 

0.97 

0.41 

0.99 

0.42 

I. 01 

0.43 

14 

0.89 

0.34 

0.91 

0.  35     0. 92 

0-35 

0.94 

0.36 

0.90 

0.37  1  0.98 

0.38 

1. 00 

0.38 

TABLE  5A.                                               [Page  271 

%. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

Difference  between  the  course  and  first  bearing— Points. 

the  course 

111(1  ^fr*f'nii(l 

bearing — 
Points. 

5 

IK 

%y2 

IK 

8 

sx 

8K 

SH 

»    1 

8% 

07 

5.06 

S'C 

4.07 

4.05 

5.10 

5.08 

sv 

3-41 

J-    J/ 

4. 10 

4.06 

5-12 

5.06 

9 

2.94 

2.88 

3-43 

3-36 

4.II 

4-03 

5-13 

5-03 

9H 

2.58 

2.51 

2  95 

2.87 

3-44 

3-34 

4.12 

3-39 

5.12 

4-97 

9>^ 

2.31 

2.  21 

2.  60 

2.49 

2.96 

2.84 

3-44 

3-30 

4. 1 1 

3-93 

5.10 

4.88 

9H 

2.  10 

1.98 

2.33 

2.19 

2.61 

2.46 

2.97 

2.79 

3-44 

3-24 

4.10 

3.86 

5-07 

4-77 

10 

1.92 

1.78 

2.  II 

1-95 

2.34 

2.16 

2.61 

2.41 

2.96 

2.74 

3-43 

3-17 

4.07 

3-76 

5-03 

4.64 

lO'i 

1.78 

I.  61 

1-93 

1-75 

2.12 

1.92 

2-34 

2. 1 1 

2.61 

2.36 

2-95 

2.67 

3-41 

3.08 

4.04 

3-65 

I0>4 

1.66 

1.46 

1.79 

1.58 

1.94 

1. 71 

2.12 

1.87 

2.34 

2.06 

2.60 

2.29 

2.94 

2.59 

3-38 

2.98 

lo^V 

1.56 

1-34 

1.67 

1-43 

1.80 

1-54 

1-95 

1.67 

2.12 

1.82 

2.. 33 

2.00 

2.58 

2.22 

2.91 

2.50 

1 1 

1.47 

1.22 

1-57 

1.30 

1.68 

1-39 

1.80 

1.50 

1.94 

1.62 

2. 1 1 

1.76 

2.31 

1.92 

2.56 

2.13 

n'+ 

1.40 

I.  12 

1.48 

1. 19 

1-57 

1.26 

1.68 

1-35 

1.80 

1.44 

1-93 

1-55 

2.10 

1.69 

2.29 

1.84 

ii'< 

1.34 

1.03 

1. 41 

1.09 

1.49 

I-I5 

1.58 

1.22 

1.68 

1.30 

1.79 

1.38 

1.92 

1.49 

2.08 

1. 61 

ii:V 

1.28 

0.95 

1-34 

1. 00 

1. 41     1.05 

1.49 

1. 10 

1-57 

1. 17 

1.67 

1.24 

1.78 

1.32 

1. 91 

1. 41 

12 

1.23 

0.87 

I.  29 

0.91 

1-35  1  0.95 

1.41 

1. 00 

1.49 

1.05 

'•57 

I. II 

1.66 

1. 17 

1.77 

1-25 

1 2^4 

I.  19 

0.80 

1.24 

0.83 

1.29 

0.87 

1-35 

0.91 

1. 41 

0.95 

1.48 

1. 00 

1.56 

1.05 

1.65 

I. II 

12}4 

I- 15 

0-73 

I.  20 

0.76 

1.24 

0.79 

1.29 

0.82 

1-35 

0.86 

1.41 

0.89 

1.47 

0.93 

1-55 

0.98 

^2)4 

I.  12 

0.67 

I.  16 

0.69 

1.20 

0.72 

1.25 

0.74 

1.29 

0.77 

1-34 

0.80 

1.40 

0.83 

1.46 

0.87 

13 

I.  09 

0.61 

I- 13 

0.63 

1. 16 

0.65 

1.20 

0.67 

1.24 

0.69 

1.29 

0.72 

1-34 

0.74 

1-39 

0.77 

i3"4 

1.07 

0.55 

I.  10 

0.57 

I-I3 

0.58 

1. 17 

0.60 

1.20 

0.62 

1.24 

0.64 

1.28 

0.66 

1.32 

0.68 

13 '2 

r.05 

0.50 

1.08 

0.51 

1. 10 

0.52 

I-I3 

0.53 

1. 16 

0-55 

1.20 

0.56 

1.23 

0.58 

1.27 

0.60 

1 3 '4 

1.03 

0.44 

I.  06 

0.45 

1.08    0.46 

I. II 

0.47 

1-13 

0.48 

1. 16 

0.50 

1. 19 

0.51 

1.22 

0.52 

14 

1.02 

0.39 

I.  04 

0.40 

1.06    0.41 

1.08 

0.41 

1. 10 

0.42 

I-I3 

0-43 

I-I5 

0.44 

1. 18 

0.45 

4 

9 

'4 

9J 

4 

9M 

10 

lox 

10/2 

10^ 

11 

loX 

97 

4-50 

lOj^ 

3 

99 

3-52 

4.91 

4-33 

1034 

3 

34 

2.87 

3-94 

3.38 

4.83 

4.14 

II 

2 

88 

2.39 

3-3° 

2.74 

3-87 

3.22 

4-74 

3-94 

11 '4 

2 

53 

2. 04 

2.84 

2.28 

3-24 

2.61 

3.80 

3-05 

4-63 

Hi 

Il'i 

2 

27 

1-75 

2.  50 

1-93 

2.79 

2.16 

3.18  i  2.46 

3-72 

2.88 

4-52 

3-49 

I  13,4 

2 

06 

1-52 

2.24 

1.66 

2.46 

1.82 

2.74  1  2.03 

3-" 

2.31 

3.63 

2.69 

4.40 

3.20 

12 

89 

'■^ 

2.03 

1.44 

2.20 

1.56 

2.41 

1. 71 

2.68 

1.90 

3-04 

2.15 

3-53 

2.50 

4.26 

3.01 

I2X 

75 

I.  18 

1.86 

1.25 

2.00 

1-34 

2.16 

1-45 

2.36 

1-59 

2.62 

1.76 

2.95 

1.98 

3-42 

2.30 

I2K 

62 

1.03 

1.72 

1.09 

1.83 

1. 16 

1.96 

•1.24 

2. 1 1 

1-34 

2.30 

1.46 

2-55 

1.62 

286 

1.82 

I2K 

53 

0.  91 

I.  61 

0.96 

1.69 

1. 01 

1.80 

1.07 

1.92 

1. 14 

2.06 

1.23 

2.24 

1-34 

2.47 

1.47 

13 

44 

0.80 

1-51 

0.84 

1.58 

0.88 

1.66 

0.92 

1.76 

0.98 

1.87 

1.04 

2.01 

I. II 

2.17 

1. 21 

13,!^ 

37 

0.71 

1.42 

0-73 

1.48 

0.76 

1-55 

0.80 

1.63 

0.84 

1.72 

0.88 

1.82 

0.94 

1.94 

1. 00 

I3K 

31 

0.  62 

1-35 

0.64 

1.40 

0.66 

1.46 

0.69 

1.52 

0.72 

1-59 

0.75 

1.67 

0.79 

1.76 

0.S3 

13^^ 

25 

0.54 

I.  29 

0-55 

1-33 

0.57 

1.38 

0.59 

1.42 

0.61 

1.48 

0.63 

1-54 

0.66 

1.62 

0.69 

14 

I. 21 

0.46 

1.24 

0.47 

1.27 

,0.49 

I-3I 

0.50 

1-35 

0.52 

1.39 

0-53 

1.44 

0-55 

1.50 

0.57 

11 

X 

UK 

11;'4 

12 

I'iX 

WA 

12 

U 

.  -| 

I2K 

4.12 

2.77 

12^4 

3-31 

2.  10 

3-96 

2.51 

123/ 

2.77 

1.65 

3.18 

1.90 

3.80    2.26 

13 

2.38 

1.32 

2.66 

1.48 

3-05 

1.69 

3.62 

2.01 

I3X 

2.  10 

1.08 

2. 29 

1. 18 

2.55 

I-3I 

2.91 

1.50 

3-44:  1-77 

13;^^ 

1.88 

0.89 

2.02 

0.95 

2.20 

1.04 

2.44 

I-I5 

2.76    1.30 

3-25 

1-53 

13^4: 

1.70 

0.73 

1. 81 

0.77 

1.94 

0.83 

2.10 

0.90 

2.31  ,  0.99 

2.61 

1. 12 

3-05 

1-31 

14 

1.56 

0.60 

1.64 

0.63 

1-73 

0.66 

1.85 

0.71 

1.99    0.76 

2.19 

0.84 

2.45 

0.94 

2.85 

1.09 

Page  272]                                                TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 
the  course 

Difference  between  the  course  an'i  first  bearing. 

and  second 
bearing. 

20° 

22° 

24° 

26° 

28° 

30°         1 

32°         1 

30° 

1.97 

0.98 

32 

1.64 

0.87 

2. 16 

I.  14 

34 

1. 41 

0.79 

1.80 

1. 01 

2.34 

I-3I 

36 

1.24 

0.73 

1-55 

0.91 

1.96 

I.  15 

2.52 

1.48 

38 

I.  II 

0.68 

1.36 

0.84 

1.68 

1.04 

2.  II 

1.30 

2.  70 

1.66 

40 

1. 00 

0.64 

1. 21 

0.78 

1.48 

0.95 

I. 81 

1. 16 

2.26 

1.45 

2.88 

1.85 

42 

0.91 

0.  61 

1. 10 

0.73 

1.32 

0.88 

1-59 

1.06 

1.94 

1.30 

2.40 

1. 61 

3-05 

2.04 

44 

0.84 

0.  58 

1. 00 

0.  69 

1. 19 

0.S3 

1.42 

0.98 

I.  70 

I.  18 

2.07 

1.44 

2.55 

1.77 

46 

0.78 

0.  56 

0.92 

0.66 

1.09 

0.  78 

I.  28 

0.  92 

1-52 

I.  09 

I. 81 

I.  30 

2. 19 

1.58 

48 

0.73 

0.54 

0.85 

0.  64 

I.  00 

0.74 

I. 17 

0.87 

1-37 

1.02 

1.62 

I.  20 

I.  92 

1.43 

50 

0.68 

0.52 

0.80 

0.  61 

0.93  ! 

0.71 

1.08 

0.83 

1.25 

0.  96 

1.46 

1. 12 

I.  71 

I-3I 

52 

0.65 

0.51 

0-75 

0.59 

0.87  : 

0.68 

1. 00 

0.79     I.  15 

0.  91 

^•33 

1.05 

1-55 

1.22 

54 

0.  61 

0.  49     0.  71 

0.57 

0.81 

0.66 

0.93 

0.  76 

1.07 

0.87 

1.23 

0.99 

1. 41 

I.  14 

56 

0.58 

0.  48     0.  67 

0.  56 

0.77 

0.64 

0.88 

0-73 

I.  00 

0.83 

I.  14 

0.95 

1.30 

1.08 

58 

0.  56 

0.  47     0.  64 

0.54 

0-73 

0.62 

0.83 

0.  70 

0.94 

0.80 

1.07 

0.90 

1. 21 

1.03 

60 

0-53 

0.  46 

0.61 

0.53 

0.69 

0. 60 

0.78 

0.68 

0.89 

0.77 

I.  00 

0.87 

I- 13 

0.98 

62 

0.51 

0.45 

0.58 

0.51 

0.66 

0.58 

0.75 

0.66 

0.84 

0.74 

0.94 

0.83 

1.06 

0.94 

64 

0.49 

0.44 

0.  56 

0.  50 

0.63 

0.57 

0.  71 

0.64 

0.80 

0.72 

0.89 

0.  80 

1. 00 

0.90 

66 

0.48 

0.43 

0.54 

0.49 

0.61 

0.56 

0.68 

0.62 

0.  76 

0.  70 

0.85 

0.78 

0.95 

0.87 

68 

0.46 

0.43 

0.  52 

0.48 

0.59 

O.S4 

0.66 

0.  61 

0-73 

0.68 

0.81 

0-75 

0.  90 

0.84 

70 

0.45 

0.42 

0.  50 

0.47 

0-57 

0-53 

0.  63 

0.59 

0.  70 

0.66 

0.78 

0.73 

0.86 

0.81 

72 

0.43 

0.41 

0.49 

0.47 

0-55 

0.52 

0.61 

0.58 

0.68 

0.64 

0.7s 

0.71 

0.82 

0.  78 

74 

0.42 

0.41 

0.48 

0.46 

0-53 

0.51 

0.59 

0.57 

0.65 

0.63 

0.  72 

0.  69 

0.79 

0.  76 

76 

0.41 

0.40 

0.46 

0.45 

0.  52 

0.  50 

0.57 

0.56 

0.63 

0.  61 

0.  70 

0.  67 

0.  76 

0.74 

78 

0.40 

0-39 

0.45 

0.44 

0.  50 

0.49 

0.  56 

0.54 

0.  61 

0.  60 

0.67 

0.66 

0.74 

0.72 

80 

0.39 

0.39 

0.44 

0.44 

0.49 

0.48 

0.54 

0-53 

0.  60 

0.59 

0.65 

0.  64 

0.71 

0.  70 

82 

0.39 

0.38 

0-43 

0.43 

0.48 

0.47 

0-53 

0.52 

0.58 

0.57 

0.63 

0.63 

0.  69 

0.  69 

84 

0.38 

0.38 

0.42 

0.42 

0.47 

0.47 

0.52 

0.51 

0-57 

0.56 

0.  62 

0.61 

0.67 

0.  67 

86 

0.37 

0.37 

0.42 

0.42 

0. 46 

0.46 

0.51 

0.51 

0-55 

0.55 

0.  60 

0.  60 

0.66 

0.  65 

88 

0.37 

0.37 

0.41 

0.41 

0.45 

0.45 

0.  50 

0.50 

0.54 

0.54 

0.59 

0.59 

0.  64 

0.  64 

90 

0.36 

0.36 

0.40 

0. 40 

0.45 

0-45 

0.49 

0.49 

0.53 

0.53 

0.58 

0.58 

0.62 

0.  62 

92 

0.36 

0.  36 

0.40 

0.40 

0.44 

0.44 

0.48 

0.48 

0.  52 

0.  52 

0-57 

0.57 

0.  61 

0.  6i 

94 

0.36 

0.35 

0.39 

0.39 

0.43 

0-43 

0.47 

0.47 

0.51 

0.51 

0.  56 

0-55 

0.  60 

0.60 

96 

0.35 

0-3S 

0.39 

0.39 

0.43 

0.43 

0.47 

0.46 

0.51 

0.  50 

0.55 

0.54 

0.59 

0.59 

98 

0.35 

0.35 

0-39 

0.38 

0.42 

0.42 

0.46 

0.46 

0.  50 

0.  50 

0-54 

0.53 

0.58 

0.57 

100 

0.35 

0.34 

0.38 

0.38 

0.42 

0.41 

0.46 

0.45 

0.49 

0.49 

0.53 

0.  52 

0.57 

0.  56 

102 

0-35 

0.34 

0.38 

0.37 

0.42 

0.41 

0.45 

0.44 

0.49 

0.48 

0.53 

0.51 

0.  56 

0-55 

104 

0.34 

0-33 

0.38 

0.37 

0.41 

0.40 

0.45 

0-43 

0. 48 

0.47 

0.  52 

0.  50 

0.  56 

0.54 

106 

0-34 

0-33 

0.38 

0.36 

0.41 

0.39 

0.45 

0-43 

0.48 

0.46 

0.52 

0.  50 

0-55 

0-53 

108 

0.34 

0.32 

0.38 

0.36 

0.41 

0.39 

0.44 

0.42 

0.48 

0.45 

0.51 

0.49 

0.55 

0.52 

no 

0.34 

0.32 

0.37 

0.35 

0.41 

0.38 

0.44 

0.41 

0.47 

0.44 

0.51 

0.48 

0.54 

0.51 

112 

0.34 

0.32 

0.37 

0.35 

0.41 

0.38 

0.44 

0.41 

0.47 

0.44 

0.  50 

0.47 

0.54 

0.  50 

114 

0.34 

0.31 

0.37 

0-34 

0.41 

0.37 

0.44 

0.40 

0.47 

0.43 

0.  50 

0.46 

0.54 

0.49 

116 

0.34 

0.31 

0.38 

0.34 

0.41 

0.37 

0.44 

0.39 

0.47 

0.42 

0.  50 

0.45 

0-53 

0.48 

118 

0.35 

0.31 

0.38 

0.33 

0.41 

0.36 

0.44 

0.39 

0.47 

0.41 

0.  50 

0.44 

0.53 

0.47 

120 

0.35 

0.30 

0.38 

0-33 

0.41 

0.36 

0.44 

0.38 

0.47 

0.41 

0.  50 

0.43 

0.53 

0.  46 

122 

0.35 

0.30 

0.38 

0.32 

0.41 

0.35 

0.44 

0-37 

0.47 

0.40 

0.  50 

0.  42 

0.53 

0.45 

124 

0.35 

0.  29 

0.38 

0.32 

0.41 

0.34 

0.44 

0.37 

0.47 

0.39 

0.  50 

0.42 

0.53 

0.44 

126 

0.36 

0.  29 

0.39 

0.31 

0.42 

0.34 

0.45 

0.36 

0.47 

0.38 

0.  50 

0.41 

0.53 

0.43 

128 

0.  36 

0.28 

0.39 

0.3' 

0.42 

0.33 

0.45 

0-35 

0.48 

0.38 

0.  50 

0.40 

0.53 

0.42 

130 

0.  36 

0.28 

0.39 

0.30 

0.42 

0.32 

0.45 

0-35 

0.48 

0.37 

0.51 

0.39 

0.54 

0.41 

132 

0.37 

0.27 

0.40 

0.30 

0.43 

0.32 

0.46 

,  0.34 

0.48 

0.36 

0.51 

0.38 

0.54 

0. 40 

134 

0.37 

0.  27 

0.40 

0.29 

0-43 

0.31 

0.46 

1  0.33 

0.49 

0.35 

0.52 

0.37 

0.54 

0.39 

136 

0.38 

0.  26 

0.  41 

0.28 

0.44 

0.30 

0.47 

0.32 

0.49 

0.34 

0.  52 

0.  36 

0-55 

0.38 

138 

0.39 

0.  26 

0.42 

0.28 

0.45 

0.30 

0.47 

0.32 

0.50 

0.33 

0.53 

0.35 

0-55 

0.37 

140 

0.39 

0.  25 

0.42 

0.  27 

0.45 

0.  29 

0.48 

;  0.31 

0.51 

0.33 

0.53 

0.34 

0.  56 

0.36 

142 

0.40 

0.  25 

0.43 

0.27 

0.46 

0.28 

0.49 

0.30 

0.51 

0.32 

0.54 

0.33 

0.  56 

0.35 

144 

0.41 

0.  24 

0.44 

0.  26 

0.47 

0.28 

0.  50 

0.  29 

0.52 

0.31 

0-55 

0.32 

0.57 

0.34 

146 

0.42 

0.  24 

0.45 

0.25 

0.48- 

0.27 

0.51 

0.28 

0-S3 

0.30 

0.  56 

0.31 

0.58 

0.32 

148 

0.43 

0.23 

0.46 

0.25 

0.49 

0.26 

0.  52 

0.27 

0.54 

0.29 

0.57 

0.30 

0.59 

0.31 

150 

0.45 

0.  22 

0.48 

0.  24 

0.  50 

0.  25 

0-53 

0.26 

0-55 

0.28 

0.58 

0.  29 

0.  60 

0.30 

152 

0.46 

0.  22 

0.49 

0.23 

0.52 

0.  24 

0-54 

0.  25 

0.57 

0.27 

0.59 

0.28 

0.  61 

0.  29 

154 

0.48 

0.  21 

0.  50 

0.  22 

0-53 

0.23 

0.  56 

0.  24 

0.58 

0.  25 

j  0.  60 

0.  26 

0.  62 

0.  27 

156 

0.49 

0.  20 

0.  52 

0.  21 

0-55 

0.  22 

0.57 

0.23 

0. 60 

0.  24 

0.62 

0.  25 

0.  64 

0.  26 

158 

0.51 

0.  19 

0.54 

0.  20 

0.57 

0.  21 

0.  59     0. 22 

0.61 

0.23 

0.63 

0.  24 

0.66 

0.25 

1     160 

0.53 

0.18 

0.56 

0. 19 

0.59 

0.20 

0.61 

0.  21 

0.63 

0.22 

0.65 

0.22 

0.67 

0.23 

TABLE  5B. 

[Page  273 

% 

Distance  of  an  Object  by  Two  Bearings 

Difference 

between 

the  course 

Difference  between  the  course  and  first  bearing.                                                              1 

and  second 
bearing. 

34° 

36° 

38° 

40° 

42° 

44° 

46°        1 

44° 

3.22 

2.24 

46 

2.69 

r-93 

3-39 

2.43 

48 

2.31 

1.72 

2.83 

2.  ID 

3-55 

2.63 

50 

2.03 

1-55 

2.43 

1.86 

2.96 

2. 27 

3-70 

2.84 

52 

1. 81 

1.43 

2.13 

1.68 

2.54 

2.01 

3-09 

2.44 

3-85 

3-04 

54 

1.63 

1.32 

I.  90 

1.54 

2.23 

1. 81 

2.66 

2-15 

3.22 

2.  60 

4.00 

3-24 

56 

1.49 

1.24 

1.72 

1.42 

1.99 

1.65 

2.33 

1-93 

2.77 

2.  29 

3-34 

2.77 

4.14 

3-43 

58 

1.37 

1. 17 

1-57 

^■33 

1.80 

1-53 

2.08 

1.76 

2.43 

2.06 

2.87 

2.44 

3-46 

2-93 

60 

1.28 

1. 10 

1-45 

I.  25 

1.64 

1.42 

1.88 

1.63 

2.17 

1.88 

2.52 

2.18 

2.97 

2.57 

62 

1. 19 

1.05 

1-34 

I.  18 

1-51 

1-34 

1.72 

1-52 

1.96 

1-73 

2.  25 

1.98 

2.61 

2.30 

64 

1. 12 

1. 01 

1-25 

1-13 

1.40 

1.26 

1.58 

1.42 

1.79 

I. 61 

2.03 

1.83 

2-33 

2.09 

66 

1. 06 

0.96 

I.  18 

1.07 

I-3I 

I.  20 

1-47 

1-34 

1.65 

I. 51 

1.85 

1.69 

2.  10 

1.92 

68 

1. 00 

0.93 

I.  II 

1.03 

1.23 

I.  14 

1-37 

1.27 

1-53 

1.42 

I.  71 

1.58 

1.92 

1.78 

70 

0.95 

0.89 

1.05  ■ 

0.99 

I.  16 

1.09 

I.  29 

I.  21 

1-43 

1-34 

1.58 

1.49 

1.77 

1.66 

72 

0.91 

0.86 

I.  00 

0-95 

I.  10 

1.05 

I. 21 

I- 15 

1.34 

1.27 

1.48 

I. 41 

1.64 

1.56 

74 

0.87 

0.84 

0.95 

0.92 

1.05 

I.  01 

I- 15 

I.  10 

1.26 

I. 21 

1.39 

1-34 

1-53 

1.47 

76 

0.84 

0.81 

0.91 

0.89 

I.  00 

0.97 

1.09 

1.06 

1.20 

I.  16 

I-3I 

1.27 

1.44 

1.40 

78 

0.80 

0.79 

0.88 

0.86 

0.96 

0.94 

1.04. 

1.02 

I.  14 

I.  11 

1.24 

I.  22 

1.-36 

1-33 

80 

0.78 

0.77 

0.S5 

0.83 

0.  92 

0.  91 

1. 00 

0.98 

1.09 

1.07 

I.  18 

I.  16 

1.28 

1.27 

82 

0.75 

0.75 

0.82 

0.81 

0.89 

0.88 

0.  96 

0.95 

1.04 

1.03 

1-13 

I.  12 

1.22 

I. 21 

84 

0.73 

0.73 

0.79 

0.79 

0.86 

0.85 

0.93 

0.  92 

1. 00 

0.99 

1.08 

1.07 

I.  17 

I.  16 

86 

0.71 

0.71 

0.77 

0.77 

0.83 

0.83 

0.89 

0.89 

0.96 

0.96 

1.04 

1.04 

I.  12 

I.  12 

88 

0.69 

0.69 

0.75 

0.75 

0.80 

0.80 

0.86 

0.86 

0.93 

0-93 

I.  00 

I.  00 

1.08 

1.07 

90 

0.67 

0.67 

0.73 

0.73 

0.78 

0.  78 

0.84 

0.84 

0.90 

0.90 

0.97 

0.97 

1.04 

1.04 

92 

0.66 

0.66 

0.71 

0.  71 

0.  76 

0.  76 

0.82 

0.82 

0.87 

0.87 

0.93 

0.93 

1. 00 

1. 00 

94 

0.65 

0.64 

0.  69 

0.  69 

0.74 

0.74 

0.79 

0.79 

0.85 

0.85 

0.91 

0.90 

0.97 

0.97 

96 

0.63 

0.63 

0.68 

0.  67 

0.73 

0.  72 

0.78 

0.77 

0.83 

0.82 

0.88 

0.88 

0.94 

0-93 

98 

0. 62 

0.62 

0.67 

0.66 

0.71 

0.  70 

0.  76 

0.75 

0.81 

0.80 

0.86 

0.  85 

0.  91 

0.  90 

1 00 

0.61 

0.60 

0.65 

0.64 

0.  70 

0.69 

0.74 

0.73 

0.79 

0.  78 

0.84 

0.83 

0.89 

0.88 

102 

0.60 

O.S9 

0.64 

0.  63 

0.68 

0.  67 

0.73 

0.  71 

0.77 

0.  76 

0.82 

0.80 

0.87 

0.85 

104 

0, 60 

0.58 

0.  63 

0.  61 

0.67 

0.  65 

0.  72 

0.69 

0.  76 

0  74 

0.80 

0.78 

0.85 

0.82 

106 

0.59 

0.57 

0.63 

0.  60 

0.66 

0.64 

0.  70 

0.68 

0.74 

0.72 

0.79 

0.  76 

0.83 

0.80 

108 

0.58 

0.55 

0.62 

0.59 

0.66 

0.  62 

0.69 

0.66 

0.73 

0.  70 

0.77 

0.74 

0.81 

0.77 

no 

0.58 

0.54 

0.  61  : 

0-57 

0.  65 

0.  61 

0.68 

0.64 

0.  72 

0.68 

0.  76 

0.71 

0.80 

0.75 

112 

0.57 

0.53 

0.61 

0.  56 

0.  64 

0.59 

0.68 

0.63 

0.71 

0.66 

0.75 

0.  69 

0.79 

0.73 

114 

0-57 

0.52 

0.  60 

0.55 

0.63 

0.58 

0.67 

0.61 

0.  70 

0.  64 

0.74 

0.68 

0.78 

0.71 

116 

0.  56 

0.51 

0.60 

0.54 

0.63 

0.57 

0.66 

0.60 

0.  70 

0.63 

0.73 

0.66 

0.77 

0.  69 

118 

0.  56 

0.  50 

0.59 

0.52 

0.63 

0-55 

0.66 

0.58 

0.69 

0.61 

0.  72 

0.  64 

0.  76 

0.67 

120 

0.  56 

0.49 

0.59 

0.51 

0.  62 

0.54 

0.65 

0-57 

0.68 

0.59 

0.  72 

0.  62 

0.75 

0.65 

122 

0.  56 

0.47 

0.59 

0.  50 

0.  62 

0-53 

0.65 

0-55 

0.68 

0.58 

0.71 

0.  60 

0.74 

0.63 

124 

0.  56 

0.46 

0.59 

0.49 

0.  62 

0.51 

0.  65 

0.54 

0.68 

0.  56 

0.71 

0.58 

0.74 

0.61 

126 

0.  56 

0.45 

0.59 

0.48 

0.  62 

0.  50 

0.  64 

0.  52 

0.67 

0.54 

0.  70 

0.57 

0.73 

0.59 

128 

0.  56 

0.44 

0.59 

0.46 

0.62 

0.49 

0.  64 

0.51 

0.67 

0-53 

0.  70 

0-55 

0.73 

0.57 

130 

0.  56 

0.43 

0.59 

0.45 

0.  62 

0.47 

0.  64 

0.49 

0.67 

0.51 

0.  70 

0.53 

0.  72 

0-55 

132 

0.  56 

0.42 

0.59 

0.44 

0.  62 

0. 46 

0.  64 

0.48 

0.67 

0.  50 

0.  70 

0.52 

0.  72 

0.54 

134 

0.57 

0.41 

0.59 

0.43 

0.  62 

0.45 

0.  64 

0.46 

0.67 

0.48 

0.69 

0.  50 

0.  72 

0.  52 

136 

0.57 

0.40 

0.  60 

0.41 

0.  62 

0.43 

0.  65 

0.45 

0.67 

0.47 

0.  70 

0.48 

0.  72 

0.  50 

138 

0.58 

0.39 

0.  60 

0.40 

0.63 

0.42 

0.65 

0.43 

0.67 

0.45 

0.  70 

0.47 

0.  72 

0.48 

140 

0.58 

0.37 

0.  61 

0.39 

0.63 

0.40 

0.65 

0.42 

0.68 

0.43 

0.  70 

0.45 

0.72 

0.46 

142 

0-59 

0.36 

0.61 

0.38 

0.63 

0.39 

0.66 

0.41 

0.68 

0.42 

0.  70 

0.43 

0.  72 

0.45 

144 

0.60 

0-35 

0.  62 

0.36 

0.  64 

0.38 

0.66 

0.39 

0.68 

0. 40 

0.71 

0.41 

0.73 

0.43 

146 

0.60 

0.34 

0.63 

0.35 

0.65 

0.  36 

0.67 

0.37 

0.69 

0.39 

0.  71 

0.40 

0.73 

0.41 

148 

0.61 

0.32 

0.63 

0.34 

0.66 

0.35 

0.68 

0.  36 

0.  70 

0.37 

0.  72 

0.38 

0.74 

0.39 

150 

0.62 

.0-31 

0.64 

0.32 

0.66 

0.33 

0.68 

0.34 

0.  70 

0.35 

0.  72 

0.36 

0.74 

0.37 

152 

0.63 

0.30 

0.65 

0.31 

0.67 

0.32 

0.  69 

0-33 

0.71 

0.33 

0.73 

0.34 

0.75 

0.35 

154 

0.65 

0.28 

0.  67 

0.  29 

0.68 

0.30 

0.  70 

0.31 

0.72 

0.32 

0.74 

0.32 

0.  76 

0.33 

156 

0.66 

0.27 

0,68  \  0.28 

0.  70 

0.28 

0.  72 

0.  29 

0.73 

0.30 

0.75 

0.30 

0.77 

0.31 

158 

0.67 

0.25 

0.69 

0.  26 

0.71 

0.27 

0.73 

0.27 

0.74 

0.28 

0.  76 

0.28 

0.78 

0.  29 

160 

0.69 

0.24 

0.71 

0.24 

0.73 

0.25 

0.74 

0.25 

0.  76 

0.  26 

0.77 

0.26 

0.79 

0.  27 

18   B 


Page  274] 

TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 

Difference  between  the  course  and  first  bearing. 

the  course 

and  second 

bearing. 

48° 

50° 

52° 

54° 

56° 

58° 

60°         1 

58" 

4.28 

3.63 

60 

3-57 

3.10 

4.41 

3.82 

62 

3-07 

2.71 

3.68 

3-25 

4.54 

4.01 

64 

2.  70 

2.42 

3-17 

2.85 

3-79 

3-41 

4.66 

4.19 

66 

2.40 

2.  20 

2.78 

2.54 

3.26 

2.98 

3.89 

3-55 

4.77 

4-36 

68 

2.17 

2.01 

2.48 

2.30 

2.86 

2.65 

3-34 

3.10 

3-99 

3-71 

4.88 

4.53 

70 

1.98 

1.86 

2.  24 

2.  10 

2-55 

2.39 

2.94 

2.  76 

3-43 

3.  22 

4.08 

3.83 

4.99 

4.69 

72 

1.83 

1.74 

2.  04 

1.94 

2.30 

2.  19 

2.  62 

2.49 

3.01 

2.86 

3-51 

3-33 

4.17    3.96 

74 

1.70 

1.63 

1.88 

I.  81 

2. 10 

2.02 

2.37 

2.  27 

2.68 

2.58 

3.08 

2.96 

3-58     3-44 

76 

1.58 

1-54 

1-75 

1.70 

1.94 

1.88 

2.  16 

2. 10 

2.42 

2.35 

2.74 

2.66 

3-14    3-05 

78 

1.49 

1-45 

1.63 

1.60 

1.80 

1.76 

1.99 

1-95 

2.  21 

2.  16 

2.48 

2.43 

2.  80     2.  74 

80 

1.40 

1.38 

1-53 

I-5I 

1.68 

1.65 

1.85 

1.82 

2.  04 

2.01 

2.  26 

2.23 

2-53 

2.49    1 

82 

1-33 

1.32 

1-45 

1.43 

1.58 

1.56 

1.72 

I.  71 

1.89 

1.87 

2.08 

2.06 

2.31 

2.29    1 

84 

1.26 

1.26 

'•37 

1.36 

1.49 

1.48 

1.62 

I.  61 

1.77 

1.76 

1-93 

1.92 

2. 13     2. 12    1 

86 

I.  21 

I.  20 

1.30 

1.30 

1. 41 

1. 41 

1-53 

1-52 

1.66 

1.65 

I.  81 

1.80 

1.98     1.97    1 

88 

I.  16 

I.  16 

1.24 

1.24 

1-34 

1.34 

1-45 

1-45 

1.56 

1.56 

1.70 

1.70 

1.84 

1.84 

90 

I.  II 

I.  II 

I.  19 

1. 19 

1.28 

1.28 

1.38 

1.38 

1.48 

1.48 

1.60 

I.  60 

1-73 

1.73 

92 

1.07 

1.07 

I.  14 

I.  14 

1.23 

1.23 

1-31 

I-3I 

I. 41 

1. 41 

1.52 

1-52 

1.63 

1.63 

94 

1.03 

1.03 

I.  10 

I.  10 

I.  18 

I. 17 

I.  26 

1.26 

1-35 

1-34 

1.44 

1.44 

1-55 

1-54 

96 

1. 00 

0.99 

1.06 

1.06 

I- 13 

I- 13 

I. 21 

I.  20 

I.  29 

1.28 

1.38 

1.37 

1.47 

1-47 

98 

0.97 

0. 96 

1.03 

1.02 

I.  10 

1.08 

1. 16 

I- 15 

1.24 

1.23 

1.32 

1-31 

1. 41 

1-39 

100 

0.94 

0.93 

1. 00 

0.98 

1.06 

1.04 

1. 12 

I.  II 

1. 19 

1. 18 

1.27 

1-25 

1-35 

1-33 

102 

0.92 

0.90 

0.97 

0-95 

1.03 

I. 01 

1.09 

1.06 

I- 15 

'•'^ 

I.  22 

1. 19 

1.29 

1.27 

104 

0.  90 

0.87 

0.95 

0.  92 

1. 00 

0.97 

i.o5 

1.02 

1. 12 

1.08 

I.  18 

1. 14 

1.25 

I. 21 

106 

0.88 

0.84 

0.92 

0.89 

0.97 

0.94 

1.03 

0.99 

1.09 

1.04 

I.  14 

1. 10 

I.  20 

I.  16 

108 

0.86 

0.82 

0.90 

0.86 

0-95 

0.90 

I.  00 

0.95 

1.05 

I.  00 

I.  II 

1.05 

I. 17 

I.  u 

no 

0.84 

0.79 

0.88 

0.83 

0-93 

0.  87 

0.98 

0.92 

1.02 

0.96 

1.08 

I. 01 

1-13 

I.  06 

112 

0.83 

0.77 

0.  87 

0.80 

0.  91 

0.84 

0-95 

0.88 

I.  00 

0-93 

I.  OS 

0.97 

1. 10 

1. 02 

114 

0.81 

0.74 

0.85 

0.78 

0.89 

0.82 

0.93 

0.85 

0.98 

0.  89 

1.02 

0.93 

1.07 

0.98 

116 

0.80 

0.  72 

0.84 

0.75 

0.88 

0.79 

0.  92 

0.82 

0.96 

0.  85 

1. 00 

0.90 

1.04 

0.94 

118 

0.79 

0.  70 

0.83 

0.73 

0.86 

0.  76 

0.90 

0.79 

0.94 

0.83 

0.98 

0.86 

1,02 

0.90 

120 

0.  78 

0.68 

0.82 

0.71 

0.85 

0.74 

0.89 

0.77 

0.91 

0.80 

0.96 

0.83 

1. 00 

0.87 

122 

0.77 

0.66 

0.81 

0.68 

0.84 

0.71 

0.87 

0.  74 

0.  90 

0.77 

0.95 

0.80 

0.98 

0.83 

124 

0.77 

0.63 

0.8c 

0.66 

0.83 

0.  69 

0.86 

0.71 

0.  90 

0.74 

0.93 

0.77 

0.96 

0.80 

126 

0.  76 

0.61 

0.79 

0.  64 

0.82 

0.66 

0.85 

0.69 

0.88 

0.71 

0.91 

0.  74 

0.95 

0.77 

128 

0.75 

0.59 

0.78 

0.  62 

0.81 

0.64 

0.  84 

0.66 

0.87 

0.69 

0.  90 

0.71 

0-93 

0.74 

130 

0.75 

0.57 

0.78 

0. 60 

0.81 

0.62 

0.83 

0.64 

0.86 

0.66 

0.  89 

0.68 

0.92 

0.71 

132 

0.75 

0.56 

0.77 

0.57 

0.80 

0.59 

0.83 

0.  61 

0.85 

0.  64 

0.88 

0.66 

0.91 

0.68 

134 

0.74 

0.54 

0.77 

0-55 

0.80 

0.57 

0.82 

0.59 

0.85 

0.61 

0.87 

0.63 

0.90 

0.65 

136 

0.74 

0.52 

0.77 

0.53 

0.80 

0-55 

0.82 

0.57 

0.84 

0.58 

0.87 

0.60 

0.89 

0.62 

138 

0.74 

0.  50 

0.77 

0.51 

0.  79 

0.53 

0.81 

0.54 

0.84 

0.  56 

0.86 

0.58 

°-!2 

0.59 

140 

0.74 

0.48 

0.77 

0.49 

0.79 

0.51 

0.81 

0.  52 

0.83 

0.54 

0.86 

0.55 

0.88 

0.57 

142 

0.74 

0.46 

0.77 

0.47 

0.79 

0.49 

0.81 

0.  50 

0.83 

0.51 

0.  85 

0.  52 

0.87 

0.54 

144 

0.75 

0.44 

0.77 

0.45 

0.79 

0.46 

0.81 

0.48 

0.83 

0.49 

0.85 

0.  50 

0.87 

0.51 

146 

0.75 

0.42 

0.77 

0.43 

0.79 

0.44 

0.81 

0.45 

0.83 

0.46 

0.85 

0.47 

0.87 

0.49 

148 

0.  76 

0.40 

0.77 

0.41 

0.79 

0. 42 

0.81 

0.43 

0.83 

0.44 

0.85 

0.45 

0.87 

0.46 

150 

0.  76 

0.38 

0.  78 

0.39 

0.80 

0. 40 

0.81 

0.41 

0.83 

0.42 

0.85 

0.42 

0.87 

0.43 

152 

0.77 

0.36 

0.78 

0.37 

0.80 

0.38 

0.82 

0.38 

0.83 

0-39 

0.85 

0.40 

0.87 

0.41 

154 

0.77 

0.34 

0.79 

0.35 

0.81 

0.35 

0.82 

0.36 

0.84 

0.37 

°-^5 

0.37 

0.87 

0.38 

^56 

0.78 

0.32 

0.80 

0.32 

0.81 

0.33 

0.83 

0.34 

0.84 

0.34 

0.86 

0.35 

0.87 

0.35 

158 

0.79 

,  0-30 

0.81 

0.30 

0.82 

0.31 

0.83 

0.31 

0.85 

0.32 

0.86 

0.32 

0.87 

0.33 

160 

0. 80  '  0. 27 

0.82 

0.28 

0.83 

0.28 

0.84 

0.29 

0.85 

0.29 

0.86 

0.30 

0.88 

0.30 

TABLE  sB. 

Distance  of  an  Object  by  Two  Bearings. 


[Page  275 


Difference 

between 

the  course 

and  second 

bearing. 


72'-' 

74 

76 

78 
8o 
82 
84 
86 
88 
90 
92 

04 
96 
98 
100 
102 
104 
106 
108 
no 

I  12 
114 
116 
118 
120 
122 
124 
126 
I2S 

134 
13" 
1 38 
140 
142 
144 
146 
148 

>52 
154 

160 


Difference  between  the  course  and  first  bearing. 


62° 


5.08 
4.25 

3.6s 
3.  20 
2.86 
2.58 
2.36 
2. 17 
2. 01 
1.88 

77  i 
67  i 
58 
50 
43 
37 
[.  32 
I.  27 
1.23 
I   19 

I- 15 
I.  12 

I.  09 

I.  07 

I.  04 

I.  02 

I.  00 

0.98 

0.97 

0.95 
0.94 

0.93 
0.92 
o.  91 
o.  90 
o.  90 

0.89 
0.89 
0.89 

0.88 
0.88 
0.88 
0.89 
0.89 
0.89 


4.84 
4.08 

3-54 

-t         T   -> 


2.81 

2.  56 

2.34 

2.17 

2.01 

1.88 

1.76 

1.66 

1-57 

1.49 

1. 41 

1-34 

1.28 

1.22 

I. 17 

I.  12 

1.07 

I.  02 

0.98 

0.94 

0.  90 

0.86 

0.83 

0.79 

0.  76 

0-73 

0.  70 

0.67 

0.  64 

0.61 

0.58 

0.55 

0.  52 

0.  50 

0.47 

0.44 

0.41 

0.39 

0.36 

0.33 

0.30 

64= 


5.18 

4-32 
3-72 
3.  26 
2.  91 
2.63 
2. 40 
2.  21 
2.05 
I.  91 
1.80 
70 
61 

53 
46 

40 

34 
29 

25 
I.  21 
I. 17 
I.  14 
I.  II 
1.08 
I.  06 
I.  04 
I.  02 
I.  00 
0.98 
0.97 
o.  96 

0-95 
0.94 

0.93 
o.  92 
o.  91 
0.91 
o.  90 
o.  90 
o.  90 
o.  90 
0.90 
o.  90 
o.  90 


4.98 

4.19 

3-63 
3.21 

2.88 
2.61 

2.39 

2.21 

2.05 

.91 

•79 
.69 

•59 
•51 
■43 
•36 
.29 

•23 

•17 
.12 

.07 

•03 
0.98 

0.94 
0.90 
0.86 
0,82 
0.79 

0^75 
0.72 
0.69 
0.66 
0.63 
0.60 

0.57 
0.54 
0.51 
0.48 

0.45 
0.42 

0-39 
0.37 
0-34 
0.31 


66° 


5.26 

4^39 
78 
31 
96 
,67 

■44 

25 
,08 


•95 
•83 
•72 
•63 

•55 
.48 

42 
•37 
•32 

■  27 

23 
.19 
.16 

•13 

.10 

08 
.05 

•03 
.02 
.00 
0.99 
0.97 
0.96 
0.95 
0.94 

0.93 

0-93 
0.92 

0.92 

0.92 

0.91 

0.91 

0.91 

0.91 


5.10 
4^30 
3-72 
3.28 

2.94 
2.66 
2.44 
2.25 
2.08 

•94 
.82 

•71 
.61 

•52 
•44 
•37 

■30 
.24 
.18 
.12 
.07 
.02 
0.98 

0.93 
0.89 
0.85 
0.82 
0.78 
0.74 
0.71 
0.68 
0.64 
0.61 
0.58 

0-55 
0.52 

0.49 

0.46 

0-43 
o  40 

0.37 
0.34 
0.31 


68= 


5-34 
4.46 

3^83 
3-36 
3.00 
2.71 
2.48 
2.28 
2.12 

.97 
,85 

■75 
.66 

■58 

■51 

■44 
•39 
■33 
.29 

•25 
.21 
.18 

•15 
.12 

.09 
.07 

•05 
•03 
.01 

.00 
0.99 
0.97 
0.96 
0.96 

0.95 
0.94 

0.94 

0.93 
093 
093 
0.93 
©•93 


70° 


5.22 

4^39 
3.80 

3^35 

2.99 

2.71 

2.48 

2.28 

2. II 

.96 

.84 

.72 

.62 

•53 

•45 

•37 

•30 

24 

.18 

.12 

.07 

.02 

0.97 

0.93 
0.88 
0.84 
0.80 
0.77 

o^73 
0.69 
0.66 
0.63 
0.59 
0.56 

o^53 
0.50 
0.47 
0.44 

0.41 
0.38 

o^35 
0.32 


5^41 

4-52 
3.88 

3^41 
3-04 
2.75 
2.51 
2.31 
2.14 
2.00 
.88 

•77 
.68 
.60 

•53 
.46 
.40 

•35 

31 

.26 

•23 
•  19 
.16 

•13 
.11 

.09 
.06 
.04 

•03 
01 
.00 
0.99 
0.98 
0.97 
0.96 
0.95 

095 
0.94 

0.94 

0.94 

0.94 


5-33 
4.48 
3.86 
3^40 
3^04 

2.75 
2.51 

2.30 

2.13 

98 
85 
-73 
■63 
•54 
•45 
•37 

■30 
.24 

•  17 
.12 

.06 
.01 
0.96 
0.92 
0.87 
0.83 
0.79 
0.75 
0.71 
0.68 
0.64 
0.61 
0.57 
0-54 
0.51 
0.48 

0.45 
0.41 
0.38 

0.35 
0.32 


12° 


5-48 

4^57 

3^93 

3-45 
3.0S 

2.78 

2.54 
2.34 
2.17 
2.03 
.90 

•  79 
.70 
.62 

•54 
.48 
.42 
•37 
•32 
.28 
.24 
.21 
.18 

•15 

.12 
.10 
.08 
.06 
.04 

•03 
.01 
.00 
0.99 
0.98 
0.97 
0.97 
0.96 
0.96 
0.95 
0.95 


5-42 
4^55 
3-92 

3-45 
3.08 

2.78 

2.53 

2^33 

2.15 

2.00 

.86 

•74 

•63 

•54 

•45 

•37 

•30 

•23 

•17 

.11 

•05 
.00 

0-95 
0.90 

0.86 
0.82 
0.77 
0.74 
0.70 
0.66 
0.62 

0.59 
0.55 
0.52 
0.49 

0.45 
o  42 

0.39 
0.36 

o^33 


u° 


u° 


5-51 
4.61 

3-97 
3^49 
,11     ^.11 


5-54 
4.62 

3-97 
3^49 


2.81 

2.57 
2.36 
2.19 
2.05 
•92 
.81 

•72 
.64 
.56 

•50 
•44 
•38 
•34 
.29 

•25 
.22 
.19 
.16 

•13 
.11 

.09 

.07 

.05 

.04 

.02 

.01 

.00 

0.99 

0.98 

0.98 

0.97 

0.97 

0.96 


2.80 

2-55 

2.34 

2.16 

2.00 

1.87 

1.74 

1.63 

I 

I 

I 

I 

1.22 

I 

I 


•54 
•45 
■37 
.29 


16 

10 

1.04 

0.99 

0.94 

0.89 

0.84 

0.80 

0.76 

0.72 

0.68 

0.64 

0.60 

0.57 

0.53 
0.50 

0.46 

0.43 
0.39 
0.36 

0.33 


59 
67 
01 

52 

14! 

84 

2^59 

2.39 

2.21 

2.07 

■94 

83 

•74 

.65 

■58 

■5' 

:-45 

[.40 

■35 
■31 

[.27 

•23 
.20 

•17 
.14 
.12 
.10 

.08 
.06 

•05 

•03 

.02 

[.01 

.00 

0.99 

0.99 

0.98 

0.98 


5-57 
4.66 
4.01 
3-52 

3-13 

2.82 

2.56 

2-35 
2.16 
2.01 
.87 

•74 
•63 
•53 
[.44 
•36 
[.28 
[.21 
.14 
.08 
.02 
0.97 
0.92 
0.87 
0.82 
0.78 
0.74 
0.70 
0.65 
0.62 
0.58 

0.54 
0.50 

0.47 

0-43 
0.40 

0.37 

o^33 


Page  276] 

TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 

Difference  between  the  course  and  first  bearing. 

the  course 

and  second 

bearing. 

78° 

80 

° 

82° 

84° 

86° 

88° 

90° 

92°        1 

88'=> 

5-63 

5-63 

90 

4.70 

4.70 

5-67 

5-67 

92 

4.04 

4.04 

4-74 

4-73 

5- 70 

5-70 

94 

3-55 

3-54 

4.07 

4.06 

4.76 

4-75 

5-73 

5-71 

96 

3-17 

3-15 

3-57 

3-55 

4.09 

4.07 

4.78 

4.76 

5-74 

5-71 

98 

2.86 

2.83 

3-19 

3.16 

3-59 

3-56 

4. 1 1 

4.07 

4.80 

4-75 

5.76 

5-70 

100 

2.61 

2.57 

2.88 

2.84 

3.20 

3.16 

3.6, 

3-55 

4.12 

4.06 

4.81 

4-73 

5-76 

5-67 

102 

2.40 

2.35 

2.63 

2.57 

2.90 

2.83 

3.22 

'^■'J 

3.62 

3-54 

4-13 

4.04 

4.81 

4.70 

5.76 

5.63 

104 

2.23 

2.  16 

2.42 

2-35 

2.64 

2.56 

2.91 

2.82 

3-23 

s-'^s  3-63 

3-52 

4-13 

4.01 

4.81 

4.66 

106 

2.00 

2.  25 

2.16 

2-43 

2.34 

2.65 

2-55 

2.92 

2.80    3.23 

3-II 

3-63 

3-49 

4-13 

3-97 

108 

I.  96 

1.86 

2.  10 

2.00 

2.26 

2.15 

2.45 

2-33 

2.66 

2.53 

2.92 

2.78 

3-24 

3.08 

3-63 

3-45 

no 

1.8s 

1-73 

I.  97 

1.85 

2. II 

1.98 

2.27 

2.13 

2.45 

2.31 

2.67 

2-51 

2.92 

2.75 

3-23 

3-04 

112 

1-75 

1.62 

1.86 

1.72 

1.98 

1.83 

2.12 

1.96 

2.28 

2. 1 1 

2.46 

2.28 

2.67 

2.48 

2.92 

2.71 

114 

1.66 

1-52 

1.76 

1. 61 

1.S7 

1. 71 

1.99 

1.82 

2.12 

1.94 

2.28 

2.08 

2.46 

2.25 

2.67 

2.44 

116 

1-59 

1.43 

1.68 

I-5I 

1.77 

1-59 

1.88 

1.69 

2.00 

1.79 

2.13 

1. 91 

2.28 

2.05 

2.46 

2.21 

118 

1.52 

1-34 

1.60 

1. 41 

1.68 

1.49 

1.78 

1-57 

1.88 

1.66 

2.00 

1.76 

2.13 

1.88 

2.28 

2.01 

120 

1.46 

1.27 

1-53 

1-33 

1.61 

1-39 

1.69 

1.47 

1.78 

1-54 

1.89 

1.63 

2.00 

1-73 

2.13 

1.84 

122 

1. 41 

I.  19 

1.47 

1.25 

1-54 

1-31 

1.62 

1-37 

1.70 

1.44 

1.79 

1.52 

1.89 

1.60 

2.00 

1.70 

124 

1.36 

I- 13 

1.42 

1. 18 

1.48 

1.23 

1-55 

1.28 

1.62 

1.34 

1.70 

1.41 

1.79 

1.48 

1.89 

1.56 

126 

1.32 

1.06 

1-37 

I. II 

1-43 

I-I5 

1.48 

1.20 

1-55 

1.26 

1.62 

I-3I 

1.70 

1.38 

1.79 

1-45 

128 

1.28 

I.  01 

1-33 

1.04 

1.38 

1.08 

1-43 

I-I3 

1.49 

1. 17 

1-55 

1.23 

1.62 

1.28 

1.70 

1-34 

130 

1.24 

0.95 

1.29 

0.98 

1-33 

1.02 

1.38 

1.06 

1.44 

1. 10 

1.49 

1. 14 

1.56 

1. 19 

1.62 

1.24 

132 

1. 21 

0.90 

1-25 

°-93 

1.29 

0.96 

1-34 

0.99 

1-39 

1.03 

1.44 

1.07 

1.49 

I. II 

1-55 

1. 16 

134 

1. 18 

0.85 

I.  22 

0.88 

1.26 

0.90 

1.30 

0.93 

1-34 

0.97 

1-39 

1. 00 

1.44 

1.04 

1.49 

1.07 

136 

I- 15 

0.80 

1. 19 

0.83 

1.22 

0.85 

1.26 

0.88 

1.30 

0.90 

1-34 

0-93 

1-39 

0.97 

1.44 

1. 00 

138 

I- 13 

0.  76 

I.  16 

0.78 

1. 19 

0.80 

1-23 

0.82 

1.27 

0.85 

1.30 

0.87 

1-35 

0.90 

1-39 

^■2} 

140 

I.  II 

0.  71 

1. 14 

0.73 

1. 17 

0.75 

1.20 

0.77 

1.23 

0.79 

1.27 

0.82 

1-31 

0.84 

1.34 

0.86 

142 

1.09 

0.67 

1. 12 

0.69 

1. 14 

0.70 

1. 17 

0.72 

1.20 

0.74 

1.24 

0.76 

1.27 

0.78 

1.30 

0.80 

144 

1.07 

0.63 

1. 10 

0.64 

1. 12 

0.66 

1. 15 

0.67 

1. 18 

0.69 

1. 21 

0.71 

1.24 

0.73 

1.27 

0.75 

146 

1.05 

0..59 

1.08 

0.60 

1. 10 

0.62 

I-I3 

0.63 

1. 15 

0.64 

1. 18 

0.66 

1. 21 

0.67 

1.24 

0.69 

148 

1.04 

0-55 

1.06 

0.56 

1.08 

0.57 

I. II 

0.59 

I-I3 

0.60 

1-15 

0.61 

1. 18 

0.62 

1. 21 

0.64 

150 

1.03 

0.51 

1.05 

0.52 

1.07 

0-53 

1.09 

0.54 

I. II 

0.55 

I-I3 

0.57 

I-I5 

0.58 

1. 18 

0.59 

152 

1.02 

0.48 

1.04 

0.49 

1.05 

0.49 

1.07 

0.50 

1.09 

0.51 

I. II 

0.52 

I-I3 

0-53 

1-15 

0.54 

154 

1. 01 

0.44 

1.02 

0.45 

1.04 

0.46 

1.06 

0.46 

1.08 

0.47 

1.09 

0.48 

I. II 

0.49 

113 

0.50 

156 

1. 00 

0.41 

1. 01 

0.41 

1.03 

0.42 

1.05 

0.43 

1.06 

0.43 

1.08 

0.44 

1.09 

0.4S 

i.ii 

0.4S 

158 

0.99 

0.37 

1. 01 

0.38 

1.02 

0.38 

1.03 

0.39 

1.05 

0.39 

1.06 

0.40 

1.08 

0.40 

1.09 

0.41 

160 

0.99 

0.34 

1. 00 

0.34 

1. 01 

0-35 

1.02 

0-35 

1.04 

0.35 

1.05 

0.36 

1.06 

0.36 

1.08 

0.37 

m 

1° 

96 

0 

98° 

100° 

102° 

104° 

106° 

108°       1 

1040 

5-74 

5-57 

106 

4.80 

4.61 

5.78 

5-51 

108 

4.12 

3-92 

4.78 

4-55 

5- 70 

5-42 

no 

3.62 

3-40 

4.  II 

3.86 

4.76 

4.48 

5.67 

5-33 

112 

3-23 

2.99 

3.61 

3-35 

4.09 

3.80 

4-74 

4.40 

5-63 

5.22 

114 

2.92 

2.66 

3.22 

2.94 

3-59 

^■fo 

4.07 

3-72 

4.70 

4-30 

5-59 

5.10 

n6 

2.66 

2.39 

2.91 

2.61 

3.20 

2.88 

3-57 

3.21 

4.04 

3-63 

4.67 

4.19 

5-54 

4.98 

118 

2.45 

2.17 

2.65 

2-34 

2.90 

2.56 

3-'9 

2.81 

3-55 

3-^3 

4.01 

3-54 

4.62 

4.08 

5-48 

4.84 

120 

2.  28 

1.97 

2.45 

2.12 

2.64 

2.29 

2.88 

2.49 

3-'7 

2.74 

3-52 

3-05 

3-97 

3-44 

4-57 

3-96 

122 

2. 12 

1.80 

2.27 

1.92 

2.43 

2.06 

2.63 

2.23 

2.86 

2.43 

3-1,4 

2.66 

3-49 

2.96 

3-93 

3-33 

124 

2.00 

1.6s 

2. 12 

1.76 

2.26 

1.87 

2.42 

2.01 

2.61 

2.16 

2.84 

2.35 

3-" 

2.58 

3-45 

2.86 

126 

1.88 

1-52 

1.99 

1. 61 

2.11 

1. 71 

2.25 

1.82 

2.40 

1-95 

2-59 

2.10 

2.81 

2.27 

3.08 

2.49 

128 

1.78 

1. 41 

1.88 

1.48 

1.98 

1.56 

2.10 

1.65 

2.23 

1.76 

2.39 

1.88 

2.57 

2.02 

2.78 

2.19 

130 

1.70 

1.30 

1.78 

1.36 

1.87 

1-43 

1.97 

I-5I 

2.08 

1.60 

2.21 

1.70 

2.36 

1. 81 

2.54 

1.94 

132 

1.62 

1.20 

1.69 

1.26 

'•77 

1.32 

1.86 

1.38 

1.96 

1.45 

2.07 

1-54 

2.19 

1.63 

2.34 

1-74 

134 

1-55 

I.  12 

1.62 

1. 16 

1.68 

1. 21 

1.76 

1.27 

1.85 

1-33 

1.94 

1.40 

2.05 

1.47 

2.17 

1.56 

136 

1.49 

1.04 

1-55 

1.07 

1.61 

1. 12 

1.68 

1. 16 

1-75 

1.22 

1.83 

1.27 

1.92 

1.34 

2.03 

1. 41 

138 

1.44 

0.96 

1.49 

0.99 

1-54 

1.03 

1.60 

1.07 

1.66 

I. II 

1.74 

1. 16 

1. 81 

1. 21 

1.90 

1.27 

140 

1.39 

0.89 

1-43 

0.92 

1.48 

0.95 

1-53 

0.98 

1-59 

1.02 

1.65 

1.06 

1.72 

1. 10 

1.79 

1. 15 

142 

1-34 

0.83 

1.38 

0.85 

1-43 

0.88 

1.47 

0.91 

1.52 

0.94 

1.58 

0.97 

1.64 

1. 01 

1.70 

1.05 

144 

1.30 

0.77 

1-34 

0.79 

1.38 

0.81 

1.42 

0.83 

1.46 

0.86 

I-5I 

0.89 

1.56 

0.92 

1.62 

0.95 

146 

1.27 

0.71 

1.30 

0-73 

1-33 

0.75    1-37 

0.77 

1.41 

0.79 

1.45    0.81  1 

1.50 

0.84 

1-54 

0.86 

148 

1.23 

0.  65 

1.26 

0.67 

1.29 

0.69    1.33 

0.70 

1.36 

0.72 

X.40 

0.74 

1.44 

0.76 

1.48 

0.78 

150 

I.  20 

0.60 

1.23 

0.61 

1.26 

0.63    1.29 

0.64 

1.32 

0.66 

1-35 

0.67 

1.38 

0.69 

1.42 

0.71 

152 

I.  18 

0.55 

I.  20 

0.56 

1.22 

0.57    1.25 

0.59 

1.28 

0.60 

I-3I 

0.61 

1.34 

0.63 

1-37 

0.64 

154 

I- 15 

0.  50 

I.  17 

0.51 

1. 19 

0.52    1.22 

0-53 

1.24 

0.54 

1.27 

0.56 

1.29 

0-57 

1.32 

0.58 

156 

I- 13 

0.46 

I- 15 

0.47 

1. 17 

0.47    1. 19 

0.48 

1. 21 

0.49 

1.23 

0.50 

1.25 

0.51 

1.28 

0.52 

158 

I.  II 

0.42 

I- 13 

0.42 

1. 14 

0.43    1. 16 

0.44 

1. 18 

0.44 

1.20 

0-45 

1.22 

0.46 

1.24 

0.47 

160 

1.09 

0.37 

I.  II 

0.38 

1. 12 

0.38    1. 14 

0.39 

I-I5 

0.39 

1. 17 

0.40 

1. 19 

0.41 

1. 21 

0.41 

TABLE  5B. 

Page  277 

Distance  of  an  Object  by  Two  Bearings. 

*- 

Difference 
between 

Difference  between  the  course  and  first  bearing.                                                      1 

and  second 
bearing. 

110°       1 

112° 

114°       1 

116°       1 

118°       1 

120° 

122° 

120° 

5.41 

4.69 

122 

4-52 

3-83 

5-34     4-53 

124 

3.88 

3.22 

4. 46     3.  70 

5.26 

4-36 

126 

3-41 

2.  76 

3-  83     3-  10 

4.  39     3-  55 

5.18 

4.19 

128 

3-04 

2.40 

3.36     2.65 

3.  78     2. 98 

4-32  !  3-41 

5.08 

4.  01 

'3° 

2.  75 

2. 10 

3. 00     2.  30 

3-31     2.54 

3.  72     2.  85 

4.25 

3-25 

4.99 

3.82 

132 

2-5" 

1.86 

2. 71      2.01 

2.  96     2.  20 

3.26 : 2.42 

3-65 

2.71 

4.17 

3.10 

4.88 

3-63 

134 

2.31 

1.66 

2.48 :  1.78 

2.67     1.92 

2.91  !  2.09 

3.20 

2.30 

3.58 

2.57 

4.08 

2.93 

136 

2. 14 

1.49 

2.28    1.58 

2.44     1.69 

2.63 

1.83 

2.86 

I.  98 

3-14 

2. 18 

3-5^ 

2.44 

13S 

2.00 

1-34 

2. 12    1. 42 

2.25  1  1.50 

2.40 

I.  61 

2.58 

1-73 

2.80 

1.88 

3.08 

2.06 

140 

1.88 

I.  21 

1.97    1.27 

2.08     1.34 

2.21 

1.42 

2.30 

1.52 

2.53 

1.63 

2.74 

1.76 

142 

1.77 

I.  09 

1.85    1. 14 

1.95      1.20 

2.05 

1.26 

2.17 

1-34 

2.31 

1.42 

2.48 

1-53 

144 

1.68 

0.  Q9 

1-75      1-03 

1.83     1.07 

1. 91 

1-13 

2.01 

I.  18 

2.13 

1.25 

2.  26 

1-33 

146 

1.60 

0.89 

1 .  66     0.  93 

1.72     0.96 

1.80 

1. 01 

1.88 

1.05 

1.98 

1. 10 

2.08 

1. 17 

14S 

1-53 

0.81 

1.58     0.84 

1.63     0.87 

1.70 

0.90 

1.77 

0.94 

1.84 

0.98 

1.93 

1.03 

150 

1.46 

0.73 

I- 51     0-75 

1.55     0.78 

1. 61 

0.80 

1.67 

0.83 

1.73 

0.87 

1,81 

0.90 

152 

1.40 

0.66 

1.44     0.68 

1.48     0. 70 

1-53 

0.  72 

1.58 

0.74 

1.63 

0.77 

I.  70 

0.80 

154 

I- 35 

0.59 

1.39     0.61 

1 .  42  '  0.  62 

1.46 

0.64 

1.50 

0.66 

1-55 

0.68 

1.60 

0.  70 

156 

I-3I 

0-53 

1-33     0.54 

1.37     0.56 

1.40 

0.57 

1.43 

0.58 

1.47 

0.60 

1.52 

0.62 

158 

1.26 

0.47 

1 .  29     0. 48 

1.32     0.49 

1-34 

0.  50 

1-37 

0.51 

1. 41 

0.53 

1.44 

0.54 

160 

1.23 

0.42 

1.25     0.43 

1.27     0.43 

I.  29 

0.44 

1.32 

0.45 

1-35 

0.46 

1.38 

0.47 

124° 

126° 

128° 

130° 

132°   . 

134° 

136° 

134° 

4.77 

3-43 

136 

3-99     2.77 

4.66 

3-23 

■3'^ 

3-43     2.29 

3-89 

2.60 

4.54 

3-04 

140 

3- 01      1-93 

3-34 

2-15 

3-79 

2.44 

4.41 

2.84 

142 

2.68      1.65 

2.94 

I. 81 

3.26 

2.01 

3.68 

2.  27 

4.28 

2.63 

144 

2.42      1.42 

2.62 

1-54 

2.86 

1.68 

3-17 

1.86 

3-57 

2.  10 

4.14 

2.43 

146 

2.21      1.24 

2.37 

1.32 

2-55 

1.43 

2.78 

1-55 

3-07 

1.72 

3-46 

1-93 

4. 00 

2.  24 

148 

2.04 

1.08 

2.  16 

1. 14 

2.30 

1.22 

2.48 

1-31 

2.  70 

1-43 

2.97 

1.58 

3-34 

1.77 

150 

1.89 

0-95 

1.99 

0.99 

2.  10 

1.05 

2.24 

1. 12 

2.40 

I.  20 

2.61 

1.30 

2.87 

1.44 

152 

1.77 

0.83 

1.85 

0.87 

1.94  1  0.91 

2.04 

0.96 

2.17 

1.02 

2.33 

1.09 

2.52 

1. 18 

154 

1.66 

0.73 

1.72 

0.  76 

1.80  '  0.  79 

1.88 

0.83 

1.98 

0.87 

2. 10 

0.92 

2.25 

0.99 

156 

1. 56     0.64 

I.  62 

0.66 

1.68  i  0.68 

1-75 

0.71 

I.  S3 

0.74 

1.92 

0.78 

2.03 

0.83 

158 

1.48     0. 56 

1-53 

0.57 

1.58     0.59 

1.63 

0.61 

1.70 

0.  64 

1.77 

0.66 

1.85 

0.69 

160 

1. 41      0.48 

1-45 

0.49 

1.49     0.51 

1-53 

0.  52 

1.58 

0.54 

1.64  '  0.  56 

I.  71 

0.58 

138° 

140° 

142° 

144° 

146° 

148° 

150° 

I48>^ 

3.85 

2.04 

150 

3.22     1. 61 

3-70     1-85 

152 

2.77     1.30 

3.09     1.45  1  3.  55  '  1.66 

154 

2.43     1.06 

2.66 

I.  16 

2.96 

1.30 

3.38 

1.48 

156 

2.17     0.88 

2.33 

0.95 

2.54 

1.04 

2.83 

1. 15 

3.22 

I-3I 

158 

1.96     0.73 

2.08 

0.78 

2.  23  !  0.  84 

2.43 

0.91 

2.69 

1. 01 

3-05 

I.  14 

160 

1. 79     0.61 

1.88 

0.64 

1 .  99     0.  68 

2.13 

0.73 

2.31 

0.79 

2.55 

0.87 

2.88 

0.98    1 

Page 

(278] 

TABLE  6 

. 

Distance  of  Objects  at  Sea  ii 
d  (in  statute  mile)  =  1.317 

1  Statute  Miles. 

V X  in  feet. 

Height, 

Dist., 

Height, 

Dist., 

Height, 

Dist., 

Height, 

Dist., 

Height, 

Dist., 

Height, 

Dist., 

Height, 

Dist., 

feet. 

miles. 

feet. 

miles. 

feet. 

miles. 

feet. 

miles. 

feet. 

miles. 

feet. 

miles. 

feet. 

miles. 

I 

1.32 

26 

6.72 

55 

9-77 

210 

19.09 

460 

28.25 

920 

39-95 

3100 

73-3 

2 

1.86 

27 

6.84 

60 

10.20 

220 

19-53 

470 

28.55 

940 

40.38 

3200 

74-5 

3 

2.28 

28 

6.97 

65 

10.62 

230 

19.97 

480 

28.85 

960 

40.  81 

3300 

75-7 

4 

2.63 

29 

7.09 

70 

11.02 

240 

20.40 

490 

29.15 

980 

41.23 

3400 

76.8 

5 

2.94 

30 

7.21 

v> 

11.40 

250 

20.82 

500 

29.45 

1000 

41.65 

3500 

77-9 

6 

3-23 

31 

7-33 

80 

11.78 

260 

21.  24 

520 

30.  03 

II 00 

43.68 

3600 

79-0 

7 

3-48 

32 

7-45 

85 

12. 14 

270 

21.64 

540 

30.  60 

1200 

45.62 

3700 

80.1 

8 

3-73 

33 

7-57 

90 

12.49 

280 

22.04 

560 

31-17 

1300 

47.48 

3800 

81.2 

9 

3-95 

34 

7.68 

95 

12.84 

290 

22.43 

580 

31-72 

1400 

49.28 

3900 

82.2 

lO 

4.  16 

35 

7-79 

100 

13-17 

300 

22.81 

600 

32.26 

1500 

51.  01 

4000 

83-3 

II 

4.37 

36 

7.90 

105 

13-50 

310 

23.19 

620 

32-79 

1600 

52.68 

4100 

84-3 

12 

4-56 

37 

8.01 

no 

13.81 

320 

23.56 

640 

33-32 

1700 

54-30 

4200 

85-4 

13 

4-75 

38 

8.12 

"5 

14.  12 

330 

23.92 

660 

33-83 

1800 

55.88 

4300 

86.4 

14 

4-93 

39 

8.22 

120 

14-43 

340 

24.28 

680 

34-34 

1900 

57-41 

4400 

87-4 

IS 

5.  10 

40 

8.33 

125 

14.72 

350 

24.64 

700 

34-  84 

2000 

58.90 

4500 

88.3 

16 

5-27 

41 

8.43 

130 

15.02 

360 

24.99 

720 

35-34 

2100 

60.35 

4600 

89-3 

17 

5-43 

42 

8.54 

135 

15-30 

370 

25-33 

740 

35-83 

2200 

61.77 

4700 

90.3 

18 

5-59 

43 

8.64 

140 

'5-58 

380 

25.67 

760 

36-31 

2300 

63.16 

4800 

91.  2 

19 

5-74 

44 

8.74 

145 

15.86 

390 

26.01 

780 

36.  78 

2400 

64.  52 

4900 

92.  2 

20 

5.89 

45 

8.83 

150 

16.13 

400 

26.34 

800 

37.25 

2500 

65.85 

5000 

93.1 

21 

6.03 

46 

8.93 

160 

16.66 

410 

26.67 

820 

37-71 

2600 

67.15 

I  mile 

95-7 

22 

6.18 

47 

9-03 

170 

17.17 

420 

26.99 

840 

38-17 

2700 

68.43 

23 

6.32 

48 

9.  12 

180 

17.67 

430 

27.31 

860 

38.62 

2800 

69.69 

24 

6.45 

49 

9.  22 

190 

18.15 

440 

27.63 

880 

39-07 

2900 

70.92 

25 

6.59 

50 

9-31 

200 

18.63 

450 

27.94 

900 

39-51 

3000 

72.13 

TABLE  7. 

Page  279 

» 

For  turning  Degrees  and  Minutes  into 

Time,  and  the  contrary. 

D. 

H.  M. 

D. 

H.  M. 

D. 

H.  M. 

D. 

H.  M. 

D. 

H.  M. 

D. 

H.  M. 

M. 

M.S. 

M. 

M.S. 

M. 

M.S. 

M. 

M.S. 

M. 

M.S. 

M. 

M.  ^. 

I 

0  4 

61 

4  4 

121 

8  4 

181 

12  4 

241 

16  4 

301 

20  4 

2 

0  8 

62 

4  8 

122 

8  8 

182 

12  8 

242 

16  8 

302 

20  8 

3 

0  12 

63 

4  12 

123 

8  12 

183 

12  12 

243 

16  12 

303 

20  12 

4 

0  16 

64 

4  16 

124 

8  16 

184 

12  16 

244 

16  16 

304 

20  16 

5 

0  20 

65 

4  20 

125 

8  20 

185 

12  20 

245 

16  20 

305 

20  20 

6 

0  24 

66 

4  24 

126 

8  24 

186 

12  24 

246 

16  24 

306 

20  24 

I 

0  28 

67 

4  28 

127 

8  28 

187 

12  28 

247 

16  28 

307 

20  28 

0  32 

68 

4  32 

1 28 

8  32 

188 

12  32 

248 

16  32 

308 

20  32 

9 

0  36 

69 

4  36 

129 

8  36 

189 

12  36 

249 

16  36 

309 

20  36 

10 

0  40 

70 

4  40 

130 

8  40 

190 

12  40 

250 

16  40 

310 
3" 

20  40 
"  20^44 

II 

0  44 

71 

4  44 

131 

844 

igV 

12  44 

251 

16  44 

12 

0  48 

72 

448 

132 

8  48 

192 

12  48 

252 

16  48 

312 

20  48 

13 

0  52 

73 

4  52 

133 

8  52 

193 

12  52 

253 

16  52 

313 

20  52 

14 

0  56 

74 

4  56 

134 

8  56 

194 

12  56 

254 

16  56 

3H 

20  56 

15   ' 

I  0 

75 

5  0 

135 

9  0 

195 

13  0 

255 

17  0 

^'i 

21  0 

16 

I  4 

76 

5  4 

136 

9  4 

196 

'3  4 

256 

17  4 

316 

21  4 

17 

I  8 

77 

5  8 

137 

9  8 

197 

13  8 

257 

17  8 

317 

21  8 

18 

I  12 

78 

5  12 

138 

9  12 

198 

13  12 

258 

17  12 

318 

21  12 

19 

I  16 

79 

5  16 

139 

9  16 

199 

13  16 

259 

17  16 

319 

21  16 

20 

I  20 

80 

5  20 

140 

9  20 

200 

13  20 

260 

17  20 

320 

21  20 

21 

I  24 

81 

5  24 

^141" 

9  24 

201 

13  24 

261 

17  24 

321 

21  24 

22 

I  28 

82 

5  28 

142 

9  28 

202 

13  28 

262 

17  28 

322 

21  28 

23 

I  32 

83 

5  32 

143 

9  32 

203 

13  32 

263 

17  32 

323 

21  32 

24 

I  36 

84 

536 

144 

9  36 

204 

13  36 

264 

17  36 

324 

21  36 

25 

I  40 

85 

5  40 

145 

9  40 

205 

13  40 

265 

17  40 

325 

21  40 

26 

I  44 

86 

5  44 

146 

9  44 

206 

13  44 

266 

17  44 

326 

21  44 

27 

I  48 

87 

5  48 

147 

948 

207 

1348 

267 

1748 

327 

21  48 

28 

I  52 

88 

5  52 

148 

9  52 

208 

13  52 

268 

17  52 

328 

21  52 

29 

I  56 

89 

556 

149 

9  56 

209 

13  56 

269 

17  56 

329 

21  56 

30 

2  0 

90 

6  0 

150 

10  0 

210 

14  0 

270 

18  0 

330 

22  0 

31 

2  4 

91 

6  4 

151 

10  4 

211 

14  4 

271 

18  4 

331 

22  4 

32 

2  8 

92 

6  8 

152 

10  8 

212 

14  8 

272 

18  8 

332 

22  8 

33 

2  12 

93 

6  12 

153 

10  12 

213 

14  12 

273 

18  12 

3ii 

22  12 

34 

2  16 

94 

6  16 

154 

10  16 

214 

14  16 

274 

18  16 

334 

22  16 

35 

2  20 

95 

6  20 

155 

10  20 

215 

14  20 

275 

18  20 

335 

22  20 

36 

2  24 

96 

6  24 

156 

10  24 

216 

14  24 

276 

18  24 

336 

22  24 

37 

2  28 

97 

6  28 

157 

10  28 

217 

1  14  28 

277 

18  28 

337 

22  28 

38 

2  32 

98 

6  32 

158 

10  32 

218 

14  32 

278 

18  32 

338 

22  32 

39 

2  36 

99 

6  36 

159 

10  36 

219 

14  36 

279 

18  36 

339 

22  36 

40 

2  40 

100 

6  40 

160 

ID  40 

220 

14  40 

280 

18  40 

340 
341 

22  40 

41 

2  44 

lOI 

6  44 

161 

10  44 

221 

14  44 

281 

18  44 

22  44 

42 

2  48 

102 

6  48 

162 

10  48 

222 

14  48 

282 

18  48 

342 

22  48 

43 

2  ^2 

103 

6  52 

163 

10  52 

223 

14  52 

283 

18  52 

343 

22  52 

44 

256 

104 

6  56 

164 

10  56 

224 

1  14  56 

284 

18  56 

344 

22  56 

45 

3  0 

105 

7  0 

165 

II   0 

225 

15  0 

285 

19  0 

345 

23  0 

46 

3  4 

106 

7  4 

166 

II   4 

226 

15  4 

286 

19  4 

346 

23  4 

47 

3  8 

107 

7  8 

167 

II  8 

227 

15  8 

287 

19  8 

347 

23  8 

48 

3  12 

108 

7  12 

168 

II  12 

228 

15  12 

288 

19  12 

348 

23  12 

49 

3  16 

109 

7  16 

169 

II  16 

229 

15  16 

289 

19  16 

349 

23  16 

50 

3  20 

no 

7  20 

170 

II  20 

230 

15  20 

290 

19  20 

350 

23  20 

51 

3  24 

III 

7  24 

1  '71 

II  24 

231 

15  24 

291 

19  24 

351 

23  24 

52 

328 

112 

728 

!  172 

II  28 

i  232 

15  28 

292 

19  28 

352 

23  28 

53 

3  32 

"3 

7  32 

173 

II  32 

1  233 

15  32 

293 

19  32 

353 

23  32 

54 

3  36 

114 

7  36 

174 

II  36 

234 

15  36 

294 

19  36 

354 

23  36 

55 

3  40 

"5 

7  40 

175 

II  40 

235 

15  40 

295 

19  40 

355 

23  40 

56 

3  44 

116 

7  44 

176 

II  44 

236 

15  44 

296 

19  44 

356 

2344 

57 

3  48 

117 

7  48 

177 

II  48 

^37 

15  48 

297 

19  48 

357 

23  48 

58 

3  52 

118 
119 

7  52 

178 

II  52 

238 

15  52 

298 

19  52 

358 

23  52 

59 

356 

756 

179 

II  56 

239 

15  56 

299 

19  56 

359 

23  56 

60 

1  4  0 

120 

8  0 

180 

12  0 

240 

16  0 

300 

20  0 

360 

24  0 

AToit'.—When  turning  seconds  of  arc  into  time,  and  vice  versa,  it  should  be  remembered  that  the  fractions  are  sixtieth'^ 
thus :  The  value  in  time  of  42"  is  not  2».48,  but  a'.JfS  —  2\8. 


Pi 

i 

u 

V 

•a 
55 

ige  280 

TABLE  8. 
Sidereal  into  Mean  Solar  Time. 

To  be  subtracted  from  a  sidereal  time  interval. 

0"^ 

Ih 

2'^ 

Sb 

4h 

5"^ 

6» 

^h 

For  seconds.  1 

w. 
o 
I 

2 

3 
4 

m.  s, 
0  0.  000 
0  0.  164 
0  0.  328 
0  0.  491 
0  0.655 

m 

0 

0 
0 
0 
0 

.     s. 
9.830 

9-993 
10.157 

10.321 

10.  485 

771.        S. 
0     19.659 
0     19.823 
0    19.987 
0    20.  151 
0    20.314 

m.     s. 
0  29.489 
0  29.653 
0  29.816 
0  29.  980 
0  30.  144 

m.     s. 
0  39.318 
0  39.  482 
0  39.  646 
0  39.810 

9  39.  974 

w.     s. 
0  49.  148 

0  49.312 

0  49. 475 
0  49. 639 

0  49. 803 

tn.     s. 
0  58.977 

0  59-  141 

'  0  59.  305 

0  59-469 

0  59. 633 

m.     s. 
I     8. 807 
I     8.971 

I     9-  135 
I     9. 298 
I     9. 462 

s. 

I 

2 

3 
4 

s. 

0.003 
.005 
.008 

.oil 

7 
8 

9 

0  0.819 
0  0.  983 
0  I.  147 
0  I. 311 
0  1.474 

0 
0 
0 
0 
0 

10.  649 
10.813 

10.  976 

11.  140 
11.304 

0    20.  478    1    0    30.  308 
0    20.  642        0    30.  472 
0    20.  806    1    0   30.  635 
0    20.  970       0   30.  799 
0   21.  134       0   30.963 

0  40.  137 
0  40.  301 
0  40.465 
0  40.  629 
0  40.  793 

0  49.  967 
0  50.  131 
0  50.  295 
0  50.458 
0  50. 622 

0  59.  796 

0  59.  960 

1  0.  124 
I     0. 288 
I     0. 452 

I     9. 626 
I     9.  790 

I     9-  954 
I   10.  118 
I   10.281 

5 
6 

7 
8 

9 

014 
.016 
.019 
.022 
.025 

lO 

II 

12 

13 
14 

0  1.638 
0  I . 802 
0  1 .  966 
0  2.  130 
0  2.  294 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

11.468 
11.632 

11-795 
"•959 
12. 123 

0   21.297 
0    21.461 
021.  625 
0    21.  789 
0    21.953 

0  31.  127 
0  31.291 

0  31.455 
0  31.618 
0  31.  782 

0  40. 956 

0   41.  I20 
0   41.  284 
0   41.448 
0   41.  612 

0  50.  786 
0  50.  950 
0  51. 114 
0  51.278 
0  51.441 

I    0.616 

I     0.  779 
I    0.943 
I     1. 107 
I     1. 271 

I  10.445 
I   10.  609 
I   10.773 
1   10.937 
I   II.  100 

10 
II 
12 

13 
14 

.  027 

.030 
.033 
.035 
.038 

IS 

16 

17 
18 

19 

0  2.457 
0  2.621 
0  2.  785 
0  2.  949 
0  3-113 

12.287 
12.451 
12.615 
12.  778 
12. 942 

0    22.  117 
0   22.  280 
0    22.  /|^/] 
0    22.  608 
0    22.  772 

0  31.946 
0  32.  no 

0  32-  274 
0  32-  438 

0  32.601 

0    41.  776     !     0     51.605 
0    41.939         0     51.   769 
0    42.103         0     51.933 
0    42.  267         0     52.  097 
0    42.  431     ,     0     52.  260 

I     1-435 
I     I-  599 
I     I.  762 
I     1.926 
I     2. 090 

I   11.264 
I   11.428 
1   11.592 
I   11.756 
I   11.920 

15 
16 

17 
18 

19 

.041 

.044 

.046 

■  049 

.052 

20 

21 

22 

23 
24 

0  3.277 
0  3.440 
0  3.  604 
0  3.  768 
0  3. 932 

0 
0 
0 
0 
0 

13. 106 

13.270 

13-434 
13- 598 
13.  761 

0   22.  936 

0  23.099 

0    23.  263 
0    23.427 
0    23.591 

0  32. 765 
0  32. 929 

0  33-  093 
0  33.257 

0  :iT,.  420 

0    42.  595          0     52. 424 

0  42.  759  '  0  52.  588 
0  42.922  1  0  52.  752 
0  43.086  '  0  52.  916 
0  43.  250     0  53. 080 

I     2.254 
I     2.418 

I     2.582 
I     2.  745 
I     2. 909 

I   12.  083 
I   12.247 
I   12.411 
I   12.575 
I   12.739 

20 
21 

22 

23 
24 

•  055 
.057 

.060 
.063 
.066 

25 
26 

27 
28 
29 

0  4. 096 
0  4.  259 
0  4. 423 
0  4.  587 
0  4-  751 

0 

0 
0 
0 
0 

13-  925 
14. 089 

14.  253 
14.417 
14.  581 

0   23.  755 
0    23.  919 
0    24.  082 
0    24.  246 
0    24.  410 

0  33. 584 

0  33-  748 
0  33.912 
0  34.  076 
0  34.  240 

0  43. 414     0  53. 243 

0  43.578     0  53.407 
0  43.  742     0  53.  571 
0  43.  905     0  53.  735 
0  44.  069  ;  0  53.  899 

I     3-073 
I     3.237 
I     3. 401 

I     3.564 
I     3.728 

I  12.903 
I   13.066 
I   13.230 
I   13-394 
1   13-558 

26 

27 
28 

29 

.068 
.071 
.074 

.076 
.079 

30 
31 

32 

33 
34 

0  4.915 
0  5.  079 
0  5.  242 
0  5.406 
0  5- 570 

0 
0 
0 
0 
0 

14.744 
14.908 
15-072 
15.236 
15.400 

0    24.  574 
0   24.  738 
0    24.  902 
0    25.  065 
0    25.  229 

0  34.  403 
0  34.  567 
0  34-  731 
0  34.  895 
0  35.059 

0  44.  233     0  54. 063 
0  44- 397     0  54. 226 
0  44. 561      0  54. 390 
0  44.  724     0  54.  554 
0  44.  888  i  0  54.  718 

I     3. 892 

I     4. 056 
I     4. 220 
I     4. 384 

I     4  547 

I  13.722 

I   13.886 
I   14.049 
I   14.213 

I   14.377 

30 
31 
32 

33 
34 

.082 
.085 
.087 

.090 

.093 

35 
36 
37 
38 
39; 

0  5-  734 
0  5.  898 
0  6.  062 
0  6.  225 
0  6.389 

0 
0 
0 
0 

0 

15-563 
15-727 
15.891 
16.055 
16.219 

0  25. 393     0  35.  223 
025.557     035.386 
0  25.721  I  0  35.550 
025.885     035.714 
0  26.  048  1  0  35. 878 

0  45.  052  :  0  54.  882 
0  45.216     0  55.046 
0  45.  380     0  55. 209 
0  45-544  '  0  55-373 
0  45.  707  1  0  55. 537 

I     4.  711 

I     4.875 
I     5-  039 
I    5. 203 
I    5.367 

I   14.541 

I   14.705 

I   14.868 
I   15.032 
I   15.196 

35 
36 
37 
38 
39 

.096 

.098 

.  lOI 

.  104 
.  106 

40 
41 
42 
43 
44 

0  6.553 
0  6.717 
0  6.  881 
0  7.045 
0  7.  208 

0 
0 
0 
0 
0 

16.383 
16. 546 
16.  710 
16.  874 
17.038 

0  26.  212 
0  26.  376 
0  26.  540 
0  26.  704 
0  26.  867 

0  36.  042 
0  36.  206 
0  36.  369 

0  36.  533 
0  36. 697 

0  45.871  1  0  55-701 

0    46.  035     ;     0    55.  865 
0    46.    199         0     56.028 

0  46.  363     0  56.  192 

0  46. 527 :  0  56. 356  1 

I    5.530 
I    5. 694 
I    5-858 
I  -  6.  022 
I     6.  186 

I   15.360 

I  15.524 
I   15.688 

I   15-851 
I   16.015 

40 
41 
42 

43 
44 

.  109 

.  112 

•115 
.117 
.  120 

46 

47 
48 

49 

0  7.372 

0  7.536 
0  7.  700 
0  7.864 
0  8.027 

0 
0 
0 
0 
0 

1 7.  202 
17.366 

17.529 
17.693 

17.857 

0  27.031 
0  27. 195 
0  27. 359 
0  27.  523 
0  27.  687 

0  36.  861 
0  37.025 
0  37.  i88 

0  37.352 
0  37.516 

0  46.  690     0  56. 520 
0  46. 854     0  56. 684 
0  47.  018     0  56.  848 
0  47. 182     0  57.011 
0  47.346  1  0  57.175  1 

I     6.350 
I     6.513 
I     6.677  ' 
I     6. 841 
I     7. 005 

I  16.179 

I  16.343 
I   16.507 

I   16.671 

I  16.834 

46 
47 
48 
49 

.123 
.  126 
.128 

•131 

.134 

50 
51 
52 
53 
54 

0  8.  191 
08.355  1 
0  8.  519  1 
0  8.  683 
0  8. 847 

0 
0 
0 
0 
0 

18.021 

18.  185     : 
18.349 
18.512 
18.  676 

0  27.  850 
0  28.014 
0  28.  1 78 
0  28.342 
0  28. 506 

0  37.680 

0  37.844 
0  38.008 
0  38.171 
0  38.  335 

0  47.510 
0  47. 673 
0  47. 837 

0  48. 001 
0  48. 165 

0  57.339 
0  57.503 
0  57.  667 

0  57.831 
0  57-994 

I     7.  169 

I     7. 332 
I     7.496 
I     7. 660 
I     7.824 

I   16.998 
I   17.  162 
I   17.326 

I   17.490 
I   17.654 

50 
51 
52 
53 
54 

.137 
.139 
.142 

.145 
.147 

55 
36 
57 
58 
59 

0  9.010 

0  9.  174 

0  9-  33^ 
0  9.  502 
0  9.  666 

0 
0 
0 
0 
0 

18.  840 
19.004 

19.  168 

19.331 
19.495 

0  28. 670 
0  28.  833 
0  28. 997 
0  29.  161 
0  29.325 

0  38.499 
0  38.  663 
0  38.827 
0  38.  991 
0  39. 154 

0  48. 329    0  58. 158  ' 
0  48. 492     0  58.  322 

0  48. 656  1  0  58. 486 

0  48.  820  '  0  58.  650 
0  48.984     0  58.814 

I     7. 988 
I     8.  152 
I     8.315 
I     8. 479 
I     8.643 

I   17.817 
I   17.981 
I   18.145 
I   18.309 
I   18.473 

p 

57 
58 
59 1 

.150 

.153 

.156 

.158 

0.  161 

TABLE  8.                   [Page  281 
Sidereal  into  Mean  Solar  Time. 

"3 

■3 

To  be  subtracted  from  a  sidereal  time  interval.                         1 

8^ 

9" 

10" 

11'^ 

12" 

13" 

14" 

15" 

For  seconds.  1 

»l. 

0 

I 

2 

-1 
J 

4 

1)1.       s. 

I  18.636 
I  18.800 
I  18.964 
I  19. 128 
I  19.  292 

tn.     s. 
I  28.466 
I  28.  630 
I  28.794 
I  28.958 
I  29.  121 

m.     s. 
I  38.296 
I  38.459 
I  38.623 
I  38.  787 
I  38.951 

m.     s. 
I  48.  125 

I  48.289 

I  48.453 
I  48.617 

I  48.  780 

>;/.     s.           m.     s. 

I  57-955  1  2  7.784 
I  58.  119  2  7.948 
I  58.282  2  8.  112 
I  58.446  2  8. 276 
I  58.610  2  8.440 

m.     s. 
2  17.614 
2  17.778 

2  17.941 
2  18.  105 
2  18.269 

ni.     s. 
2  27.443 
2  27.  607 

2  27.  771 
2  27.935 
2  28.  099 

s. 
I 

2 

3 
4 

s. 

0.003 
.005 
.008 
.  on 

5 

0 

7 
8 

9 

I  19.456    I  29.285 
I  19.619    I  29.449 
I  19.783    I  29.613 
I  19.947    I  29.777 
I  20. 1 1 1  I  29. 940 

I  39-115 
I  39.279 

I  39.442 
I  39.  606 
I  39.  770 

I  48.944 
I  49.  108 
I  49-272 
I  49-436 
I  49.  600 

I  58.774  2  8.603 
I  58. 938  2  8.  767 
I  59.  loi  ■  2  8.931 
I  59.265  1  2  9.095 
I  59.429  2  9.259 

2  18.433 
2  18.597 
2  18.761 
2  18.  924 
2  19.088 

2  28.263 
2  28.426 
2  28.  590 
2  28.  754 
2  28.918 

5  .014 

6  .016 

7  .019 

8  .  022 

9  .  025 

10 

II 

12 

'3 
14  , 

I  20.  275  1  I  30.  104 
I  20.  439   I  30.  268 
I  20.602   I  30.432 
I  20.  766   I  30.  596 
I  20.  930   I  30.  760 

I  39-934 
I  40.  098 
I  40.  261 
I  40.425 
I  40.589 

I  49.  763 

I  49-927 
I  50.091 
I  50.255 
I  50.419 

I  59.593  2  9.423 
I  59.  757  2  9.  58b 

1  59.  921  2  9.  750 

2  0.084  2  9. 914 
2  0.248  2  10.078 

2  19.252 
2  19.416 
2  19.580 

2  19.744 
2  19.  907 

2  29.  082 
2  29. 245 
2  29.  409 
2  29.573 
2  29.  737 

10  i  .027 

11  .  030 

12  .033 

13  -035 

14  !  .038 

15 

i6 

17 
iS 

19 

I  21.  094 
I  21.258 
I  21.422 
I  21.585 
I  21.749 

I  30.923 
I  31.087 
I  31.251 

1  31-415 
I  31.579 

I  40.  753 
I  40.917 
I  41.081 

I  41.244 
I  41.408 

I  50.583 
I  50.746 
I  50. 910 
I  51.074 
I  51.238 

2  0.412 

2  0.576 
2  0.  740 
2  0. 904 
2  1.067 

2  10.  242 
2  10.405 
2  10.  569 

2  10.733 
2  10.897 

2  20.  071 
2  20.  235 
2  20.  399 
2  20.  563 
2  20.  727 

2  29. 901 

2  30.  065 
2  30.  228 
2  30.  392 
2  30- 556 

15  .041 

16  .044 
171  . 046 

18  .049 

19  .052 

20 
21 

22 

23 
24 

I  21.913 

I  22.077 
I  22.241 
I  22.  404 
I  22.568 

I  31.743 
I  31.906 
I  32.070 
I  32.234 
I  32.398 

I  41.572 
I  41.736 
I  41.900 
I  42. 064 
I  42.  227 

I  51.  402 

I  51-565 
I  51.729 

I  51.893 

I  52.057 

2  1.231 

2  1.395 
2  1.559 
2  1.723 
2  1.887 

2  II.  061 
2  11.225 
2  11.388 
2  II. 552 
2  II.  716 

2  20.  890   2  30.  720 
2  21.054   2  30.  884 
2  21.  218   2  31.  048 
2  21. 382   2  31.  211 
2  21.546  ;  2  31.375 

20  .  055 

21  ,  -057 

22  1  . 060 

23  ;   .063 

24  .066 

25  !   .068 

26  . 071 

27  !   .074 

28  .076 

29  _.079_ 

30  1  .  082 

31  .085 

32  .087 

33  -  090 

34  . 093 

35  ■  .096 

36  . 098 

37  • loi 

38  .104 

39  . 106 

40  .  109 

41  .112 

42  .115 

43  -117 

44  i  -  120 

25 
26 

27 
28 

29 

I  22.  732 
I  22.896 
I  23.  060 
I  23.224 

I  23.387 

I  32.562 
I  32.  726 
I  32.889 

I  33-053 
I  33.217 

I  42.391 

I  42.555 
I  42.719 
I  42.883 

I  43.047 

I  52.221 

I  52-385 
I  52.548 
I  52.712 
I  52.876 

2  2. 050 
2  2.214 
2  2.378 
2  2.542 
2  2.  706 

2  11.880 
2  12.  044 
2  12.208 
2  12.371 
2  12.535 

2  21.709   2  31.539 
2  21.  873   2  31.  703 
2  22.  037  ;  2  31.  867 
2  22.  201    2  32.031 
2  22.365   2  32.  194 

3" 
31 

32 

34 

I  23.551    I  33.381 

I  23.715  :  I  33.545 
I  23.  879  !  I  IT,.  708 
I  24.043  !  I  33.872 
I  24.207  1  I  34.036 

I  43-210 
I  43-374 
I  43-538 
I  43.  702 
I  43.866 
I  44.029 
I  44-  193 
I  44-357 
I  44.521 
I  44.685 
I  44.849 
I  45- 012 
I  45.176 
I  45-340 
I  45.504 
I  45.668 
I  45-832 

I  45-995 
I  46,159 
I  46.323 

I  53.040 
I  53.204 
I  53.368 
I  53.531 
I  53.695 

I  53.859 
I  54,023 

I  54.187 

I  54.351 

I  54.514 

I  54.678 

I  54.842 

I  55. 006 

I  55-170 

I  55-333 

I  55.497 
I  55.661 
I  55.825 
I  55-989 
I  56. 153 

2  2. 869 

2  3-033 
2  3- 197 
2  3-361 
2  3-525 

2  12.699 
2  12.863 
2  13.027 
2  13.  191 
2  13-354 

2  22. 529 
2  22.692 
2  22.  856 
2  23.020 
2  23.  184 

2  32-358 
2  32. 522 
2  32.686 
2  32.850 
2  33-013 
2  33-177 

2  33-  341 

2  33-  505 
2  33.669 

2  33-833^ 
2  33.996 
2  34.  160 
2  34.  324 
2  34-488 
2  34.652 

35 
36 

37 
S^ 
39 

I  24.370 

I  24.534 
I  24.  698 
I  24.862 
I  25.026 

I  34.  200 
I  34.364 
I  34.528 
I  34.691 

I  34-855 
I  35.019 
I  35-  ^83 
I  35-347 
I  35-5" 
I  35-674 

I  35-838 
I  36. 002 
I  36. 166 
I  36-330 
I  36-493 

2  3.689  2  13. 518 
2  3. 852  2  13.682 
2  4.  016  1  2  13.  846 
2  4. 180  2  14.010 
2  4.344  ;  2  14.173 

2  23.  348 
2  23.  512 
2  23.675 
2  23.839 
2  24.  003 

40 

41 
42 

43 

44 

I  25. 190 

I  25.353 
I  25.517 

I  25.681 

I  25.845 

2  4.508 : 2  14.337 

2   4.672   2  14.  501 
2   4.835  ,  2  14.665 
2   4.  999  !  2  14.  829 

2  5. 163  :  2  14. 993 

2  24.  167 
2  24.331 
2  24.495 
2  24.  658 
2  24.  822 

45 
46 

47 

48 

49 

I  26.  009 
I  26.  172 
I  26.336 
I  26.  500 
I  26. 664 

2   5-327 
2   5.491 

2   5.655 
2   5.818 
2   5.  982 

2  15.  156 

2  15.320 

2  15.484 
2  15.648 
2  15.812 

2  24.986 
2  25. 150 
2  25.314 
2  25.477 
2  25.  641 

2  34.816 
2  34-979 
2  35- 143 
2  35-307 
2  35-471 

46 

47 
48 

49 

.123 

.  126 

.128 

.131 
•  134 

50 
51 

52 
53 
54 

55 
56 

11 

59 

I  26,828   I  36.657 
I  26.992   I  36.821 
I  27.155   I  36.985 
I  27.319   I  37.149 
I  27.483   I  37.313 

I  46.487 
I  46.651 
I  46.815 

I  46.978 
I  47.  142 

I  47.306 

I  47.470 
I  47.634 

I  47-797 
I  47.961 

I  56.316 
I  56. 480 
I  56.644 
I  56.808 
I  56.972 

I  57. 136 
I  57.299 

I  57.463 
I  57.627 

I  57-791 

2  6.  146 

2   6.310 
2   6.474 

2  6. 637 
2  6. 801 
2  6. 965 

2   7.  129 
2   7.  293 

2  7-457 

2   7.  620 

2  15.976 
2  16.  139 
2  16.303 
2  16.467 
2  16.631 

2  25.805 
2  25.  969 
2  26. 133 
2  26.  297 
2  26.460 

2  35-635 
2  35-  798 
2  35-962 
2  36.  126 
2  36.  290 

50 
51 

52 
53 
54 

.137 
-139 
.  142 

•  145 
.147 

I  27.647 
I  27.811 
I  27.975 
I  28.  138 
I  28.302 

I  37.476 

I  37.640 
I  37.804 
I  37.968 
I  38-  132 

2  16.795 
2  16.959 
2  17.  122 
2  I  7.  286 
2  17.450 

2  26.  624 

2  26.  788 
2  26.  952 
2  27.  116 
227.  280 

2  36.454 
2  36.618 
2  36-  781 
2  36-945 
2  37-  109 

55  .150 

56  .  153 

57  -156 

58  .  158 

59  0. 161 

Page  282 

TABLE  8. 
Sidereal  into  Mean  Solar  Time. 

"3 

u 

•a 

To  be  subtracted  from  a  sidereal  time  interval.                                                               1 

le^ 

l^h 

IS** 

i9^ 

20" 

21h 

22^ 

23'^ 

For  seconds.  1 

w. 
o 

I 

2 

3 
4 

m.     s. 
2  37-  273 
2  37.437 
2  37.601 
2  37.  764 
237.  928 

m.     s. 
2  47.  102 
2  47.266 

2  47-430 
2  47.  594 

2  47-  758 

m. 

2 

2 

2 

2 

2 

J. 

56. 932 

57.096 
57.  260 
57-424 
57-  587 

m.    s. 
3    6. 762 

3    6.925 
3     7. 089 
3     7. 253 
3     7.417 

m.     s. 
3   16.591 
3  16.  755 
3  16.919 
3  17-083 
3  17.246 

m.     s. 
3  26.421 
3  26.  585 
3  26.  748 
3  26.912 
3  27.076 

m.     s. 
3  36.250 
3  36-414 
3  36.578 
3  36.  742 
3  36.906 

m.     s. 

3  46.  080 
3  46-  244 
3  46.  407 
3  46.571 
3  46.  735 
3  46-  899 
3  47-063 
3  47-  227 
3  47-  390 
3  47-  554 

s. 

I 
2 

3 
4 

5 
6 

7 
8 

9 

s. 

0.003 
.005 
.008 
.on 

5 
6 

7 
8 

9 

2  38.  092 
2  38.  256 
2  38.  420 

2    38.  584 

2  38.  747 

2  47.  922 
2  48.  085 
2  48.  249 
2  48.413 
2  48.  577 

2 
2 
2 
2 
2 

57-  751 
57-915 
58.079 

58-  243 
58. 406 

3     7.581 
3     7-745 
3     7-  908 
3    8.072 
3    8.236 

3  17.410 
3  17.574 
3  17.738 
3  1 7.  902 
3  18.066 

3  27.240 
3  27.404 
3  27-  568 
3  27-  731 
3  27-  895 

3  37.069 
3  37-  233 
3  37-  397 
3  37.561 
3  37-  725 

.014 
.016 
.019 
.022 
.025 

lO 

II 

12 

13 

14 

2  38.911 

2  39-075 
2  39.  239 

2  39-403 
2  39-  566 

2  48.  741 
2  48.  905 
2  49. 068 
2  49.232 
2  49. 396 

2 
2 

2 
2 

2 

58.  570 

58-  734 

58.  898 

59-  062 

59.  226 

3    8. 400 
3    8.564 
3    8.728 
3    8. 891 
3    9.055 

3  18.229 

3  18.393 
3  18.557 
3  18.721 
3  18.885 

3  28.059 
3  28.223 
3  28.  387 
3  28. 550 
3  28.  714 

337.889 
3  38.052 
3  38.216 
3  38-  380 
3  38- 544 

3  47-  718 
3  47-882 
3  48.046 
3  48.  210 
3  48.  373 

10 
II 

12 

13 
14 

.027 

.030 

.033 

.035 
.038 

15 
i6 

17 
i8 

19 

2  39-  730 
2  39-894 
2  40.  058 
2  40.  222 
2  40.  386 

2  49.  560 
2  49.  724 
2  49.  888 
2  50.051 
2  50-215 

2 
2 
2 
2 

3 

59-  389 
59-  553 
59-717 
59-  881 
0.045 

3    9.219  1  3  19.049 
3    9.383     3  19.212 
3    9.547     3  19-376 
3    9.710     3  19-540 
3    9-874     3  19-704 

3  28.  878 
3  29.042 
3  29.  206 
3  29-370 
3  29.  533 

3  38-  708 
338-871 
3  39-035 
3  39-  199 
3  39-  363 

3  48.  537 
3  48-  701 
3  48.  865 
3  49-  029 
3  49-  193 

15 
16 

17 
18 

19 

.041 
.044 
.046 

•049 
.052 

20 
21 
22 

23 
24 

2  40.  549 
2  40.  713 
2  40.  877 
2  41.  041 
2  41.205 

2  50-379 
2  50-  543 
2  50.  707 
2  50.  870 
2  5-034 

3 

3 
3 

-^ 

3 

0.209 

0.372 

0-536 
0.  700 
0.864 

3  10.  038     3  19.  868 
3  10.  202     3  20. 032 
3  10.  366     3  20. 195 
3  10.  530     3  20.  359 
3  10.693  !  3  20.523 

3  29.697 
3  29.861 
3  30-025 
3  30-  189 
3  30-  353 

3  39.  527 
3  39-691 
3  39-  854 
3  40.018 
3  40.  182 

3  49-  356 
3  49-  520 
3  49-  684 
3  49-  848 
3  50-012 

20 
21 

22 

23 
24 

.055 
.057 
.060 

.063 
.066 

25 
26 

27 

28 

29 

2  41.369 
2  41.532 
2  41.696 
2  41.  860 
2  42.  024 

2  51.  198 
2  51.362 
2  51. 526 
251.  690 

2  51-853 

3 

3 
3 
3 
3 

1.028 
I.  192 
1-355 
1-519 
1.683 

3  10.857 
3  II. 021 
3  "-185 
3  "-349 
3  11-513 

3  20.687 
3  20.851 
3  21.014 
3  21.178 
3  21.342 

3  30-516 
3  30.  680 

3  30-844 
3  31-008 
3  31-172 

3  40.  346 
3  40.510 
3  40.  674 
3  40.  837 
3  41.001 

3  50-175 
3  50-339 
3  50-503 
3  50-667 
3  50.831 

25 
26 

27 
28 

29 

.068 
.071 

.074 
.076 

.079 

30 
31 
32 

33 
34 

2  42.  188     2  52.017 
2  42.352     2  52. 181 
2  42.515     2  52.345 
2  42.  679  1  2  52.  509 
2  42.  843  1  2  52.  673 

3 
3 
3 
3 
3 

1.847 
2.  on 
2.174 

2.  338 
2.  502 

3  11.676     3  21.  506 
3  II.  840     3  21.670 
3  12.  004     3  21.834 
3  12.168     3  21.997 
3  12.332  '  3  22.161 

3  31-336 
3  31-499 
3  31-663 
3  31-827 
3  31.991 

3  41-165 
3  41.329 
3  41.493 
3  41.657 
3  41.820 

3  50.995 
3  51.158 
3  51-322 
3  51-486 
3  51.650 

30 
31 

32 

33 
34 

.082 
.085 
.087 
.090 

•093 

3| 
36 

37 

38 

39 

40 

41 
42 

43 
44 

2  43. 007     2  52.  836 
2  43.  171      2  53.  000 
2  43-  334     2  53.  164 
2  43. 498  I  2  53. 328 
2  43.  662     2  53.  492 

3 
3 
3 
3 
3 

2.666 
2.830 
2.994 
3.157 
3-321 

3  12.496 
3  12.659 
3  12,823 
3  12.987 
3  13-151 

3  22.  325 
3  22.489 
3  22.653 
3  22.817 
3*22. 980 

3  32. 155 
3  32.318 
3  32.482 
3  32.  646 
3  32.810 

3  41-984 
3  42. 148 
3  42.312 
3  42.476 
3  42. 639 

3  51.814 
3  51-978 
3  52.  141 
3  52.305 
3  52.469 

35 
36 
37 
38 
39 

.096 
.098 

.  lOI 

.  104 
.  106 

2  43.  826     2  53.  656 
2  43-990     2  53.819 
2  44.154     2  53.983 
2  44.317     2  54.147 
2  44.481      2  54-3" 

3 
3 
3 
3 
3 

3-485 

3.649 

3-813 

3-977 
4.140 

3  13.315     3  23.144 
3  13.478     3  23-308 
3  13.642     3  23.472 
3  13.806     3  23.636 
3  13-  970     3  23. 800 

3  32.974 
3  33-  138 
3  33-301 
3  33-  465 
3  33-  629 

3  42.  803     3  52.  633 
3  42-967     3  52-797 
3  43-131     3  52.961 
3  43-  295     3  53.  124 
3  43-  459  ;  3  53-  288 

40 
41 
42 
43 
44 

.  109 
.  112 

.115 
.117 
.  120 

46 

48 
49 

50 
51 
52 
53 
54 

2  44.645 
2  44.  809 
2  44-  973 
2  45- 137 
2  45-  300 

2  45.464 
2  45.628 
2  45.  792 

2  45-  956 
2  46.  120 

2  54-475 
2  54.  638 
2  54. 802 
2  54. 966 
2  55. 130 

3 
3 
3 
3 
3 

4-304 
4.468 
4.632 
4.796 
4.960 

3  14-  134     3  23.  963 
3  14.  298     3  24.  127 
3  14.461     3  24.291 
3  14.625     3  24.455 
3  14.789     3  24.619 

3  33-  793 
3  33-957 
3  34- 121 
3  34-284 
3  34-448 

3  43-  622 
3  43-  786 
3  43-950 
3  44-114 
3  44.  278 

3  53.452 
3  53-616 
3  53-  780 
3  53-943 
3  54.  107 

45 
46 

47 
48 

49 

.123 
.  126 
.128 

.131 
.134 

2  55-294 
2  55-458 
2  55.621 

2  55-  7S5 
2  55.949 

3 
3 
3 
3 
3 

5-123 
5-287 
5-451 
5-615 
5-779 

3  14.  953     3  24.  782 
3  15.117     3  24.946 
3  15.281      3  25.  no 
3  15.444     3  25.274 
3  15.608     3  25.438 

3  34-612 
3  34-  776 
3  34.940 
3  35.  104 
3  35-267 

3  44.  442  1  3  54.  271 
3  44-605     3  54-435 
3  44-  769     3  54-  599 
3  44-  933     3  54-  763 
3  45-  097  :  3  54-  926 

50 
51 

52 
53 
54 

•137. 

.139 

.142 

.145 
.147 

11 

59 

2  46.283     2  56.  113 
2  46.447  1  2  56.277 
2  46.  611      2  56.441 
2  46-  755  '  2  56. 604 
2  46.  939  1  2  56.  768 

3 
3 
3 
3 
3 

5.942 
6.  106 
6.  270 

6-  434 
6.598 

3  15-772     3  25-602 
3  15-  936     3  25.  765 
3  16.  100     3  25.929 
3  16.264     3  26.093 
3  16.427  1  3  26.257 

3  35-431 
3  35- 595 
3  35-  759 
3  35-923 
3  36.086 

3  45-261     3  55.090 
3  45-425     3  55-254 
3  45-588     3  55-418 
3  45-  752  •  3  55-  582 
1  3  45-916  1  3  55-746 

11 

59 

-150 

-153 
.156 

.158 

0.  161 

TABLE  9. 

Page 

283 

Mean  Solar  into  Sidereal  Time. 

1-.* 

on 
C 
n 

III. 

To  be  added  to  a  mean  time  interval. 

Ob 

l'^ 

2h 

3" 

4h 

III.      s. 

5^ 

e^ 

^u 

For  seconds. 

in. 

.f. 

III. 

.f. 

m. 

s. 

III.      s. 

III.      s. 

III.      s. 

///.     s. 

I 

•. 

O 

0 

0.  000 

0 

9.  856 

0 

19.713 

0  29.  569 

0  39.426 

0  49. 282 

0  59. 139 

I     8. 995 

I 

0 

0.  164 

0  1 

0.021 

0 

19-877 

0  29.  734 

0  39. 590 

0  49.  447 

0  59.303 

I     9.  160 

I      0 

003 

2 

0 

0.329 

0  1 

0.  185 

0 

20.  041 

0  29. 898 

0  39.  754 

0  49.  611 

0  59.467 

I     9. 324 

2 

005 

0 

0.493 

0  1 

0.349 

0 

20.  206 

0  30.  062 

0  39.919 

0  49-  775 

0  59. 632 

I     9. 488 

3 

008 

4 
5 

0 

0.657 

0  1 

0.514 

0 

20. 370 

0  30.  227 
0  30739T 

0  40.  083 

0  49.  939 

0  59.796 

0  59. 960 

I     9. 652 
I     9.817 

4  i 
5 

oil 
014 

0 

0.821 

0  1 

0.678 

0 

20.  534 

0  40. 247 

0  50.  104 

6 

0 

0.986 

0  1 

0.842 

0 

20.  699 

0  30.  555 

0  40.412 

0  50. 268 

I     0.  124 

I     9.981 

6 

016 

7 

0 

I.  150 

0  1 

I.  006 

0 

20.  863 

0  30-  719 

0  40.  5  76 

0  50.432 

I      u.  289 

I     ID.  145 

7 

019 

8 

0 

1-314 

0  1 

I.  171 

0 

21.  027 

0  30. 884 

0  40.  740 

9  50. 597 

I     0. 453 

I     10.310 

8 

022 

9 

0 

1.478 

0  1 

i.335_ 

0 

21.  191 

0  31.048 
0  31.  212 

0  40. 904 
0  41.069 

0  50.  761 
0  50.  925 

1     0.617 
I     0.  782 

I     10.474 
I     10.638 

9  ' 
10 

025 
027 

10 

0 

1.643 

0  1 

1.499 

0 

21.356 

II 

0 

1.807 

0  ) 

1.663 

0 

21.520 

0  31.376 

0  41.233 

051.  089 

I     0. 946 

I     10.  802 

II 

030 

12 

0 

I. 971 

0  J 

1.828 

0 

21.684 

0  31.541 

0  41.397 

0  51-254 

I     I.  no 

I     10.967 

12  ' 

033 

13 

0 

2.136 

0  1 

1.992 

0 

2 1 .  849 

0  31-  705 

0  41.  561 

0  51.418 

I     1.274 

I     11. 131 

13 

036 

14 

15 

0 

2.  300 

0  1 

2. 156 

0 

22.013 

0  31.869 

0  41.  726 

051. 582 
0  51.746 

I     1.439 
I     1.603 

I     11.295 

14 
15 

038 
041 

0 

2.464 

0 

2.321 

0 

22.177 

0  32. 034 

0  41.  890 

I   11.459 

i6 

0 

2.628 

0  J 

2.485 

0 

22. 341 

0  32. 198 

0  42. 054 

0  51.911 

I     I.  767 

1   11.624 

16 

044 

17 

0 

2-793 

0  ] 

2.649 

0 

22. 506 

0  32. 362 

0  42.  219 

0  52.  075 

I     1.932 

I   11.788 

17 

047 

iS 

0 

2-957 

0  1 

2,813 

0 

22.  670 

0  32. 526 

0  42.  383 

0  52.  239 

I     2. 096 

1   11.052 

18 

049 

19 

20 

0 

3.  121 

0  1 

2.978 

0 

22. 834 

0  32.691 

_°_i2:.5l7_ 

0  52.  404 

I     2. 260 

I   12.  117 

19 

052 
055      1 

0 

3-285 

0  J 

3.142 

0 

22. 998 

0  32.855 

0  42.  711 

0  52.  568 

I     2. 424 

I   12.  2S1 

20 

21 

0 

3-450 

0 

3.306 

0 

23.  163 

0  33.019 

0  42. 876 

0  52.  732 

I     2. 589 

1   12.445 

21 

057     1 

22 

0 

3.614 

0  ] 

3-471 

0 

23.  327 

0  33- 183 

0  43-  040 

0  52.896 

I     2.  753 

I   12.609 

22 

060   n 

23 

0 

3-778 

0  1 

3-635 

0 

23.491 

0  7:1.  348 

0  43.  204     0  53.061 

I     2.917 

I   12.774 

23 

063   1 

24 

0 

3-943 

0  1 

3-799 

0 

23. 656 

0  33.512 

0  43. 368     0  53. 225 

I     3.0^1 

I   12.938 

24 

0G6   1 
068   j 

25 

0 

4.107 

0  ] 

3-  963 

0 

23.  820 

0  33. 676 

0  43.  533     0  53. 389 

I     3. 246 

I   13. 102 

25 

26 

0 

4.271 

0  1 

4.128 

0 

23.  984 

0  33.  841 

0  43-  697     0  53. 554 

I     3.410 

I   13.266 

26 

071    I 

27 

0 

4-435 

0  1 

4.292 

0 

24. 148 

0  34.005 

0  43.861     0  53.718 

I     3-574 

I   13-431 

27 

074  i 

28 

0 

4.600 

0  1 

4.456 

0 

24-313 

0  34.  169 

0  44.  026     0  53.  882 

I     3-  739 

I   13.595 

28 

077 

29 

0 

4.764 

0 

4.620 

0 

24-  477 

0  34.  333 

0  44.  190 
0  44-  354 

0  54.  046 

I     3. 903 

J  J  3-  759 
I  13.924 

29 

30 

079 
0S2 

30 

0 

4.928 

0  1 

'4^^785 

0 

24. 641 

0  34-498 

0  54-211 

I    4. 067 

31 

0 

5-093 

0  J 

4-949 

0 

24.  805 

0  34.  662 

0  44.518  '  0  54.375 

I     4.231 

I  14.088 

31 

085 

32 

0 

5-257 

0  ) 

5.  113 

0 

24.970 

0  34.  826 

0  44.  683     0  54.  539 

I     4. 396 

I  14.252 

32 

088 

33 

0 

5-421 

0  1 

5-278 

0 

25.134 

0  34-  990 

0  44.  847 

0  54.  703 

I     4. 560 

I   14.416 

33 

090 

34 

0 

5.58s 

0  ] 

5-442 

0 

25.  298 

0  35.  155 

0  45.011 

0  54.868 

I    4.724 

I  .4.581 
I  14.745 

34 

35 

093 

096 

35 

0 

5-750 

0  1 

5.606 

0 

257463" 

0  35-319 

0  45.176 

0  55-  032 

I     4. 888 

36 

0 

5-914 

0  J 

5.770 

0 

25.627 

0  35-483 

0  45-  340     0  55.  196 

I     5-053 

I  14-909 

3'J 

099 

37 

0 

6.078 

0  ) 

5-935 

0 

25.  791 

0  35. 648 

0  45.  504  j  0  55. 361 

I     5.217 

I  15-073 

37 

lOI 

38 

0 

6.242 

0  1 

6.099 

0 

25-955 

0  35.812 

0  45.668 

0  55- 525 

I     5.381 

I  15.238 

38 

104 

3_9 

0 

6.407 

0  1 

[6.  263 

0 

26.  120 

0  35.976 

0  45-  833 

0  55-  689 

I     5-546 

I  15-402 
I  15.566 

39   _ 
40 

io7_ 
no 

40 

0 

6.571 

0  1 

16.427 

0 

26. 284 

0  36.  140 

0  45. 997 

0  55.853' 

I     5.710 

41 

0 

6-735 

0 

6.592 

0 

26.448 

0  36.305     0  46.  161 

0  56.018 

I     5-874 

I  15-731 

41 

112 

42 

0 

6.900 

0 

6.756 

0 

26.612  1  0  36.469  1  0  46.325 

0  56. 182 

I     6.038 

I  15-895 

42 

115 

43 

0 

7.064 

0 

16.920 

0 

26.  777 

0  36. 633  ;  0  46. 490 

0  56. 346 

I     6. 203 

I  16.059 

43 

118 

44 

0 

7.228 

0 

17.085 

0 

26. 941 

0  36-  798 

0  46. 654 

0  56.510 

I     6.367 

I  16.223 

44 

120 

45 

0 

7.392 

0 

[7.249 

0 

27.105 

0  36. 962 

0  46. 818 

0  56.675 

I     6.531 

I  16.388 

45 

123 

46 

0 

7-557 

0 

17.413 

0 

27.  270 

0  37. 126 

0  46. 983 

0  56-839 

I     6.695 

I  16.552 

46 

126 

47 

0 

7.721 

0 

17.577 

0 

27.  434 

0  37. 290  1  0  47. 147 

0  57.003 

I     6. 860 

I  16.716 

47 

129 

48 

0 

7.885 

0 

17.742 

0 

27-  598 

0  37-455 

0  47.311 

0  57. 168 

I     7. 024 

I  16.881 

48 

131 

49 

0 

S.  049 

0 

17.906 

0 

27.  762 

0  37.619 

0  47. 475 

0  57-332 

I     7.  188 

I  17.045 

49  : 

134 

50 

0 

872X4 

0 

[8.070 

0 

27.927' 

0  37.  783 

0  47. 640 

0  57.496 

I     7-  353 

I  17.209 

50 

137 

51 

0 

8-378 

0 

[8. 234     0 

28.091 

0  37.947 

0  47.  804 

0  57.660 

I     7-517 

I  17.373 

51 

140 

52 

0 

8.542 

0 

18.  399 

0 

28.  255 

0  38. 112 

0  47.968 

0  57.  825 

I     7. 681 

I  17.538 

52 1 

142 

53 

0 

8-707 

0 

18.563 

0 

28. 420 

0  38.  276 

0  48. 132 

0  57.989 

I     7.845 

I  17.702 

53  ! 

145 

54 

0 

8.871 

0 

18.  727 

0 

28.  584 

0  38.440 

0  48.  297 

0  58. 153 

I    8.010 

1  17.866 

54  ! 

148 

55 

0 

9-035 

0 

18.892 

0 

28.  748 

0  38.605 

0  48.461 

0  58. 317 

I    8.174 

I  18.030 

55 

151 

56 

0 

9.199 

0 

19.056 

0 

28.912 

0  38.  769     0  48.  625 

0  58.482 

I    8.338 

I  18.195 

56 

153 

57 

0 

9-364 

0 

19.  220 

0 

29.077 

0  38.  933     0  48.  790 

0  58. 646 

I     8. 502 

I  18.359 

57 

156 

58 

0 

9.528 

0 

19- 384 

0 

29.  241 

0  39-  097     0  48.  954 

0  58.810 

I     8. 667 

1   18.523 

58 

159 

59 

0 

9.692 

0 

19-  549 

0 

29-  405 

0  39.262  1  0  49.  118 

0  58.975 

I     8. 831 

I  18.688 

59  j  0 

162 

Page  284 

TABLE  9. 

Mean  Solar  into  Sidereal  Time. 

To  be  added  to  : 

I  mean  time  interval. 

81^ 

9^ 

IQi^ 

U'' 

12h 

13h 

14h 

15'» 

For  seconds.  1 

m. 

m.     s. 

m.     s. 

m.     s. 

m.     s. 

m. 

s. 

m.     s. 

m.     s. 

»?.  i'. 

s.        s 

0 

I  18.852 

I  28.708 

I  38-  565 

I  48.421 

58.278 

2  8.  134 

2  17.991 

2  27.847 

I 

I  19.016 

I  28.873 

I  38.729 

I  48 

585 

58.442 

2  8.298 

2  18.155 

2  28.011 

I   0 

003 

2 

I  19.  180 

I  29.037 

I  38.893 

I  48 

750 

58.  606 

2  8.463 

2  18.319 

2  28. 1 76 

2 

005 

1 

J 

I  19-345 

I  29.201 

I  39.058 

I  48 

914 

58.  771 

2  8.627 

2  18.483 

2  28.340 

3 

008 

4 

I  19.509 

I  29.365 

I  39.222 

I  49 

078 

58-  935 

2   8.791 

2  18.648 

2  28. 504 

4 

oil 

S 

I  19.673 

I  29.530 

I  39.386 

I  49 

243 

59- 099 

2   8.956 

2  18.812 

2  28.668 

5 

014 

6 

I  19.837 

I  29.694 

I  39.550 

I  49 

407 

59-  263 

2   9.  120 

2  18.976 

2  28. 833 

6 

016 

7 

I  20.  002 

I  29.858 

I  39-715 

I  49 

571 

59. 428 

2   9.  284 

2  19.141 

2  28.997 

7 

019 

8 

I  20.  166 

I  30.022 

I  39.879 

I  49 

735 

59- 592 

2   9.  448 

2  19.305 

2  29. 161 

8 

022 

9 

I  20.330 

I  30.  187 
I  30-351 

I  40.043 

I  49 

900 

59-  756 

2   9.  613 

2  19.469 

2  29. 326 

9 

025 

lO 

I  20.495 

I  40.207 

1  50 

064 

59. 920 

2   9.777 

2  19.633 

2  29.490 

10 

027 

II 

I  20.  659 

I  30-515 

I  40.372 

I  50 

228 

2 

0.085 

2   9.941 

2  19.  798 

2  29. 654 

11 

030 

12 

I  20.823 

I  30.  680 

I  40.536 

I  50 

393 

2 

0.249 

2  10.  105 

2  19.  962 

2  29.818 

12 

033 

13 

1  20.  987 

I  30.844 

I  40.  700 

I  50 

557 

2 

0.413 

2  10.  270 

2  20.  126 

2  29. 983 

13 

036 

14 

I  21.  152 

I  31.008 

I  40.865 

I  50 

721 
885 

2 

0.578 

2  .10.434 

2  20.  290 

2  30- 147 

14 

038 

15 

I  21.316 

I  31.172 

I  41.029 

I  50 

2 

0.742 

2  10.598 

2  20.455 

2  30.311 

15 

041 

lb 

I  21.480 

I  31-337 

I  41-193 

I  51 

050 

2 

0. 906 

2  10.763 

2  20.  619 

2  30.476 

16 

044 

17 

I  21.644 

I  31-501 

I  41-357 

I  51 

214 

2 

1.070 

2  10.927 

2  20.  783 

2  30. 640 

17 

047 

18 

I  21.  809 

I  31.665 

I  41-522 

I  51 

378 

2 

1-235 

2  II.  091 

2  20.  948 

2  30.804 

18  ' 

049 

19 

I  21.973 

I  31.829 

I  41.686 

I  51 

542 

2 

1.399 

2  11.255 

2  21.  112 
2  21.276 

2  30.968 

19  , 

052 

20 

I  22.  137 

I  31-994 

I  41.  850 

I  51 

707 

2 

1-563 

2  11.420 

2  31-133 

20 

055 

21 

I  22.  302 

I  32.  158 

I  42.015 

I  51 

871 

2 

1.727 

2  11.584 

2  21.  440 

2  31.297 

21 

057 

22 

I  22.  466 

I  32.322 

I  42.179 

I  52 

035 

2 

1.892 

2  11.748 

2  21.  605 

2  31-461 

22 

060 

23 

I  22.  630 

I  32.487 

I  42.343 

I  52 

200 

2 

2.056 

2  H.9I2 

2  21.  769 

2  31.625 

23 

063 

24 

I  22.794 

I  32.651 

I  42.507 

I  52 

364 

2 

2.  220 

2  12.077 

2  21.933 

2  31-  790 

24 

066 

25 

I  22.959 

I  32.815 

I  42.672 

I  52 

528 

2 

2.385 

2  12.241 

2  22. 098 

2  31-954 

25 

068 

26 

I  23.  123 

I  32.979 

I  42.836 

I  52 

692 

2 

2-549 

2  12.405 

2  22.  262 

2  32. 118 

26 

071 

27 

I  23.287 

I  33-144 

I  43-000 

I  52 

857 

2 

2-713 

2  12.  570 

2  22.  420 

2  32.  283 

27 

074 

2b 

I  23.451 

I  33-308 

I  43.  164 

I  53 

021 

2 

2.877 

2  12.734 

2  22  590 

2  32.447 

28 

077 

29 

I  23.616 

I  33-472 

I  43-329 

I  53 

185 

2 

3.042 

2  12.898 

2  22.  755 

2  32. 611 

29 

079 

30 

I  23.780 

I  33-637 

I  43-493 

I  53 

349 

2 

3.206 

2  13.  062 

2  22.919 

2  32.  775 

30 

082 

31 

I  23.944 

I  33.801 

I  43.657 

I  53 

514 

2 

3-370 

2  13.227 

2  23.  083 

2  32.  940 

31 

085 

32 

I  24.  109 

I  33-965 

I  43.822 

I  53 

678 

2 

3-534 

2  13-391 

2  23.  247 

2  33.  104 

32 

088 

33 

I  24.273 

I  34.  129 

I  43.986 

I  53 

842 

2 

3-699 

2  13.555 

2  23.412 

2  33-  268 

33 

090 

34 

I  24.437 

I  34-294 

I  44. 150 

I  54 

007 

2 

3-863 

2  13.  720 

2  23.576 

2  33-432 

34 

093 

35 

I  24.  601 

I  34.458 

I  44-314 

I  54 

171 

2 

4.027 

2  13.884 

2  23.  740 

2  33- 597 

35 

096 

3(3 

I  24.  766 

I  34.622 

I  44-479 

I  54 

335 

2 

4.192 

2  14.048 

2  23.905 

2  33-  761 

36 

099 

37 

I  24.930 

I  34.  786 

I  44-643 

I  54 

499 

2 

4.356 

2  14.  2X2 

2  24.  069 

2  33-  925 

37 

lOI 

3« 

I  25.094 

I  34-951 

I  44.807 

I  54 

664 

2 

4.520 

2  14.377 

2  24.  233 

2  34-090 

38 

104 

39 

I  25.259 

I  35-115 

I  44-971 

I  54 

828 

2 

4.684 

2  14.541 

2  24.397 

2  34-  254 
2  34-418 

39 

107 

40 

I  25.423 

I  35.279 

I  45-  136 

I  54 

992 

2 

4.849 

2  14.705 

2  24.  562 

40 

no 

41 

I  25.587 

I  35-444 

I  45.300 

I  55 

156 

2 

5-013 

2  14.  869 

2  24.  726 

2  34.  582 

41 

112 

42 

I  25.  751 

I  35.608 

I  45-464 

I  55 

321   2 

5-177 

2  15.034 

2  24.  890 

2  34-  747 

42 

115 

43 

I  25.916 

I  35-772 

I  45-629 

I  55 

485 

2 

5-342 

2  15.  198 

2  25.054 

2  34-911 

43  \ 

118 

44 

I  26.  080 

I  35-936 

I  36.  lOI 

I  45-793 
I  45-957 

I  55 

649 
814 

2 

5.506 

2  15.362 

2  25.  219 

2  35-075 

44 

120 

4.S 

I  26.  244 

I  55 

2 

5.670 

2  15.527 

2  25.383 

2  35- 239 

45 

123 

46 

I  26.  408 

I  36.265 

I  46.  I21 

I  55 

978 

2 

5.834 

2  15.691 

2  25.547 

2  35-404 

46 

126 

47 
4S 

I  26.573 

I  36.429 

I  46.286 

I  56 

142 

2 

5.999 

2  15.855 

2  25.  712 

2  35- 568 

47 

129 

I  26.737 

I  36-593 

I  46.450 

I  56 

306 

2 

6.163 

2  16.  019 

2  25.876 

2  35-  732 

48 

131 

49 
50 

I  26.901 
I  27.066 

I  36-  758 
I  36.922 

I  46.  614 
I  46.  778 

I  56 
I  56 

47* 

2 

6.327 

2  16.  184 

2  26.  040 

2  35.897 

49 

134 

635 

2 

6.491 

2  16.348 

2  26.  204 

2  36.061 

50 

137 

51 

I  27.230 

I  37.086 

I  46.943 

I  56 

799 

2 

6.656 

2  16.  512 

2  26.  369 

2  36-225 

■=;' 

140 

52 

I  27.394 

I  37-251 

I  47.  107 

I  56 

964 

2 

6.820 

2  16.  676 

2  26.  533 

2  36-  389 

52 

142 

53 

I  27.558 

I  37-415 

I  47.271 

I  57 

128 

2 

6.984 

2  16.  841 

2  26.  697 

2  36-  554 

53 

145 

54 

I  27.  723 

I  37.579 

I  47.436 

I  57 

292 

2 

7.149 

2  17.005 

2  26.861 

2  36-  718 

54 

148 

55 

I  27.887 

I  37-  743 

I  47. 600 

I  57 

456 

2 

7.313 

2  17.  169 

227.  026 

2  36.882 

55 

151 

5<^ 

I  28.051 

I  37.908 

I  47.764 

I  57 

621 

2 

7.477 

2  17.334 

2  27.  190 

2  37-047 

56 

153 

57 

I  28.215 

I  38.072 

I  47-928 

I  57 

785 

2 

7.641 

2  17.498 

2  27.354 

2  37-211 

57 

156 

5« 

I  28.380 

I  38.236 

I  48.093 

I  57 

949 

2 

7.806 

2  1 7.  662 

2  27.519 

2  37-  375 

58 

159 

59 

I  28.544 

I  38.400 

I  48-257 

I  58-113 

2 

7.970 

2  17.826 

2  27.683 

2  37-  539 

59  i  0 

lt)2 

^ 

TABLE  9.                                                [Page 
Mean  Solar  into  Sidereal  Time. 

285 

u 

ji 

c 

To  be  added  to  a  mean  time  interval. 

onds. 

16" 

l^h 

18" 

19" 

20" 

21" 

22" 

23" 

For  sec 

m. 
0 
I 

2 

-t 
0 

4 

m.     s. 
2  37.  704 

2  37.868 
2  38.  032 
2  38. 196 
2  38.  361 

m.     s. 

2   47.  560 

2  47-  724 
2  47.  889 
2  48-053 
2  48.  2 1 7 

W.       J. 

2    57.417 

2    57-581 

2  57-  745 
2  57-909 
2  58-074 

m.     s. 
3     7.273 

3     7-437 
3     7.602 

3     7-  766 

3     7-  930 

m.     s. 
3  i7-i2g 
3  17-294 
3  17-458 
3  17.622 

3  17-787 

m.     s. 
3  26.986 
3  27.  150 
3  27-315 
3  27.479 
3  27-643 

m.     s. 
3  36.842 
3  37-007 
3  37-171 
3  37-335 
3  37-500 

m.     s. 
3  46. 699 

3  46-  863 
3  47-  027 
3  47-  192 
3  47-  356 

s. 

1   i  0 
2 

3 
4 

r. 

003 
005 
008 
on 

I 

7 
S 

9 

2  38.  525 
2  38.689 
2  38.854 
2  39.018 
2  39.  182 

2  48. 381 

2  48.  546 
2  48.  710 
2  48.874 
2  49-039 

2  58.238 
2  58. 402 
2  58. 566 

2  58.  731 
2  58.  895 

3    8. 094 
3    8.259 
3    8.423 
3    8.587 
3    8.751 

3  17.951 
3  18. 115 
3  18.279 

3  18.444 
3  18.608 

3  27.807 
3  27-972 
3  28.  136 
3  28.  300 
3  28.464 

3  37-664 
3  37-828 
3  37-992 
3  38-  157 
3  38-321 

3  38-485 
3  38-649 
3  38-814 
3  38-  978 
3  39-  142 

3  47.  520 

3  47.  685 
3  47.849 
3  48.013 

3  48-177 

5  t 
6 

7 
8 

9 

014 

016 
019 

022 
025 

10 
II 
12 

13 
14 

2  39-346 
2  39-511 
2  39-675 
2  39-  839 
2  40.  003 

2  49. 203 

2  49-  367 

2  49-531 
2  49.  696 
2  49.  860 
2  50.  024 
2  50.  188 

2  50-353 
2  50-517 
2  50.681 

2  59.059 

2  59-224 
2  59-  388 
2  59-552 
2  59-716 

3    8.916 
3    9-  080 
3    9-244 
3    9-  409 
3    9-573 

3  18.  772 
3  1S.937 
3  19.  loi 
3  19-265 
3  19-429 

3  19-594 
3  19-758 
3  19-922 
3  20. 086 
3  20.251 

3  28.  629 
3  28.  793 
3  28.957 
3  29.  122 
3  29.  286 

3  48-342 
3  48-  506 
3  48.670 
3  48-  834 
3  48-999 

10 

11 
12 

13 
14 

027 
030 

033 
036 
038 

041 

044 

047 
049 
052 

15 

16 

17 

iS 

19 

2  40.  168 

2  40.  332 
2  40.  496 
2  40.  661 
2  40.  825 

2  59.  881 

3  0. 045 
3    0. 209 

3    0.373 
3    0.538 

3    9.737 
3    9.901 
3  10. 066 
3  10. 230 
3  10.394 

3  29.450 
3  29.614 
3  29-  779 
3  29-943 
3  30-  107 

3  39-307 
3  39-471 
3  39-635 
3  39-  799 
3  39-964 

3  49. 163 

3  49-  327 
3  49-492 
3  49- 656 
3  49- 820 

15 

16 

17 

18 

19 

20 
21 

22 

23 

24 

2  40.  989 

2  41-  153 
2  41.318 

2  41.482 
2  41.  646 

2  50.  846 
2  51.010 

2  51-174 
2  51-338 
2  51-503 

3    0.  702 
3    '0.866 
3     1-031 
3     I-  195 
3     1-359 

3  10.559 
3  10.723 
3  10.887 

3  11-051 
3  II. 216 

3  20.415 

3  20.579 
3  20.  744 
3  20. 908 
3  21.072 

3  30-271 
3  30-436 
3  30.  600 

3  30-  764 
3  30-929 

3  40.  128 
3  40-292 

3  40-456 
3  40.  621 

3  40.  785 

3  49-  984 
3  50-  149 
3  50.313 
3  50.477 
3  50-642 

20 
21 

22 

23 
24 

055 
057 
060 
063 
066 

25 
26 

27 

28 
29 

30 
31 
32 
33 
34 

36 
37 
38 
39 

2  41.  810 

2  41-975 
2  42.  139 

2  42.  303 

2  42.468 

2  51.667 
2  51.831 
2  51-995 
2  52.  160 

2  52-  324 

3     1-523 
3     1.688 

3     1-852 
3     2.016 
3    2.  181 

3  11.380 
3  "-544 
3  1 1  -  708 
3  11-873 
3  12.037 

3  21.236 
3  21.401 

3  21.565 
321.  729 
3  21.893 

3  31-093 
3  31-257 
3  31-421 
331-586 
3  31-750 

3  40-949 
3  41-114 
3  41-278 
3  41-442 
3  41.  606 

3  50.806 
3  50-970 
3  51.134 
3  51-299 
3  51-463 

26 
27 
28 
29 

30 
31 
32 
33 

34 

068 
071 
074 

077 
079 

082 
085 
088 
090 

093 

2  42.  632 
2  42.  796 
2  42.  960 
2  43-  125 
2  43-  289 
2  43-453 
2  43-617 
2  43-  782 
2  43-946 
2  44.  1 10 

2  52.488 
2  52-653 
2  52-817 
2  52.  981 

2  53-  145 

3    2.345 
3     2. 509 
3    2.673 
3     2.83§ 
3     3-002 
3    3.166 
3     3. 330 
3     3-495 
3     3-659 
3    3-823 

3  12.201 
3  12.366 
3  12.530 
3  12.694 
3  12.858 

3  22.058 
3  22. 222 
3  22.386 
3  22.551 
3  22.715 
3  22.879 
3  23.043 
3  23.  208 
3  23-372 
3  23. 536 

3  31-914 
3  32-078 
3  32-243 
3  32-407 
3  32-571 

3  32-  736 
3  32-900 
3  33-064 
3  33-  228 
3  33-393 

3  41-771 
3  41-935 
3  42.099 
3  42.  264 

3  42.428 

3  51-627 
3  51-791 
3  51-956 
3  52. 120 
3  52-2S4 

2  53-310 

2  53-474 
2  53-638 
2  53-803 
2  53-967 

3  13.023 
3  13-187 
3  13-351 
3  13-515 
3  13-680 

3  42-  592 
3  42-  756 
3  42-921 
3  43-085 
3  43-  249 

3  52-449 
3  52-613 
3  52- 777 
3  52-941 
3  53. 106 

35  i 

36! 

37 

38 

39 

.096 

-099 
.  lOI 
.  104 
.107 

40 

41 

42 

43 

44 

45 
46 

47 
48 
49 

2  44-  275 
2  44-439 
2  44- 603 
2  44-  767 
2  44-932 
2  45.096 
2  45.  260 
2  45-425 
2  45-  589 
2  45-  753 

2  54-  131 
2  54-295 
254.  460 
2  54-624 
2  54.  788 

2  54-952 
2  55- "7 
2  55-281 

2  55-445 
2  55.610 

3     3-988 
3    4  152 
3     4-316 
3    4. 480 

3    4.64s 
3    4-  809 
3     4-973 
3     5-137 
3    5-302 
3    5.466 

3  13-844 
3  14.008 

3  14-173 
3  14-337 
3  14.501 

3  23.  700 
3  23-  86s 
3  24.029 
3  24.  193 
3  24-358 

3  33-557 
3  33-  721 
3  33-  886 
3  34-050 
3  34-214 

3  43-413 
3  43-578 
3  43-  742 
3  43-  906 
3  44-071 

3  53.270 
3  53.434 
3  53- 598 
3  53.  763 
3  53.927 

40 
41 
42 
43 
44 

.  no 
.  112 

- 115 
.  118 
.  120 

3  14.665 
3  14.830 
3  14.994 
3  15.158 
3  15.322 

3  24-  522 
3  24.686 
3  24.850 
3  25.015 
3  25-  179 

334-378 
3  34-  543 
3  34-  707 
3  34-  871 
3  35-035 

3  44-235 
3  44-  399 
3  44-  563 
3  44-  728 
3  44-  892 

3  54-091 
3  54-256 
3  54-420 
3  54.584 
3  54.  748 

46 

47 
48 
49 

.123 
.126 
.  129 

.131 
.134 

50 
51 
52 
53 
54 

2  45-917 
2  46.082 
2  46.  246 
2  46.410 
2  46.  574 

2  55-  774 
2  55-938 
2  56. 102 
2  56.267 
2  56.431 

3    5.630 
3    5.795 
3    5.959 
3    6.123 
3    6.287 

3  15-487     3  25-343 
3  15-651   1  3  25.508 
3  15-815  !  3  25-672 
3  15.980     3  25.836 
3  16.  144     3  26. 000 

3  35- 200 
3  35-364 
3  35-528 
3  35-  693 
3  35-857 

3  45-056 
3  45-  220 
3  45-  385 
3  45-  549 
3  45-713 

3  54-913 
3  55.077 
3  55.241 
3  55-405 
3  55-570 

50 
51 
52 
53 
54 

-137 

.  140 

142 

-145 
148 

11 
11 

59 

2  46.  739 
2  46-903 
2  47.067 

2  47-  232 
2  47.  396 

'  2  56.595 
2  56.  759 
2  56. 924 
2  57.088 

1  2  57-252 

3     6.452 

3    6.616 

3    6.  780 

13    6.944 

1  3     7. 109 

3  16.  308     3  26.  165 
3  16.472  1  3  26.329 
3  16.637  ,  3  26.493 
3  16.  801  1  3  26.657 
3  16.965  1  3  26.822 

3  36.021 
3  36-  185 
3  36-350 
3  36-514 
3  36.  078 

3  45-  878 
3  46.  042 
3  46.  206 
3  46.  370 
3  46.  535 

3  55-  734 
3  55-898 
3  56. 063 
3  56-227 
3  56.391 

55 
56 
57 
58 
59  ,  0 

151 

153 
156 
159 
162 

Page  286]                                              TABLE  lo. 

True  Rising  and  Setting. 

6 

•a 

3 
-t-t 

Declination. 

•a 
3 

■^ 

0° 

1° 

2° 

3° 

40 

5° 

6° 

70 

8° 

90 

10° 

11° 

12° 

13° 

14° 

15° 

o 

O 

I 
2 

3 
4 

A.  in. 

6  0 
0 
0 
0 
0 

h.  ftt. 
6  0 
0 
0 
0 
0 

h.  nt. 

6  0 
0 
0 
0 

h.  tn. 

6  0 
0 
0 

h.  m. 

6    0 
0 

I 
I 
I 

A.  m. 

6  0 

0 

I 
I 
I 

h.  m. 

6    0 

0 

I 
I 
2 

A.  m. 

6    0 

0 

I 
I 
2 

A.  m. 
6  0 

I 
I 
2 
2 

A.  tn. 
6  c 

I 
I 
2 
3 

A.  m. 
6  0 

I 
I 
2 
3 

h.  m. 

6    0 
I 
2 
2 
3 

A.  m. 

6    0 
I 
2 
3 
3 

A.    tK. 

6  0 
I 
2 
3 
4 

A.  m. 
6  0 
I 
2 
3 
4 

A.  m. 
6    0 

I 
2 
3 
4 

0 
0 
I 
2 
3 
4 

5 
6 

7 
8 

9 

60   60 
0  !    0 
0     0 
0     I 
0     I 

6  I 

6  I 

2 

2 

6  I 
2 
2 
2 
3 

6  2 
2 
2 
3 
3 

6  2 
3 
3 
3 
4 

6  2 
3 

3 
4 
4 

6  3 
3 
4 
5 
5 

6  3 
4 
4 

6  4 

4 
5 
6 
6 

6  4 

5 
5 
6 

7 

6  4 

S 
6 

7 
8 

6  5 
6 
6 

7 
8 

6  S 
6 

7 
8 

9 

6  S 

6 
8 

9 
10 

5 
6 

7 
8 

10 
II 
12 
13 
i4_ 

15 
16 

17 
18 

19 

lO 

II 

12 

13 
14 

6061 
0     I 
0     I 
0  ^    I 
0     I 

6  I 
2 
2 
2 
2 

6  2 
2 
3 
3 
3 

6  3 
3 
3 
4 
4 

6  4 
4 
4 
5 
S 

6  4 

5 
S 
6 
6 

6  S 

6 
7 

6  6 
6 
7 

6  6 

7 
8 
8 
9 

6  7 

8 

9 

9 

10 

6  II 
12 
12 
13 
14 

6  8 

9 

9 

10 

II 

6  12 
13 
14 
14 
15 

6  9 

9 
10 
II 

12 

6  9 
10 
II 
12 
13 

6  10 
II 
12 
13 
14 

6  II 
12 

13 
14 
15 

15 
16 

17 
18 

'9. 

20 

21 

22 

23 

24 

6  0 
0 
0 
0 
0 

6  I 

6  2 
2 
2 
3 
3 

6  3 
3 
4 
4 
4 

6  4 
S 
5 
5 
6 

6  5 
6 
6 
7 
7 

6  6 
7 

8 

6  8 

8 

9 

9 

10 

6  9 

9 
10 
10 
II 

6  10 
10 
II 
12 
13 

6  13 
14 
15 
16 

17 

6  14 

15 
16 

17 
18 

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55 
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22 
29 
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7  49 
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17 

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38 
53 

9  13 
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19 

44 

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25 

49 

10  25 

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54 

10  28 

12  0 

9  58 
10  31 

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10  34 
12  0 

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75 
76 

77 
78 

79 

6 

-a 
3 

0°    1° 

2° 

3° 

4 

50 

60 

70 

8° 

»° 

10° 

11° 

12° 

13° 

14° 

15° 

Declination. 

■ 

TABLE  10. 

[Page  287  | 

« 

True  Rising 

and  Setting. 

3 

Declination. 

4J 

■a 
3 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

o 

/(.  HI. 

A.   m. 

h.  in. 

A.  m. 

A.  tn. 

A.  tn. 

A.  m. 

A.  tn. 

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A.  tn. 

A.  tn. 

A.  tn. 

A.  tn. 

0 

o 

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2 

2 

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2 

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2 

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4 

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12 

12 

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16 

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16 

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13 

14 

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16 

17 

18 

19 

20 

21 

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23 

24 

25 

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15 

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18 

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20 

21 

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24 

25 

26 

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1 3 

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17 

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20 

21 

22 

24 

25 

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29 

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16 

17 

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20 

21 

22 

23 

24 

25 

27 

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29 

30 

32 

33 

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15 

15 

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6  22 

6  24 

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6  34 

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19 

20 

21 

23 

24 

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29 

31 

32 

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35 

37 

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16 

17 

20 

21 

23 

24 

26 

27 

28 

30 

31 

33 

34 

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37 

39 

41 

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21 

23 

24 

26 

27 

29 

30 

32 

33 

35 

36 

38 

40 

42 

43 

18 

19 

23 

24 

26 

27 

29 

30 

32 

34 

35 

37 

39 

40 

42 

44 

46 

19 

20 

6  24 

6  26 

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632 

634 

6  36 

6  37 

6  39 

641 

6  43 

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20 

21 

25 

27 

29 

30 

32 

34 

36 

38 

39 

41 

43 

45 

47 

49 

51 

21 

22 

27 

28 

30 

32 

34 

3b 

3« 

40 

41 

43 

45 

48 

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52 

54 

22 

23 

28 

30 

32 

34 

36 

38 

39 

42 

44 

46 

48 

50 

52 

54 

57 

23 

24 
25 

29 

31 

33 

35 

37 

39 

41 

44 

46 

48 

50 

52 

55 

57 

7  0 

24 

631 

6  33 

635 

637 

6  39 

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6  48 

6  50 

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6  55 

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25 

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39 

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28 

29 
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37 
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31 

40 

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59 

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14 

18 

21 

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32 

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14 

18 

21 

25 

32 

33 

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14 

17 

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28 

33 

34 
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54 

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13 
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17 

20 

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32 

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6.53 

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5 

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12 

16 

19 

23 

27 

31 

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18 

22 

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17 

21 

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7  32 

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7  51 

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58 

7  2 

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10 

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18 

22 

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31 

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17 

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15 

19 

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29 

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7  16 

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19 

24 

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34 

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7 

14 

20 

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18 

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17 

22 

28 

33 

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51 

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10 

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24 

31 

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50 

7  20 

7  25 

7  31 

7  37 

7  43 

7  55 

8  2 

8  8 

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51 

23 

29 

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13 

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28 

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26 

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8  38 

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9  18 

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55 

50 

41 

48 

55 

8  3 

11 

19 

27 

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55 

9  5 

16 

28 

41 

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57 

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52 

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16 

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15 

27 

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57 

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49 

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5 

14 

22 

32 

41 

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13 

25 

38 

53 

10  10 

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59 

54 

8  2 

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20 

29 

39 

49 

9  0 

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24 

37 

52 

10  9 
10  28 

29 

10  55 

56 

59 

60 

7  59 

8  8 

8  17 

8  26 

8  36 

8  47 

8  58 

9  9 

9  22 

9  35 

9  SI 

10  8 

12  0 

60 

61 

8  5 

14 

24 

34 

44 

55 

9  7 

20 

34 

49 

10  7 

27 

54 

12  0 

61 

62 

II 

20 

31 

42 

53 

9  1 

18 

32 

47 

10  S 

26 

54 

12   0 

62 

t>3 

17 

27 

38 

5° 

9  2 

16 

30 

46 

10  4 

25 

S3 

12  0 

b3 

04 

24 

35 

47 

59 

13 

28 

44 

10  2 

24 

52 

12  0 

04 

65 

8  32 

8  44 

857 

9  10 

9  25 

9  42 

10   0  '  10  22 

10  51 

12  0 

65 

66 

40 

53 

9  7 

23 

39 

58 

21       50 

12  0 

66 

6; 

50 

9  4 

20 

37 

56 

10  19 

49 

12  0 

67 

08 

9  I 

17 

34 

54 

10  17 

47 

12   0 

68 

69  _ 
70 

14 
9  28 

31 
9  48 

51 

10  15 

46 

12  0 

_«'9 
70 

10  13 

10  44 

12  0 

71 

45 

10  10 

43 

12  0 

71 

72 

10  8 

41 

12  0 

72 

73 

39 

12  0 

73 

74_ 
75 

12  0 

_74 
75 

76 

76 

77 

77 

7S 

7a 

79 

79 

6 
■a 
3 

3 

3 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

26° 

26° 

27° 

28° 

29° 

30° 

Declination. 

Page  288]                                                TABLE  ii. 

For  reducing  the  Time  of  the  Moon's  passage  over  the  Meridian  of  Greenwich  to  the  Time  of  its  passage  over 
any  other  Meridian.     The  numbers  taken  from  this  Table  are  to  be  added  to  the  Time  at  Greenwich  in  West 
Longitude,  but  subtracted  in  East. 

Ship's 
Lon. 

Daily  variation  of  the  moon's  passing  the  meridian. 

Ship's 
Lon. 

w 

42' 

44/ 

46' 

48' 

50' 

52' 

54' 

56' 

58' 

60' 

62' 

64' 

66' 

o 

0 

5 

lO 

IS 

20 

25 
30 

1 

0 
I 
I 

2 
2 

3 
3 

/ 

0 

I 
I 
2 
2 
3 
3 

/ 

0 

1 
1 
2 
2 

3 
4 

0 

I 
I 
2 

3 

3 
4 

/ 

0 
I 
I 

2 

3 
3 

4 

/ 

0 
I 
I 
2 
3 
3 
4 

/ 

0 
1 
I 

2 

3 
4 
4 

1 

0 
I 
I 

2 

3 
4 
4 

/ 

0 
I 
2 
2 

3 

4 

5 

0 

I 
2 
2 

3 
4 

5 

0 
I 

2 

2 

3 
4 
5 

0 
I 

2 

3 
3 
4 
5 

/ 

0 

I 
2 

3 
4 
4 
S 

/ 

0 

1 
2 

3 
4 
5 

5 

0 
0 

5 
10 

15 
20 

25 
30 

35 
40 

45 
50 
55 
60 

65 
70 

■    11 

85 
90 

95 
100 

105 

35 

40 

45 
50 
55 

4 

4 
5 
6 
6 

4 

5 

6 

4 
5 

I 

7 

4 

I 

6 

7 

5 
5 
6 

7 
7 

1 

6 

6 

7 
8 

7 
7 
8 

7 
8 

9 

6 
6 

7 
8 

9 

6 

7 
7 
8 

9 

6 

7 
8 

9 
9 

6 

7 
8 

9 
10 

6 

7 
8 

9 
10 

60 

65 

70 

11 

7 
7 
8 
8 
9 

7 
8 
8 
9 
9 

9 
9 

ID 

8 
8 

9 
10 
10 

8 
9 
9 

ID 
II 

8 

9 
10 

ID 
II 

9 

9 

10 

11 

12 

9 
10 
10 
11 
12 

9 

ID 
II 
12 
12 

ID 
10 
11 
12 

13 

10 
11 
12 
12 

13 

10 
II 
12 

13 

14 

17 
1.5 
12 
13 
14 

u 
12 

13 
14 
IS 

85 
90 

95 
100 

105 

9 
10 
II 
II 
12 

10       10 

10  ;     11 

11  12 

12  12 
12          13 

II 
II 
12 

■  13 
13 

II 
12 

13 
13 
14 

12 
12 

13 

14 
15 

12 

13 
14 
14 
15 

13 

13 

\l 

16 

14 
14 

\i 

17 

14 
IS 
16 

17 
17 

IS 

;i 

17 
18 

17 

i8 
19 

16 
16 

17 
18 

19 

no 

IIS 
120 

125 
130 

12 

13 
13 
14 
14 

13 
13 
14 
15 
15 

13 

14 
15 
15 
16 

14 

IS 

15 
16 

17 

IS 

IS 

16 
17 
17 

'A 

17 
17 
18 

16 

17 
17 
18 

19 

16 

17 
18 

19 
19 

17 

18 

19 

19 
20 

18 
19 
19 
20 
21 

18 

19 
20 
21 
22 

19 
20 
21 
22 
22 

20 
20 
21 

2.2 

23 

20 
21 

22 

23 
24 

no 

115 

120 

125 
130 

13s 

140 

145 
150 

155 

135 
140 

145 
150 
155 
160 

i6S 
170 

175 
180 

16 
17 
17 
18 
18 
19 
19 
20 

16 
16 

17 

17 
18 

16 

17 
18 
18 
19 

17 

18 

19 
19 
20 

18 
19 
19 

20 

21 

19 
19 
20 
21 
22 

19 
20 
21 
22 
22 

20 

21 
22 
22 

23 

21 
22 

23 
23 
24 

22 
23 
23 
24 

25 

22 

23 
24 

26 

23 
24 

26 
27 

24 

26 

27 
28- 

25 
26 

27 
27 
28 

19     '     20 

19  20 

20  21 

20  21 

21  22 

20 
21 
22 
22 

23 

21 

22 
23 

23 
24 

22 

23 
24 

24 

25 

23 
24 

25 
25 

26 

24 
25 

26 
27 

26 
26 

27 
28 

26 

27 
27 
28 
29 

27 
27 

28 
29 
30 

28 

28 

29 
30 
31 

28 
25 
3& 
31 
32 

29 
30 
31 
32 
33 

160 

165 
170 

180 

40^ 

42' 

44/ 

46' 

48' 

50' 

52' 

54' 

56' 

58' 

60' 

62' 

64' 

66' 

TABLE  12.                                               [Page  289 

For  finding  the  variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon'?  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of 
the  pige  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column.     Also  for  finding  the  Variation 
of  t  le  Moon's  Declination  in  seconds  of  time,  the  motion  in  one  minute  being  given  at  the  top,  and  the 
numbers  in  the  side  column  being  taken  for  seconds. 

M. 

I 

2 

3 
4 
5 

Horary  motion. 

M. 

1" 

2- 

r' 

4// 

5'^ 

6'^ 

^// 

8^' 

9" 

W 

11^^ 

t2'' 

W 

14// 

W 

w 

W 

18^' 

19' 

0 

0 

0 
0 
0 

0 

0 
0 
0 
0 

0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

0 

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0 
0 

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0 
0 

0 
0 
0 

0 
0 
0 

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0 

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0 

0 

0 

0 
0 
I 

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I 

0 

0 
I 

I 
I 

0 

I 
I 

I 
I 

0 
I 
I 

I 
I 

0 
I 
I 
I 
I 

0 
I 

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I 
2 

0 

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I 
2 

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2 

3 

4 
5 

6 

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0       0 
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2 
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2 
2 
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2 
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2 
2 

3 

2 
2 
2 
2 

3 

2 
2 
2 

3 
3 

2 
2 
2 

3 
3 

2 
2 
3 
3 
3 

6 

7 
8 

9 

ID 

II 

12 

13 
14 
15 

0  1    0 
0       0 
0  1    0 
0       0 
0       I 

2 

2 
2 

2 

2 
2 
2 
2 

2 

2 
2 
2 
2 

2 

2 
2 
2 

3 

2 
2 
2 
3 
3 

2 
2 
3 
3 
3 

2 
3 
3 
3 
3 

3 
3 
4 
4 
4 
4 
4 
5 

3 
3 
3 

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4 

3 
3 
3 
4 
4 

3 
3 

4 
4 
4 

3 
4 
4 
4 
5 

3 

4 
4 
4 
5 

II 
12 

13 
14 
15 

i6 

17 
i8 

19 
20 

21 

22 

23 
24 
25 
26 

27 
28 

29 
30 

31 

32 
33 
34 
35 

0 

0 
0 

0 

0 
0 

0 

0 
0 
0 

* 

2 
2 
2 

2 
2 
2 
2 
2 

2 
2 
2 

2 
2 

2 
2 
2 

3 
3 

2 

3 

3 
3 
3 

3 
3 
3 
3 
3 

3 
3 

3 
3 
4 

3 
3 

4 
4 
4 

3 
4 

4 
4 
4 

4 

4 
5 

1 

4 
5 
5 
5 
5 

5 
S 
5 

i 

5 
5 

6 

S 

i 

6 
6 

16 

17 
18 

19 
20 

2 

2 
2 
2 

2 

2 
2 
2 
2 

2 

2 
2 
2 

3 

2 
3 
3 
3 
3 

3 

3 
3 
3 
3 

3 

3 
3 
4 
4 

4 
4 
4 
4 
4 

4 

4 
4 

4 
5 

4 
4 
5 

5 
5 

5 
5 
5 
5 
5 

5 

5 
5 
6 
6 

i 

6 
6 
6 

6 
6 
6 
6 
7 

6 
6 

7 
7 

7 

6 
7 
7 

7 

7 

8 

21 

22 

23 
24 
25 

0 

0 
0 
0 

2 
2 
2 
2 
2 

2 
2 
2 
2 
3 

3 
3 
3 
3 
3 

3 
3 
3 
3 
4 

3 

4 
4 
4 
4 

4 
4 
4 
4 
5 

4 
5 
5 

5 
5 

5 
5 
5 

5 

6 
6 

6 
6 
6 
6 

7 

6 
6 

7 
7 
7 
7 

8 
8 

7 
7 
7 
7 
8 

7 
7 

8 

7 
8 
8 
8 
9 

8 
8 
8 
9 
9 

8 

9 

9 

9 
10 

26 

27 
28 
29 
30 

'  I            I 

2 

2 
2 
2 
2 

2 
2 
2 
2 
2 
2 
2 

3 
3 
3 

3 
3 
3 
3 
3 

3 
3 
3 
3 
4 

4 
4 
4 
4 
4 

4 
4 
4 
5 
5 

S 
5 
5 
5 
5 

I 

6 
6 
6 

5 

i 

6 
6 

6 
6 
6 
6 
6 

6 
6 

7 
7 
7 

7 
7 

7 

r 

8 

8 
8 
8 
9 
9 

8 

9 

9 

9 

9 

10 

10 

10 

ID 
II 

9 

9 

9 

10 

10 

9 
10 

ID 
10 
II 

ID 

10 
10 

II 
II 

31 

32 

33 
34 
35 

36 

37 
38 

39 
40 

41 

42 

43 
44 
45 

2 

2 
2 
2 
2 

3 

3 
3 
3 
3 

4 

4 
4 
4 
4 

4 
4 

4 
5 
5 

5 

I 

5 
5 

6 
6 
6 

7 
7 

7 
7 
8 
8 
8 

8 
8 
8 
8 
9 

8 

9 

9 

9 

9 

10 

10 

10 

10 

II 

9 

9 
10 
10 
10 

10 
10 
II 
II 
II 

II 
II 
II 
12 
12 

II 

12 
12 
12 
13 

36 
37 
38 
39 
40 

T      1           ¥ 

I           2 

2 
2 
2 
2 
2 

3 
3 
3 
3 
3 
3 
3 
3 
3 
3 

3 

4 
4 
4 
4 

4       5 

4       5 
4       5 

4  5 

5  5 

6 
6 
6 

6 
6 
6 

7 
7 

7 
7 
7 

8 
8 
8 

8 
8 

8 
8 
9 
9 
9 

9 

9 

9 

10 

10 

10  1     II 

11  II 

II          u 

II        12 
II        12 

12        12 
12        13 
12        13 

12  1     13 

13  !    14 

13 
13 

14 
14 
14 

41 

42 

43 
44 
45 

46 

47 

48 

49 
50 

1          2          2 
I          2          2 
I           2          2 
12           2 
123 

4  1    5       5 
4       5       5 
4       5       6 
4       5       6 
4       5,6 

6 

6 
6 

7 
7 
7 
7 
8 

8 
8 
8 
8 
8 

8  9 

9  9 
9      10 

9      10 
9      10 

10 
10 
10 
II 
II 

II 
II 
II 
II 
12 

12 
12 
12 
12 

13 

12 

13 
13 
13 
13 
14 
14 
14 
14 
15 

13 
13 
14 
14 
14 

14 
14 
14 
15 
IS 

15 
15 
15 
16 

16 

46 

47 
48 

49 
50 

51 

52 

53 
54 
55 

I          2 
I          2 
I           2 
I           2 
I           2 

3 
3 
3 
3 
3 
3 
3 
3 
3 

3 

3 
3 
4 
4 
4 

4 

4 
4 
5 
5 

5       6 
5       6 

5  6 

6  6 

' 

8 
8 
8 
8 

8 

9 
9 
9 
9 
9 

9 
10 
10 

10 
10 

10 
10 
II 
II 
II 

n 
II 
II 
12 

12 

12 
12 
12 
13 
13 

13 
13 

14 
14 

14 
IS 
IS 

15 
16 

16 
16 
17 

16 
16 
17 
17 

17 
18 
18 
18 

19 
19 

51 

52 
53 
54 
55 
'56" 

'i 

59 
60 

56 

57 
58 

60 

1           2 
I           2 

I           2 
I           2 
I           2 

4 
4 
4 
4 
4 

5       f 
5       6 

5       6 
5       6 

7 

7 
7 
7 
7 

I 

8 
8 
8 

8 
9 
9 
9 
9 

9 
10 
10 
10 
10 

10     II 

10  II 

11  12 
II      12 
II      12 

12 
12 

:i 

13 

13 
13 
•4 
14 
14 

14 
14 
15 
15 
15 

15 

!l 

16 

16       17 
16  '     17 

16  17 

17  18 
17       18 

Page  290 

TABLE  12. 

\ 

For  findinc:  the  Variation  ( 

Df  the  Sun's 

Right 

Ascension, 

of  the 

Declination 

of  the  Equation  of  Time,  or  of  the  f 

Moon's 

Right  Ascension,  in  any  number  of  minutes  0 

f  time 

,  the  Horary  Motion  be 

ng  Ri 

ven  at 

the  top  of  ! 

the  pag 

e  in  seconds,  and  the  number  of  minutes 

of  time  in  the  sid 

z  column.  Also  for  finding  ih 

e  Variation  1 

of  the 

Moon's  Declination  in  seconds  of 

time, 

the  m 

otion 

in  one  minute  be 

ng  given  at  the  top,  and  the  | 

numbei 

s  in  the  sic 

Je  column  being  taken  for  seconds. 

1 

Horary  motion. 

M. 

M. 

W 

21  '  22'^ 

! 

23'^ 

24^^ 

25^^ 

W 

IV' 

28'^ 

29'^ 

w 

^V 

32^' 

33'^ 

w 

35'^ 

w 

I 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

I 

I 

I 

I 

I 

I 

I 

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2 

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2 

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2 

2 

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2 

2 

2 

2 

3 

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I 

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2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

4 

5 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

3 

5 

6 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

4 

4 

b 

7 

2 

2 

3 

3 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4 

7 

8 

3 

3 

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3 

3 

3 

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4 

4 

4 

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4 

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5 

8 

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5 

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5 

9 

10 

3 

4 

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4 

4 

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5 

5 

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b 

6 

b 

b 

10 
II 

II 

4 

4 

4 

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4 

5 

5 

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5 

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6 

6 

6 

6 

6 

6 

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12 

4 

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7 

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13 

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5 

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6 

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7 

7 

7 

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7 

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8 

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14 

15 
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5 

5  1  6 

6 

6 

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8 

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8 

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15 
lb 

5 

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18 

18 

19 

20 

21 

21 

22 

23 

23 

24 

25 

2b 

2b 

44 

45 

15 

16 

17 

17 

18 

19 

20 

20 

21 

22 

23 

23 

24 

2S 

2b 

2b 

27 

45 

46 

15 

16 

17 

18 

18 

19 

20 

21 

21 

22 

23 

24 

25 

25 

2b 

27 

28 

4b 

47 

16 

16 

17 

18 

19 

20 

20 

21 

22 

23 

24 

24 

25 

2b 

27 

27 

28 

47 

48 

16 

17 

18 

18 

19 

20 

21 

22 

22 

23 

24 

2S 

2b 

2b 

H 

28 

29 

48 

49 

16 

17 

18 

19 

20 

20 

21 

22 

23 

24 

25 

25 

2b 

27 

28 

29 

29 

49 

50 

17 
17 

18 
18 

18 

19 

20 

21 

22 

23 

23 

24 

2S 

2b 

27 

28 

28 

29 

30 

50 
51 

51 

19 

20 

20 

21 

22 

23 

24 

2S 

2b 

26 

27 

28 

29 

30 

31 

■^2 

17 

18 

19 

20 

21 

22 

23 

23 

24 

2S 

2b 

27 

28 

29 

29 

30 

31 

52 

53 

18 

19 

19 

20 

21 

22 

23 

24 

25 

2b 

27 

27 

28 

29 

30 

31 

32 

53 

54 

18 

19 

20 

21 

22 

23 

23 

24 

25 

2b 

27 

28 

29 

30 

31 

32 

32 

54 

55 
"56 

18 
19 

J9^ 
20 

20 

21 

22 

23 

24 

25 

2b 

27 

28 

28 

29 

30 

31 

32 

33 

55 
56 

21 

21 

22 

23 

24 

2S 

26 

27 

28 

29 

30 

31 

32 

33 

34 

57 

19 

20 

21 

22 

23 

24 

25 

2b 

27 

28 

29 

29 

30 

31 

32 

33 

34 

57 

5^ 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

5» 

59 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

30 

31 

32 

33 

34 

35 

59 

60 

20 

21   22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

3t> 

bo 

TABLE  12. 

Page  291 

For  finding  the  Variation  of  the  Sun's 

Right  Ascension,  of  the  Declination, 

of  the 

Equation  0 

'  Time,  or  of  the 

Mooij's  Right  Ascension,  in  any  number  of  minutes  of  time,  the 

Horary  Motion  being  gi 

ven  at  the  top  of 

the  page  in  seconds,  and  the  number 

•  of  minutes 

of  time  in  the  side  column.  Also  for  find 

na  the  Variation 

of  the  Moon's  Dechnation  in 

secon 

ds  of  time, 

the  motion 

in  one  minute  being  given  at  the  top,  and  the  1 

numbers  in  the  side  column  being  taken  for  seconds. 

1 

Horary  motion. 

M 

M 

I 

sv 

38^' 

39^' 

40^^ 

41// 

ir' 

43'^ 

44// 

W 

w 

47// 

I 

49^' 

5»'' 

51'' 

52'' 

53" 

I 

I 

I 

I 

I 

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I 

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I 

I 

I 

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I 

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2 

I 

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I 

I 

I 

I 

I 

I 

2 

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T 

J 

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5 

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ID 

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ID 
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13 

8 

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9 

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9 

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10 

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9 

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10 

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12 

12 

12 

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14 

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10 

10 

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12 

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13 

13 

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15 
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12 

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13 

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14   14 

15 

15 

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12 

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13 

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lb 

lb 

18 

19 

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12 

13 

13 

13 

14 

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15 

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lb 

lb 

lb 

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19 

20 

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13 

13 

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14 

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14 

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16 

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17 

17 

17 

18 

20 

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13 

13 

14 

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15 

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lb 

lb 

lb 

17 

17 

18   18 

18 

19 

21 

22 

14 

14   14 

15 

15 

15 

lb 

lb 

17 

17 

17 

18 

18 

18   19 

19 

19 

22 

23 

H 

15  1  15 

15 

lb 

lb 

lb 

17 

17 

18 

18 

18 

19 

19   20 

20 

20 

23 

24 

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15   16 

16 

lb 

17 

17 

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18 

18 

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20 

20   20 

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25 

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17 

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18 

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20 

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16 

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20 

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17 

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18 

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19 

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17 

18 

18 

19 

19 

20 

20 

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23 

23   24 

24 

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29 

18 

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20 

21 

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22 

22 

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23 

24 

24   25 

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29 

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19 

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20 

20 

20 

21 

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22 

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27   27 

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20 

21 

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29 

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21 

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23 
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24 

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30 

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35 
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26 

27 

28 

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29 

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30   31 

31 

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37 

23 

23 

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27 

27 

28 

28 

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30 

30 

31   31 

32 

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37 

3« 

23 

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27 

27 

28 

29 

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30 

30 

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32   32 

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24 

25   25 

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27 

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28 

29 

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30 

31 

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33   i  33 

34 

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25 

25 
26 

26 

27 

27 

27 

28 

29 

29 

30 

31 

31 

32 

33 

33  i  34 

35 

35 

40 
41 

41 

25 

27 

28 

29 

29 

30 

31 

31 

32 

33 

33 

34  :  35 

36 

36 

42 

26  j  27   27 

28 

29 

29 

30 

31 

32 

32 

33 

34 

34 

35  '    36 

36 

37 

42 

43 

27  27   28   29 

29 

30 

31 

32 

32 

33 

34 

34 

35 

36   37 

3Z 

38 

43 

44 

27  28   29   29 

30 

31 

32 

32 

33 

34 

34 

35 

36 

37   37 

38 

39 

44 

45 
46 

28  29  f  29   30 

31 
31 

32 
32 

32 

33 

33 

34 

35 

35 

36 

37 

38   38 

39 

40 

45 

28  29 

30   31 

34 

35 

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36 

37 

3^ 

38  !  39 

40 

41 

46 

47 

29  1  30 

31   31 

32 

33 

34 

34 

35 

36 

37 

3^ 

38 

39  '  40 

41 

42 

47 

48 

30  30   31  '  32 

33 

34 

34 

35 

36 

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39 

40   41 

42 

42 

4h 

49 

30  31   32   33 

33 

34 

35 

36 

n 

3^ 

38 

39 

40 

41   42 

42 

43 

49 

50 
51 

31  32 
31  32 

33 
33 

33 

34 

35 

36 

37 

38 

38 

39 

40 

41 

42  1  43 

43 

44 

50 
51 

34 

35 

36 

37 

37 

38 

39 

40 

41 

42 

43   43 

44 

45 

52 

32  33 

34   35 

36 

36 

37 

38 

39 

40 

41 

42 

42 

43   44 

45 

4b 

52 

53 

33  34 

34   35 

36 

37 

38 

39 

40 

41 

42 

42 

43 

44  i  45 

4b 

47 

53 

54 

33  34  1  35  i  36 

37 

38 

39 

40 

41 

41 

42 

43 

44 

45  ;  46 

47 

48 

54  1 

55 
16 

34 
35 

35   36 
35   36 

37 

38 

39 

39 

40 

41 

42 

43 

44 

45 

46  1  47 

48 

49 

55 
56 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

^z  i  48 

49 

49 

57 

35 

36   37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48   48 

49 

50 

57 

5« 

36 

37   38 

39 

40 

41 

42 

43 

44 

44 

45 

46 

47 

48   49 

50 

51 

5^ 

59 

3b 

37   38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49   50 

51 

52 

59 

60 

37  ,  3^  .  39 

40 

41 

42 

43 

44 

45 

4b 

47 

48 

49 

50   51 

52 

53 

60 

Page  292]                   TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon's  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of 
the  page  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column.  Also,  for  finding  the  Variation 
of  the  Moon's  Declination  in  seconds  of  time,  the  motion  in  one  minute  being  given  at  the  top,  and  the 
numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

5i'' 

55'^ 

m' 

5r' 

58'^ 

59'' 

60'^ 

W 

6r' 

63^' 

W 

65'^ 

66^^ 

er^ 

68^^ 

69^' 

W 

I 
2 

3 
4 
5 
6 

7 
8 

9 
10 

I 

2 

3 
4 
5 

I 
2 

3 
4 
5 

1 
2 

3 
4 
5 

2 

3 
4 
5 

I 

2 

3 
4 
5 

I 
2 

3 
4 
5 

I 
2 

3 
4 
5 

I 

2 

3 
4 
5 

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2 
3 
4 
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1 

2 

3 
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2 

3 
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2 

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2 

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2 

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2 
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2 
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65 
66 
67 

P 
65 
66 

67 
68 

(>4 
66 

67 
68 
69 

P 
67 

68 

69 

70 

56 

11 

59 
60 

TABLE  12.                   [Page  293 

For  finding  the  Variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon's  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of 
the  page  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  cohunn.  Also  for  finding  the  Variation 
of  the  Moon's  Dechnation  in  seconds  of  time,  the  motion  in  one  minute  being  given  at  the  top,  and  the 
numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

71' 

vy 

W 

W 

15'' 

W 

IV 

IS'' 

19'' 

80'^ 

81'^ 

S2" 

83'^ 

s^" 

85^' 

86'^ 

SI" 

I 

2 

3 
4 
5 

I 
2 
4 

5 
6 

I 
2 

4 

I 

2 
4 

I 
2 
4 
5 
6 

I 

3 
4 

5 
6 

I 

3 

4 

1 

I 

3 
4 

1 

I 

3 
4 
5 
7 

I 

3 
4 
5 
7 

1 

3 
4 
5 
7 

I 

3 

4 
5 
7 

I 

3 
4 
5 
7 

I 
3 
4 
6 

7 

I 

3 
4 

6 

7 

I 

3 
4 
6 

7 

I 

3 
4 
6 

7 

I 

3 
4 
6 

7 

I 

2 

3 

4 
5 

6 

7 
8 

9 

10 

I 

9 
II 
12 

7 

8 

10 

II 

12 

7 

9 

10 

II 
12 

7 

9 

10 

II 

12 

8 

9 
10 
II 

13 

8 
9 

ID 
II 

13 

8 
9 

ID 
12 
13 

8 

9 
10 
12 

13 

8 

9 
II 
12 
13 

8 

9 
II 
12 

13 

8 

9 
II 
12 
14 

8 

ID 
II 
12 

14 

8 

ID 
II 
12 
14 

8 
10 
II 

13 

14 

9 
10 
II 

13 

14 

9 

ID 
II 

13 

14 

9 
10 
12 

13 
15 

6 

7 
8 

9 
10 

II 

12 

13 
14 
15 

13 
14 
15 
17 
18 

13 
14 
16 

17 
18 

13 

\l 

17 
18 

14 
15 
16 
17 
19 

14 

'A 

18 
19 

14 

15 
16 
18 
19 

14 
15 
17 

18 

19 

14 
16 

17 
18 
20 

14 
16 

17 
18 
20 

15 
16 

17 
19 
20 

18 

19 
20 

18 

19 
21 

15 
17 
18 

19 
21 

15 
17 
18 
20 
21 

16 

17 
18 
20 
21 

16 
17 
19 
20 
22 

16 
17 

19 

20 

22 

II 
12 

13 
14 
15 

i6 

17 
i8 

19 

20 

19 
20 
21 
22 
24 

19 
20 
22 

23 

24 

19 
21 
22 

23 
24 

20 
21 
22 

23 

25 

20 
21 

23 
24 

25 

20 
22 

23 

24 

25 

21 
22 

23 
24 
26 

21 

22 
23 

25 
26 

21 

22 

24 

25 
26 

21 

23 
24 
25 
27 

28 
29 

31 
32 

33 

22 

23 
24 

26 
27 

22 
23 

25 
26 

27 

22 

24 

26 
28 

22 
24 
25 

27 
28 

23 

24 
26 

28 

23 
24 
26 

27 
29 

23 

26 
28 
29 

16 

17 
18 

19 
20 

21 

22 

23 
24 
25 

26 

27 
28 

30 

26 
28 
29 
30 

26 
27 
28 
29 
30 

26 

27 
28 

30 

31 

26 
28 
29 
30 
31 

27 
28 

29 
30 
32 

27 
28 

30 
31 
32 

27 
29 
30 
31 
33 

28 
29 
30 
32 
33 

28 
30 
31 
32 
34 

29 

30 
31 
33 
34 

29 

30 
32 

33 

35 

36' 

37 

39 

40 

42 

29 
31 
32 
34 
35 

30 
31 
33 

34 
35 

30 
32 

33 
36 

30 
32 
33 

36 

21 
22 
23 
24 

25 

26 
27 
28 
29 
30 

31 
32 
35 

36 

31 

32 
34 
35 
36 

32 
33 
34 
35 
37 
38 

39 
40 

41 
43 

32 
33 

36 
37 

33 
34 

38 

33 
34 
35 
37 
38 

33 
35 
36 
37 
39 

34 

38 
39 

36 
37 
38 
40 

36 
37 
39 
40 

38 
39 
41 

36 

37 
38 
40 

41 

36 
38 
39 
41 
42 

37 
38 
40 

41 

43 

37 
39 
40 

42 
43 

38 

39 
41 

42 

44 

26 

27 
28 
29 
30 

31 

32 

33 
34 
35 
36 

11 

39 
40 

37 
38 

39 
40 

41 

37 
38 
40 

41 

42 

38 
39 
41 
42 

43 

39 
40 

41 
43 
44 

39 
41 
42 

43 
44 

40 

41 
42 

44 
45 

40 
42 
43 
44 
46 

41 
42 

43 

45 
46 

41 

43 
44 
45 
47 

42 

43 
45 
46 
47 

42 
44 

46 
48 

43 
44 
46 
47 
48 

43 

46 
48 
49 

44 
45 
47 
48 
50 

44 
46 

47 
49 
50 

46 
48 
49 
51 

31 

32 
33 
34 
35 

43 

44 

45 
46 

47 

43 
44 
46 
47 
48 

44 

46 
47 
49 

44 
46 

47 
48 
49 

46 
48 
49 
50 

46 

47 
48 
49 
51 

46 
47 
49 
50 
51 

47 
48 
49 
51 
52 

47 
49 
50 
51 

53 

48 
49 
51 
52 
53 

49 
50 
51 
53 
54 

49 
51 

52 
53 
55 

50 
51 

53 
54 
55 

50 
52 
53 

11 

51 

52 
54 
55 
57 

52 
53 
54 
56 
57 

52 
54 
55 

■11 

36 
37 
38 
39 
40 

41 

42 

43 
44 
45 
46 

47 
48 
49 
50 

51 

52 
53 
54 
55 
56 
57 
58 

60 

49 
50 
51 

52 
53 

56 
57 
58 
59 
60 
62 

64 

65 
66 
67 

69 

70 

71 

49 
50 

52 
53 
54 

50 
51 
52 
54 
55 

51 

52 
53 
54 
56 

51 

53 
54 

11 

52 

53 
54 
56 
57 

53 

54 

55 

5^ 
58 

53 

11 

57 
59 

54 
55 

11 

59 

11 

57 
59 
60 

55 

57 
58 

61 

56 
57 
59 
60 
62 

57 
58 

61 
62 
64 

65 
66 
68 
69 

57 

59 
60 
62 

63 

58 
60 
61 
62 
64 

60 
62 

63 
65 
66 
67 
69 
70 

72 

59 
61 

62 

64 

65 

67' 

68 

70 

71 

73 

74 

75 

77 

78 

80 

41 
42 

43 
44 
45 
46 
47 
48 
49 
50 

51 

52 
53 

It 

55 

^8 
58 

60 

56 

11 

60 
61 

11 

62 

58 

60 
61 

63 

60 
61 
62 

63 

59 
60 
62 

63 
64 

60 
61 
62 
64 

65 

61 

62 

P 
65 
66 

61 
64 
67 

62 

P 
65 
66 

68 

P 
64 

66 

67 

68 

64 
66 
67 
69 
70 

P 
67 

68 

69 

71 

61 
62 

64 
65 

66 

62 

63 
64 
66 
67 

64 
65 
67 
68 

64 

65 
66 

68 

69 

65 
66 

67 
68 
70 

65 
67 
68 
69 

71 

66 
68 
69 

70 
72 

67 
68 
70 

71 

72 

68 
69 

71 

72 

73 

69 
70 

72 
73 
74 

70 

71 

72 
74 
75 

71 

72 
73 

11 

71 

73 

76 

77 

72 
74 
75 
77 
78 

73 

75 
76 

77 
79 

67 
68 
70 

71 

72 

68 

69 

71 
72 

73 

69 

70 
72 

73 
74 

70  1  71 

71  72 

73  73 

74  75 

75  1  76 

72 

73 
74 
76 
77 

73 

74 
75 
77 
78 

74 

11 

78 
79 

76 
77 
79 
80 

76 

77 
78 
80 
81 

77 
78 

79 
81 

82 

77 

79 
80 
82 

83 

81 

84 

79 
81 
82 
84 
85 

80 
82 
83 
85 
86 

81 

83 
84 
86 

87 

50 
57 
58 

60 

Page  294 

TABLE  12. 

For  finding  the  Variation  of  the  Sun's 

Right  A  cension,  of  the  Declination 

of  the  Equation  of  Time,  or  of  the 

Moon's  Right  Ascension,  in  any  nu 

mber  ( 

3f  minutes  of  time 

,  the 

Horar 

y  Motion  being  given  at  the  top  of 

the  page  in  secon 

ds,  and  the 

aumbe 

r  of  minutes  of  time  in 

the  side  column.  Also  for  finding  the  Variation  1 

of  the  Moon's  Dechnation  in 

seconds  of 

time,  the  motion 

in  one  minute  beine  eiven  at  the  top,  and  the  1 

numbers  in  the  side  column  being  taken  for  seconds. 

1 

Horary  motion. 

M. 

M. 
I 

88'^ 

89^^ 

90^' 

91^^ 

92'' 

93^^ 

w 

95'' 

96^^ 

9r' 

98'^ 

99'^ 

100^' 

101'' 

102'  103  ' 

104" 

2 

I 

I 

I 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2    2 

2 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

0 

0 

3 

3 

3 

3    3 

3 

2 

3 

4 

4 

5 

5 

S 

S 

S 

5 

5 

<; 

5 

5 

i   5 

5 

5    S 

5 

3 

4 

b 

b 

6 

6 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7    7 

7 

4 

5 

7 

7 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 
10 

8 

8 

9    9 

9 
10 

5 
6 

6 

9 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

10   10 

7 

10 

10 

II 

II 

II 

II 

II 

II 

II 

II 

II 

12 

12 

12 

12   12 

12 

7 

8 

12 

12 

12 

12 

12 

12 

13 

13 

13 

13 

13 

13 

13 

13 

14   14 

14 

8 

9 

13 

13 

14 

14 

14 

14 

14 

14 

14 

15 

15 

15 

15 

15 

15 

15 

16 

9 

ID 

15 

IS 

15 

IS 

IS 

16 

16 

16 

16 

16 

16 

17 

17 

17 
19 

17 
19 

17 

17 
19 

10 

II 

16 

16 

17 

17 

17 

17 

17 

17 

18  i  18 

18 

18 

18 

19 

II 

12 

18 

18 

18 

18 

18 

19 

19 

19 

19   19 

20 

20 

20 

20 

20 

21 

21 

12 

13 

19 

19 

20 

20 

20 

20 

20 

21 

21 

21 

21 

21 

22 

22 

22 

22 

23 

13 

14 

21 

21 

21 

21 

21 

22 

22 

22 

22 

23 

23 

23 

23 

24 

24 

24 

24 

14 

^5 

22 

22 

23 

23 

23 

23 

24 

24 

24 

24 

25 

25 

"  26 

25 

25 

27 

26 
27 

26 
27 

26 
28 

15 

16 

23 

24 

24 

24 

25 

25 

25 

25 

26 

26 

26 

27 

16 

17 

25 

25 

26 

26 

26 

26 

27 

27 

27 

27 

28 

28 

28 

29 

29 

29 

29 

17 

18 

2b 

27 

27 

27 

28 

28 

28 

29 

29 

29 

29 

30 

30 

30 

31 

31 

31 

18 

•9 

28 

28 

29 

29 

29 

29 

30 

30 

30 

31 

31 

31 

32 

32 

32 

33 

33 

19 

20 

29 

30 

30 

3" 

31 
32 

31 

31 

32 

32 

32 

33 

33 

33 

34 

34 

34 

35 
.36 

20 
21 

21 

31 

31 

32 

32 

33 

33 

33 

34 

34 

34 

35 

35 

35 

36 

36 

22 

32 

33 

33 

33 

34 

34 

34 

35   35 

36 

3b 

3b 

37 

37 

37 

38 

38 

22 

23 

34 

34 

35 

35 

35 

3b 

3^ 

36 

37 

37 

38 

38 

38 

39 

39 

39 

40 

23 

24 

35 

3b 

3^ 

36  !  37 

37 

38 

38 

38 

39 

39 

40 

40 

40 

41 

41 

42 

24 

23 

37 
38 

37 
39 

3^ 
39 

38  !  38 

39 

39 

40 

40 

40 

41 

41 

42 

42 

43 

43 
45 

43 
45 

25 
26 

26 

39 

40 

40 

41 

41 

42 

42 

42 

43 

43 

44 

44 

27 

40 

40 

41 

41 

41 

42 

42 

43 

43 

44 

44 

45 

45 

45 

4b 

4b 

47 

27 

28 

41 

42 

42 

42 

43 

43 

44 

44 

45 

45 

46 

46 

47 

47 

48 

48 

49 

28 

29 

43 

43 

44 

44 

44 

45 

45 

46 

4b 

47 

47 

48 

48 

49 

49 

50 

50 

29 

30 

44 
45 

45 
46 

45 
47 

4b 

46 

47 

47 

48 

48 

49 

49 

SO 
SI 

SO 

52 

51 
S2 

51 
S3 

52 
.53 

52 
54 

30 
31 

31 

47 

48 

48 

49 

49 

SO 

50 

SI 

32 

"^l 

47 

48 

49 

49 

50 

50 

51 

51 

52 

52 

53 

53 

54 

54 

55 

55 

32 

33 

48 

49 

50 

50 

SI 

SI 

52 

52 

53 

53 

54 

54 

55 

Sb 

5b 

57 

57 

33 

34 

50 

50 

SI 

52 

52 

S3 

S3 

54 

54 

55 

5b 

5b 

57 

57 

58 

58 

59 

34 

35 
36 

51 

53 

52 
53 

53 

54 

S3 

54 

54 

55 

55 

SO 

57 

57 

58 

58 

59 
61 

60 
61 

60 
62 

bi 
62' 

35 

55 

55 

56 

56 

57 

58 

58 

59 

59 

60 

36 

37 

54 

55 

5i> 

5b 

57 

57 

58 

59 

59 

60 

60 

61 

62 

62 

b3 

64 

64 

37 

3« 

5^^ 

5^ 

57 

58 

58 

59 

60 

60 

61 

61 

62 

63 

63 

64 

65 

65 

66 

38 

39 

57 

5«- 

59 

59 

60 

60 

61 

62 

62 

63 

64 

64 

65 

66 

66 

67 

68 

39 

40 

59 

•59 

60 

61 

61 

62 

63 

63 

64 

65 
66 

65 

67 

66 

67 

67 

68 
^0" 

69 

69 
71 

40 

41 

60 

61 

62 

62 

63 

64 

64 

65 

66 

68 

68 

69 

70 

41 

42 

b2 

b2 

63 

64 

64 

65 

66 

67 

67 

68 

69 

6q 

70 

71 

71 

72 

73 

42 

43 

^3 

b4 

<^5 

bS 

66 

67 

67 

68 

69 

70 

70 

71 

72 

72 

73 

74 

75 

43 

44 

b5 

b5 

bb 

67 

67 

68 

69 

70 

70 

71 

72 

73 

73 

74 

75 

76 

76 

44 

45 

bb 

b7 
68 

68 
69 

68 

69 

70 

71 

71 

72 

73 

74 

75 

74 

75 

76 

77 

77 

"78" 

77 

78 

45 

46 

by 

70 

71 

71 

72 

73 

74 

74 

76 

77 

79 

80 

46 

47 

b9 

70 

71 

71 

72 

73 

74 

74 

75 

76 

77 

78 

78 

79 

80 

81 

81 

47 

48 

70 

71 

72 

73 

74 

74 

75 

76   77 

78 

78 

79 

80 

8i 

82 

82 

83 

48 

49 

72 

73 

74 

74 

75 

76 

77 

78   78 

79 

80 

81 

82 

82 

83 

84 

85 

49 

50 

73 

74 
76 

75 

76 

77 

78 
79 

78 

79 

80 

81 

82 

83 
84 

83 

84 
86 

85 
87" 

86 

87 

SO 

51 

75 

77 

77 

78 

80 

81 

82 

82 

83 

85 

88 

88 

51 

52 

7b 

77 

7« 

79 

80 

81 

81 

82 

83 

84 

85 

86 

87 

88 

88 

89 

90 

52 

53 

7« 

^9  1  80 

80 

81 

82 

83 

84 

85 

86 

87 

87 

88 

89 

90 

91 

92 

53 

54 

79 

80   81 

82 

83 

84 

8s 

86 

86 

87 

88 

89 

90 

91 

92 

93 

94 

54 

55 
56 

81 
82 

82 
13 

«3 
84 

83 

84 

85 
87 

86 
88 

87 
89 

88 

89 

90 

91 

92 

93 

94 

94 

95 
97 

55 
56 

^5 

86 

90 

91 

91 

92 

93 

94 

95 

96 

H 

84 

85   86 

86   87 

88 

89 

90   91 

92 

9i 

94 

95 

qb 

97 

98 

99 

57 

5« 

^5 

86   87 

88 

89 

90 

91 

92   93 

94 

95 

96 

97 

98 

99 

100 

lOI 

58 

59 

^7 

88  j  89 

90 

90 

91 

92 

93   94 

95 

9b 

97 

98 

99 

100 

lOI 

102 

59 

60 

88 

89   90 

91 

92 

93 

94 

95   96 

97 

98 

99 

100   lOI 

102 

103 

104 

60 

TABLE  12.                   [Page  295, 

For  finding  the  Variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon's  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of 
the  page  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  fintling  the  Variation 
of  the  Moon's  Declination  in  seconds  of  time,  the  motion  in  one  minute  being  given  at  the  top,  and  the 
numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

105'^ 

106^^ 

107^^ 

108'^ 

109^^ 

110^^ 

111'^ 

112^^ 

113^^ 

114^^ 

115^' 

116^^ 

nr' 

118^^ 

I 

2 

3 
4 
5 

2 

4 
5 
7 
9 

2 
4 
5 
7 
9 

2 
4 
5 
7 
9 

2 
4 
5 
7 
9 

2 
4 
5 
7 
9 

2 

4 
6 

7 
9 

2 

4 
6 

7 
9 

2 

4 
6 

7 
9 

2 

4 
6 
8 
9 

2 

4 

6 

8 

10 

2 

4 

6 

8 

10 

2 

4 

6 

8 

10 

2 
4 

6 
8 

ID 

2 

4 

6 

8 

10 

I 

2 

■> 

4 
5 

6 

7 
8 

9 

lO 

II 

12 

14 
16 
18 

II 
12 

14 
16 
18 

II 
12 

14 
16 
18 

II 

13 

14 
16 

18 

II 

13 
15 
16 
18 

II 

13 
15 
17 
18 

II 

13 
15 
17 
19 

II 
13 

15 
17 
19 

II 

13 
15 
17 
19 

II 

13 
15 
17 
19 

12 
13 
IS 
17 
19 

12 
14 
IS 
17 
19 

12 

14 
16 
18 
20 

12 

14 
16 
18 
20 

6 

9 
10 

n 
12 
13 
14 
15 
16 

17 
18 

19 
20 

II 

12 

13 
14 
15 

19 
21 

23 

25 
26 

19 
21 

23 

25 
27 

20 
21 

*  23 

25 
27 

20 

22 

23 
25 
27 

20 
22 
24 
25 
27 

20 
22 

24 
26 

28 

20 
22 

24 
26 
28 

21 
22 

24 
26 
28 

21 

23 

24 
26 

28 

21 

23 
25 
27 
29 

21 
23 
25 
27 
29 

21 

23 
25 
27 

29 

21 

23 
25 
27 
29 

22 

24 
26 
28 
30 

i6 

17 
iS 

19 

20 

28 

30 
32 
33 
35 

28 

30 
32 
34 
35 

29 
30 
32 
34 
36 

29 

31 
32 

36 

29 

31 
33 
35 
36 

29 
31 

33 
35 
37 

30 
31 
33 

35 
37 

30 
32 
34 
35 
37 

30 
32 
34 
36 
38 

30 
32 
34 
36 
38 

31 
33 

36 
38 

31 

33 
35 
37 
39 

31 

33 
35 
37 
39 

31 

33 
35 
37 
39 

21 

22 
23 
24 
25 
26 

27 
28 
29 
30 

37 
39 
40 

42 
44 

37 
39 
41 
42 
44 

37 
39 
41 
43 
45 

38 
40 

41 
43 
45 

38 
40 

42 
44 
45 

39 
40 

42 

44 
46 

39 
41 
43 
44 
46 

39 
41 
43 
45 
47 

40 
41 

43 
45 
47 

40 
42 

44 
46 

48 

40 

42 

44 
46 

48 

41 

43 
44 
46 

48 

41 
43 

45 
47 
49 

41 
43 
45 
47 
49 

21 

22 

23 

24 
25 

46 
47 
49 
51 
53 

46 

48 

53 

46 
48 
50 
52 
54 

47 
49 
50 

52 
54 

47 
49 
51 

53 
55 

48 
50 
51 
53 

55 

48 

50 

.  52 

It 

49 
50 
52 

H 
56 

49 
51 

53 
55 
57 

49 
51 

53 
55 
57 

50 
52 

54 

58 

59 
61 

67 

50 
52 
54 

58 

51 
53 
55 
57 
59 

51 

53 
55 
57 
59 

26 

27 
28 

29 
30 

31 

32 

34 
35 

56 
60 

6i 

55 

11 

60 
62 

55 
57 

61 
62 

56 
58 

59 
61 

63 

56 

60 
62 
64 

57 
59 
61 

62 
64 

11 

61 

63 
65 

58 
60 
62 

P 
65 

60 
62 
64 
66 

59 
61 

63 
67 

60 
62 
64 
66 
68 

60 
62 
64 

66 
68 

61 

P 
65 
67 

69 

31 
32 
33 
34 
35 

36 

37 
38 

39 
40 

63 

65 
67 

68 

70 

54 
67 
69 
71 

64 
66 
68 
70 

71 

65 
67 

68 

70 

72 

67 
69 
71 

73 

66 
68 
70 
72 
73 

67 
68 
70 
72 
74 

67 

69 
71 
73 
75 

68 
70 
72 

73 

75 

68 

70 

72 

74 
76 

69 
71 
73 

75 
77 

70  ;   70 

72  72 

73  '   74 
75    76 
77    78 

71 

73 
75 
77 
79 

36 
37 
38 
39 
40 

41 

42 
43 
44 
45 

72 

74 
75 
77 
79 

72 

74 
76 

78 
80 

73 
75 
77 
78 
80 

74 
76 

77 
79 
81 

71 
76 

78 

80 

82 

75 
77 

83 

76 

80 
81 

83 

77 
78 
80 
82 
84 

77 
79 
81 

83 
85 

78 
80 
82 

84 
86 

79 
81 
82 

84 
86 

79    80 
81    82 
83    84 
85    86 
87    88 

81 
83 
85 
87 
89 

41 

42 

43 
44 
45 

46 

47 
48 
49 
50 

81 
82 

84 
86 
88 

81 
83 

85 
87 
88 

82  i   83 

84  !  85 

86  \      86 

87  88 
89    90 

84 
85 
87 
89 
91 

84 

86 
88 
90 
92 

f5 
89 

91 
93 

86 
88 
90 
91 
93 

95 
97 
99 

lOI 

103 

87 
89 
90 
92 
94 

87 
89 

91 
93 

95 

88 
90 
92 

94 
96 

89    90 
91    92 
93    94 
95    96 
97    98 

90 
92 

94 
96 
98 

46 

47 
48 

49 
50 

51 

52 
53 
54 
55 

89 
91 
93 
95 
96 

90 
92 
94 
95 
97 

91    92 
93  :   94 

95  '   95 

96  97 
98    99 

93 
94 
96 

98 
100 

94 
95 
97 
99 

lOI 

94 

98 
100 
102 

96 

98 

100 

102 

104 

97 
99 

lOI 

103 
105 

98 
100 
102 
104 
105 

99    99 

Id     lOI 

102   103 
104   105 
106   107 

100 
102 
104 
106 
108 

51 

52 
53 
54 
55 

56 

57 
58 

59 
60 

98 
100 
102 
103 

105 

99    100    lOI 
Id   102   103 
102   103   104 
104   105   106 
106   107   108 

102   103 

104  105 

105  106 
107   108 
109   110 

104 

105 
107 
109 
III 

105 
106 
108 
no 

112 

105 

107 

109 
III 
113 

106 
108 
no 
112 
114 

107 
109 
III 
113 
115 

108   109 
no   in 
112   113 

114   "5 
116   117 

no 
112 
114 
n6 
118 

56 

11 

59 
60 

Page  296]                    TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon's  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of 
the  page  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation 
of  the  Moon's  Declination  in  seconds  of  time,  the  motion  in  one  minute  being  given  at  the  top,  and  the 
numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

lir^ 

120^^ 

121^^ 

122^' 

123^^ 

124^^ 

125^^ 

126^^ 

nv 

128^^ 

129^^ 

130^^ 

131^^ 

132^^ 

I 
2 

3 
4 

5 
6 

7 
8 

9 
10 

2 

4 

6 

8 

10 

2 

4 
6 
8 

ID 

2 

4 

6 

8 

10 

2 

4 

6 

8 

10 

2 

4 

6 

8 

10 

2 

4 

6 

8 

10 

2 

4 
6 
8 

ID 

2 

4 

6 

8 

II 

2 
4 

6 

8 

li 

2 

4 
6 

9 
n 

2 

4 
6 

9 
II 

2 
-  4 

7 

9 
II 

2 
4 
7 
9 
II 

2 
4 
7 
9 
II 

I 
2 

3 
4 
5 

12 

14 
16 
18 
20 

12 

14 
16 
18 
20 

12 

14 
16 
18 
20 

12 

14 
16 
18 
20 

12 

14 
16 
18 
21 

12 
14 
17 
19 
21 

13 
15 
17 
19 
21 

13 
15 
17 
19 
21 

13 
15 
17 
19 
21 

13 
15 
17 
19 
21 

13 
15 
17 
19 
22 

13 
15 
17 
20 

22 

13 
15 
17 
20 
22 

13 

15 
18 

20 

22 

6 

7 
8 

9 
10 

II 
12 

13 
14 
15 

22 

24 
26 
28 
30 

22 
24 
26 
28 
30 

22 
24 
26 
28 
30 

22 

24 
26 
28 

31 

23 

25 
27 

29 
31 

23 

25 
27 

29 
31 

23 

25 
27 

29 
31 

23 

25 
27 

29 
32 

23 

25 
28 

30 
32 

26 
28 

30 
32 

24 
26 

28 

30 
32 

24 

26 

28. 

30 

33 

24 
26 
28 

31 
33 

24 
26 
29 

31 
33 

II 

12 

13 
14 
15. 
16 

17 
18 

19 
20 

16 

17 

18 

19 
20 

32 

36 
38 
40 

32 

34 

3^ 
38 
40 

32 

34 
36 
38 
40 

33 
35 
37 
39 
41 

33 
35 
37 
39 
41 

33 
35 
37 
39 
41 

33 

35 
38 
40 

42 

36 
38 
40 
42 

34 

38 
40 
42 

34 

38 
41 
43 

34 
37 
39 
41 
43 

35 
37 
39 
41 
43 

35 
37 
39 
41 
44 

35 
37 
40 
42 
44 

21 

22 

23 

24 

25 

42 

44 
46 
48 
50 

42 

44 
46 
48 
50 

42 

44 
46 

48 

5° 

43 

45 
47 
49 
51 

43 
45 
47 
49 
51 

43 
45 
48 
50 
52 

44 
46 

48 

50 

52 

44 
46 
48 
50 
53 

44 
47 
49 
51 
53 

45 
47 
49 
51 
53 

45 
47 
49 
52 
54 

46 
48 
50 
52 
54 

46 
48 

50 
52 
55 

46 
48 
51 
53 
55 

21 

22 

23 
24 
25 

26 

27 
28 

29 
30 

52 

H 
56 

58 

60 

52 

54 
56 

60 

52 
54 
56 
58 
61 

53 

55 
57 

61 

53 
55 
57 
59 
62 

54 

5^ 
58 

60 

62 

5t 
56 

60 
63 

55 

57 

59 
61 

63 

55 
57 
59 
61 
64 

55 
58 
60 
62 
64 

5^ 

58 

60 
62 

65 

56 

59 
61 

63 
65 

57 

61 

63 
66 

57 
59 
62 
64 
66 

26 

27 
28 

29 
30 

31 
32 
33 
34 
35 

61 

63 

65 
67 

69 

62 
64 
66 
68 
70 

P 

65 
67 

69 
71 

P 

P 
67 

69 

71 

64 
66 
68 
70 

72 

64 
66 
68 
70 
72 

65 
67 
69 

71 

73 

75 
77 

79 
81 

83 

P 
67 

69 

71 

74 

66 
68 

70 
72 
74 

66 
68 
70 
73 

75 

67 
69 
71 

73 

75 

P 
69 

72 

74 
76 

68 

70 

72 

74 

76 

68 
70 

73 
75 
77 

31 

32 
33 
34 
35 

36 

37 
38 

39 
40 

71 

73 
75 
77 
79 

72 
74 

78 
80 

73 

75 
77 

79 
81 

73 
75 
77 

79 
81 

74 
76 

78 
80 
82 

74 
76 

79 
81 

83 

76 

78 
80 
82 
84 

76 
80 

85 

77 

79 
81 

83 
85 

11 

82 

84 
86 

78 
80 

82 

85 
87 

79 
81 

l^ 
85 

87 

79 
81 

84 
86 
88 

36 
37 
38 

39 
40 

41 

42 
43 
44 
45 

81 

83 
85 
87 
89 

82 

84 
86 
88 
90 

^3 
85 

87 
89 
91 

83 

85 

89 
92 

84 
86 
88 
90 
92 

f5 
87 

89 

91 

93 

85 
88 
90 
92 
94 

86 
88 
90 
92 
95 

87 
89 
91 
93 
95 

87 
90 

92 
94 
96 

88 
90 
92 
95 
97 

89 
91 
93 
95 
98 

90 
92 
94 

9^ 
98 

100 

103 

105 

107 

109 

90 

92 

95 

97 

99 

Id 

103 

106 

108 

no 

41 
42 

43 
44 
45 
46 

47 
48 
49 
50 

46 

47 
48 

49 
50 

91 
93 
95 
97 
99 

92 

98 
100 

93 
95 
97 
99 

lOI 

94 
96 

98 
100 
102 

94 
96 

98 
100 
103 

95 
97 
99 

lOI 

103 

96 

98 

xoo 

102 

104 

97 
99 

lOI 

103 

105 

97 

99 

102 

104 

106 

98 
100 
102 

105 
107 

99 

lOI 

103 

105 
108 

100 
102 
104 
106 
108 

51 

52 
53 
54 
55 

lOI 

103 
105 
107 
109 

102 
104 
106 
nl 
no 

103 

105 
107 
109 
III 

104 
106 
108 
no 
112 

105 
107 
109 
III 

"3 

105 
107 
no 
112 
114 

106 

108 

no 
"3 
"5 

107 
109 
III 

116 

108 
no 
112 
114 
116 

109 
III 

"3 
115 
117 

110 
112 
114 
116 
118 

III 

113 
"5 
117- 
119 

121 
124 
126 
128 
130 

in 
114 
116 
118 
120 
^122 
124 
127 
129 
131 

112 
114 
117 
119 
121 
123 
125 
128 
130 
132 

51 

52 
53 
54 
55 
56 
57 
58 
59 
60 

56 
57 
58 
59 
60 

III 

H3 

115 

117 

119 

112 
114 
116 
118 
120 

"3 

115 
117 

119 

121 

114 
116 
J18 
120 
122 

"5 
117 

119 

121 

123 

116 
118 
120 
122 

124 

117 
119 
121 
123 
125 

118 

120 
122 
124 
126 

119 
121 

123 
125 

127 

119 
122 
124 
126 

128 

120 

123 

125 
127 
129 

TABLE  12.                   [Page  297 

For  finding  the  Variation  of  the  Sun's  Right  Ascension,  of  the  Declination,  of  the  Equation  of  Time,  or  of  the 
Moon's  Right  Ascension,  in  any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of 
the  page  in  seconds,  and  ilie  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation 
of  the  Moon's  Declination  in  seconds  of  time,  the  motion  in  one  minute  being  given  at  the  top,  and  the 
numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

133''  134'' 

135" 

136" 

137'^ 

138" 

139" 

140" 

141" 

142" 

143" 

144" 

145" 

146" 

I 

2 

3 

4 
5 
6 

7 
S 

9 

10 

1 1 

12 
13 
14 
15 
16 

17 

i<S 

19 
20 

2 

4 

7 

9 

II 

2 
4 
7 
9 
II 

2 

S 

7 

9 

II 

2 

5 

7 

9 
II 

2 

5 

7 

9 

II 

14 
16 
18 
21 

23 

2 

5 

7 

9 

12 

2 

5 

7 

9 
12 

16 

19 
21 

23 

2 

5 

7 

9 

12 

2 
5 
7 
9 
12 

2 

5 

7 

9 
12 

2 

5 

7 

10 

12 

2 

5 
7 

10 
12 

2 

5 
7 

ID 
12 

2 
5 
7 

10 
12 

I 
2 

3 
4 
5 

13 
16 

18 

20 

22 

13 
16 

18 
20 
22 

14 
16 
18 
20 
23 

14 
16 
18 
20 
23 

»4 
16 
18 
21 
23 

14 
16 

19 
21 

23 

14 
16 

19 
21 

24 

14 
17 
19 
21 

24 

14 
17 
19 
21 

24 

14 
17 
19 
22 
24 

>5 
17 

19 
22 
24 

15 
17 

19 
22 

24 

6 

7 
8 

9 
10 

24    25 

27  !  27 
29   29 
31   31 
33    34 

25 
27 
29 
32 
34 
36 
38 
41 
43 
45 

25 
27 
29 
32 
34 

25 
27 
30 
32 
34 

25 
28 

30 
32 

35 

25 
28 

30 
32 
35 

26 
28 
30 
33 
35 

26 
28 

31 
33 

35 

26 
28 

31 

33 
36 

26 
29 

31 
33 
36 

26 
29 

31 
36 

27 
29 

31 

36 

27 
29 
32 
34 
37 

II 

12 

13 
14 
15 

35 
38 
40 
42 
44 

36 
38 
40 
42 
45 

36 
39 
41 
43 
45 

37 
39 
41 

43 
46 

37 
39 
41 
44 
46 

37 
39 
42 

44 
46 

37 
40 
42 
44 
47 

38 
40 
42 

45 
47 

38 
40 

43 
45 
47 

38 
41 
43 
45 
48 

38 

41 

43 
46 

48 

39 
41 
44 
46 

.48 

39 
41 
44 
46 

49 

16 

17 

18 

19 
20 

21 
22 

23 

24 
25 
26 

27 
28 
29 
30 

47 
49 
51 
53 
55 

47 
49 
51 
54 
56 

47 
50 
52 

56 

48 
SO 
52 
54 
57 

48 
50 
53 
55 
57 

59 
62 
64 
66 
69 

48 
51 

11 

58 

49 
51 

56 
58 

49 
51 
54 
56 
58 

49 

52 

56 
59 

50    50 
52    52 
54    55 
57    57 
59    60 

50 
53 

55 

60 

51 

53 

$ 

60 

51 
54 
56 
58 
61 

21 

22 

23 
24 
25 

58 
60 
62 
64 
67 

58 
60 

P 
65 

67 

59 
61 

63 
65 
68 

59 
61 

63 
66 
68 

60 
62 
64 
67 
69 

60 
63 

? 
67 

70 

61 

65 
68 
70 

61 

'd 

68 
71 

62    62 
64    64 
66    67 
69    69 
71    72 

62 

67 
70 
72 

63 

65 

68 
70 
73 

63 
66 

68 

71 

73 

20 

27 
28 
29 
30 

31 
32 

34 
35 
3~6 
37 
38 
39 
40 

31 

32 
-» -, 

34 
35 

69 
71 

73 
75 
78 

69 
71 

76 
78 

70 

72 
74 
77 
79 

70 

73 
75 
77 
79 

71 
73 
75 
78 
80 

71 

74 
76 

78 
81 

72 
74 
76 

79 
81 

72 

75 

77 

79 
82 

73 
75 
78 
80 
82 

73 
76 

78 
80 

83 

74 
76 

79 
81 

83 

74 
77 
79 
82 

84 

75 

77 
80 

82 
85 

75 
78 
80 

85 

36 
37 
38 
39 
40 

80 
82 

84 

86 

.  89 

80 
83 
85 
87 
89 

81 

83 
86 
88 
90 

82 

84 
86 
88 
91 

82 

84 

f7 
89 

91 

83 
85 
87 
90 
92 

88 
90 

93 

84 
86 
89 

91 
93 

85 

89 
92 
94 

85 
88 
90 
92 
95 

86 
88 
91 
93 
95 

86 

89 
91 

96 

87 
89 
92 

94 
97 

88 
90 
92 

95 
97 

41 
42 
43 
44 
45 

91 
93 
95 
98 
100 

92 

94 
96 

98 

lOI 

92 

95 

97 

99 

101 

93 

95 

97 
100 

102 

94 
96 

98 
100 
103 

94  1   95 

97  :   97 
99   100 

101   102 

104   104 

96 

98 
100 
103 

105 

96 
99 

lOI 

103 
106 

97    98 

99   100 

102   102 

104   105 

107   107 

98 

lOI 

103 
106 
108 

99 
102 
104 
106 
109 

100 
102 

105 
107 
no 

41 
42 
43 
44 
45 

46 

47 
48 
4') 
50 

102   103 
104   105 
106   107 
109   109 
III   112 

104 
106 
108 
no 
"3 

104 
107 
109 
III 

"3 

105 
107 
no 
112 
114 

106 
108 
no 
113 
"5 

107 
109 
III 
114 
116 

107 
no 
112 
114 
117 

108 
no 

"3 
115 
118 

109 
in 

"4 
n6 
118 

no 
112 
114 
117 
119 

no 

"3 
"5 
n8 
120 

in 
114 
116 
118 
121 

112 
114 
117 
119 
122 

46 

47 
48 
49 
50 

51 

S2 

53 
54 
55 
56 
57 
58 

59 

60 

113   114 
115   116 
117   118 
120   121 
122   123 

"5 
117 
119 
122 
124 

116 
118 
120 
122 
125 

116 
119 
121 

126 

117 
120 
122 
124 
127 

118 
120 
123 

125 

127 

119 
121 
124 
126 
128 

120 
122 

125 
127 
129 

121 
123 
125 
128 
130 

122  j  122 
124   125 
126   127 
129   130 
131  1  132 

123 
126 
128 

131 

133 

124 
127 
129 

131 
134 

51 

52 
53 
54 
55 

124   125   126  i  127   128  '  129 
126   127   128   129   130   131 
129   130   131  1  131  i  132  i  133 
131    132  1  133   134  1  135  1  136 
^33       134   135   136   137   138 

130 

132 
134 
137 
139 

131 

133 
135 
138 
140 

132 

136 

139 
141 

133 

135 

137 
140 

142 

133   134 
136   137 
138  i  139 
141   142 

143  1  144 

135 
138 
140 

143 

145 

136 

139 
141 
144 
146 

56 

57 
58 

59 
60 

Page  298 

TABLE  12 

1 

For  finding 

the  Variation  of  the  Sun's  Ri 

ght  Ascension,  of  the 

Declination,  of  the  Equation 

of  Time,  or  of  the 

Moon's  R 

ight  A 

jcension,  in  an 

y  number  of  minutes  of  time,  the  Horary 

Motion 

being 

given  at  the  top  of 

the  page  i 

n  secoi 

ds,  and  the  number  of  minutes  of  time  in  the  side 

column 

.  Also  for  hnding  th 

e  Variation  1 

of  the  M 

aon's  Dedinat 

ion  m 

seconds  of  time,  the  motion 

m  one 

minute  being 

given 

at  the  top,  and  the  | 

numbers 

n  the  side  column  being  taken  for  seconds. 

1 

Horary  motion. 

M. 

M. 
I 

147// 

148^^ 

149'^ 

150^^ 

151^^ 

152^' 

153'^ 

154^^ 

155^^ 

156^^ 

157'^ 

158'^ 

159'^ 

160^' 

I 

2 

2 

2 

3 

'  3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

2 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

2 

3 

7 

7 

7 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

3 

4 

10 

ID 

ID 

10 

10 

10 

10 

10 

10 

10 

10 

II 

II 

II 

4 

5 

12 

12 

12 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

5 

6 

15 

15 

15 

15 

15 

15 

15 

15 

16 

16 

16 

16 

16 

16 

6 

7 

17 

17 

17 

18 

18 

18 

18 

18 

18 

18 

18 

18 

19 

19 

7 

8 

20 

20 

20 

20 

20 

20 

20 

21 

21 

21 

21 

21 

21 

21 

8 

9 

22 

22 

22 

23 

23 

23 

23 

23 

23 

23 

24 

24 

24 

24 

9 

10 

25 

25 

25 

25 

25 

25 

26 

26 

26 

26 

26 

26 

27 

27 

10 

II 

.  27 

27 

27 

28 

28 

28 

28 

28 

28 

29 

29 

29 

29 

29 

n 

12 

29 

30 

30 

30 

30 

30 

31 

31 

31 

31 

31 

32 

32 

32 

12 

13 

32 

32 

32 

33 

33 

33 

33 

33 

34 

34 

34 

34 

34 

35 

13 

14 

34 

35 

35 

35 

35 

35 

3^ 

36 

36 

36 

37 

37 

37 

37 

14 

15 
i6 

37 
39 

37 

37 

38 

38 

38 

38 

39 

39 

39 

39 

40 

40 

40 

15 

39 

40 

40 

40 

41 

41 

41 

41 

42 

42 

42 

42 

43 

16 

17 

42 

42 

42 

43 

43 

43 

43 

44 

44 

44 

44 

45 

45 

45 

17 

i8 

44 

44 

45 

45 

45 

46 

46 

46 

47 

47 

47 

47 

48 

48 

18 

19 

47 

47 

47 

48 

48 

48 

48 

49. 

49 

49 

50 

50 

50 

51 

19 

20 

49 

4^ 

50 

50 

50 

51 

53 

51 

51 

52 

52 

52 

53 

53 

53 

20 

21 

51 

52 

52 

53 

53 

54 

54 

54 

55 

55 

55 

^t 

56 

21 

22 

54 

54 

55 

55 

55 

56 

56 

56 

57 

57 

58 

58 

58 

59 

22 

23 

56 

57 

57 

58 

58 

58 

59 

59 

59 

60 

60 

61 

61 

61 

23 

24 

59 

59 

60 

60 

60 

61 

61 

62 

62 

62 

63 

63 

64 

64 

24 

25 

61 

62 

62 

63 

63 

63 

64 

64 

65 

65 

65 

66 

66 

67 

25 
26 

26 

64 

64 

65 

65 

65 

66 

66 

67 

67 

68 

68 

68 

69 

69 

27    66 

67 

67 

68 

68 

68 

69 

69 

70 

70 

71 

71 

72 

72 

27 

28    69 

69 

70 

70 

70 

71 

71 

72 

72 

73 

73 

74 

74 

75 

28 

29    71 

72 

72 

73 

73 

73 

74 

74 

75 

75 

76 

7b 

P 

77 

29 

30    74 

74 

75 

77 

75 
78 

76 

76 

77 

77 

78 
80 

78 
81 

79 

79 
82 

80 

80 

30 

31    76 

76 

78 

79 

79 

80 

81 

82 

^3 

31 

32 

78 

79 

79 

80 

81 

81 

82 

82 

83 

83 

84 

84 

85 

85 

32 

33 

81 

81 

82 

83 

8s 

84 

84 

85 

85 

86 

86 

87 

87 

88 

33 

34 

83 

84 

84 

85 

86 

86 

87 

87 

88 

88 

89 

90 

90 

91 

34 

35 

86 

86 

87 

88 

88 

89 

89 

90 

90 

91 

92 

92 

93 

93 

35 

36 

88 

89 

89 

90 

91 

91 

92 

92 

93 

94 

94 

95 

95 

96 

36 

37 

91 

91 

92 

93 

93 

94 

94 

95 

96 

96 

97 

97 

98 

99 

H 

38 

93 

94 

94 

95 

96 

96 

97 

98 

98 

99 

99 

100 

lOI 

lOI 

38 

39 

96 

96 

97 

98 

98 

99 

99 

100 

lOI 

lOI 

102 

103 

103 

104 

39 

40 

98 

99 

99 

100 

101 

lOI 

102 

103 

103 

104 

105 

105 

106 

107 

40 

41 

100 

lOI 

102 

103 

103 

104 

105 

105 

106 

107 

107 

108 

109 

109 

41 

42 

103 

104 

104 

105 

106 

106 

107 

108 

109 

109 

no 

III 

III 

112 

42 

43 

105 

106 

107 

108 

108 

109 

no 

no 

III 

112 

"3 

"3 

114 

"5 

43 

44 

108 

109 

109 

no 

III 

III 

112 

113 

114 

114 

"5 

116 

117 

117 

44 

45 
46 

no 

III 

112 
~"4^ 

113 

113 

114 

"5 

116 

116 

117 

118 

119 

119 

120 

45 

"3 

"3 

115 

116 

117 

117 

118 

119 

120 

120 

121 

122 

123 

46 

47 

115 

116 

117 

118 

118 

119 

120 

121 

121 

122 

123 

124 

125 

125 

47 

48 

118 

118 

119 

120 

121 

122 

122 

123 

124 

125 

126 

126 

127 

128 

48 

49 

120 

121 

122 

123 

123 

124 

125 

126 

127 

127 

128 

129 

130 

131 

49 

50 

123 

123 

124 

125 

126 

127 

128 

128 

129 

130 

131 

132 
134 

133 
135 

133 
136 

50 
51 

51 

125 

126 

127 

128 

128 

129 

130 

131 

132 

133 

133 

52 

127 

128 

129 

130 

131 

132 

133 

133 

134 

'35 

13b 

137 

138 

139 

52 

53 

130 

131 

132 

133 

133 

134 

135 

136 

137 

138 

139 

140 

140 

141 

53 

54 

132 

133 

134 

135 

136 

137 

138 

139 

140 

140 

141 

142 

i43 

144 

54 

55 

135 

136 

137 

138 

138 

139 

140 

141 

142 

143 

144 

145 

146 

147 

55 

56 

137 

138 

139 

140 

141 

142 

143 

144 

145 

146 

147 

147 

148 

149 

56 

57 

140 

141 

142 

143 

143 

144 

145 

146 

147 

148 

149 

150 

151 

152 

57 

5« 

142 

143 

144 

145 

146 

147 

148 

149 

150 

151 

152 

153 

154 

155 

58 

59 

145 

146 

147 

148 

148 

149 

150 

151 

152 

153 

154 

1^5 

15b 

157 

59 

60 

147 

148 

149 

150 

151 

152 

153 

154 

155 

156 

157 

158 

159 

160 

60 

TABLE 

13- 

Page  299 

V 

For  finding  the  Sun's  Right  .Vscension 

for  any  given  number  of  hours. 

Horary  va- 
riation. 

Number  of  hours. 

si 

X 

1 

2 

3 

4 

5 

6 

1 

8 

9 

10 

11 

12 

s. 

1/ 

/.■ 

// 

II 

// 

II 

II 

II 

II 

II 

// 

II 

s. 

8.  50 

8.S 

17- 0  '  25.5  1  34.0 

42.5 

SI.O 

59-5 

68.0 

76.5 

85.0 

93-5 

102.0 

8.50 

'^-  55 

8.6 

17.  I 

25-  7     34-  2 

42.8 

51-3 

59-9 

68.4 

77.0 

85-5 

94-  I 

102.  6 

8.55 

<S.  60 

S.  6 

17.2 

25-8  ;  34-4 

43- 0 

51.  b 

60.  2 

68.8 

77.4 

86.0 

94.6 

103.2 

8.60 

S.65 

8.7 

17-3 

26.  0     34.  6 

43-3 

51-9 

60.6 

69.2 

77-9 

86.5 

95-2 

103.8 

8.65 

S.  70 

:s.  75 

8.7 

■  S.  8" 

17.4     26.1  j  34.8 
17-5     26.3  !  35.0 

43-5 
43-8" 

52.2 
52-5 

60.  9 
"6T.3 

69.6 
70.0 

78.3 

87.0 
87.5 

95-7 
96-3 

104.4 
105.0 

8.  70 

78.8 

8.75 

8.  So 

8.8 

17.6     26.4     35.2 

44.0 

,52.8 

61.6 

70.4 

79.2 

88.0 

96.8 

105.6 

8.  So 

8.  85 

8.9 

17-7 

26.6 :  35.4 

44-3 

53-1 

62.0 

70.8 

79-7 

88.5 

97-4 

106.2 

8.85 

8.  qo 

8.9 

17.8 

26.7 

35-6 

44-.'; 

53-4 

62.  3 

71.2 

80.  I 

89.0 

97-9 

106.8 

8.90 

_    ^-95 
q.  00 

9.0 

9.0 

17.9 
18.0 

26.9 
27. 0 

35-8 
•36.0 

44.8 
45- 0 

53-7 

62.  7 

63.  0 

71.6 
72.  0 

80.6 
81.0 

89.  5 

98.5 
99.0 

107.4 
108.  0 

8.95 

54- 0 

90.0 

9.00 

9.05 

9.1 

18.  I 

27. 2 

36.2 

45-3 

54-3 

63-4 

72.4 

81.5 

90-5 

99-6 

108.6 

9-05 

Q.  10 

9.  I 

18.2 

27-3 

36-4 

45-5 

54-6 

63-7 

72.8 

81.9 

91.  0 

100.  I 

109.  2 

9.  10 

9-  15 

9.2 

IS.  3 

27-5 

36.6 

45-8 

54-9 

64.  I 

73-2 

82.4 

91-5 

100.  7 

109.  8 

9-15 

9.  20 

9.2 

18.4 

27.6 
"27.8 

36.8 

46.  0 

55-2 

64.4 

73.6 

82.8 
8.3-3 

92.0 
92.5 

101.2 
101.8 

110.4 
in.  0 

9.20 

9-25 

9-3 

18.5 

37- 0 

46-3 

55-5 

64.8 

74.0 

9-25 

9-3° 

9-3 

18.6 

27.9 

37-2 

46.5 

55-8 

65.1 

74-4 

8,3-7 

93-0 

102.3 

in.  6 

9-30 

9-35 

9.4 

IS.  7 

28.1 

37-4 

46.8 

56-1 

65-5 

74.8 

84.2 

93-5 

102.  9 

112.  2 

9-35 

9.40 

9.4 

18.8 

28.2 

.37-6 

47.0 

56.4 

65.8 

75-2 

84.6 

94-0 

103.4 

112.8 

9.40 

9-45 
9-50 

9-5 
9-5 

18.9 

28.4 

37-8 

47-3 

56.7 
57- 0 

66.2 
66.5 

75:_6 
76.0 

85.1 
85.S 

94-5 
95-0 

104.0 

"3-4 
114.0 

9-45 
9-50 

19.0 

28.5 

38.0 

47-.'; 

104.5 

9-55 

9.6 

19. 1 

28.7 

38.2 

47.8 

57-3 

66.9 

76.4 

86.0 

95-5 

105.  I 

114.6 

9-55 

9.  60 

9.6 

19.2 

28.8 

38.4 

48.0 

57.6 

67.2 

76.8 

86.4 

96.0 

105.  6 

115.  2 

9.60 

9-65 

9-7 

19-3 

29.0 

38.6 

48.3 

57.9     67.6 

77.2 

86.9 

96.5 

106.  2 

"5-8 

9-65 

9.70 

9-7 

19.4 

29.  I 

38-8 

48.5 

58.  2     67. 9 

77.6 
78.0 

87-3 
87.8 

97-0 

106.  7 

116.  4 

117.  0 

9.70 
9-75 

9-75 

9.8 

19-5 

29- 3 

39- 0 

48.8 

58.  5 

68.3 

97-5 

107.3 

9.  80 

9.8 

19.6 

29.4 

39-2 

49.0 

58.8 

68.6 

78. 4 

88.2 

98.0 

107.8 

117.6 

9.  So 

9-85 

9.9 

19.7 

29.6 

39-4 

49-3 

59-1 

69.0 

78.8 

88.7 

98.5 

108.  4 

118.  2 

9.85 

9.90 

9.9 

19.8 

29.7 

39-6 

49-5 

59-4 

69-3 

79.2 

89.1 

99.0 

108.  9 

118.8 

9.90 

9-95 
10.  00 

10.  0 
10.  0 

19.9 

29.  9     39.  8 

49.8 

59-7 

69.7 

79.6 
80.0 

89.6 

99-5 

109.5 

'19-4 
120.0 

9.95 

20.  0 

30.  0     40.  0 

50.  0 

60.  0 

70.0 

90.  0 

100. 0 

no.  0 

10.  00 

10.  05 

10.  I 

20.  I 

30.2 

40.  2 

50-  3 

60.3 

70.4 

80.4 

90.5 

100.  5 

no.  6 

120.  6 

10.  05 

10.  10 

10.  I 

20.  2 

30.3 

40.4 

50-5 

60.6 

70.7 

80.8 

90.9 

lOI.O 

III.  I 

121.  2 

10.  10 

If).  15 

10.  2 

20.3 

30-5 

40.  6 

50.8 

60.  9     71.  I 

81.2 

91.4 

loi.  5 

III. 7 

121. 8 

10.  15 

10.  20 

10.  2 

20.4 

30.6 

40.  8 

Si.o 

61.2 

71.4 

81.6 

91.8 

102.0 

112.  2 
112.8 

122.4 

10.  20 
10.  25 

10.  25 

10.3 

20.5 

30.8 

41.  0 

51-3 

61.5 

71.8 

82.0 

92.3 

102.5 

123.0 

10.30 

10.3 

20.6 

30-9 

41.2 

SI- 5 

61.8 

72.1 

82.4 

92.7 

103.0 

"3-3 

123.6 

10.30 

10.  35 

10.4 

20.  7 

31- I 

41.4 

51.8 

62.  I      72.  5 

82.8 

93-2 

103.5 

"3-9 

124.2 

10.35 

10.40 

10.4 

20.8 

31.2 

41.  6 

52.0 

62.  4     72.  8 

83.2 

93.6 

104. 0 

"4-4 

124.8 

10.  40 

10.45 

10.5 

20.  9 

31-4 

41.8 

52.3 

62.  7  i  73.  2 

83.6 
"84.0 

94.1 
94-5 

104.5 

115. 0 
"5-5 

125.4 
126.  0 

10.45 
10.  50 

10.  50 

10.5 

21.  0 

31-5 

42.  0 

52.5 

63-  0     73-  5 

105.0 

10.55 

10.6  . 

21.  I 

31-7 

42.2 

52.8 

63-3     73-9 

84.4 

95- 0 

105-5 

116. 1 

126.6 

10.55 

10.  60 

10.6 

21.  2 

31.8 

42.4 

53-  0 

63.6     74.2 

84.8 

95-4 

106.  0 

116.  6 

127.  2 

10.  60 

10.  65 

10.7 

21.3 

32.0 

42.  6 

53-  3 

63.9     74.6 

85.2 

95-9 

106.  5 

117.  2 

127.8 

10.  65 

10.  70 

10.7 

21.4 

32.1 

42.8 

53-5 

64.  2     74. 9 

85.6 

96.3 

107.0 

"7-7 
1 18.  3 

128.4 

10.  70 

10.75 

10.8 

21-5 

32-3 

43- 0 

5.3.8 

64-5 

75-3 

86.0 

96.8 

107.5 

129.0 

10.75 

10.80 

10.8 

21.6 

32-4 

43.2 

54- 0 

64.8 

75-6 

86.4 

97.2 

108.0 

118.  8 

129.6 

10.80 

1 0.  85 

10.9 

21.7 

32.6 

43-4 

54-3 

65. 1 

76.0 

86.8 

97-7 

108.5 

119.4 

130.  2 

10.85 

10.  90 

10.9 

21.8 

32.7 

43-6 

.54-5 

65-  4  '  76-3 

87.2 

98.1 

109.0 

119.9 

130.8 

10.  90 

10.95 

II. 0 

21.9 

32.9 

43-8 

54-8 

65.  7     76.  7 

87.6 

98.6 
99.0 

109.5 
no.  0 

120.  5 
121. 0 

131-4 
132.0 

10.95 

II.  00 

II. 0 

22.0 

33- 0 

44.0 

55.0  !  66.  0     77.0 

88.0 

n.  00 

II.  05 

II. I 

22. 1 

33-2 

44.2 

55-3     66.3  ;  77.4 

88.4 

99-5 

no.  5 

121. 6 

132.6 

II.  05 

II.  10 

II.  I 

22.  2 

33-3 

44.4 

55-5     66.6 

77-7 

88.8 

99.9 

III.O 

122.  I 

133-2 

II.  10 

II. 15 

II.  2 

22.3 

33-  5 

44.6 

55.8  1  66.9 

78.1 

89.2 

100.4 

III. 5 

122.  7 

133-8 

II. 15 

II.  20 

11.  2 

22.4 

33- b 

44-8 

56. 0     67.  2 
56-3     67.5. 

78.4 

89.6 

100.8 

lOI.  3 

112.0 

123.2 

134-4 

11.  20 
11.25 

u.  25 

"•3 

22.  5 

33-8 

45.0 

78.8 

90.0 

112.  5 

123.8 

135-0 

11.30 

"•3 

22.6 

33-9 

45-2 

56.  5     67.  8  j  79.  I 

90.4 

loi.  7 

113. 0 

124.3 

135- b 

11.  30 

"•35 

II. 4 

22.7 

34-1 

45-4 

56.  8     68.  I      79.  5 

90.8 

102.  2 

113- 5 

124.9 

136.2 

".35 

1 1. 40 

II. 4 

22.8 

34-2 

45.6 

57.0     68.4     79.8 

91.  2 

102.6 

114. 0 

125.4 

136.8 

n.40 

11.45 

II-5 

22.  9 

34-  4  1  45-  8 

57.3  1  68.  7  ,  80.2 

91.6 

103.  I 

1 14.  5 

126.  0 

137-4 

"•45 

Page  300]                                                  TABLE  13. 

For  finding  the  Sun's  Right  Ascension  for  any  given  number  of  hours. 

Number  of  hours. 

13 

14 

15 

16 

n 

18 

19 

20 

21 

22 

23 

24 

s. 

8.50 

8.55 

8.60 
8.65 
8.70 

no.  5 

111.  2 
III. 8 

112.  5 

113.  I 

119. 0 
119.  7 
120.4 

121. 1 
121. 8 

11 

127-5 
128.3 
129.0 
129.8 
130-5 

136.0 
136.8 
137-6 
138.4 
139.2 

144.5 
145-4 
146. 2 

147-1 
147-9 

II 

153-0 

153-9 
154.8 

155-7 
156.6 

II 

161.  5 

162.  5 

163.4 
164.4 

165.3 

II 

170.0 
171. 0 
172. 0 
173.0 
174.0 

II 

178.5 
179-6 
180.6 
181.  7 
182.7 

II 

187.0 
188. 1 
189.2 

190.3 
191-4 

II 

195-5 
196.7 

197.8 
199-0 
200. 1 

II 

204.0 
205.  2 
206.4 
207.6 
208.8 

s. 

8.50 

8.55 

8.60 
8.65 
8.70 

8.75 

8.80 
8.85 
8.90 

8.95 

113.8 

1 14.  4 

115.  I 

II5-7 
116. 4 

122.  5 

123.  2 
123.9 

124.  6 

125-3 

131-3 
132.0 

132.8 

133-5 
134-3 

140.0 

140.  8 

141.  6 
142.4 
143-2 

148.8 
149.6 
150.5 
151.3 
152.2 

157-5 
158-4 

159-3 
160. 2 
161. 1 

166.3 
167.2 
168.2 
169. 1 
170. 1 

175-0 
176.0 
177-0 
178.0 
179-0 

183.8 
184.8 

185.9 
186.9 
188.0 

192.5 
193-6 
194-7 
195-8 
196.9 

201.  3 
202.4 
203.6 
204.7 
205.9 

210.0 
211.  2 
212.4 
213.6 
214.8 

8.75 

8.80 
8.85 
8.90 

8.95 

9.00 

9-05 

9. 10 

9-15 
9.  20 

117. 0 

117.  7 

1 18.  3 
119. 0 

119.  6 

126.0 
126.  7 
127.4 
128.  I 
128.8 

135-0 

135-8 

136-5 

137-3 
138.0 

144.0 
144.8 

145-6 
146.4 
J47-2 

153-0 
153-9 
154-7 
155-6 
156.4 

162.0 
162. 9 
163-8 

164-7 
165.6 

171.0 
172.0 
172-9 
173-9 
174.8 

180.0 
181.0 
182.0 
183.0 
184.0 

189.0 
190. 1 
191. 1 
192.  2 
193.2 

198.0 

199.1 
200.2 
201.3 
202.4 

207.0 
208.2 

209.3 
210.  5 

211. 6 

216.0 
217.2 
218.4 
219.  6 
220.8 

9.00 

9-05 

9. 10 

9-15 

9.20 

9-25 
9.30 

9.35 
9.40 

9.45 

120.3 
120.  9 
121. 6 
122.  2 
122.9 

129.5 
130.  2 
130.9 
131. 6 

132^  3 

138.8 

139.5 
140.3 

141. 0 

141.  8 

148.0 
148.8 
149.6 
150.4 
151. 2 

157.3 
158.1 
159.0 
159.8 
160.7 

166.5 
167.4 
168.3 
169. 2 
170. 1 

175-8 
176.7 

177-7 
178.6 

179-6 

185.0 
186.0 
187.0 
188.0 
189.0 

194.3 

195-3 
196.4 

197.4 

198-5 

203-5 
204.6 
205.7 
206.8 
207.9 

212.8 
213.9 

215.  I 

216.  2 
217.4 

222.0 
223.2 
224.4 
225.6 
226.8 

9-25 
9-30 

9-35 
9.40 

9-45 

9-50 

9-55 
9.60 

9.65 

9.70 

123.5 

124.2 
124.8 

125.5 
126.  I 

i33^o 

133^7 
134^4 
135- I 
135-8 

142.5 

143.3 
144.0 

144.8 
145-5 

152.0 
152.8 
153-6 
154.4 
155-2 

161.5 
162.4 
163.2 
164. 1 
164.9 

171. 0 

171-9 
172.8 

173-7 
174.6 

180.5 
181.5 
182.4 
183.4 

184.3 

190.0 
191. 0 
192.0 
193.0 
194.0 

199-5 
200.  6 

20I.6 

202.  7 
203.7 

209.0 
210.  I 
211. 2 
212.3 
213.4 

218.5 

219-7 
220.8 

222.0 

223.  I 

228.0 
229.  2 
230.4 
231.6 
232.8 

9-50 

9.55 
9.60 

9-65 
9-  70 

9.75 
9.80 
9.85 
9.90 
9.95 

126.8 
127.4 
128.  I 
128.7 
129.4 

136.  5     146.  3 
137.2  !  147.0 

137.9  '  147.8 
138.6!  148.5 

139^3     149-3 

156.0 
156.8 
157.6 
158.4 
159.2 

165.8 
166.6 

167.5 
168.3 
169. 2 

175-5 
176.4 

177-3 
178.2 

179-1 

185.3 
186.3 

187.2 

188.  I 

189. 1 

195.0 
196.0 
197.0 
198.0 
199.0 

204.8 
205.8 
206.9 
207.9 
209.0 

214-5 
215.6 
216.  7 
217.8 
218.9 

224.3 
225.4 

226.  6 

227.  7 
228.9 

234-0 
235.2 
236.4 
237.6 
238.8 

9.75 
9.  bo 

9-85 
9.90 

9-95 

10.00 
10.  05 
10.  10 
10.  15 
10.20 

130.0 
130.7 

131.3 
132.0 
132.6 

140.0     150.0 
140.  7  '  150.  8 

141. 4     151-5 
142.  I      152.3 
142.8  ,   153.0 

160.0 
160.8 
161. 6 
162.4 
163.2 

170.0 
170.9 

171-7 
172.6 

173-4 

180.0 
180.9 
181. 8 
182.7 
183-6 

190.0 
191.  0 
191.9 
192.9 
193.8 

200.0 
201.0 
202.0 
203.0 
204.0 

210.0 
211. 1 
212. 1 
213.  2 
214.2 

220.0 

221.  I 

222.  2 
223.3 
224.4 

230.0 

231.2 

232.3 

233-5 
234.6 

240.0 
241.  2 
242.4 
243.6 
244.8 

10.00 
10.  05 
10.  10 
10.15 
10.  20 

10.25 

10.30 

10.35 

10.40 

10.45 

133.3 
133-9 
134.6 

135-2 
135^9 

143-5     153-8 

144.2  154.5 

144.9     155-3 
145.6     156.0 

146.3  156.8 

164.0 

164.8 
165.6 
166.4 
167.  2 

174-3 

175-1 
176.0 

176.8 

177-7 

184.5 

185-4 
186.3 
187.2 
188.  I 

194.8 
195-7 
196-7 
197.6 
198.6 

205.0 
206.0 
207.0 
208.0 
209.0 

215-3 
216.3 
217.4 
218.4 
219-5 

226.  6 
227.7 
228.8 
229.9 

235-8 

236.9 
238. 1 
239.2 
240.4 

246.0 

247-2 
248.4 
249.6 
250.8 

10.  25 

10.30 

10.35 
10. 40 

10.45 

10.  50 

10.55 
10. 60 

10.  65 

10.  70 

136.5 
137-2 
137-8 
138-5 
139-1 

147.01   157.5 
147-7'   158.3 

148.4    !     159.0 
149.   I         159.8 
149.8        160.5 

168.0 
168.8 
169.  6 
170.4 
171.  2 

178.5 
179.4 
180.2 
181. 1 
181. 9 

189.0 
189.9 
190.  8 

191-7 
192.6 

199- 5 
200.  5 
201.4 
202.4 

203.3 

210.0 
211. 0 
212.0 
213.0 
214.0 

220.5 
221.6 
222.6 
223.7 
224.7 

231.0 
232.  I 
233-2 

234-3 
235-4 

241-5 
242.7 
243.8 
245.0 
246.  1 

252.0 
253-2 

254.4 

255-6 
256.8 

10.  50 

10.55 
10.  60 
10.  65 
10.  70 
10.75 
10.80 
10.85 
10.90 
10.95 

ic'.75 
10.  80 

10.85 

10.  90 

10.95 

139.8 
140.4 
141.  I 
141.  7 
142.4 

150.5  161.  3        172.0 
151.  2       162.0       172.8 

151.  9  '   162.  8  i   173.6 

152.6  163.5     174.4 

153-3     164.3     175-2 

182.8 
183.6 
184.5 
185.3 
186.2 

193-5 
194.4 

195-3 
196.  2 

197-1 

204.3 
205.2 
206.2 
207. 1 
208.1 

215.0 
216.0 
217.0 
218.0 
219.0 

225.8 
226.8 
227.9 
228.  9 
230.0 

236-5 
237.6 

238.7 
239.8 

240.9 

247-3 
248.4 

249.6 

250.7 
251.9 

258.0 
259.2 
260.4 
261.6 
262.8 

11.00 
11.05 
II.  10 
II. 15 
11.20 

143.0     154. 0(  165.0     176.0 
143  7'   154-7'  165.8     176.8 

144.3    155.4    166.5 !  177-6 
145. 0    156. 1    167. 3    178.4 

145. 6     156. 8     168.0     179.2 

187.0 
187.9 
188.7 
189.6 
190.4 

198.0 
198.9 
199.8 

200.  7 

201.  6 

209.0 
210.0 
210.  9 
211. 9 
212.8 

220.0 
221.0 
222.0 
223.0 
224.0 

231.0 
232. 1 

233-1 
234.2 
235.2 

242.0 
243.1 
244.2 

245-3 
246.4 

247-5 
248.6 

249.7 

-250.  8 

251-9 

253-0 
254-2 
255-3 

2qf .  . 

257-6 

264. 0 
265.2 
266.4 
267.6 
268.8 

11. 00 
11.05 
II.  10 
11.15 
II.  20 

11.  25 
11.30 

"•35 
11.40 

"•45 

146.  3     157.  5     168.8  1  180.  0 

146.  9     158.  2     169.  5  1  180.  8 

147.  6  ;  158.9     170.  3     181.  6 

148.  2  1  159.  6     171.  0     182.4 
148.91  160.31  1 71 -8     183.2 

191. 3  202.5 
192. 1 1 203.4 

193.  O!    204.3 
193.8       205.  2 

194.  7       206.  I 

213.8 
214.7 

215-7 
216.6 
217.6 

225.0 
226. 0 
227. 0 
228.0 
229.0 

236-3 
237-3 
238.4 

239-4 
240.5 

258.8 

259-9 
261.  I 
262.2 
263.4 

270.0 
271.2 
272.4 
273.6 
274.8 

11.25 
11.30 

"•35 
11.40 

11.45 

TABLES  14,  15,  16. 

Page  301 

TABLE  14. 

TABLE  15. 

Dip  of  the  Sea 

Dip  of  the  Sea  at  different  Distances  from  the  Observer. 

Horizon. 

T3 

a 

1-)  (U 

p 

Height  of  the  Eye  above  the  Sea  in  Feet. 

Height 
of  the 
Eye. 

Dip  of  the 
Horizon. 

.  5 

10 

15 

20 

25 

30 

35 

40 

Dip. 

Dip. 

Dip. 

Dip. 

Dip. 

Dip. 

Dip. 

Dip. 

Feet. 

/     // 

M. 

M. 

M. 

M. 

M. 

M. 

M. 

M. 

I 

0  59 

1  23 

2 

X 

II 

23 

34 

45 

57 

68 

79 

91 

3 

I  42 
I  58 

% 

6       1       12 

17 

23 

28 

34 

40 

45 

4 

% 

4 

8 

12 

IS 

19 

23 

27 

30 

5 
6 

7 
8 

2  II 

2  24 
2  36 
2  46 

2  56 

3  06 
3  15 
3  24 

I 

3 

6 

9 

12 

IS 

17 

20 

23 

IX 

3 

5 

7 

10 

12 

14 

16 

19 

I>^ 

3 

4 

6 

8 

10 

12 

14 

16 

9 
10 
II 

2 

2 

4 

5 

7 

8 

9 

II 

12 

^%. 

2 

3 

4 

6 

7 

8 

9 

10 

3  , 

2 

3 

4 

5 

6 

7 

8 

9 

12 

3>^ 

2 

3 

4 

5 

6 

6 

7 

8 

13 
14 
15 

3  32 
3  40 
3  48 

4 
5 

2 

2 

3 

4 

4 

5 
4 

5 
S 

6 
6 

7 
6 

7 
7 

3 

6 

2 

3 

4 

4 

5 

s 

6 

6 

16 
17 

3  55 

4  02 

Note  to  Table  15. — The  numbers  of  this  Table  below  the  black  line? 

are  the 

18 

4  09 

same  as  are  given  in  Table  14,  the  visible  horizon,  corresponding  to  those 

heights, 

19 
20 
21 

4  16 
4  23 
4  29 

not  being  so  far  distant  as  the  land. 

22 

4  36 

TABLE  16. 

23 

4  42 

The  Sun's  Parallax  in 

24 

4  48 

Altitude. 

25 
26 

27 

4  54 

5  00 
5  06 

Sun's  Alt. 

Sun's  Paral- 
lax. 

28 
29 
30 

5  " 

5  17 
5  22 

D. 

S. 

35         5  48 

0 

9 

40         6  12 

ID 

9 

45         6  36 

20 

8 

50         6  56 

30 

8 

55         7  16 

40 

7 

60         7  35 

50 

6 

65          7  54 

55 

5 

7" 

8    12 

60 

4 

75 

8  29 

65 

4 

80 

8  46 

70 

3 

85 

9  02 

•75 

2 

90 

9  18 

80 

2 

95 

9  33 

85 

I 

100 

9  48 

90 

0 

Page  302]                                                TABLE  17. 

Parallax  in  Altitude  of  a  Planet. 

•a  nv 

0    0    0    0    10  0    rOvO    ON  N    u-iOO    11    Tft--.  0    N    rfvO  00    O    M    ■^^  CC    O 
i-i    N    fOCO^'^'^^^^lJ^  tnvO  vO  VO    t^  t^  t^  t^  t^CO  CO  00  00  00    On 

« 

0 

a 
— 

V-l 

0 

X 

a 

c 

0 

N 

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0 

X 

V 

V 

in  u->  ro  O   OS  t^vO   -^roM   O   Ovt^uT+N   "   OOO   t~»vO  ir^Tj-  c)   «   o 
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MNNNnNNi-">-<>-<"i-i>-i>-i-ii-i 

r^  t^  ii-1  m  N   w  O   OnOO  r^  "^  ■^  ro  N  '-   OnOO  J^  t^vo  iri  tJ-  ro  N  "-i  O 

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^  VO   -^  ro  >-<   O   OsOO   t^'O  tn  r)-  ro  11   O   O\0<0   f^vO  in  i/^  tI"  ro  N   i-<   O 
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NNNMt^i-i>-i>-<"i-iwi-i'-i»-i 

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ro  CO  N   O   OsOO   t^vo  vr>  Tj-  ro  N   •-   O   OM>0  »^vO  vOmTj-roNNiiO 
NNNN>-iwi-H'-ii-i««i-.«i-i 

V 
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N   N   w   OsOO  t^^  vo  ■<1-  -"d-  ro  N   m   O   OnOO  t^\0  mmrJ-rON  N   m   O 
NNNi-Hi-ii-ii-ii-<«i-(i-ii-i«-i-i 

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1—1 
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2 

On  OnOO  vOvOmTj-roN   N   "   O   OnOO   r-»^0  vO   mm'^trorON   i-i   i-   O 

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GC 

00  00   •-'•vO  m-+rorON   w  O   O   OsOO  *^vo  ^O  m'i-TfrDrOM   "-«  '-'   O 

K  t^vo   mThrONNMOO   OsOO  t^  t~.>0  miOTf'^rON   N   m   -i   O 

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vOvOmTj-roN   N   "-I   O   O   ONOO  00  t>«\0  mu-)ThT}-r'5r'iN   N   ii   i-   O 

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lOinrhrONi-ii-iOOON  OnOO   t^  t^vO   lOLrl■^^fOco^^   M   »-•   <-*   O 

T)-'*r«lNi-ii-iOOON  CT\00  t^  I^vO  u-iirT<t'*fOrON   M   w   —   O   O 

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h-  i-c  O   O   OnOO  00  00  t^  t^vo  vO  mmt'^rororON  N   N  i-i   "   O   O 

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00 

00  00  00   t^  I^vO  >0\0»movnTfi*-Tj-rOroNNMM>-i-i'-"i-<0    O 

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t^  t^  »^\0  ^omu-)mm'J--^Tl-r<-)rOrONNNN>-i-ii-ii-'000 

0 

V 
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ir)iOiO'^'^Tt-'>!j-fr>rOf<^r<1PONNNMNwi-i>HwwwOOO 

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m 

TABLES  18 

,   19. 

Page  303 

%■ 

TABLE  18. 

TABLE  19. 

Augmentation  of  the  Moon's  Semi-diameter. 

Augmentation  of  the  Moon's  Hor.  Par. 

c  o 

D  's  semi-diameter. 

1 

£i 

0     . 

■«  C 
0  0 

P  's  Hor.  Parallax. 

14^ 

15' 

16' 

\v 

kl 

•  r:  a> 

53' 

57' 

61' 

<^ 

m' 

^" 

30'^ 

0' 

30' 

0' 

J 

0 

// 

// 

II 

o 

II 

II 

II 

// 

II 

// 

o 

0. 1 

0. 1 

0. 1 

0. 1 

0.2 

0.  2 

0 

0.0 

0.0 

0.  0 

2 

0.6 

0.6 

0.7 

0.7 

0.8 

0.8 

2 

0.0 

0.0 

0.0 

4 

I.O                    I.  I 

1.2 

1-3 

1.4 

1-5 

4 

0. 1 

0. 1 

0. 1 

6 

15 

1.6 

1.7 

1.9 

2.0 

2. 1 

6 

0. 1 

0. 1 

0. 1 

8 

2.0 

2. 1 

2.3 
2.8 

2.4 

2.6 

2.7 

8 

0.2 

0.2 

0.2 

lO 

2.4 

2.6 

3-0 

3-? 

3-4 

10 

0-3 

0.3 

0.4 

12 

2.9 

3-5 

3-3 

3-6 

3-8 

4.0 

12 

o.S 

0-5 

0-5 

14 

3-^ 

3.6 

3-9 

4.1 

4.4 

4-7 

14 

0.6 

0.7 

0.7 

i6 

3-8 

4.1 

4.4 

4.7 

5.0 

5-3 

16 

0.8 

0.9 

0.9 

iS 

4-3 

4.6 

4-9 

5-2 

5.6 

5-9 

18 

1.0 

1. 1 

1. 1 

20 

4-7 

5.1 

5-4 

5-8 

6.1 

6.5 

20 

1.2 

1,3 

1.4 

22 

5-2 

5-5 

5-9 

6.  3 

6.7 

7-1 

22 

1-5 

1.6 

1-7 

24 

5-6 

6.0 

6.4 

6.8 

7-3 

7-7 

24 

1.7    1        1.9 

2.0 

26 

6.0 

6.5 

6.9 

7.4 

7.8 

8.3 

26 

2.0            2.2 

2-3 

28 

6.5 

6.9 

7-4 

7-9 

8.4 

8.9 
9-5 

28 

2.3 

2.5 

2.6 

30 

6.9 

7.3 

7.9 

8.4 

8.9 

30 

2.6 

2.8 

3-0 

32 

7-3 

7.8 

8. 3 

8.9 

9.4 

10. 0 

32 

2.9 

3-1 

3-4 

34 

7.7 

8.2 

8.8 

9.4 

10. 0 

10.6 

34 

3-3 

3-5 

3-8 

^^ 

8.1 

8.6 

9.2 

9.8 

10.5 

II.  I 

36 

3-6 

3-9 

4.1 

38 

8.4 

9.0 

9-7 
10. 1 

10.3 

10.9 

II. 6 

38 

4.0            4.3            4.6      1 

40 

8.8 

9.4 

10.  7 

II. 4 

12.  I 

40 

4.3 

4.6 

5-0 

42 

9.2 

9.8 

10.5 

II. 2 

II. 9 

12.6 

42 

4.7 

5-0 

5-4 

44 

9-5 

10.  2 

10.9 

II. 6 

12.3 

13-1 

44 

5-0 

5-4 

5-8 

46 

9.8 

10.5 

II. 3 

12.0     i       12.8 

13.6 

46 

5-4 

5.8 

6.2 

48 

10.  2 

10.9 

II. 6 

12.4    1       13.2 

14.0 

48 

5-8 

6.2 

6.6 

50 

10.  5 

II. 2 

12.0 

12.8 

13.6 

14.4 

50 

6.1 

6.6 

7-1 

52 

10.  8 

"•5 

12.3 

13- I 

14.0 

14.9 

52 

6.5 

7.0 

7-5 

54 

II.  I 

II. 8 

12.7 

13-5 

14.4 

15-3 

54 

6.8 

7.4 

7-9 

56 

II-3 

12. 1 

13.0 

13.8 

14.7 

15.6 

56 

7.2 

7.7 

8.3 

58 

II. 6 

12.4 

13-3 

14. 1 

15- 1 

16.0 

58 

7.5 

8.1 

8.6 

60 

II. 8 

12.7 

^3-5 

14.4 

15-4 

16.3 

60 

7.8 

8.4 

9.0 

62 

12.  I 

12.9 

13.8 

14.7 

15-7 

16.6 

62 

8.1 

8.8 

9.4 

64 

12.3           13.2 

14.  I 

15.0 

16.0 

16.9 

64 

8.4 

9-1 

9-7 

66 

12.5 

13-4 

14-3 

15-2 

16.2 

17.2 

66 

8.7 

9-4 

10. 0 

68 

12.7 

13-6 

14.  5 

15-5 

16.5 

17-5 

68 

9.0 

9-7 

10.3 

70 

12.9 

13.8 

14.7 

15-7 

16.7 

17.7 

70 

9.2 

9-9 

ID.  6 

72 

13.0 

13-9 

14.9 

15-9 

16.9 

17.9 

72 

9-5 

10.2 

10.9 

74 

13- I 

14.  I 

15.0 

16.0 

17. 1 

18. 1 

74 

9-7 

10.4 

II.  I 

76 

13-3 

14.2 

15.2 

16,2 

17.2 

18.3 

76 

9.8 

10.6 

"•3 

78 

13-4 

14-3 

15-3 

16.3 

17.4 

18.4 

18.6' 

78 

lO.O 

10.8 

"•5 

80 

13-5 

14.4 

15-4 

16.4 

17-5 

80 

10.  I 

10.  9 

II. 7 

82 

13-5 

14-5 

15-5 

16.5 

17.6 

18.7 

82 

10.3     1       II. 0           II. 8      1 

84 

13.6    i       14.6 

15-6 

16.6 

17.6 

18.7 

84 

10.3 

II.  I     ,       II. 9      1 

86 

13.6           14.6 

15-6 

16.6 

17-7 

18.8 

86 

10.4 

11,2 

12.0 

88 
90 

13-7 

14.6 

15.6 

16.  7 

17.7 

18.8 

88 

10.4 

II. 2 

12.0 
12.0 

13-7 

14.  6 

15.6 

16.7 

17.7 

18.8 

90 

10.5 

"•3 

Page  304 

TABLE  20. 

Mean  Refraction. 

Barometer  30  inches.    Fahrenheit's  Thermometer  5c 

)». 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 
Altitude. 

Mean  Re- 

Apparent 

Mean  Re- 

Altitude. 

fraction. 

Altitude. 

fraction. 

Altitude. 

fraction. 

fraction. 

Altitude. 

fraction. 

O       ' 

/      '/ 

0     / 

/     // 

0     ' 

/    // 

0      ' 

/     // 

0     ' 

'     II 

9  30 

5  35-1 

15     0 

3  34- 1 

25     0 

2      4.4 

42     0 

I     4.7 

o    o 

36  29.  4 

35 

5  32.4 

10 

3  31-7 

10 

2     3-4 

20 

I     3-9 

I      o 

24  53-  6 

40 

5  29-6 

20 

3  29.4 

20 

2      2.5 

40 

I     3.2 

2       O 

18  25.5 

45 

5  27-0 

30 

3  27-1 

30 

2       1.6 

43     0 

I     2.4 

3    o 

14  25.  I 

50 

5  24.3 

40 

3  24.8 

40 

2      0.  7 

20 

I     1.7 

4    o 

II  44.4 

55 

5  21.7 

50 

3  22.6 

50 

I    59.8 

40 

I     1.0 

5     o 

9  52-0 

10    0 

5  19-2 

16     0 

3  20.5 

26     0 

I    58.9 

44    0 

I    0.3 

5 

9  44.0 

5 

5  16.7 

ID. 

3  18.4 

10 

I    58.1 

20 

0  59.6 

lO 

9  36-  2 

10 

5  H-2 

20 

3  16.3 

20 

I  57-2 

40 

0  58.9 

15 

9  28.6 

15 

5  11-7 

30 

3  14-2 

30 

1  56.4 

45    0 

0  58.2 

20 

9  21.2 

20 

5    9-3 

40 

3  12.2 

40 

I  55-5 

20 

0  57.6 

25 

9  14.  0 

25 

5    6.9 

50 

3  10.3 

50 

I  54-7 

40 

0  56.9 

5  3° 

9     7.0 

10  30 

5    4-6 

17      0 

3     8.3 

27     0 

I  53-9 

46    0 

0  56.2 

35 

9    0.  I 

35 

5    2.3 

10 

3    6.4 

10 

I  53-1 

20 

0  55.6 

40 

8  53-4 

40 

5    0.0 

20 

3    4-6 

20 

I  52-3 

40 

0  55.0 

45 

8  46.8 

45 

4  57.8 

30 

3    2.8 

30 

I  515 

47    0 

0  54-3 

50 

8  40.4 

50 

4  55.6 

40 

3      I.O 

40 

I  50:7 

20 

0  53-7 

55 

8  34.2 

55 

4  53-4 

50 

2  59.2 

50 

I  50.0 

40 

0  53- 1 

6    0 

8  28.0 

II     0 

4  51-2 

18      0 

2  57-5 

28     0 

I  49.2 

48    0 

0  52.5 

5 

8  22.1 

5 

4  49-1 

10 

2  55.8 

20 

I  47-7 

49    0 

0  50.6 

10 

8  16.2 

10 

4  47-0 

20 

2  54-1 

40 

I  46.  2 

50    0 

0  48.9 

15 

8  10.5 

15 

4  44-9 

30 

2  52-4 

29     0 

I  44-8 

51     0 

0  47.2 

20 

8    4.8 

20 

4  42-9 

40 

2  50.8 

20 

I  43-4 

52    0 

0  45.5 

25 
6  30 

7  59-3 

25 

4  40-9 

50 

2  49.2 

40 

I  42.  0 

53    0 

0  43-9 

7  53-9 

II  30 

4  3^-9 

19      0 

2  47-7 

30     0 

I  40.6 

54    0 

0  42.3 

35 

7  48.7 

35 

4  36.9 

10 

2  46.  I 

20 

I  39-3 

55    0 

0  40.  8 

40 

7  43-5 

40 

4  35- 0 

20 

2  44.6 

40 

I  38.0 

56    0 

0  39-3 

45 

7  38.4 

45 

4  33-1 

30 

2  43-1 

31      0 

I  36-7 

57    0 

037.8 

50 

7  33-5 

50 

4  31-2 

40 

2  41.6 

20 

I  35-5 

58    0 

0  36.4 

55 

7    0 

7  28.6 

55 

4  29.4 

50 

2  40.  2 

40 

I  34.2 

59    0 

0  35- 0 

7  23.8 

12    0 

4  27.5 

20      0 

2  38.8 

32      0 

I  33-0 

60    0 

0  33-6 

5 

7  19-2 

5 

4  25-7 

10 

2  37-4 

20 

I  31.8 

61     0 

0  32.3 

10 

7  14-6 

10 

4  23.9 

20 

2  36.  0 

40 

I  30.7 

62    0 

0  31.0 

15 

7  10.  I 

15 

4  22.  2 

30 

2  34.6 

33    0 

I  29.5 

63    0 

0  29.  7 

20 

7    5-7 

20 

4  20.4 

40 

2  33-3 

20 

I  28.4 

64    0 

0  28.4 

25 
7  30 

7     1-4 

25 

4  18.7 

50 

2  32.0 

40 

I  27.3 

65    0 

0  27.  2 

6  57-1 

12  30 

4  17- 0 

21       0 

2  30-7 

34    0 

I  26.  2 

66    0 

0  25,9 

35 

6  53.0 

35 

4  15-3 

10 

2  29.4 

20 

I  25.1 

67    0 

0  24.7 

40 

6  48.9 

40 

4  13-6 

20 

2  28.  I 

40 

I  24.  I 

68    0 

0  23.6 

45 

6  44.9 

45 

4  12.0 

30 

2  26.9 

35    0 

I  23.1 

69    0 

0  22.4 

50 

6  41.  0 

50 

4  10.4 

40 

2  25.7 

20 

I  22.0 

70    0 

0  21.2 

55 

6  37-1 

55 

4    8.8 

50 

2  24.5 

40 

I  21.0 

71     0 

0  20. 1 

8    0 

6  33-3 

13    0 

4     7. 2 

22      0 

2  23.3 

36    0 

I  20.  I 

72    0 

0  18.9 

5 

6  29.  6 

5 

4    5-6 

10 

2  22.  I 

20 

I   19.  I 

73    0 

0  17.  8 

10 

6  25.9 

10 

4    4-  I 

20 

2  20.  9 

40 

I   18.2 

74    0 

0  16.  7 

15 

6  22.3 

15 

4    2. 6 

30 

2  19.8 

37    0 

I   17.2 

75    0 

0  15.6 

20 

6  18.8 

20 

4     1. 0 

40 

2  18.7 

20 

I   16.3 

76    0 

0  14.5 

25 

___6  15.3 
6  II.  9 

25 

3  59-6 

50 

2  17-5 

40 

I  15.4 

77    0 

0  13-5 

8  30 

13  30 

3  58.1 

23    0 

2  16.4 

38    0 

I  14-5 

78    0 

0  12.4 

35 

6    8.5 

35 

3  56.6 

10 

2  15-4 

20 

I  13.6 

79    0 

0  II. 3 

40 

6    5-2 

40 

3  55-2 

20 

2  14.3 

40 

I  12.7 

80    0 

0  10.3 

45 

6    2. 0 

45 

3  53-7 

30 

2  13- 3 

39    0 

I  II. 9 

81     0 

0    9. 2 

50 

5  58.8 

50 

3  52-3 

40 

2  12.2 

20 

I   II. 0 

82    0 

0    8.2 

55 
9    0 

5  55-7 
5  52-6 

•      55 

3  50.9 

50 

2  II. 2 

40 

I  10.  2 

83    0 

0     7.2 

14    0 

3  49-5 

24    0 

2  10.  2 

40    0 

I    9.4 

84    0 

0    6.  I 

5 

5  49-6 

10 

3  46.8 

10 

2    9. 2 

20 

I     8.6 

fl    ° 

0    5-1 

10 

5  46.6 

20 

3  44-2 

20 

2    8.2 

40 

I     7-8 

86    0 

0    4.  I 

15 

5  43-6 

30 

3  41-6 

30 

2     7.2 

41     0 

I     7.0 

87    0 

0    3.1 

20 

5  40-7 

40 

3  39- 0 

40 

2    6. 2 

20 

I     6.2 

88    0 

0    2.0 

25 

5  37-9 

50 

3  36-5 

50 

2    5-3 

40 

I     5-4 

89    0 

0     1.0 

9  30 

5  35-1 

15    0 

3  34-1 

25     0 

2    4.4 

42    0 

I    4.7 

90    0 

0    0.0 

TABLE  21. 

Page  305 

^ 

Correction  of  the  Mean  Refraction  for  the  Height  of  the  Baromete 

r. 

"  Mean  refraction. 

Barom. 

Barom. 

0' 

v 

2' 

V 

4' 

%' 

6' 

V 

8' 

9' 

10^ 

Subtract. 

Acid. 

0" 

1  1 

:tO" 

0" 

11 

30" 

0"    30" 

0" 

// 

30" 

II 

0" 

30" 

0" 



30" 

0" 

30" 

0" 

30" 

0" 

30" 

0"     30" 

0" 

//  1   // 

1    " 

II 

'/ 

II 

/; 

II . 

II 

';            // 

// 

27.  50 

0 

2 

S 

7 

ID      12 

15 

17 

20 

23 

25 

28 

30 

33 

35 

38   I40 

43 

45  1  48 

51 

27-55 

0 

2 

5 

7 

ID 

12 

15 

17 

20 

22 

25 

27 

30 

32 

35 

37  i40 

42 

45  '  47 

50 

27.  60 

0 

2  1  5 

7 

10 

12 

14 

17 

19 

22 

24 

27     29 

31 

34 

36    39 

41 

44     46 

49 

27.65 

0 

2  1  5 

7 

9 

12 

14  i  16 

19 

21 

24 

26  ,28 

31 

33 

36  :  38 

40 

43     45 

48 

27.70 

27-75 

0 
0 

2!  5 
2     4 

7 

7 

9 

11 

14 
13 

lb 

18 

21 

23 

25  !28 

30 

32 

35  :37 
34    36 

39 
39 

42     44 

41"    43 

47 

9!  u 

16 

18 

20 

23  25  27 

29    32 

46 

27.  80 

0 

2     4 

7 

9     " 

13:  15 

18 

20 

22      24      27      29 

31 

33    35 

38 

40     42 

45 

27- S5 

0 

2     4 

6 

9     II 

13'  15 

17 

19 

22      24      26  i    28 

30 

32  135 

37 

39     41 

44 

27.90 

0 

2  1  4 

^ 

8    10 

13 

^5 

17 

19 

21   23   25  !  27 

30 

32    34 

3b 

38     40 

43 

2  7-95 

0 

2 

2 

4 

^ 

8    10 
8     10 

12 
12 

J4^ 
14 

lb 

16" 

18   1  21  ,    23      25  i    27 

29 !  31    2,i 

28   30  :  32 

35 
34 

37     39 
36     38 

42 

28.  00 

0 

4 

6 

18    '  20      22      24 

26 

41 

28.  05 

0 

2  1  4 

b 

8!-  10 

12 

14 

lb 

18      20      22      24 

25 

27   29   31 

?>2, 

35     37 

39 

28.  10 

0 

2      4 

b 

8|    9 

" 

13 

15 

17      19     21    : 23  '   25 

27    29  ;3i     2,2, 

34     36 

38 

28.  15 

0 

'   . .2  1  4 

2  Y 

b 

.  71    9 

II  j    13 

15 

17    ,19 

20    22    24    26    28    30    32 

34     36 

37 

28.  20 

0' 

5 

5 

71-  9 
7      9 

rilj3 

10 1 12 

14 

14 

16  ji8 
16  1 18 

20    22    24    25  i  27  1 29 
19    21     23    25     26    28 

31 
30 

2i     35 
32     34 

36 

28.25 

0 

35 

2S.30 

0 

2    3 

3 

7      8 

10  i  12 

14 

15    17 

19    21 

22    24    26    27 

29 

31      iZ 

34 

28.  35 

0 

2  i  3 

5 

7 

8 

10  12 

13 

15     17 

18    20    22    23    25     27 

28 

30     32 

33 

28.  40 

0 

2!3 

5 

b 

8 

10  II 

13 

14    16    18    19    21    23    24    261  27 

29     31 

32 

28.45 

28.  50 

0 
0 

-^li 

5 

4 

6 

6 

8 

9 i  ji 

^9 '  10 

12     14     16     17    19'  20    22    23    25  I  27 
12^  14    15     17     18    20  i  21     23  '  24    26 

28     30 

31 

27     29 

30 

31-50 

2S.  55 

0 

I      3 

4 

6      7 

9  10 

12     13     15     16     17    19    20    22    23'  25 

26     28 

29 

31-45 

28.  Oo 

0 

I  1  3 

4 

6      7 

8    10 

II     13     14     15     17     18    20    21     23    24 

25     27 

28 

31.40 

28.  65 

0 

•  :  3 

4 

5      7 

8:       9 

II     12     14     15     16     18     19    20    22  i  23 

25     26 

27 

31-35 

28.  70 

"  28.  75" 

0 

0 

^L    3 
I     2 

.__4 

4 

5      6 

8|    9 
7      9 

10  j  12  i  13  i  14    16    17    18    20    21 !  22 

10    II     13    14    15     16    18    19    20    21 

24     25 

23     24 

26 

31-30 

5      6 

25 

31-25 

28.  80 

0 

I      2 

4 

5      6 

7      8 

10    II     12    13    14    16    17    18    19 

21 

22     23 

24 

31.20 

28.85 

0 

I      2 

3 

5      6 

7      8 

9    10    12     13     14     IS     16    17     19 

20 

21      22 

23 

31-  15 

28.90 

0 

I     2 

3 

4,     5 

7,    8 

9    10    II     12     13     14    16    17    18 

19 

20     21 

22 

31.  10 

28.  95 

29.  00 

0 

0 

I     2 
I      2 

1 

3 

4!     5 

4      5 

6'     7 

8j         9     1    II:      12     113         14         15          16         17 

18 

19     20 

21 

20" 

_31-o5 
31.00 

8      9     10     II     12     13 

14     15     16 

17 

18     19 

29.05 

0 

I      2 

3 

4      5 

6 

7 

8      9     10 

II     11     12     13     14    15     16 

17      18 

19 

30-95 

29.  10 

0 

I      2 

4      4 

5      6 

7      8      9     10     II     12     13 

14    15     15 

16      17 

18 

30.90 

29.15 

0 

I      2 

3       4 

5      6 

7      8      9      9     10     II     12     13     14     15 

15       lb 

17 

30-85 

29.  20 
29.  25" 

0 

I     2 

2 

3      4 

3^     4 

5i    6 
4      5 

6 

6 

78      9    10 
7    ^8  ^8      9 

10      II  ;    12       13;    14 

10       II       II       12       13 

15       15 

14      14 

lb 
1.5" 

30.  80 
'30-75  ' 

0 

I      I 

2 

29.30 

0 

I      I 

2 

3      3 

4      5 

6 

6788 

9       10       II       II        12 

13   1    13 

14 

30-  70 

29-35 

0 

I      I 

2 

3      3 

4      5 

s 

6 

7      78      9      9     10     10     II 

12        13 

13 

30-65 

29.40 

0 

I      I 

2 

2      3 

4      4 

5 

5677889     10     10 

II         12 

12 

30.60 

29.45 

0 

I      I 

o-l-i 

2 

_A_3. 
2      2 

3^     4_ 

3'     3 

4 

5  : 

6|    6  1    7 

7  1    8,     8      9 

"7"     7'     8      8 

9 

10        II 

u 

10^ 

30-55 
30.50 

29.  50 

0 

4'     5 

5      6      6 

9 

9      10 

29-  55 

0 

0     I 

2      2 

1              "» 

445556677 

8 

8       9 

9 

30-45 

29.  60 

0 

0     I 

2      2 

2      3 

344455666 

7 

7       8 

8 

30.40 

29.  05 

() 

0     I 

I      2 

2      2 

334445556 

b 

6       7 

7 

30-  35 

29.  70 

29-75 

0 
0 

0     I 
0     0 

I       I 
I       I 

2      2  , 
I       2  : 

2i    3  1    31    3  i   4      4 
2I    2  1    3:     3  '    3      3  ' 

4     5:5 

4      4      4 

4- 

5       6 

5       5 

b 

30-30 

5 

30-25 

29.80 

0 

0     0 

I       I 

I       I 

222      2      2      3 

3      3      3 

3 

4       4 

4 

30.20 

29.85 

0 

0     0 

0 

I       I 

I       I 

I  ■     12      22      2 

222 

3 

3       3 

3 

30-15 

29.  ()0 

0 

0     0 

0 

0      0 

I 

I  ; 

III       1       I       I 

1 ,    2  ;   2 

2 

2       2 

2 

30-  lo 

29.  95 
30.00 

0 
0 

0     0 

0 
0 

0      0 
0  To 

0"  1  30" 

0 

0 

0 

0      I 

^  i    ' 

I  , 

I 

1       I 

I 

I        I 

0       0 

I 

30-05 

0 
30" 

0 

0 

0 

0 

0  j 
30"  1 

0 

0 

0 

0      0 

0 

0 

Q 

30.00 

0" 

30" 

0" 

30" 

0" 

0" 

30" 

0" 

30"  1  0" 

30" 

0" 

30" 

0"     30" 

0" 

! 

Add. 
Barom. 

Haroni. 

( 

)'              1 

l^ 

V 

V 

4^     1     5^           6'     1      V          W     \ 

9' 

10' 

Mean  refraction. 

20    B 


Page  306] 

TABLE 

22. 

Correction  of  the  Mean  Refraction  for  the  Height 

of  the  Thermometer. 

Ther 

M 

ean  refraction.  • 

Ther. 

0' 

V 

%' 

V 

4^ 

-5' 

6^ 

V 

8^ 

9^ 

10' 

Add. 

Add. 

0" 

30" 

0" 

30" 

0" 

30" 

0" 

30" 

0" 

30" 

0"  j  30" 

0" 

30" 

0" 

30" 

0" 

/; 

30" 

0" 

30" 

II 

0" 

o 

// 

// 

// 

II 

II 

II 

/.' 

II 

.'/ 

II 

// 

" 

//     // 

// 

II 

If 

II 

II 

c 

—  lO 

0  4 

8 

12 

16  20   24 

28 

33 

37 

41 

46 

SO  55 

60 

65 

70 

75 

80 

85 

90 

~IO 

—  8 

0  4 

8 

12 

15'  19   23 

27 

31 

3^) 

40 

44 

48  53 

58 

b2 

67 

72 

77 

82 

87 

-  8 

—  6 

0 

4 

7 

II 

15  :  19  22 

2b 

30 

34 

38 

42 

47  51 

55  1  60 

64 

69 

74 

79 

84 

-  6 

—  4 

0 

4 

7 

II 

14  18  '  22 

25 

^l 

33 

37  i  41 

45  ]  49 

53  ;  57 

b2 

bb 

71 

P 

80 

—  4 

—  2 

0 

3 
3 

-7_ 

7 

10 
10 

14 
13 

17  21 

16 !  20 

24 

28 

31 

30 

35  j  39 
34  i  37 

43  1  47 
41  1  45 

51  55 

59  '  64  b8 
57"r6r  65" 

72 
69 

77 
74 

—  2 

O 

0 

23 

27 

49 

53 

0 

2 

0 

3 

0 

9 

12 

16    19 

22 

25 

29 

32  \   36 

39  43 

47  50 

54  58  i  62 

66 

70 

2 

4 

0 

3 

b 

9 

12 

15    18 

21 

24 

28 

31  !  34 

37  \   41 

44  1  48 

52  S5  '  59 

63 

67 

4 

6 

0 

3 

b 

8 

II 

14  i  17 

20 

23 

2b 

29  32 

36  !  39 

42  46 

49  ;  53  \   56  60 

t'4 

6 

8 

0 

3 

5 

^ 

II 
10 

14  :   16 
13  I   15 

19 
18 

22 
21 

25 
24 

28  31 
26  29 

34  !  37 
32  1  35 

40 
38" 

43 
41 

47  ;  50  54  57 

61 

8 

lO 

0 

3 

5 

8 

44  i  48  !  51 

54 

58 

10 

11 

0  2 

5 

7 

10 

13     15 

18 

20 

23 

26  I  28 

31  1  34 

37 

40  43  j  46  1  49 

S3 

5<^ 

II 

12 

0  2 

5 

7 

10 

12    15 

17 

20 

22 

25  \   28 

30  33 

36  j  39  1  42  1  45 

48 

51 

54 

\2 

13 

0   2 

5 

7 

9 

12    14 

17 

19 

22 

24  !  27 

30  32 

35  i  38  1  41  !  44 

47 

SO 

S3 

13 

14 

0  2 

5 
4 

7 
7 

9 
9 

II 

14 

lb 

19 

21 

24 

2b 

29  i  31 

34 

37 
36 

40  42 

45 

48 

51 

14 

IS 

0   2 

13 

16 

18 

20 

23 

25 

28  j  30 

33 

38  I  41 

44 

47 

50 

IS 

i6 

0   2 

4 

b 

9 

II    13 

15 

18  20 

22 

25 

27  29 

32 

35  !  37  40 

43 

45 

48 

16 

17 

0  '  2 

4 

b 

8 

10   13 

15 

17  i  19 

21 

24 

26  1  29 

31 

33  !  36  i  39 

41 

44 

47 

17 

iS 

0   2 

4 

b 

8 

10   12 

14 

16  1  19 

21 

23 

25  i  28 

30 

32 

35  1  37 

40 

43 

45 

18 

19 

0 

2 
2 

4 
4 

b 
6 

8 
8 

10  1  12 

14 

16  18 

20 

22 
22 

24  27 

29 
28 

31 
30 

34 
53 

3f> 

39 

41 

44 

19 

20 

0 

9 

II 

13 

IS  17 

19 

24 

26 

35 

37 

40 

42 

20 

21 

0   2 

4 

5 

7 

9 

"  1  13 

IS 

17 

19 

21 

23  25 

27 

29  31 

34 

3^ 

38 

41 

21 

22 

0   2 

3 

5 

7 

9 

II   12 

14 

lb 

18 

20 

22  24 

2b 

28  :  30  !  32 

35 

37 

39 

22 

23 

0  1  2 

3 

5 

7 

8 

10 

12 

14 

15 

17 

19 

21  i  23 

25 

27  1  29  i  31  j  33 

36 

38 

23 

24 
25 

0   2 
0   2 

3 
3 

5 
5 

b 
6 

8 

10 

II 

13 

IS 

17 

18 

20 

22 

24 
23 

26  28 

25  1  27 

30 

32 

34 
33 

3f 

24 

9 

II 

13 

14 

16 

18 

19 

21 

29 

31 

35 

25 

26 

0   I 

3 

4 

b 

7 

9 

II 

12 

14 

15 

17 

19 

20 

■32  ,  24  1  26   28 

29 

31 

33 

26 

^? 

0   I 

3 

4 

b 

7 

9 

10 

12  13 

15 

10 

18  19 

21    23   25   26 

28 

30 

32 

27 

28 

0   I 

3 

4 

5 

7 

8 

10 

II  12 

14 

IS 

17  19 

20   22  i  23   25 

27 

29 

30 

28 

29 

0 

I 
I 

3_ 
2 

4 
4 

5 
5 

b 
6 

8 

9 

II 
10 

12 

13 

IS 

16  1  18 

19 
18 

21 

22  24 

2b 
24 

27 
26 

29 
28 

29 
30 

30 

0 

7 

II 

13 

14 

15  1  17 

20 

21  23 

31 

0   I 

2 

3  5 

6   7 

8 

9  II 

12 

13 

15   16 

17 

19  I  20  1  22 

23 

25 

26 

31 

32 

0   I 

2 

3  4 

6 

7 

8 

9  10 

II 

13 

14  15 

i6  i  18  i  19  j  20 

22 

23 

25 

32 

5i 

0   I 

2 

3  4 

5 

b 

7 

8   ID 

II 

12 

13   14 

15  i  17  i  18  !  19 

2fN 

22 

23 

3i 

34 

0 

2 
2 

3 

4 

^ 

b 
6 

7 
6 

8 

y 

9 

10 

II 
10 

12   13 
"  1  13 

14 
14 

lb 

17 

18 
17 

19 

21 

22 

34 

35 

0 

3  4 

8 

9 

15 

16 

18 

19 

20 

35 

3b 

0 

2 

3i  3 

4  '  S 

6 

7   8 

9 

10 

II   12 

13 

14 

15  1  16 

17 

18 

19 

36 

^l 

0 

2 

2   3 

4   5 

b 

6   7 

8 

9 

10  II 

12 

13 

14 

15 

lb 

17 

iS 

37 

3^ 

0 

2 

3 

4   4 

5 

6   7 

7 

8 

9  10 

II 

12 

13 

13 

14 

IS 

10 

38 

39 

0 

_2   3 
2  '  2 

3   4 

3l  4 

5 
4 

S 
S 

b 

7 

8 

8   9 

10   II 

II 

12 

13 

14 

15 

39 
40 

40 

0 

6 

6 

7 

8   8 

9  10 

10 

II 

12 

13  13 

41 

0 

2 

2 

3   3   4 

4 

S 

6 

6 

7   7 

8   9 

9  1  10 

II 

II 

12 

41 

42 

0 

0 

I   2 

2   3  !  3 

4  1  4 

S 

S 

6   7 

7   8 

8   9 

9 

10 

1 1 

42 

43 

0 

0 

2 

2 

3   3 

3  i  4 

4 

5 

5   6 

6  1  7  i  7  1  8 

8 

9 

9 

43 

44 

0 

0 

0 



_1 
I 

2 

2   3 

3  :  3 

4 

4 

4   5 

5 

6  1  6  1  7 

7 

8 

S 

44 

45 

0 

I 

2   2 

2   3 

3 

3 

4  !  4 

4 

5 

S   6 

6 

6 

7 

45 

46 

0 

0 

0 

I    I 

11,2 

2   2 

2 

2 

3 

3 

4 

4 

4   4 

5 

5 

5 

46 

47 

0 

0 

0 

I    I 

I   1,1 

I 

2 

2 

2 

2 

2 

3 

3 

3   3 

4 

4 

4 

47 

48 

0 

0  0 

Q   0 

I  j  I 

I 

I 

I 

I 

I 

I 

2 

2 

2 

2 

2 

2 

2 

3 

48 

49 

0 

0  :  0 

0 
0 

30" 

0 

0   0 

0 

0 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 
0 

30" 

I 

49 

50 

0 

0 

30" 

0 
0" 

0 

0   0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 
0" 

0 
30" 

0 
0" 

0 

50 

Add. 
Ther. 

0" 

0" 

30"  0"  30" 

1 

0" 

30" 

0" 

30" 

0"  30" 

1 

0" 

30" 

0" 
10^ 

Add. 
Ther. 

Q 

)' 

1' 

2'     3' 

4' 

W 

6^ 

V 

8' 

9^ 

M 

ean  refract 

on. 

TABLE  22. 

Page 

307 

Correction 

of  the  Mean  Refraction  for  the  Height 

of  the  Thermometer. 

Mean  refraction. 

Then 
Subt. 

Ther. 
Subt. 

0' 

1' 

2 

/ 

3 

' 

4' 

5' 

6' 

%' 

8^ 

9' 

10^ 

0" 

30" 

II 

0" 

II 

30" 

0" 

30" 

0" 

30" 

0" 

30" 

0" 

30" 

0" 

30" 

0" 

// 

30" 

0" 

30" 

II 

0" 

30" 

0" 

0 

It 

;/ 

" 

II 

// 

// 

II 

// 

ii 

II 

II 

II 

// 

.  // 

(/ 

II 

II 

0 

50 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

50 

51 

0 

0 

0 

0 

0 

0 

0 

0 

0 

I 

I 

1 

I 

I 

I 

I 

I 

I 

I 

I 

I 

51 

52 

0 

0 

0 

0 

0 

I 

I 

I 

I 

I 

I 

I 

I 

2 

2 

2 

2 

2 

2  '      2 

3 

52 

53 

0 

0 

0 

I 

I 

I 

I 

I 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3   4 

4 

53 

54 

0 

0 

0 



I 

I 

I 

2 

2 

2 

2  !  T 

3 
4 

3 
4 

3 
4 

4 

5 

4 

5 

4 
5 

5   5 

5 

54 
55 

55 

0 

0 

I 

I 

2 

2 

2 

3   3   3 

6 

6  1  6 

50 

0 

0 

I 

2 

2 

2 

3 

3   4   4 

4 

5 

5 

b 

b 

6 

7 

7'  8 

56 

57 

0 

0 

2 

2 

2 

'> 

J 

3 

4   45 

5 

b 

0 

*6 

7 

8 

8 

8 

9 

57 

58 

0 

0 

I 

2 

2 

3 

3 

4 

4   5  1  5 

b 

b 

7 

7 

8 

9 

9 

10 

ID 

58 

59 

0 

2 
2 

■  2 

3 

3 
3 

4 

4 

5   S  1  6 

5   6  :  7 

b 

7 

7 

'8 

8 
9 

8 
9 

9 

10 

II 

II 
12 

12 

59 
60 

60 

0 

2 

3 

4 

5 

10 

11 

13 

61 

0 

2 

3 

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4 

5 

6  ,  7   7 

8 

9 

9 

10  II 

12 

12 

13 

14 

61 

62 

0 

2 

3 

3 

4 

5 

b 

6  !  7   8 

9 

9 

ID 

II  i  12 

13 

14 

15 

15 

62 

63 

0 

2 

3 

4 

5 

5 

6 

7i  8  1  8 

9 

10 

II 

12  1  13 

14 

15 

lb 

17 

63 

64 
65^ 

0 

0 

T 

2 

2 

2 

3 

3 

4 

5 
5 

6 
6 

7 
7 

7 
8 

8 

9 

10  '■ 
II 

II 
12 

12 

13 

13  1  14 

14  15 

15 
16 

16 

17 

18 

64 

3 

4 

9 

10 

17 

18 

19 

65 

66 

0 

2 

3 

4 

5 

5 

6 

7 

8 

9  10 

II 

12 

14 

15   lb 

17 

18 

19 

20 

66 

67 

0 

2 

3 

4 

5 

6 

7 

8 

9  10  II 

12 

13 

14 

16   17 

18 

19 

20 

22 

67 

68 

0 

2 

3 

4 

5 

b 

7 

8 

9 

II   II 

13 

14 

15 

16 

18 

19 

20 

22 

23 

68 

69 

0 

2 

3 

3 

4 
5 

5 
6 

7 
7 

8 

9 

10 

II 

12 

13 

14 

IS 
16 

lb 
17 

J  7 

19 

20 
21 

21 

23 

24 

69 

7^ 

0 

2 

8 

9 

ID   12 

12 

18  20 

22 

24 

25 

70 

71 

0 

2 

4 

5 

b 

7 

8   10 

II   12   13 

15 

lb 

18 

19  20 

22 

23  25 

27 

71 

72 

0 

2 

4 

5 

^ 

8 

9  10 

II    13   14 

lb 

17 

18 

20  21 

23 

25 

2b 

28 

72 

73 

0 

3 

4 

5 

7 

8 

9  II 

12  1  13   14 

lb 

18 

19 

21 

22 

24 

2b 

27 

29 

73 

74 
75 

0 

0 

- 

3 

3 

4 

4 

5 

6 

7 
7 

8 

8 

10 

II 

12  1  14   15 

13  14  '    16 

17 
18 

18 
19 

20 
'21 

22 

22 

23 

24 

25 
20 

27 
28 

28 
29 

30 
31 

74 

75 

10 

II 

76 

0 

I   3 

4 

6 

7 

9 

10  12 

13   15   16 

18 

20 

22 

23 

25 

27 

29  31 

32 

76 

77 

0 

3 

5 

6 

8 

9 

II   12 

14   16   17 

19 

21 

22 

24 

2b 

28 

30  32 

34 

77 

7« 

0 

1 

3 

5 

6 

8 

9 

II   13 

14  j  16   18 

20 

21 

23 

25 

27 

29 

31 

33 

35 

78 

79 
80 

0 
0 

-1 

3 

5 
5 

6 
7 

8 
8 

10 
10 

11  j3 

12  14 

IS  :  17   18 
15   17   19 

20 
21 

22 

23 

24 
25 

2b 

28 

30 
31 

32 

34 

3^ 

79 

2  3 

27  :  29 

33 

35 

37 

80 

81 

0 

2 

3 

5 

7 

9 

ID 

12  14 

16   18   20 

21 

24 

2b 

28 

30 

32 

34 

3(^ 

38 

81 

82 

0 

2 

4 

5 

7 

9 

II 

13   14 

16   18   20 

22 

24 

2b 

28 

31 

33 

35 

37 

40 

82 

83 

0 

2 

4 

5 

7 

9 

11 

13   15 

17   19   21 

23 

25 

27 

29 

31 

34 

3(^ 

38 

41 

83 

84 

0 

0 

2 

4 

'6 

8 
8 

_9 
10 

II 
12 

13 
14 

IS 
16 

17   19  ;  21 

23 

24 

2b 
26 

28- 
29 

30 

32 

35 

?,7 
38 

39 

40 

42 

84 

2  4 

18   20 

22 

31 

33 

36 

43 

85 

86 

0 

2 

4 

6 

8 

10 

12 

14  16 

18   20 

23 

25 

27 

29 

32 

34 

37 

39 

42 

44 

86 

87 

0 

2 

4 

6 

8 

10 

12 

14 

17 

19   21 

23 

25 

28 

30 

32 

35 

38 

40 

43 

45 

87 

88 

0 

2 

4 

6 

8 

10 

13 

15 

17 

19   21 

24 

2b 

28 

31 

33 

2^ 

38 

41 

44 

46 

88 

89 
90 

0 

0 

2 

4 

6 

"7 

9 

II 

13 

13 

15 
16 

17 
18 

20   22 

24 

27 
27 

29 
30 

32 
32 

34 

35 

37 
38 

39 

40 

42 
43 

45 
-46' 

48 

89 

2  4 

9 

II 

20   23   25 

49 

90 

91 

0 

2 

4 

■7 
/ 

9 

II 

14 

lb 

18 

21   23 

25 

28 

31 

33 

3t> 

39 

41 

44 

47 

50 

91 

02 

0 

2 

5 

7 

9 

II 

14 

lb 

19 

21   24 

2b 

29 

31 

34 

37 

39 

42 

45  1  48 

51 

92 

93 

0 

2 

5 

7 

9 

12 

14 

17 

19 

22   24 

27 

29 

32 

35 

37 

40 

43 

46 

49 

52 

93 

94 
95 

0 
0 

2 

2 

5 
5 

7 

7 

10 

10' 

12 
12 

14 
15 

17 
17 

J9_ 
20 

22  ,  25 
22   25 

27 
28 

30 
30 

33 
33 

35 
36 

38 

41 

44 

47 
48 

50 
51 

53 

94 

39 

42 

45 

54 

95 

96 

0 

2 

5 

7 

10 

12 

15 

18 

20 

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09 
100 

Sul.t. 
Ther. 

0 

3 

3 
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5 
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8 
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30" 

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13 
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45 
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0' 

1' 

»2 

/ 

3 

/ 

i' 

5' 

6' 

V 

8' 

9' 

10^ 

Mean  refraction. 

Page  308] 


TABLES  23,  24. 


TABLE  23. 

Correction  of  the  Moon's  Altitude  foi 

•  parall 

ax  and  1 

efrac- 

tion  corresponding 

to  a   mean   val 

le   of  t 

he   hori 

zontal 

parallax,  57'  30". 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

Corr. 

0 

0 

/ 

0 

/ 

0 

/ 

10 

51 

31 

48 

51 

■  35 

71 

18 

II 

52 

32 

47 

52 

35 

72 

17 

12 

52 

33 

47 

53 

34 

73 

17 

13 

52 

34 

4b 

54 

33 

74 

16 

14 

52 

35 

46 

55 

32 

75 

15 

15 

52 

3^ 

45 

5^ 

32 

76 

14 

16             52 

37 

45 

57 

31 

77 

13 

17      !      52 

3« 

44 

5« 

30 

7« 

12 

18      1      52 

39 

44 

59 

29 

79 

II 

19      1      52 

40 

43 

60 

28 

80 

10 

20 

51 

81 

21 

51 

41 

42 

61 

27 

9 

22             51 

42 

42 

62 

26 

82 

8 

23 

51 

43 

41 

63 

26 

«3 

7 

24 

50 

44 

40 

64 

25 

84 

6 

25 

50 

45 

40 

bS 

24 

«S 

5 

26 

50 

46 

39 

66 

23 

86 

4 

27 

49 

47 

S« 

67 

22 

«7 

3 

28       (       49 

48 

3« 

68 

21 

88 

2 

29       ,       49 

49 

37 

69 

20 

89 

I 

30             48 

50 

3<^ 

70 

19 

90 

0 

TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude. 

Barometer  30  inches. — Fahrenheit's  Thermometer  50°. 


Moon's 
app.  alt. 


Horizontal  parallax. 


o 
lo 
20 

30 
40 

50 

o 
10 
20 

30 
40 

50 

o 
10 
20 

30 
40 

50 

o 
10 

20 

30 
40 

50 

o 
10 

20 

3« 

40 
50 


Correction  for  seconds  of 
parallax.— Add. 


o 

10  i 

20 

30 
40 
50 

o 

10 

20 

30 
40 

50 

o 

10 
20 

30 
40 

50 

o 

10 
20 

30 
40 

50 

o 
10 

20 

30 
40 

49 


r' 

4^^ 

^" 

It 

It 

II 

2 

4 

6 

12 

14 

16 

22 

24 

26 

32 

34 

36 

42 

44 

46 

52 

54 

56 

Corr. 

for 

minute 

of  alt. 


2 
12 
22 

32 
42 

52 
2 
12 
22 
32 
42 
52 
2 
12 
22 
32 
42 
52 
2 
12 
22 

32 
42 
51 


4  6 

14  16 

24  26 

34  36 


44 

46 

54 

56 

4 

6 

14 

16 

24 

26 

34 

36 

44 

46 

54  56 

4  6 

14  16 

24  26 

34  36 

44  46 

54  56 

4  6 

14  16 

24  26 

34  36 

44  46 

53  55 


8 
18 
28 
38 

i  48 
58 

'  8 
18 
28 
38 
48 

JS 
8' 
18 
28 

38 
48 
58 
8" 
18 
28 

38 
48 
58 
8 
18 
28 

48 
57 


Add. 
I'  I" 
2   I 


TABLE  24. 

Page  309 

Correction  of  the  Moon's  Apparent  Altitude. 

, 

*■ 

Barometer  30  inches.— Fahrenheit's  Thermometer  50°. 

Moon's 

Horizontal  parallax 

Correction  for 
paralla.x.- 

seconds  of 
-Add 

Corr. 
for 

app.  alt. 

1 

j 

54'    55' 

56' 

57'    58' 

59' 

60' 

1 

61' 

0" 

2" 
II 

4" 
II 

6" 

8" 

of  alt. 

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>  // 

/  /'   /  // 

1    II 

/  II 

It 

/' 

II 

Add. 

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9 

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8 

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7  I 

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18   0 

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53  10  54  7 

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10 

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15 

17 

20 

22     19 

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8  i    5  !    2 

20 

19 

21 

23 

25 

27 

9  I 

30 

21     18 

15 

12       10 

6     3 

0 

30 

29 

30 

32 

34 

3b 

40 

20     17 

14  i 

10     8 

4      I 

54  58 

40 

38 

40 

42 

44 

4b 

50 

18     15 

12 

50  10 

9 

51  7 

6 

2  53  59 

56 

50 

48 

50 

SI 

53 
6 

55 
8 

19   0 

48  16  49  13 

52  4 

53  0  53  57 

54  55 

0 

0 

2 

4 

10 

15     12 

8 

5  !    2 

52  59  •        55 

53 

10 

10 

II 

13 

15 

17 

20 

13     10 

6 

3  \          0 

57  1    53 

51 

20 

19 

21 

23 

25 

27 

20 

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5 

2 

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55  I    51 

49 

30 

29 

30 

32 

34 

3b 

40 

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3 

0 

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53     49 

47 

40 

38 

40 

42 

44 

4b 

50 

9     5 

2 

5058 

55 

51     48 

45 

50 

48 

50 

51 

53 

55 

Page  310j                    TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude. 

Barometer  30  inches. — Fahrenheit's  Thermometer  50°. 

- 

0  y. 

Correction  for  seconds  of 

Corr. 

Moon's 
app.  alt. 

Horizontal  parallax. 

0  I-. 

0  c^ 

1)  £1, 

parallax. — Add 

for 
minute 
of  alt. 

54' 

55' 

56' 

57' 

58' 

59' 

60' 

61' 

0" 

1 

2" 

4" 

6" 

8" 

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50  56 

51  52 

52  49 

53  45 

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0 

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4 

6 

8 

I' 

0" 

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5  i 

2 

58 

55 

51 

47 

43 

40 

10 

9 

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13 

15 

17 

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56 

52 

49 

45 

41 

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53 

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48  7  i  49  0 

49  53 

50  45  51  38  \    0 

0   2 

5 

7 

lO 

26  :       18         II 

3  48  56 

49  i    40  ,   34 

10 

9   10 

12 

14 

16 

20 

22  1    14  1    7  1  47  59  1    52 

44 

36  :    29 

20 

17  1  19 

21 

23 

24 

30 

18  1    10  ]    2 

55    47 

39 

31  ;     24 

30 

26 

28 

3° 

31 

33 

40 

14     6  !  46  58 

51    43 

35 

27  1   20 

40 

35 

37 

38 

40 

42 

50 

iJ  !    3  I    55 

47     39     31 

23        15 

50 

44 

45 

47 

49 

SI 

__ 



TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude. 
Barometer  30  inches. — Fahrenheit's  Thermometer  50°. 


[Page  311 


Moon's 
app.  alt. 


30  o 
10 

20 

30 
40 

, 5o_ 

31  o 
10 
20 

30 
40 

32  o 
10 

20 

30 

40 

__    50 

33  o 
10 
20 

30 
40 

50 


34  o 

ID 
20 

30 
40 

50 

35  o 

ID 
20 

30 
40 
50 


36  O 

10 
20 

30 
40 

_       50 

37  o 
10 
20 


40 

i° 

38  o 
10 
20 

3" 
40 

SO 

39  o 

ID 

20 

30 
40 

50 


Horizontal  parallax. 


W 


I      II 
45  6 

2 

44  58 
54 
50 
45 


55' 

56' 

sr 

58' 

59' 

60' 

/  '/ 

/  // 

/   /; 

/  // 

'  // 

/  // 

61' 


45  57 
54 
SO 
46 

42 
38 


44  41 

37 

r:, 

28 

24 
20 


45  33 
29 


46  50 
46 
42 
37 
33 
29 

46  24 
20 


44  15 
II 

7 

43  S8 

___S4_ 

43  48 

44 

40 

35 
30 

43  21 
16 
II 

6 

I 

42  56 


24 

15 

20    II 

16     7 

II 

2 

45  7 

4558 

3 

53 

47  42 

38 

34 
29 
25 
21 

'47^16' 
12 

7 

46  58 


53 


48  34 

30 
26 

21 

17 
12 

IE' 7" 

47  58 
54 
49 
44 


49  26 
22 
18 

"i 


48  59 

54 

49 

45 
40 

35 


44  58 

53 

48 

14 

44  39 
34 
30 

25 
20 

15 


42  52 

47 
42 

37 
32 

27 

42  22 

17 
12 

7 
I 

4L_S^ 

41  51 
46 

41 
35 
30 
25 


44  II 

6 
I 

43  56 

51 

46 

43  41 
36 
31 
26 
21 
16 


48 
44 
39 

34_ 

45  29 
25 
20 

15 
10 

_5_ 
45  o 
44  55 
50 

.45 
40 

.  ,  35 

44  30 
25 
20 

15 
10 

4 


41  19 

14 
8 

3 
40  58 

_52 
40  47 
42 
36 
30 
25 
19 


43  II 

5 
o 

42  55 
50 
44 

42  39 
34 
29 

23 
18 
12 


43  59 
54 
48 

43 
38 
32 

43  27 
21 
16 
II 

5 
42  59 


42  7 
2 

41  56 
51 
45 
39 


41  33 
28 

23 
17 
II 

5 


42  54 
49 
43 

38 
32 
26 

42  20 

15 
9 
3 

41  57 
51 


46  49 

44 
39 
34 
29 
24 


47  40 

35 
30 

25 
20 

15 


4831 
26 

21 

16 

II 

6 


50  18 

13 
9 
4 
o 

_49  55 
49  SO 

45 
40 

36 

31 
26 


51  10 

6 

I 

50  56 

52 

47 


46  19 

15 
10 

5 
o 

45  55_ 

45  50 

45 
40 

35 
30 
24^ 

45  19 

14 

9 

3 

44  58 

53 


47  10 

5 
o 

46  55 
50 
45_ 

46  40 
34 
29 
24 
19 
L4 

46  9 

3 

45  58 

52 

47 

42 


48  o 

47  55 
50 
45 
40 
35 


47  30 
24 
19 

13 

8 

3 


49  22 

17 

II 

6 

48  56 
48  50 

45 
40 

35 
30 
24 

19 

14 

9 

3 

4758 

52 


50  42 

37 
32 
27 
22 

17 


50  13 

8 

2 

49  57 
52 
47 


48 


49  41 
36 
31 

25 
20 

14 


Vi 


44  48 

45  37 

42  )    31 

37 

25 

31 

20 

26 

14 

20 

8 

44  15 

9 

4 

43  58 

53 

47 

43  41 
36 
30 

24 
iS 

13 

43  7 
I 

42  55 
49 
43 
37 


45  3 

44  57 

52 

46 

40 

34 

44  29 


46  58 
52 
47 
41 
36 

__3^ 

46  25 

19 

14 

8 

2 

45  56 
51 


47  47 
41 
36 
30 
25 
19 


49  9 

3 
48  58 

52 
47 
42 

48  36 
30 
25 
19 
14 
8 


47  14 

48  2 

8 

47  56 

2 

SO 

46  56 

44 

50 

39 

44 

33 

45 


45 


45 
40 

34 
28 
22 
16 


46  39 

27 
21 

15 
9 

3 


46 


23 

10 

45  57 

'7        ^ 

51 

12  1  44  58 

45 

6  i    52 

39 

0 
43  54 

46 

33 

44  40 

45  27 

48  1    34 

21 

42 

28 

15 

36 

22 

8 

30 

16 

2 

23 

9 

44  55 

47  27 
21 

15 
9 

_46  57 
46  51 
45 
38 
32 
26 
20 


46  13 
7 
I 

45  54 
48 
42 


o 
10 
20 

30 
40 

SO 

o 

10 

20 

30 
40 

5_o 

o 

10 

20 

30 
40 

50 

o 
10 

20 

30 

40 

50 

o 
10 

20 

30 
40 

_5o 

o 

10 

20 

30 
40 

i° 

o 
■10 
20 

30 
40 

JO 

o 
10 
20 

30 
40 

JO 

o 
10 

20 

30 
40 

o 
10 
20 

30 
40 

50 


Correction  for  seconds  of 
parallax. — Add. 


6" ;  8" 


o 

9 
17 
26 

35 
43_ 

o 

9 
17 
26 

34 
43_ 

o 

8 

17 

25 
34 

4?_ 

o 

8 
17 

25 

33 

_42_ 

o 

8 

17 

25 

?,i 

41_ 

o 

8 

16 

24 

33 

41 

o 

8 

16 

24 

32 

o 

8 

16 

24 
32 
40 

o 


2 
10 

19 

28 

36 
45 

2" 
10 
19 

27 
36 

44 


3 
12 

21 

29 


5   7 
14   16 

23 
31 


2 

10 

19 

27 

35 

44 

2 

10 

18 

27 
35 

2 

10 
18 
26 

35 
43 

2 
10 
18 
26 
34 
42 

2 
10 
18 
26 

34 
42 


24 

33 
38  40  42 
47  49  50 

5  ,  7 
14  I  15 
21  j  22  24 
29  31  32 

38  i  39  :  41 
46    48^1  50 

7 


3 
12 


3 
12 

20 

29 

37 


36 
_44 

1 

II 


2 
10 

17 

25 
33 

2 

s   9 
16  '  17 

23 :  25 


3 
II 

19 
27 
35 

_43 
3 


II 


31 

33 

39 

41 

0 

2 

8 

-  9 

15 

17 

23 

25 

31 

32 

39 

40 

35 

41 

3 
II 


46  47 


5 

14  15 

22  I  24 

30  i  32 
39 


41 
49 

315  7 
12  I  13  I  15 
20  22  .  23 
28  30  32 
37  i  38  I  40 
45  i  47  i  48 

3  j  5  i  7 

12  !  13  1  15 

20  21  j  23 

28  30  31 


40 
48 


38 
46 

5   7 
13  15 


20  21  23 


28  I  29 
36  38 
44  46 


19  20 

27  I  28 


36 

44 


5 
12 


19  I  20 

26  I  28 

34  !  36 

42  I  43 


31 
39 
47 
6 
14 
23 
31 
39 
47 


5 

13 

21 

29 
37 

45 

5 
II  j  13 

19  !  21  i  22 

27  j  29    30 

35  i  37  38 

43  I  45 

3  I  5 
13 


46 


6 

14 
22 

30 
38 
46 


(  orr. 

for 
minute 
of  alt. 


Sub. 
1'  o" 
2   I 


6 

14 

22 
29 
37 
45 


I 

2 
2 

3 
3 
4 
4 


o 
I 
I 

2 
2 

3 
3 

4 
4 


1  I 

2  I 

T.    2 


1  I 

2  I 

3  2 

4  2 

5  3 


Page 

312] 

TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude. 

Barometer 

30  inches.— Fahrenheit's  Thermometer  50°. 

Moon's 

Horizontal  parallax. 

t4H 

Correction  for  seconds  of 
parallax.  — Add. 

Corr. 

for 

app.  alt. 

fes 

minute 

54' 

/    // 

55' 

56' 

sr 

58' 

59' 

60' 

61' 

1)  a 

0" 

2" 

4" 

6" 

8" 

of  alt. 

o   / 

/  /; 

/  // 

/  // 

/  II 

/  // 

/  // 

/  // 

n 

// 

// 

II 

II 

II 

Sub. 

40  0 

40  14 

41  0 

41  46 

42  32 

43  18 

44  4 

44  50 

4536 

0 

0 

2  i  3 

5 

6 

6' 

3" 

10 

8 

40  54 

39 

25 

II 

43  57 

43  1   29 

10 

8 

9  i  II 

12 

14 

7 

4 

20 

2 

48 

33 

19 

5 

50 

36  j   22 

20 

15 

17 

18 

20 

21 

8 

5 

30 

39  56 

42 

28 

13 

42  59 

44 

30    16 

30 

23 

24 

2b 

27 

29 

9 

5 

40 

50 

-  36 

22 

7 

53 

38 

24 

9 

40 

3? 

32 

34 

35 

37 

50 

45 
39  39 

30 

16 

I 
41  55 

47 
42  41 

32 

18 

3 

50 

38 

40 

41 

3 

43 
5 

44 
6 

41  0 

40  24 

41  ID 

43  26 

44  " 

4456 

0 

0 

2 

10 

33 

18 

4 

49 

^i 

19 

4 

49 

ID 

8 

9 

II 

12 

14 

20 

27 

12 

40  58 

43 

28 

13 

43  58 

43 

20 

IS 

17 

18 

20 

21 

30 

21 

6 

51 

36 

22 

7 

51 

37 

30 

23 

24 

2b 

27 

29 

40 

16 

0 

45 

30 

16 

0 

45 

30 

40 

3° 

32 

33 

35 

3b 

50 

10 

39  54 
39  48 

39 

40  33 

24 

9 

42  53 

42  47 

38 

23 

50 

38 
0 

39 

41 

42 

44 

42  0 

39  i 

41  17 

42  2 

43  31 

44  16 

0 

I 

3 

4 

6 

10 

3«  5« 

42 

27 

II 

41  56 

41 

25 

10 

10 

7 

9 

10 

12 

13 

I 

I 

20 

52 

3f> 

21 

5 

50 

34 

18 

3 

20 

15 

lb 

18 

19 

21 

2 

I 

30 

46 

30 

14 

40  58 

43 

27 

II 

43  56 

30 

22 

•24 

25 

27 

28 

3 

2 

40 

40 

24 

8 

5? 

3<= 

21 

5 

49  40 

30 

31 

33 

34 

3b 

4 

2 

50 

34 

18 
39  12 

2 
39  56 

46 
40  40 

30 

14 

42  58 
42  52 

42 
4336 

50 

37 

38 

40 

41 

43 
6 

5 
6 

3 
4 

43  0 

38  28 

41  24 

42  8 

0 

0 

I 

3 

4 

10 

22 

6 

50 

34 

18 

I 

45 

29 

ID 

7 

9 

10 

12 

13 

7 

4 

20 

16 

38  59 

43 

27 

II 

41  54 

38 

22 

20 

15 

lb 

18 

19 

20 

8 

5 

30 

10 

53 

37 

20 

5 

48 

31 

15 

30 

22 

23 

25 

26 

28 

9 

5 

40 

4 

47 

30 

14 

40  58 

41 

24 

8 

40 

29 

3J 

32 

34 

35 

50 

37  57 

41 

24 
39  18 

7_ 
40  I 

51 

34 

.17 

42  10 

I 

50 

37 

38 

39 

3 

41 

42 

44  0 

37  51 

38  35 

40  44.  41  27 

4254 

0 

0 

I 

4 

6 

10 

45 

28 

II 

39  54 

37   .    20  1    3 

4b 

ID 

7 

9 

10 

II 

13 

20 

3« 

21 

4 

47 

30 

13 

41  56 

39 

20 

14 

16  1  17 

19 

20 

30 

32 

15 

38  58     41 

24 

7 

49 

32 

30 

21 

23 

24 

2b 

27 

40 

26 

9 

51  1    34 

17 

0 

42 

25 

40 

29 

30 

31 

33 

34 

50 

20 

2 

44  j    27 

10  40  53 

35 

18 
42  II 

50 

3t) 

37 

39 

40 

41 

6 

I 

I 

45  0 

37  14 

37  56 

38  38  39  21 

40  3  t  40  46 

41  28 

0 

0 

I 

3 

4 

10 

7 

49 

31     14 

39  56  1    39 

21 

3 

10 

7 

8 

10 

II 

13 

2 

I 

20 

0 

43 

25  1    7 

49     32 

14  :  41  56 

20 

14 

15 

17 

18 

20 

3 

2 

30 

36  54 

37 

18  !    I 

43  !    25 

7  i   49 

30 

21 

23 

24 

25 

27 

4 

3 

40 

48 

30 

"  i  38  54 

36  1    18 

0 

42 

40 

28 

30 

3i 

,32 

34 

5 

3 

50 

46  0 

41 

36  35 

23 

37  17 

4 
37  .58 

47 

29  1    II 

40  52 

34 

0 

J5_ 
0 

J7_ 

I 

38 

39 

41 
6 

b 
7 

4 
5 

38  40 

39  22 

40  4 

40  45  i  41  27 

3 

4 

10 

29 

10 

51 

33 

15 

39  57 

38  1   20 

10 

7 

8 

10 

II 

12 

8 

5 

20 

22 

3 

44 

26 

8 

49 

31 

12 

20 

14 

15 

17 

18 

19 

9 

b 

30 

16 

30  57 

38 

20 

I 

42 

24 

5 

30 

21 

22 

23 

25 

2b 

40 

9 

50 

32 

13 

38  54 

35 

17 

4058 

40 

28 

29 

30 

32 

33 

50 

2 

43 

25 
37  18 

6 

47 

28 

9 
40  2 

50 
4043 

0 

35 
0 

3b 
I 

37 
3 

39 
4 

40 
5 

47  0 

35  56 

36  37 

37  59 

38  40 

39  21 

10 

49 

30 

II 

52 

34 

14 

39  55 

3<^ 

10 

7 

8 

10 

II 

12 

20 

42 

23 

4 

45 

26 

6 

47 

28 

20 

14 

15 

lb 

18 

19 

30 

36 

17 

36  57 

•38 

19 

38  59 

40 

21 

30 

20 

22 

23 

24 

2b 

40 

30 

10 

50 

31 

12 

52 

32 

13 

40 

27 

29 

30 

3J 

33 

50 

23 

35  16 

3 

35  56 

43 
36  36 

24 

5 

45 

25 

5 

50 

34 

35 

37 

38 

4 

39 

5 

I 

I 

48  0 

37  17 

37  57  38  37 

39  17  1  39  58 

0 

0 

I 

3 

10 

10 

50 

30 

10 

50    30 

10    50 

10 

7 

8 

9 

II 

12 

2 

I 

20 

T 

J 

43 

23 

2 

43  1  .  22 

2 

42 

20 

13 

15 

lb 

17 

19 

3 

2 

30 

34  56 

3^' 

16 

36  55 

35 ;     15 

38  55 

34 

30 

20 

21 

23 

24 

25 

4 

3 

40 

49 

29 

9    48 

28 

8 

48 

27 

40 

27 

28 

29 

31 

32 

5 

3 

50 

42 

22 

I 

41 

.  21 

0 

40 

19 

50 

33 

35 

3t) 

37 

39 

6 

7 

4 
5 

49  0 

34  35 

35  15 

35  54 

36  34 

37  13 

37  53 

38  32 

39  II 

0 

0 

I 

3 

4 

5 

10 

29 

8 

47 

27 

6 

46 

25 

4 

10 

7 

8 

9 

10 

12 

8 

5 

20 

22 

I 

40  !    20 

36  59 

38 

17 

38  5^^ 

20 

13 

14 

lb 

17 

18 

9 

b 

30 

15 

34  54 

33 

12 

51 

30 

9 

48 

30 

20 

21 

22 

23 

25 

40 

8 

47 

26 

5 

44 

23 

2 

41 

40 

2b 

27 

29 

30 

3'. 

50 

I 

40 

19 

35  58 

36  i,   15 

37  54 

33 

50 

33 

34 

35 

3b 

38 

TABLE  24.                   [Page  313 

Correction  of  th 

e  Moon's  Apparent  Altitude. 

% 

Barometer 

30  inches.— Fahrenheit's  Thermometer  50°. 

Correction  for  seconds  of 

c  ,,  1 

Moon's 
app.  alt. 

I 

horizontal  parallax 

• 

parallax. — Add. 

f 

54'    55' 

50' 

5r 

58' 

59' 

60'   61' 

0  a 

II 

0" 

2" 

4" 

6" 

8" 
II 

of  alt.  1 

J   / 

/  //     // 

/  ,/ 

1  II 

/  // 

/  // 

/  II   \   1     II 

// 

II 

II 

II 

50  0 

33  54  :  34  33 

35  n 

35  50 

36  29 

37  8 

37  46  '  38  25 

0 

0 

I 

3 

4 

5 

10 

47  '    26 

4 

43 

21 

0 

38    17 

10 

b 

8 

9 

10 

12 

20 

sO     19 

34  57 

3^ 

14 

36  53    31     9 

20 

13 

14 

15 

17 

18 

30 

33     II 

49 

28 

6 

45    23     I 

30 

19 

20 

22 

23 

24 

40 

26     4 

42 

20 

35  58 

37     IS  37  53 

40 

2b 

27 

28 

29 

31 

50 

19 

33   57 
33   50 

35 
34  28 

13 

35  6 

51 

29     7 

45 
37  37 

_5o 
0 

32  33 

J5 

3 

3t) 

4 

37 
5 

Sub.  1 
I'  I"  1 

51   0 

33   12 

35  44 

36  22  36  59 

0 

I 

10 

5    43 

21 

3458 

3b 

14    51    29 

10 

b 

8 

9 

10 

II 

2 

I 

20 

32  58 

3^^ 

13 

50 

28 

6     43    21 

20 

13 

14 

15 

lb 

iS 

2 

30 

51 

29 

6 

43 

21 

35  58    36    13 

30 

19 

20 

21 

23 

24 

4 

1 

J 

40 

44  1    22 

33  59 

3^ 

14 

50    28     5 

40 

25 

2b 

28 

29 

30 

5 

4 

50 

37   I    14 

51 
33  44 

28 
34  21 

6 

42    20  ,  36  57 

50 

31 

33_ 
I 

34 
2 

35 
4 

3b 
5 

b 

7 
8 

4 

5 
6 
6 

52  0 

32  30  33  7 

3458 

35  35  36  12  36  49 

0 

0 

10 

23     0 

3b 

^3 

50 

27     4    41 

10 

b 

7 

9 

10 

II 

20 

15  1  32  52 

29 

6 

43 

19  35  56    33 

20 

12 

13 

15 

lb 

17 

9 

30 

8  '    45 

21 

33  58 

35 

II    48    24 

30 

18 

20 

21 

22 

23 

40 

3« 

14 

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24 

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27 

29  58 

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26 

27  28 

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30 

4 

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27  14  27  45 

28  16 

2847 

29  18 

29  49 

30  20  30  51 

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0 

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3 

10 

6     37 

7 

38 

9 

40 

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10 

5   6   7 

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27  59 

30 

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31 

2 

33 

20 

10 

II   12 

13 

14 

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51     21 

51 

22 

2853 

23 

29  54 

24 

30 

15 

16  17 

18 

19 

40 

43  1    13 

43 

14 

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14 

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15 

40 

20 

21  22 

23 

24 

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35     5 

35 

5 

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6 

36 

6 

50 

25 

26  27 

29 

30 

Page  314]                    TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude. 

Barometer  30  inches. — Fahrenheit's  Thermometer  50° 

• 

Correction  for  seconds  of  1 

Corn 

for 

Moon's 

Horizontal  parallax. 

parallax. — Add. 

54^ 

55^ 

56^ 

5r 

58^ 

59^ 

60^ 

er 

0  ci 

<U  Q. 

W' 

"y' 

4// 

<6" 

8^^ 

of  alt. 

0  / 

/  // 

/  // 

/  // 

1  II 

/  // 

/  // 

/  // 

/  // 

II 

II 

II 

II 

II 

II 

60  0 

26  26 

26  57  1  27  27  1  27  57 

28  27 

28  57 

29  27 

29  57 

0 

0 

1 

2 

3 

4 

ID 

19    49  '    19  !•   49 

19 

49 

18 

48 

10 

5   6 

7 

8 

9 

20 

II     41     II     40 

10 

40 

9 

39 

20 

10   II 

12 

13 

14 

30 

3  '        32     2     31 

I 

31 

0 

30 

30 

15   16 

17 

18 

19 

40 

25  55    24  ,  26  53    23 

27  53 

22 

28  51 

21 

40 

20 

21 

22 

23 

24 

61  0 

47     16  1    45     14 

44 

13 

42 

12 

50 

25 

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28 

29 

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26   8   26  37  ;  27   6 

27  36 

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2834 

29  3 

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31 

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27  56 

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28  54 

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49 

18 

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16 

45 

20 

10 

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12 

12 

13 

30 

15     43 

12 

40 

ID 

38     7 

35 

30 

14 

15 

lb 

17 

18 

40 

7  :    35 

4 

32 

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29 

27  58 

26 

40 

19 

20 

21 

22 

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2§ 

4 

50 

24  59    27  ;  25  55 

24 

26  52 

20 

49 

17 

50 

24 

25 

26 
2 

27 
3 

62   0 

24  50  1  25  19  1  25  47  26  15 

26  43  !  27  II  27  40 

28  8 

0 

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10 

42     10    38     6 

34  1    2 

30 

27  58 

10 

5   6 

6 

7 

8 

>?,o 

34     2     29  25  57 

25 

26  53 

21 

49 

20 

9 

10 

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12 

12 

30 

26  24  54    21  1    49 

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12 

40 

30 

14 

15 

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17 

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8 

3b 

3 

31 

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20 

21 

22 

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10 

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32 

25  59 

27 

26  54 

21 

50 

23 

24 

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2 

2b 

27 

63  0 

24  2 

24  29 

24  56 

25  23 

25  51 

26  18 

26  45 

27  12 

0 

0 

3 

4 

10 

23  54  !   21 

48     15  1    42 

9 

36 

1 
0 

10 

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5 

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7 

8 

20 

46    13 

39     6  [    33 

0 

27 

26  54 

20 

9 

10 

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12 

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30 

37     4     31  24  58 

24  25  51 

18 

45 

30 

13 

14 

15 

lb 

17 

40 

29  23  55  1    22     49 

IS 

42 

8 

35 

40 

18 

19 

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21 

22 

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20    47 

13 

24  5 

40 

6 

33  !  25.59 

26 

50 

22 

23 

24 

25 

2b 

64  0 

23  12  ,  23  39 

24  32  '  24  58  '  25  24  !  25  50 

26  17 

0 

0 

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2 

3 

3 

10 

4  '         31 

23  57  1   23 

49  i    15' 

41 

8 

10 

4 

5 

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7 

8 

20 

22  56     22 

48    14 

40  !    6 

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25  58 

20 

9  1  10 

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12 

30 

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31  24  57 

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Sub. 

65  0 

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10 

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7 

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6    31  i  22  56    21 

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25  i    48 

12 

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50 

20 

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20  41  1  21  5 

21  28  21  52  22  15  22  39 

23  2 

23  26 

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0 

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2 

2 

3 

10 

^T,     20  56  i    19    43     6     29  22  52  [    16 

10 

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5 

5 

6 

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43     7 

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30 

16    39     2    25    48  1  •  n 

34  22  57 

30 

12  1  12 

13 

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15 

40 

8    30  20  53     16 

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24 

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40 

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lb 

17 

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19  59    21    44     7 

30  21  52 

15 

37 

50 

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20 

21 

22 

22 
^3~ 

68  0 

19  50  ,  20  13 

20  35 

20  58 

21  21 

t  21  43 

22  5  22  28 

0 

0 

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10 

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27 

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5 

b 

7 

20 

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40 

2 

24 

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9 

20 

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9 

9 

10 

30 

25  '    47 

9    31 

20  53 

15 

37 

21  59 

30 

II  !  12 

13 

13 

14 

40 

16     38 

0    22 

44  i    5 

27 

49 

40 

15 

lb 

lb 

17 

18 

50 
69  0 

7    29 

19  51     13 

34 

20  56 

17 

39 

50 

18 

19 

20 

I 

21 
2 

21 

18  59  \   19  21 

19  42  20  4 

20  25 

20  47 

21  8 

21  30 

0 

0 

I 

3 

10 

50    12    33  19  55  !   16 

37 

20  59 

20 

10 

4 

4 

5 

b 

b 

20 

42     3 

24    45  •          7 

28 

49 

10 

20 

7 

8 

8 

9 

10 

30 

33  .  18  54 

15  ,   36 

19  57 

18 

39 

0 

30 

II 

II 

12 

13 

13 

40 

24    45 

6  ;   27 

48 

9 

29 

20  50 

40 

14 

15 

15 

lb 

17 

50 

16  ;   37  j  18  57    18 

39 

0 

20 

41 

50 

18 

18 

19 

20 

20 

TABLE  24. 

Page  315 

Correction  of  the  Moon' 

s  Apparent  Altitude. 

V 

Barometer  30  inches.— Fahrenheit's  Thermometer  50= 

Moon's 
app.  alt. 

Horizontal  parallax. 

C  g 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 
for 

54' 

55' 

56' 

57'    58' 

59' 

60' 

61' 

0  c< 
C/5 

0" 

2" 

4" 
II 

6" 

/; 

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of  alt. 

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20 

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44 

II  56 

8 

20 

4 

4 

5 

5  i  ^ 

30 

34 

46 

10  58 

10 

22 

34 

46 

II  58 

30 

6 

b 

7 

7 :   8 

40 

25 

37 

48 

0 

12 

24 

3b 

48 

40 

8 

8 

9 

9  >  10 

50 

16 

28 

39 

10  51 

3 

15 

26 

38 

50 

10 

10 

II 

II  1  12 

I   I 

79  0 

10  7 

10  19 

10  30 

10  42 

10  53 

II  5 

II  16 

II  28 

0 

0 

0 

I 

10 

9  5« 

9 

21 

32 

43 

10  55 

6 

17 

10 

2 

2 

3 

3  i  3 

20 

49 

0 

II 

22 

a 

44 

10  56 

7 

20 

4 

4 

4 

5   5 

30 

40 

9  50 

I 

12 

23 

34 

45 

10  56 

30 

b 

b 

b 

7 

7 

40 

31 

41 

9  52 

3 

13 

24 

35 

4b 

40 

7 

8 

8 

8 

9 

50 

22 

32 

43 

9  54     4 

15 

25 

3b 

50 

9 

10 

10 

10  II  1 

Page  316 

TABLE  24. 

Correction  of  the  Moon 

's  Apparent  Altitude. 

Barometer 

30  inches. — Fahrenheit's  Thermometer  5c 

>°. 

Moon's 
app.  alt. 

Horizontal  parallax. 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 
for 

0  2 

minute 

O        ' 

54^ 

55' 

56' 

sr 

58' 

59' 

60' 

61' 

0  rv 
C/3 

0" 

2" 

4" 

6" 

8" 

of  alt. 

/   // 

/   // 

/   // 

/  // 

/   // 

/   // 

/      ;/ 

/    // 

II 

// 

'    // 

" 

II 

80     0 

9  13 

9  23 

9  34 

9  44 

9  55 

10    5 

ID    15 

10  26 

0 

0 

0 

I 

I 

I 

10 

^    3 

14 

24 

34 

45 

9  55 

5 

15 

10 

2 

2 

2 

3 

3 

20 

8  54 

i     0    4 

14 

24 

35 

45 

9  55 

5 

20 

3 

4 

4 

4 

5 

30 

45 

!     8  55 

,    5 

1     15 

25 

35 

45 

9  54 

30 

5 

5 

6 

6 

6 

40 

3<^ 

46 

855 

0    5 

15 

25 

35 

44 

40 

7 

7 

7 

8 

8 

50 

27 

37 

46 

8  56 

6 

15 

25 

34 

50 

8 

9 

9 

9 

ID 

81      0 

8  18 

827 

837 

8  46 

8  56 

9    5 

9  14 

9  24 

0 

0 

0 

I 

I 

I 

10 

9 

18 

27 

3b 

46  !    8  55 

4 

13 

10 

I 

2 

2 

2 

3 

20 

7  59 

8 

■  17 

26 

36 

45 

8  54 

3 

20 

3 

4 

4 

4 

30 

50 

7  59 

8 

17 

26 

35 

44 

852 

30 

4 

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5 

5 

1     6 

40 

41 

50 

7  59 

8 

17 

25 

34 

42 

40 

6 

b 

b 

7 

50 

32 

41 

49 

758 

7 

15 

24 

32 

50 

7 

8 

1     8 

8 

9 

82     0 

7  23 

7  31 

7  40 

7  48 

7  57 

8    5 

8  13 

8  22 

0 

0 

1     0 

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I 

10 

14 

22 

30 

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47 

7  55 

3 

II 

10 

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2       2 

2 

2 

20 

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12 

20 

28 

37 

45 

7  52 

0 

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6  55 

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19 

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35 

42 

7  50 

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5 

5 

40 

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6  54 

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10 

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5 

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7 

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7 

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6  43 

6  50 

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7    5 

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19 

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2 

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20 

9 

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30 

37  1         44 

Ml 

6  58 

20 

2 

3  1     3 

3 

J 

2      2 

30 

0 

7 

13 

•      20 

27           34 

41 

48 

30 

3 

4  i     4 

4 

4 

3    3 

40 

5  51 

5  58 

4 

II 

18 

24 

31 

38 

40 

5 

5       5 

5 

6 

4    4 

50 

42 

49 

5  55 

I 

8 

14 

21 

27 

50 

6 

6       6 

6 

7 

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84    0 

5  33 

5  39 

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5  52 

5  58 

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10 

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36 

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48 

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2 

2 

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28  !         34 

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30 

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7 

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29 

35 

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0 

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4  53 

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3 

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20 

18 

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30 

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14 

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25 

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26 

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2  47 

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2  53 

2  56 

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37 

40 

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2  55 

2  58 

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20 

28 

31 

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36 

39           42 

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47 

20 

I 

I 

I 

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30 

19 

21 

24 

26 

29           32 

34 

37 

30 

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2 

2 

2 

40 

10 

12  , 

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17 

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24 

27 

40 

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2 

2 

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3  ! 

5 

7 

9  !         12 

14 

16 

50 

2 

2 

2 

3 

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45 

47 

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10 

0 

0       0 

0 

0 

20 

32 

34 

3b 

38 

39           41 

43 

44 

20 

I 

I 

I 

I 

I 

30 

23 

25 

26 

28 

29           31 

32 

34 

30 

I 

I 

I 

I 

I 

40 

14 

15 

16 

19 

20 

21 

22 

24 

40 

I 

I 

I 

I 

I 

50 

5 

6 

1 

7 

9 

ID 

II 

12 

13 

50 

I 

I 

I 

2 

2 

89    0 

0  56 

0  57 

0  58 

0  59 

10          II 

I     2 

I     3 

0 

0 

0 

0 

0 

0 

10 

46 

47 

48 

49  1 

0  50       0  51 

0  51 

0  52 

10 

0 

0 

0 

0 

0 

20 

H 

37 

^v 

39 

40                40 

41  : 

42 

20 

0 

0 

0 

0 

0 

30 

28 

28 

28 

29 

30                30 

31 

31 

30 

0 

0 

0 

0 

0 

40 

19 

19 

'9 

19 

20 

20 

21 

21 

40 

0 

0 

0 

0 

0 

50 

9 

10   ! 

10 

1 

ID 

10 

10 

10 

ID 

50 

I 

I 

I 

I 

I 

TABLE  25. 

[Page  317 

Table  showing  the  variation  of  the  altitude  o 

f  an  object  arising 

from  a  change  of  100  seconds  in  the  declina- 

tion.     If  the  change  move  the  body 

toward  the  elevated  pole  apjily  the  correction  to  the  altitude  with  the  | 

signs  in  the  Table  ;  otherwise,  chang 

e  the  signs. 

i 

c 

41 

Q 
o 

1) 

3 
< 

Latitude  of  same  name  as  declination. 

Latitude  of  different  name  from  declination. 

d 

.2 

70° 

60° 

50° 

40° 

30° 

20° 

10° 

0° 

10° 

20° 

30° 

40° 

50° 

60°     70° 

3 

< 

Q 

0 

// 

II 

II 

II 

II 

II 

II 

II 

II 

// 

// 

II 

" 

II 

II 

0 

0 

o 

94 

87 

7^ 

64 

50 

34 

17 

0 

17 

34 

50 

64 

76 

87 

94 

0 

ID 

95       88 

Z^ 

f§  ^    51 

35 

18 

0 

18 

35 

51 

65 

78 

88 

9S 

10 

20 

100       92 

82 

68  i     53 

36 

18 

0 

18 

36 

S3 

68 

82 

92      100 

20 

30 

1  100 

88 

74  ■     57 

39 

20 

0 

20 

39 

57 

74 

88  i  100  1 

30 

0 

40 

100 

84  1     65 

45 

22 

0 

23 

45 

65  i    84 

100 

40        0 

50 

100       78 

53 

27 

0 

27 

53 

78  '  100 

50 

60 

100 

68 

35 

0 

35 

68 

100 

60 

70 

100 

51 

0 

51 

100 

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87 

94 

70  j 

0 

94 

^7 

77 

^ 

50 

34 

17 

0 

17 

34 

50 

64 

77 

0 

10 

95 

87 

77 

65       50 

34 

17 

—  I 

18 

35 

51 

66 

78 

88  1     96 

10 

20 

99       91 

81 

67  1     52 

35 

17 

—  I 

19 

37 

54 

69  !    83 

93 

lOI 

20 

30 

107       98 

87 

73       56 

38 

18 

—    2 

22 

41 

59  i     76  i    90 

102 

30 

2 

40 

III  ;    98 

82       63 

42 

20 

—    2 

25 

47 

68 

86  !  102 

40          2 

50 

116 

97       74 

50 

24 

-  3 

30 

57 

81 

103  1 

50    i 

bo 

124  1     95 

64 

30 

-  5 

40 

73 

103  1          i 

60  ! 

70 

{  139 

92 

43 

—  8 

59 

108 

50 

70 

0 

94       87       77 

64  1     50 

34 

17 

0 

17 

34 

64       77 

87 

94 

0 

10 

94       87       77 

64  1     50 

34 

lb 

—  I 

19 

36 

52  t    67  1     79  1     89  1    97 

10  ! 

20 

98       90       79 

66 

51 

34 

lb 

~'  3 

21 

39 

56       71  j    84 

95 

103 

20 

30 

105       96 

85 

70 

54 

36 

lb 

—  4 

24 

44 

62  j     78 

93 

104 

30 

4 

40 

1  107 

94 

78 

59 

39 

17 

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29 

51 

71 

90 

106 

40     4 

50 

III 

92 

70 

45 

19 

-  8 

35 

62  ;     86 

109 

50 

bo 

117 

88 

5^^ 

23 

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47 

81      112 

60 

70 

127 

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32 

—  19 

70 

119 

70 

0 

94       87 

77 

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50 

34 

17 

0 

17 

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87 

94 

0  1 

10 

94       87 

76 

64      49 

33 

lb 

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20 

37       53       67       80 

90 

98 

10  ^ 

20 

97       89       78 

65  1    50 

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22 

40       57  i     ^^,       86 

96 

104 

20 

30 

103       94       83 

69  i    52 

34 

14 

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2b 

46       64       81       95 

107  i 

30 

6 

40 

105       92 

fo       57 

2,'^ 

14 

—  9 

32 

54       74  i     93      109 

40       6 

50 

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88 

bb 

41 

15 

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40 

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bo 

III 

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51 

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70 

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80 

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35  !     50 

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98  ,  106 

20 

30 

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32 

12 

—  8 

28 

48       66  !     83       97 

109 

30 

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113 

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118 

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100 

10 

20 

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100 

20 

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30 

50       69       86 

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30 

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10 

20 

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29 

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20 

12 

30 

99       90       78       64       47 

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30 

40 

108       98       84       68       49 

28 

5 

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40 

12 

50 

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70 

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3 

70°     60°     50°     40°     30° 

20° 

10° 

0° 

10° 

! 
20°     30°     40° 

50°     60° 

70° 

(U 

Latitude  of  same  name  as  d 

eclinati 

on. 

Latitude  of  different  name  from  declination. 

Itituc 
eclin 

Q 

< 

<       0   I 

Page  318] 

TABLE  25.                                                                      1 

Table  showing  the  variation  of  the  altitude  of  an  object  arising  from  a  change  of  loo  seconds  in  the  declina-  | 

tion.     If  the  chonge  move  the 

body  toward  the  elevated  pole,  apply  the  correction  to  the  altitude  with  the 

signs  in  the  Table;  otherwise, 

change  the  signs. 

o     Declination. 

(U 

■a 

3 

0 

Latitude  of  same  name  as  declination. 

Latitude  of  different  name  from  declination. 

■  1 

■  .2 

3         .S 

<      Q 

w 

60° 

50° 

40° 

30° 

20° 

10° 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

II 

II 

II 

// 

// 

II 

II 

// 

II 

// 

/'        /' 

II 

II 

0       0 

0 

97 

f^ 

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5? 

35 

18 

0 

18 

35 

52 

66       79 

89 

97 

0 

10 

94 

86 

76  1     63 

48 

31          H 

—     4 

23 

40 

57 

72  1     85  1     95 

103 

10 

20 

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86 

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27         10 

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45 

64      80      93     104 

20 

30 

97 

89 

77       62 

45  i      26  i        6 

—  14 

35  i    55 

74  \    91      106 

30 

14 

40 

106 

96 

82       66 

46  1      25  1        2 

—  21 

44        67   !     88   ;    107 

1 

40  !  14 

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109 

93  \     73 

50  !      25  ;  -  2 

-  30 

58 

85 

no 

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60 

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41  :     58  !     73       86 

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104 

10 

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48  i     66  I     82       95 

106 

20 

30 

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87 

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109 

30 

16 

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80  !    63 

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40  J  16 

50 

106 

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47 

21        —    6 

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54 

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60 

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112 

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102 

92 

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96 

116 

40     18 

50 

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50 

60 

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lO 

20 

93 

85 

74  '     60 

43 

25           6 

-   13 

33 

52       70 

86 

100 

20 

30 

94 

85 

73  !     58 

40 

21           0 

—  21 

42 

63       82      100 

30 

20  !  40 

100 

90 

76  i     59 

39 

17     -  6 

-  31 

55 

78     100 

40     20 

i  ^° 

100 

83       63 

39 

13  1  -15 

-  43 

72 

100  ; 

50 

1  60 

100       74 

43 

ID       — 26 

-  63 

100 

60 

|7o_ 

-   — 

% 

100 

56 
54 

6 

-46 

— 100 

70  j 

83  1    69 

37 

19 

0 

19 

37 

54 

69 

83 

-93 

lOI 

0  i 

'  10 

96 

88 

77       63 

48 

30  1       12 

-     7 

26 

45 

62 

78 

91 

102 

10 

:  20 

93 

^5 

73       59 

43 

25  •        5 

-  15 

35 

54 

72 

88 

103 

1 

20 

1  30 

94 

85 

72  !     57 

39 

19     —  2 

—  23 

45 

66 

86 

103 

30 

22   1  40 

98 

88 

74  1     57 

36 

14     —  9 

-  34 

58 

82     104 

40     22 

■  50 

no 

97 

80       60 

36 

9  !  —19 

-48 

11 

106  i 

50 

60 

117 

95 

68 

38 

4 

—33 

-  70 

107 

! 
1 

60 

'   70 

95" 

131 

92 

47 

—  3 

-56 

—  III 

19 

70 

0 

84       70 

55  '     37 

19 

0 

Zl 

55 

70 

84 

95 

103 

0  ! 

10 

97 

88 

77       64 

48        30         11 

—     8 

27 

46 

63  (     79 

93 

104 

10 

20 

93 

^5 

73       59 

42        24          4 

-   16 

36 

56 

74  !     91 

105 

20 

30 

93 

84 

71       56 

38  :     18—4 

—  26 

48 

69 

89  ,  107 

30 

24      40 

97 

86 

72       54 

34           12       —12 

-  37 

62 

86 

109 

40   24 

f 

107 

93 

77       56 

32          5     -23 

-  53 

83 

III 

1 

50  : 

!    60 

112 

91       64 

32  :  —  2    —39 

-  77 

"5 

60  ; 

7P_. 
0 

96 

123       83 

85  i     72 

38  -13    -67 

—  122 

1 

105 

70 

56     38      19 

0 

19 

38 

56       72 

"85~ 

96 

0 

10 

98 

89 

78       64 

48      30      II 

-    9 

28 

47 

65  i    81  i    95 

106 

10 

20 

95 

85 

73       59 

41      23        3 

—  18 

38 

58 

77       94     108 

20 

30 

93 

l^ 

70       54 

36      16—6 

-  28 

50 

72 

92      III 

30 

2b      40 

96 

85 

70       52 

32       9    —16 

-  41 

66 

91 

114 

40     26 

5° 

105 

92 

74       53 

28       I  ,  —28 

-  58 

88 

117 

50 

60 

108 

86       58 

27 

-  8  i  -46 

-  84 

123 

60 

70 

115 

75 

29 

-23     -78 
20°      10° 

-134 

10° 

70 

'    a 
i  .2 

^      1 
5       SJ 

a 
0 

03 

T3 

7«° 

60° 

50° 

40° 

30° 

0° 

20° 

30° 

40° 

50° 

60° 

70° 

leclir 
Ititu 

Latitude  of  same  n 

line  as  declination. 

Latitude  of  different  name  from  declination. 

I  a  ■  < 

<l«    1 

TABLE  26. 

[Page  319  | 

^ 

Variation  of  the  Sun's  Altitude  in  one  minute  from  noon. 

Latitude. 

Declination  01 

a  different  name  from  the  latitude. 

■a 
3 

0° 

1     1° 

2° 

3° 

4° 

5° 

6° 

1° 

8° 

9° 

10° 

ir 

o 

II 

!     " 

// 

II 

II 

i 

u 

II 

II 

/ ' 

0 

0 

o 

28.1 

22.4  '      18.  7 

16.0 

14.0 

12.4 

II.  I 

10. 1 

0 

I 

28.1 

22.4 

18.  7        16.0 

14.0 

12.4 

II.  2 

10. 1 

9-3 

I 

2 

28.1 

22.4 

18.7 

16.0        14.0 

12.5 

II. 2 

10.  2 

9-3 

8.6 

2 

3 

28.1 

22.4 

18.7 

16.0 

14.0        12.5 

II.  2 

10. 2 

9-3 

8.6 

8.0 

3 

4 

28.1 

22.4 

A-L. 

16.0 

14. 0 

12.5  i      II. 2 

10,2 

9-3 

9-3 
8.6 

8.6 
8.  0 

8.0 

"7.4 

7-4 

4 

5 

22.4 

iSTf- 

16.0 

14. 0 

12.5 

II. 2          10.2 

7.0 

5 

6 

18.7 

16.0 

14.0 

12.5 

II.  2 

10.2            9.3 

8.6 

8.0 

7-5 

7.0 

6.6 

6 

7 

16.0 

14. 0 

12.4 

II.  2 

10.  2 

9.3         8.6 

8.0 

7-5 

7.0 

6.6 

6.2 

7 

8 

14.0 

12.4 

II. 2 

10.2 

9-3 

8.  6         8. 0 

7-5 

7.0 

6.6 

6.2 

5-9 

8 

9 

A^-A^ 

II. 2 

10.2 

9-3 

8.6 

8.  0         7.  5 

7.0 

6.6 

6.2 

5-9 

5-6 

9 

lO 

II.  I 

10. 1 

9-3 

8.6 

8.0 

7. 4         7-  0 

6.6 

6.2 

5-9 

5-6 

5-3 

10 

II 

10. 1 

§•3 

8.6 

8.0 

7-4 

7.  0         6.  6 

6.2 

5-9 

5-6 

5-3 

5-1 

II 

12 

9.2 

8.5 

7-9 

7-4 

7.0 

6. 5         6. 2 

5-9 

5-6 

5-3 

5-0 

4.8 

12 

13 

8.5 

7-9 

7-4 

6.9 

6.5 

6.  2         5.  8 

5-6 

5-3 

5-0 

4.8 

4.6 

13 

14 

7-9 

7-4 

6.9 

6.5 
6.1 

6.2 
5-8 

-     5.8:       5.5  ,_ 
5-5         5-3 

5-3 

5-0 

5-0 
4.8 

4.8 
4.6 

4.6_ 
4.4 

4.4 
4.2 

14 
15 

15 

7.3 

6.9 

"  ^-  5 

i6 

6.8 

6.5 

6.1 

5-8 

5-5 

5.2         5.0 

4.8 

4.6 

4.4 

4.2 

4.1 

16 

17 

6.4 

6.1 

5-S 

5-5 

5-2 

5.0        4.8 

4.6 

4.4 

4.2 

4-1 

3-9 

17 

i8 

6.0 

5-  7 

5-5 

5-2 

5-0 

4.  8         4. 6 

4.4 

4.2 

4.  I 

3-9 

3-8 

18 

20 

5-7 

5-4 

5-2 

4-9 
4-7 

4-7 
4-5 

4-5         4-4 
4. 3         4-2 

^4-2^ 

4.0 

4.0 
3-9 

3-9 
3.8^ 

3-8 
3-6 

3.6 
3-5 

19 

20 

5-4 

51 

4.9 

21 

51 

4.9 

4-7 

4-5 

4-3 

4.  2         4. 0 

3-9 

3-7 

3-6 

3-5 

3-4 

21 

22 

4.9 

4-7 

4-5 

4-3 

4.  I 

4. 0         3-9 

3-7 

3-6 

3-5 

3-4 

3-3 

22 

23 

4.6 

4.4 

4.3 

4.  I 

4.0 

3-8         3-7 

3-6 

3-5 

3-4 

3-3 

3-2 

^3 

24 

4.4 

4.2 

4.1 

4.1 
3-9 

3-9 
3-8 

3-8 
'3-7 

3-  7  .      3-6 
3-5         3-4 

3-5 
3-3 

3-4 

3-2 

3-3    : 

3-1 

3-2 
3-1 

3-1 

3.0 

2% 

25 

4.2 

26 

4.0 

3-9 

^•? 

3-t> 

3-5 

3-4         3-3 

3-2 

3-1 

3-0 

3-0 

2.9 

26 

27 

3-9 

3-7 

3-6 

3-5 

3-4 

3-3         3-2 

3-1 

3-0 

2.9 

2.9 

2.8 

27 

28 

3-7 

3-6 

3-5 

3-4 

3-3 

3-2         3-1 

3-0 

2.9 

2.8 

2.8 

2-7  \ 

28 

29 
30 

3-5 
3-4 

„3.4  i 

3-3  1 

3-2 

3-1 

3-1         3-  0 

2.9 

2.8 

2.8 

2.7 

2.6  i 

29 
'  30 

3-3  i 

3-2  1 

31 

3-0 

3.0        2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5  ' 

31 

3-3 

3-2 

3-1 

3-0 

2.9 

2.9         2.8 

2.7 

2.6 

2.6 

2.5 

31 

32 

31 

3-1 

3-0 

2.9 

2.8 

2.8         2.7 

2.6 

2.6 

2-5 

2-5 

2.4 

32 

33 

3-0 

2.9 

2.9 

2.8 

2.7 

2.7         2.6 

2-5 

2.5 

2.4 

2.4 

2-3 

33 

34 

2.9 

2.8 

2.8 
2.7 

2.7 
2.6 

2.6 

2-5 

2.6         2.5 
2.5         2.4 

2.5 

2.4 

2.4 

2.3 

2.2 

„_  2.3 

2.2 

34 

35 

35 

"2.8 

'2.7 

2.4 

2-3 

2.3 

36 

2.7 

2.6 

2.6 

2-5 

2-5 

2.4         2.4 

2-3 

2.3 

2.  2 

2.  2 

2.  I 

36 

37 

2.6 

2-5 

2-5 

2.4 

2.4 

2.3         2.3 

2.  2 

2.  2 

2.  2 

2.  I 

5>..  I 

37 

38 

2-5 

2.5 

2.4 

2.4 

2-3 

2.3         2.2 

2.2 

2.  I 

2.  I 

2.  I 

2.0 

38 

39 

2.4 

2.4  , 
2.3 ' 

2.3 
2.2 

2.3 

2.  2 

2.  2 

2.  2 

2. 1 
2. 1 

2.  I 
2.0 

2.  I 
2.0 

2.  0 

2.0 

2.0 

_39  _ 

40 

2-3 

2.  2 

2.  I 

2.  o~ 

1-9 

1.9 

40 

41 

2-3 

2.  2 

2.  2 

2.  I 

2.  I 

2.1         2. 0 

2.0 

1-9 

1.9 

1-9 

I.  8 

41 

42 

2.  2 

2.  I 

2.  I 

2.  I 

2.0 

2.0         2.0 

1-9 

1.9 

1-9 

1.8 

1.8 

42 

43 

2.  I 

2.  I 

2.  0 

2.  0 

2.0 

1.9         1.9 

1.9 

1.8 

1.8 

1.8 

1-7 

43 

44  _. 

2.  0 

2.0 

2.  0 

1.9 

1.9 

1.9         1.8 

1.8 

1.8 

1-7 

1-7 

1-7 

44 

'  45 

2.  0 

1.9 

1-9 

1-9 

1.8 

1.8         1.8 

1.7" 

1-7 

1-7 

•■7 

i;6 

45 

46 

1.9 

1.9 

1.8 

I.  8 

1.8 

1.7         1.7 

1-7 

1-7 

1.6 

1.6 

1.6 

46 

47 

1.8 

1.8 

1.8 

1-7 

1-7 

1-7         1.7 

1.6 

1.6 

1.6 

1.6 

1.6 

47 

48 

1.8 

1-7 

1-7 

1-7 

1-7 

1.6         1.6 

1.6 

1.6 

1.6 

1-5 

1-5 

48 

49 
50 

1-7 

1-7 

1-7 

1.6 

1.6 

1.6         1.6 

1-5 
1-5 

1-5 
1-5 

1-5 
1-5 

1-5 
1.4 

1-5 

49 

1.6 

1.6' 

1.6 

1.6 

1.6 

I- 5         1-5 

1.4 

50 

52 

1-5 

1-5 

1-5 

1-5 

1-5 

1.4         1.4 

1.4 

1.4 

1.4 

1.4 

1-3 

52 

54 

1.4 

1.4 

1.4 

1.4 

1-4 

1-3         1-3 

1-3 

1-3 

1-3 

1-3 

1-3 

54 

5^ 

1-3 

1-3 

1-3 

1-3 

1-3 

1.3         1.2 

I.  2 

1.2 

I.  2 

I.  2 

I.  2 

56 

58 
60  ' 

1.2 

1.2  , 

I.  2 

1.2 

I.  2 

1.2         1.2 

I.  I 

1. 1 

I.  I 
I.  0 

I.  I 
I.  0 

I.  I 

I.O 

58 
"  60 

1. 1 

1. 1 

I.I  i 

1. 1 

I.  I 

I.I          I.I 

I.  I 

I.O 

62 

I.O 

I.O 

I.O 

I.  0 

I.O 

I.O              I.O 

I.O 

I.O 

I.O 

I.O 

0.9 

62 

64 

I.O 

0.9 

0.9 

0.9 

0.9 

0.  9         0. 9 

0.9 

0.9 

0.9 

0.9 

0.9 

64 

66 

0.9 

0.9 

0.9 

0.9 

0.8 

0.  8         0. 8 

0.8 

0.8 

0.8 

0.8 

0.8 

66 

68 

0.8 

0.8 

0.8 

0.8 

0.8 

0.  8         0.  8 

0.8 

0.8 

0.7 

0.7 

0.7! 

68 

70 

0.7 
0° 

0  7 

0.7 

0.7 

0.7 
4° 

0.  7         0.  7 

0.7 

r 

0.7 

0.7 
9° 

0.7 
10° 

0.7 

n° 

70 

■l°^^i 

2°     i 

3° 

5° 

6° 

Page  320 

TABLE  26. 

Variation  of  the  Sun 

's  Altit 

ude  in  one  minute  from  noon 
nt  name  from  the  latitude. 

Latitude. 

Declination  of  a  differe 

u 

•0 

3 
1-1 

12° 

13° 

14° 

15° 

16° 

n° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

o 

// 

1/ 

// 

" 

// 

// 

//         // 

II 

// 

// 

II 

II 

C 

o 

9.2 

^•5 

7.9 

7-3 

6.8  ' 

6.4 

6.0  1    5.7 

5-4 

5-1 

4.9 

4  6 

4.4 

0 

I 

8.5 

7-9 

7-4 

6.9 

6.5 

6.  I 

5-7  i    5-4 

5-1 

4.9 

4-7 

4.4 

4.2 

I 

2 

7-9 

7-4 

6.9 

6.5 

6.1 

5.8 

5-5       5-2 

4-9 

4-7 

4.5 

4-3 

4.1 

2- 

3 

7-4 

6.9 

6.5 

6.1 

5-8 

5-5 

5-2       4-9 

4-7 

4-5 

4-3 

4.1 

3-9 

3 

4 
5 

7.0 
675 

6.5 
6.2 

6.2 

5.8 

5-5 

5-2 

5-2       5-0 

4-7 
4.5 

4-5 
4.3 

4-3       4-1 
4.  2       4.  0 

4.0 

3.8 

4 

5-8 

5-5 

5-0       4.8 

3-8 

3-7 

5 

6 

6.2 

5-8 

5-5 

5-3 

5-S 

4.8       4.6       4.4 

4.2 

4-0       3.9 

3-7 

3-6 

6 

7 

5-9 

5-6 

5-3 

5-0 

4.8 

4. 6       4. 4       4.  2 

4.0 

3-9       3-7 

3-6 

3-5 

7 

8 

5.6 

5-3 

5-^ 

4.8 

4.6 

4.4  i    4.2       4.0 

^■1, 

3-7       3-6 

3-5 

3-4 

8 

_9  _ 

10 

5-3 
5-S 

5-0 

4.8" 

4.8 
4-6 

4.6 
4.4 

4.4 

4.  2       4. 1 

3-9 

3-8 
3-6 

3-  6       3-  5 
3-5       3-4 

3-4 
3-3 

3-3 
3-2 

9 

4.2 

4-1  !     3-9       3-8 

ID 

II 

4.8 

4.6 

4.4 

4.2 

4.1 

3-2 

3-8        3-6 

3-5 

3-4       3-3 

3-2 

3-1 

II 

12 

4.6 

4-4 

4.3 

4.1 

3-9 

3-8 

3-7       3-5 

3-4 

3-3       3-2 

3-1 

3-0 

12 

13 

4.4 

4-3 

4.1 

3-9 

3-8 

3-7 

3-5       3-4 

3-3 

3-2       3-1 

3-0 

2.9 

13 

14 
15 

4.2 
4.  I 

4.1 
3-9 

3-9 
3.8 

3-8 
.3-7 

.    3.7 
3-5 

3-5 
3-4 

3-4       3-3 

3.2 

3-1  1    3-0 

2.9 
2.  8 

2.8 
2.8 

14 
15 

3-3       3-2 

3-1 

"3.0 

^•§ 

lb 

3-9 

3-8 

3.7 

3-5 

3-4 

3-3 

3-2       3.1 

3-0 

2.9 

2.8 

2.8 

2.7 

16 

17 

3-« 

3-7 

•3-5 

3-4 

3-3 

3-2 

3-1       3-0 

2.9 

2.8 

2.8 

2.7 

2.6 

17 

i8 

3-7 

3-5 

3-4 

3-3 

3-2 

3-1 

3.0       2.9 

2.9 

2.8 

2.7 

2.6 

2.5 

18 

19 

3-5 

3-4 
3-3 

3-3 

3-2 

3-1 

3-0 

2.9       2.9 

2.8 

2.7 
2.6 

2.6 

2.6 

2.5 

19 

20 

3-4 

3-2 

3-1 

3-0 

2.9 

2. 9  ;    2. 8 

2.6 

2.5 

2,4 

20 

21 

3-3 

3-2 

3-1 

3-0 

2.9 

2.8 

2.  8  i     2.  7 

!    2.6 

2.6 

2.5 

2.4 

2.4 

21 

22 

3-2 

3-1 

3-0 

2.9 

2.8 

2.8 

2.7 

2.6 

-2.6 

2-5 

2.4 

2.4 

2.3 

22 

23 

3-1 

3-0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.4 

2.4 

2.3 

2.3 

23 

24 

3-0 

2.9 
2.8 

2.8 
2.-7 

2.8 

2.7 

2.6 

2.5 

2-5 

j    2.4 

2.4 

2.3 

2.3 

2.2 

24 

25 

2.9 

2.7 

2.6 

2.5 

2.5 

2.4 

!  2.4 

2.3 

2.3 

2.2 

2.2 

25 

26 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.  I 

2.  I 

26 

27 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.2 

2. 2    1      2.  I 

2.  I 

2.  I 

27 

28 

2.6 

2.6 

2.5 

2.5 

2.4 

2.3 

2-3 

2.  2 

2.2 

2.  I          2.  I 

2.  I 

2.  0 

28 

29 
30 

2.6 

2.5 

2.4 

2.4 

2.3 

2-3 

2.2 

2.  2 

2. 1 

2.  I          2.0 

2.0 

2.  0 

29 

2.5 

2.4 

2.4 

2.3 

2.3 

2,2 

2,2 

2. 1 

2. 1 

2. 0    i      2.0 

2.0 

1-9 

30 

31 

2.4 

2.4 

2-3 

2-3 

2.2 

2.  2 

2.  I 

2.  I 

2.0 

2.0          2.0 

1.9 

1.9 

31 

32 

2-3 

2.3 

2.  2 

2.  2 

2.  2 

2.  I 

2.1       2.0 

2.0 

1.9          1.9 

1-9 

1.8 

32 

33 

2-3 

2.  2 

2.2 

2.  I 

2.  I 

2.  I 

2.  0       2.  0 

'•9 

1.9 

1.9 

1.8 

1.8 

33 

34 
35 

2.  2 

2.2 

2.  I 
2.  I 

2.  I 

2.0 

2.0          2.0           1.9 

1-9 

1.9 

1.8 

1.8 

1.8 
1-7 

34 
35 

2.2 

2.  I 

2.0 

2.0 

2.0 

1.9       1.9 

1     1.8 

1.8 

1.8 

1-7 

36 

2.  I 

2.  I 

2.0 

2.0 

1.9 

1.9 

1.9  i     1.8 

;    1.8 

1.8 

1-7 

1.7 

1-7 

36 

37 

2.0 

2.0 

2.0 

1,9 

1.9 

1.9 

1.8       1.8 

1    1.8 

1-7 

1-7 

1-7 

1.6 

37 

3« 

2.  0 

1-9 

1.9 

1-9 

1.8 

1.8 

1.8  j     1.8 

1-7 

1-7 

1-7 

1.6 

1.6 

38 

39 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8       1.7  1     1.7 

1     1.7 

1.6 

1.6 

1.6 

1.6 
1-5 

39 
40 

40 

1-9 

1.8 

1.8 

1.8 

1.7 

1. 7  1    1.7       1.7 

1     1.6 

1.6 

1.6 

1.6 

41 

1.8 

1.8 

1.8 

1.7 

1-7 

1. 7       1.6       1.6 

'     1.6 

1.6 

1-5 

1-5 

1-5 

41 

42 

1.8 

1-7 

1-7 

'•l 

;    ^-7 

1.6       1.6 

1.6 

1.6 

1-5 

1-5 

1-5 

1-5 

42 

43 

1-7 

1-7 

^•l 

1.6 

1.6 

1.6       1.6 

1-5 

1-5 

1-5 

1-5 

1.4 

1.4 

43 

.    44 

1-7 

1.6 

1.6 

1.6 

1.6 

i.S       1.5 

I- 5 

'     1-5 

1.4 

1.5 

1.4 

1.4 

1.4 

44 

45 

1.6 

1.6 

1.6 

1-5 

1-5 

1-5       1-5 

1-5 

1.4 

1.4 

1.4 

1.4 

45 

46 

1.6 

1.6 

1-5 

1-5 

1-5 

1.5       1.4       1.4 

1.4 

1.4       1.4 

1-3 

1-3 

46 

47 

••5 

1-5 

1-5 

1.5 

1.4 

1.4       1.4 

1.4 

1.4 

1-3       1-3 

1-3 

1-3 

47 

48 

1-5 

1-5 

1.4 

1.4 

1.4 

1.4  ,     1.4 

1.4 

1-3 

1-3       1-3 

1-3 

1-3 

48 

49 

1.4 

1.4 

1.4 

1.4 

1-4 

1-3  '     1.3 

1-3 

1-3 

1-3        1-3 

1.2 

1.2 

49 

50 

1.4 

1.4 

1.4 

1-3 

1-3 

1-3        1-3 

1-3 

1-3 

1.3        1.2 

I.  2 

I.  2 

50 

52 

1-3 

1-3 

1-3 

1-3 

1.3 

1.3        1.2 

I.  2 

I.  2 

I.  2        I.  2 

I.  I 

I.  I 

52 

54 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2        1.2 

I.  I 

I.  I 

I.I        I.I 

I.  I 

I.  I 

54 

56 

I.  2 

I.  I 

1. 1 

I.I 

I.  I 

I.  I  j     1. 1 

1. 1 

i     ^"  ' 

1. 1        1.0 

1.0 

1.0 

56 

5« 

I.  I 

I.  I 

1. 1 

I.I 

!     1.0 

1.0       1.0 

1.0 

1.0 

1.0       1.0 

1.0 

1.0 

58 

60 

I.  0 

I.O 

I.  0 

1.0 

1.0 

1.0       1.0 

0.9 

0.9 

0. 9       0. 9 

0.9 

0.9 

60 

62 

0.9 

0.9 

0.9 

0.9 

0.9 

0.  9       0. 9 

0.9 

0.9 

0. 9       0. 9 

0.9 

0.8 

62 

64 

0.9 

0.9 

0.9 

0.9 

0.8 

0.  8       0.  8 

0.8 

0.8 

0.  8       0.  8 

0.8 

0.8 

64 

66 

0.8 

0.8 

0.8 

0.8 

0.8 

0.  8       0. 8 

0.8 

0.8 

o.  7  ;     0.  7 

0.7 

66 

68 

0.  7 

0.7 

0.7 

0.7 

0.7 

0.  7       0.  7       0.  7 

0.7 

0.7  : 

68 

70 

0.7 

12" 

0.7 
13° 

0.7 
14° 

0.6 

0.6 

0.  6       0.  6       0.  6 

70 

15° 

16° 

ir  '  18° 

19° 

'   20° 

21°   !   22° 

23° 

24° 

TABLE  26 

Page 

321 

^k 

Variation  of  the  Su 

n's  Altitude  in  one  minute  from  noon. 

3 

• 

Declination  of  the  same  name  as  the  latitude. 

B 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

r 

8° 

9° 

10° 

11° 

C 

II 

II 

// 

// 

II 

II 

II 

II 

II 

II 

II 

II 

0 

o 

28.1 

22.4 

18.7 

16.0 

14.0 

12.4 

II.  I 

10. 1 

0 

I 

28.0 

22.4 

18.6 

16.0 

13-9 

12.4 

II.  I 

I 

2 

28.0 

22.3 

18.6 

15.9 

13-9 

12.3 

2 

3 

27.9 

22.3 

18.5 

15.8 

13.8 

3 

4 

28.1 

27.8 

22.2 

18.5 

15-8 

4 
5 

5 

22.4 

28.0 

27.7 

22. 1 

18.4 

6 

18.7 

22.4 

28.0 

27.6 

22.0 

6 

7 

16.0 

18.6 

22.3 

27.9 

27.4 

7 

S 

14.0 

16.0 

18.6 

22.3 

27.8 

8 

9 

12.4 

13.9 

15.9 

18.5 

22.2 

27.7 

9 

10 

II.  I 

12.4 

13-9 

15.8 

18.5 

22. 1 

27.6 

10 

II 

10.  I 

II.  I 

12.3 

13.8 

15.8 

18.4 

22.0 

27.4 

II 

12 

9.2 

10.  I 

II.  I 

12.3 

1.3.8 

15.7 

18.3 

21.9 

27.3 

12 

13 

«.5 

9.  2 

10. 0 

II. 0 

12.2 

13.7 

15.  b 

18.2 

21.7 

27.1 

13 

14 

7-9 

8-5 

-9-2 

10. 0 

10.9 

12. 1 

13.6 
12. 1 

15.5 

13-5 

18.0 

21,6 

26.9 

14 

15 

7-3 

7.8 

8.4 

9.1 

9.9 

10.9 

15-4 

17.9 

21.4 

26.  7 

15 

16 

6.8 

7-?, 

7.8 

8.4 

9.1 

9.8 

10.8 

12.0 

13.4 

15.3 

17.8 

21.3 

16 

17 

6.4 

6.8 

7.  2 

7.8 

8.3 

9.0 

9.8 

10.7 

II. 9 

n-2, 

15.2 

17.6 

17 

18 

6.0 

6.4 

6.8 

7.2 

7.7 

8.3 

8.9 

9.7 

10.  6 

II. 8 

13.2 

15.0 

18 

19 

5-7 

6.0 

6.3 

6.7 

7.2 

7.6 

8.2 

8.9 

9.6 

10.6 

II.  7 

13. 1 

19 

20 

5-4 

5-7 

6.0 

6.3 

6.7 

7- J 

7.6 

8.1 

8.8 

§■5 

10.5 

II. 6 

20 

21 

5-1 

5-4 

5-6 

5-9 

(5-3 

6.6 

7.0 

7-5 

8.1 

8.7 

^•5 

10.4 

21 

22 

4-9 

51 

5-3 

S-^ 

5-9 

6.2 

6.6 

7.0 

7-5 

8.0 

8.6 

9-4 

22 

23 

4.6 

4.8 

5-0 

5-3 

5-5 

5-8 

6.1 

^•5 

6.9 

^4 

7-9 

8.5 

23 

24 

4.4 

4.6 

4.8 

5-0 

5-2 

5.5 

5.8 
5-4 

6.1 

5-7 

6.4 
6.0 

6.8 
6.4 

7.3 

6.8 

7.8 

24 

25 

4.2 

4.4 

4.6 

4.7 

S-o 

5-2 

7.2 

25 

26 

4.0 

4.2 

4-3 

4-5 

4.7 

4.9 

5-1 

5-4 

5-7 

6.0 

6-3 

6.7 

26 

27 

3-9 

4.0 

4.1 

4-3 

4.5 

4.7 

4-9 

^•l 

5-3 

5-b 

5-9 

6.2 

27 

28 

3-7 

3.8 

4.0 

4.1 

4-3 

4.4 

4.6 

4.8 

5-0 

5-3 

5-5 

5.8 

28 

29 

3-5 

3-7 

3.8 

3-9 

4.1 

4.2 

4.4 

4.6 

4-7 

5-0 

5.2 

5-5 
5-1 

29 

30 

3-4 

3-5 

3-6 

3.7 

3-9 

4.0 

4.2 

4-3 

4.5 

4-7 

4.9 

30 

31 

2,-2, 

3-4 

3-5 

3.b 

■h-1 

3-8 

4.0 

4.1 

4-3 

4.4 

4.6 

4.8 

31 

•T7 

J- I 

3-2 

3-3 

3-4 

3-5 

3-7 

3.8 

3-9 

4-1 

4.2 

4-4 

4.6 

32 

33 

3-0 

3-1 

3-2 

2,-2, 

3.4 

3-5 

3-6 

3.7 

3-9 

4.0 

4.2 

4-3 

2>2 

34 

2.9 

3-0 

3.1 

3-2 

3-2 

3-3 

3-4 

3.b 

3.7 

3.8 

3.9 

3-7 

4.  I 

34 

35 

2.8 

2.9 

3  ° 

3.0 

3-1 

3-2 

3-3 

3-4 

3-5 

3-6 

3-9 

35 

3b 

2.7 

2.8 

2.8 

^•% 

3-0 

3-1 

3-2 

3-3 

3-4 

3-5 

3-6 

3-7 

Z^ 

37 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 

3-0 

3-1 

3-2 

3-i 

3-4 

3-5 

37 

3« 

2-5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3-0 

3-0 

3-2 

3-2 

Z-i 

38 

39 

2.4 

2-5 

2.5 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 
2.8 

3-  0 
2.  9 

3-1 

3-2 

3-2 

3-^ 

_39 
40 

40 

2.3 

2.4 

2.4 

2-5 

2.6 

2.6 

2.7 

2.7 

41 

2-3 

2-3 

2.4 

2.4 

2^5 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

41 

42 

2.  2 

2.  2 

2-3 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.6 

2.7 

2.8 

42 

43 

2.  I 

2.  I 

2.  2 

2.  2 

2-3 

2.3 

2.4 

2.4 

2.5 

2-5 

2.6 

2.7 

43 

44 

45 

2.0 

2.1 

2.  I 

2.  I 

2.2 

2,2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.4 

2-5 

2.4 

44 
45 

2.0 

2.0 

2.0 

2.  I 

2.  I 

2,2 

2.2 

2.2 

2.3 

2.3 

4b 

1.9 

1.9 

2.0 

2.  0 

2.0 

2.  I 

2. 1 

2.  2 

2.2 

2.  2 

2.3 

2-3 

46 

47 

1.8 

1-9 

1.9 

1-9 

2.  0 

2.0 

2.0 

2.  I 

2.  I 

2. 1 

2.2 

2.2 

47 

48 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.  I 

2.  I 

48 

49 

1.7 

1-7 

1.8 
1.7 

1.8 
1.7 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 
~i.9' 

2.0 
1.9 

2.  I 

49 

50 

1.6 

1-7 

1.8 

1.8 

1.8 

1.8 

1.9 

2.0 

50 

52 

1-5 

1.6 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1-7 

1.8 

1.8 

1.8 

52 

54 

1.4 

1.4 

1-5 

1-5 

1-5 

1-5 

1-5 

1.6 

1.6 

1.6 

1.6 

1-7 

54 

5(' 

'•3 

••3 

1.4 

1.4 

1-4 

I. -4 

1.4 

1.4 

1-5 

1-5 

1-5 

1-5 

5(^ 

5« 

I.  2 

I.  2 
I.  I 

1-3 
I.  2 

1-3 
I.  2 

i-3_ 
1.2 

1-3 
1.2 

1-3 

1-3 

1.3 

1.2 

1.4 
1.2 

1.4 

1.4 

58 

60 

I.  I 

1.2 

1.2 

1.3 

1.3  1 

60 

62 

I.  0 

I.  0 

I.  I 

1. 1 

I.  I 

I.  I 

I.  I 

I.  I 

I.I 

I.  I 

I.  2 

I.  2 

62 

64 

I.  0 

1. 0 

I.  0 

I.O 

1.0 

I.  0 

1.0 

1.0 

1.0 

I.  0 

1.0 

1. 1 

64 

60 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

I.  0 

66 

68 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.9 

0.9 

68 

7(j 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.8 
8° 

0.8 
9° 

0.8 

0.8 

70 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

10° 

11° 

I^M^ 

21  B 


Page 

(322] 

TABLE  26. 

Variation  of  the  Sun's  Altitude  in 

one  minute  from  noon. 

3 

■■§ 

1-1 

Declination  of  the  same  name  as  the  latitude. 

1) 

12° 

13° 

14° 

15° 

16° 

n° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

o 

// 

II 

II 

ji 

II 

II 

II 

II 

II 

II 

II 

II 

II 

o 

9.2 

8.5 

7-9 

7-3 

6.8 

6.4 

6.0 

S-7 

5-4 

5-1 

4.9 

4.6 

4.4 

0 

I 

10. 1 

9.2 

8.5 

7.8 

7-3 

6.8 

6.4 

6.0 

5-7 

5-4 

5-1 

4.8 

4.6 

I 

2 

II.  I 

10. 0 

9.2 

8.4 

7.8 

7-5 

6.8 

b.3 

6.0 

.5.0 

5-3 

5-0 

4.8 

2 

3 

12.3 

II. 0 

lO.O 

9.1 

8.4 

7.8 

7.2 

6.7 

b.3 

5-9 

5-0 

5-3 

5-0 

4 

13- « 

12. 2 

10.9 

9-9 

9.1 

8-3 

7.7 

7.2 

6.7 

0.3 

5-9 

5-5 

5-2 
5-5 

4 
5 

5 

15-7 

13-7 

12.  I 

10.9 

9.8 

9.0 

8.3. 

7.6 

7-1 

6.6 

6.2 

5-8 

6 

18.  3 

15.6 

13.6 

12.  I 

10.8 

9.8 

8.9 

8.2 

7.6 

7.0 

6.6 

6.1 

5-8 

6 

7 

21.9 

18.2 

15-5 

13-5 

12.0 

10.  7       9.  7 

8.9 

8.1 

7-5 

7.0 

6.5 

6.1 

7 

8 

27.3 

21.7 

18.0 

15-4 

13-4 

II.  9     10.6 

9.6 

8.8 

8.  I 

7-5 

6.9 

6.4 

8 

9 

27.1 

21.6 

17.9 

15-3 

13-3      "-8 

10.6 

9-5 

8.7 

8.0 

7-4 

6.8 

9 

lO 

26.9 

21.4 

17.8 

15.2  1  13.2 

II. 7 

10.5 

9-5 

8.6 

7-9 

7-3 

10 

II 

26.  7 

21.3 

17.6  1  15.0 

13- 1 

II. 6 

10.4 

9.4 

8.5 

7.8 

II 

12 

26.5 

21.  I 

17-5 

14.9 

13.0 

II. 5 

10.3 

9-3 

8.4 

12 

13 

26.2 

20.9 

^1-7> 

14.8 

12.  8 

"•3 

10.  I 

9.2 

13 

H 

26.0 

20.  7 

17.1 

14.6 
16.9 

12.7 

II. 2 

10.  0 

1  + 

IS 

25-7 

20.4 

14.4 

12.5 

11.  I 

15 

i6 

26.5 

25.4 

20.  2 

16.7 

14-3 

12.4 

16 

17 

21.  I 

26.2 

25.1 

20.  0 

16.  s 

14.  I 

17 

i8 

17-5 

20.9 

26.0 

24.8 

19.7 

16.3 

18 

19 

14.9 

17.3 

20.  7 

25-7 

24-5 

19-5 

19 

20 

13.0 

14.8 

17. 1 

20.4 

25-4 

24.2 

20 

21 

II-5 

12.8 

14.  6 

16.9 

20.2 

25-1 

21 

22 

10.3 

"•3 

12.  7 

14.4 

16.7 

20.0 

24.8 

22 

23 

l-^ 

10.  I 

II.  2 

12.5 

14-3 

lb.  5 

19.7 

24-5 

23 

24 

8.4 

9.2 

10.  0 

II.  I 

12.4 

14.1 

16.  3 

19.5 

24.  2 

24 

25 

7-7 

8.3 

9.0 

9.9 

10.9 

12.2  :  13.9 

16. 1 

19.2 

23.8 

25 

26 

7-1 

7.6 

8.2 

8.9 

9.8 

10.  8      12.  I 

13-7 

15-9 

18.9 

23-5 

26 

27 

6.6 

7.0 

7.5 

8.1 

8.8 

9.6      10.6 

II. 9 

13-  5 

15-0 

18.6 

23.1 

27 

28 

6.2 

('•S 

7.0 

7.4 

8.0 

8.  7       9.  5 

10.5 

II.  7 

13-3 

15-4 

18.3 

22.  7 

28 

29 

5-7 

6.1 

6.4 

6.9 

7-3 

7. 9  ;    8.  6 

9.4 
8.4 

10.3 

"•5 

13- I 

15- 1 

18.0 

29 

30 

5-4 

5-7 

6.0 

6.4 

6.8 

7.2 

7.8 

9.2 

10. 1 

"•3 

12.8 

14.9 

30 

31 

5-1 

5-3 

5-b 

5-9 

b.3 

6.7 

7.1 

1-1 

8-3 

9.0 

10.  0 

II.  I 

12.  6 

31 

32 

4.« 

5-0 

5-2 

5-5 

5.8 

6.2 

0-5 

7.0 

7-5 

8.1 

8.9 

9.8 

10.  9 

32 

33 

4.5 

4-7 

4-9 

5-' 

5-4 

5-7 

6.1 

6.4 

6.9 

7-4 

8.0 

8.7 

9.6 

2,2, 

34 

4.3 

4.4 

4.6 

4.8 

5-1 

5-3 

S-b 

5-9 

^-■3 

6.8 
6.2 

7-3 
676 

7-1 

8.6 

34 

35 

4.0 

4.2 

4.4 

4.5 

4.7 

5-0 

5-2 

5-5 

5-8 

1-7 

35 

3b 

3.« 

4.0 

4.1 

4-3 

4-5 

4-7 

4.9 

5-i 

5-4 

5-7 

6.1 

0.5 

7.0 

30 

H 

3.0 

3.« 

3-9 

4.0 

4.2 

4.4       4.6 

4.8 

5.0 

5-3 

5-0 

6.  0 

6.4 

37 

3« 

3-4 

3-6 

3-7 

3-« 

4.0 

A-  I       4- 3 

4.5 

4-7 

4.9 

5-2 

5-5 

5.8 

38 

39 

3-3 

3-4 

3-5 

3-0 

3.« 

3.9       4.0 

4.2 

4.4 

4.6 

4.8 

5-1 

5-4 

39 

40 

3-1 

3-2 

3-3 

3-4 

3.6 

3-7 

3-8 

4.0 

4.1 

4-3 

4-5 

4-7 

5-0 

40 

41 

3-0 

3-1 

3-2 

3-3 

3-4 

3-5 

3-b 

3-7 

3-9 

4.0 

4.2 

4.4 

4.6 

41 

42 

2.9 

2.9 

3-0 

31 

3-2 

3-3 

3-4 

3-5 

3-7 

3.8 

4.0 

4-1 

4-3 

42 

43 

2.7 

2.8 

2.9 

3-S 

3-0 

3-1 

3-2 

3-3 

3-5 

3-0 

3-7 

3-9 

4.0 

43 

44 

2.6 

2.7- 

2.7 

2.8 

2.9 

3-0 

3-1 

3-2 

3-3 

3-4 

3-5 

3-0 
3-4 

3-8 

44 

45 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3-° 

3-1 

3-2 

3-3 

3-5 

45 

46 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3-0 

.3-1 

3-2 

.3-3 

46 

47 

2-3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2.9 

2.9 

3-0 

3-1 

47 

48 

2.2 

2.  2 

2-3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.  7 

2.8 

2.9 

3-0 

48 

49 

2.  I 

2. 1 

2.2 

2.  2 

2-3 

2.3 

2.4 

2.4 

2-5 

2.6 

2.6 

2.7 

2.8 

49 

50 

2.0 

2.0 

2.  I 

2.  I 

2.2 

2.2 

2.3 

2-3 

2.4 

2.4 

2.5 

2.6 

2.6 

50 

52 

1.8 

1.9 

1.9 

1-9 

2.0 

2.0 

2.  I 

2.  I 

2.  I 

2.  2 

2.  2 

2.3 

2.4 

52 

54 

1-7 

1-7 

1-7 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.  I 

2.  I 

54 

56 

1-5 

1.6 

1.6 

1.6 

1.6 

1-7 

1.7 

1-7 

1.8 

1.8 

1.8 

1.9 

1.9 

56 

5« 

1.4 

1.4 

1-5 

1-5 

1-5 

1-5 

1-5 

1.6 

1.6 

1.6 

1.6 

1.7 

1-7 

1-5 

58 

60 

1-3 

1-3 

1-3 

1-3 

1.4 

1.4 

1.4 

1.4 

1.4 

1-5 

1-5 

1-5 

60 

62 

I.  2 

I.  2 

1.2 

(     '-^ 

I.  2 

1.2 

1-3 

1-3 

1-3 

1-3 

1-3 

1-3 

1.4 

62 

64 

I.  I 

I.  I 

I.  I 

'     I.  I 

1. 1 

1. 1 

I.  I 

I.  2 

1.2 

I.  2 

1.2 

1.2 

I.  2 

64 

66 

I.  0 

I.O 

I.  0 

1.0 

1.0 

1.0 

1.0 

I.  0 

1.0 

I.  I 

1. 1 

1. 1 

I.  1 

66 

68 

0.  9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

1.0 

I.  0 

68 

70 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 
17° 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.9 

70 

12° 

13° 

14° 

15° 

16° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

». 

TABLE  27. 

Page 

323 

To  reduce  the  numbers  of  Table  26  to  other  given  intervals  of  time  from  noon. 

Time  from  noon. 

s. 

o 

s. 

0' 

V 

r 

3' 

16.0 

5'    '    6' 

r 

8^ 

9' 

10^ 

iv 

12' 

0.0 

I.  0 

4.0 

9.0 

25. 0     36. 0    49. 0 

64. 0 

81.0 

100. 0 

121. 0 

144.0 

0 

I 

0.  0 

1.0 

4.1 

9 

I 

16.  I 

25. 2     36. 2     49. 2 

64-3 

81.3 

100.3 

121. 4 

144.4 

I 

2 

0.  0 

1. 1 

4-1 

9 

2 

16.3 

25-3     36.4     49-5 

64-5 

81.6 

100.  7 

121. 7 

144.8 

2 

3 

0.0 

I.  I 

4.2 

9 

3 

16.4 

25-  5     36.  6  1  49.  7 

64.8 

81.9 

lOI.O 

122. 1 

145.2 

3 

4 

0.0 

1. 1 

4-3 

9 

4 

16.5 

25.  7     36.  8     49.  9 

65.1 

82.2 

101.3 

122. 5 

145-6 

4 

5 

0.0 

1.2 

4-3 

9 

5 

16.7 

25.8     37.0  1  50.2 

65-3 

82.5 

101.7 

122. 9 

146. 0 

5 

6 

0.0 

1.2 

4.4 

9 

6 

16.8 

26.0     37.2     50.4 

65.6 

"  82.8 

102.  0 

123.2 

146.4 

6 

7 

0.  0 

I.  2 

4-5 

9 

7 

16.9 

26.2     37.4  1  50.6 

65.9 

83.1 

102.3 

123.6 

146.8 

7 

8 

0.  0 

1-3 

4.6 

9 

8 

17.  I 

26.4     37.6     50.9 

66.1 

83.4 

102.  7 

124. 0 

147-2 

8 

9 

0.  0 

1-3 

4.6 

9 

9 

17.2 

26.5     37.8     51.  I 

66.4 

83-7 

103.  0 

124-3 

147.6 

9 

lO 

0.0 

1.4 

4-7 

10 

0 

17.4 

26.7     38.0     51.4 

66.7 

84.0 

103.4 

124.7 

148.  0 

10 

II 

0.0 

1.4 

4.8 

10 
10 

I 
2 

17-5 
17.6 

26.9     38.2     51.6 

27.0      38.4  :   51.8 

67.0 
67.2 

84-3 

_i°3i_L 

125.1 

148.4 

u 

12 

0.0 

1.4 

4.8 

84.  6 

104.0 

125.4 

148.8 

12 

13 

0.0 

1-5 

4.9 

10 

3 

17.8 

27.  2     38.  6     52.  I 

67.  5 

84.9 

104.4 

125.8 

149.2 

13 

14 

0. 1 

1-5 

5-0 

10 

5 

17.9 

27-4     38.9     52-3 

67.8 

85-3 

104.7 

126. 2 

149-7 

14 

15 

0. 1 

1.6 

5- 1 

10 

6 

18.  I 

27.6     39.1      52.6 

68.1 

85.6 

105.  I 

126.6 

150.  1 

15 

i6 

0. 1 

1.6 

5-1 

10 

7 

18.2 

27-  7     39-  3     52.  8 

68.3 

85-9 

105.4 

126. 9 

150.5 

16 

17 

0. 1 

1.6 

5-2 

10 

8 

18.3 

27-9     39-5     53- 0 

68.6 

86.2 

105-7 

127-3 

150-9 

17 

i8 

0. 1 

1-7 

5-3 

10 

9 

18:5 

28.  I     39-  7     53-  3 

68.8 

86.  s 

106.  I 

127.7 

151-3 

18 

19 

0. 1 

1.7 

5-4 

II 

0 

18.6 

28.  3     39-  9     53-  5 

69.2 

86.8 

106. 4 

128. 1 

151.  7 

19 

20 

0.1 

1.8 

5-4 

II 

I 

18.8 

28. 4     40. 1     53.  8 

69.4 

87.1 

106.8 

128.4 

152.  I 

20 

21 

0. 1 

1.8 

5-5 

II 

2 

18.9 

28.  6     40.  3     54.  0 

69.7 

87.4 

107.  I 

128.8 

152.5 

21 

22 

0. 1 

1.9 

5-6 

II 

3 

19. 1 

28.  8     40.  5     54.  3 

70.0 

87.7 

107.5 

129. 2 

152.9 

22 

23 

0. 1 

1-9 

5-7 

II 

4 

19.2 

29.  0     40.  7     54.  5 

70.3 

88.0 

107.8 

129.  6 

153.3 

23 

24 

0.2 

2.0 

5-! 

II 

6 

19.4 

29.2     41.0     54.8 

70.6 

88.4" 

108.  2 

130.0 

153-8 

24 

25 

0.  2 

2.0 

5-8 

II 

7 

19-5 

29.3     41.2     55.0 

70.8 

88.7 

108.5 

130.3 

154-2 

25 

26 

0.  2 

2.  I 

5-9 

II 

8 

19.7 

29.5     41.4     55.3 

71.  I 

89.0 

108.9 

130.7 

154.6 

26 

27 

0.  2 

2.  I 

6.0 

II 

9 

19.8 

29.7     41.6     55. 5 

71.4 

f9-3 

109.  2 

131.  1 

155-0 

27 

28 

0.  2 

2.  2 

6. 1 

12 

0 

20.0 

29.9     41.8     55.8 

71-7 

89.6 

109.  6 

131-5 

155-4 

28 

29 

0.2 

2.2 



6.2 

12 

I 

20. 1 

30. 1     42. 0     56. 0 

72.0 

89.9 

109.9 

131-9 

155.8 

29 

30 

0.  2 

2.  2 

6.2 

12 

2 

20.  2 

30.  2     42.  2     56.  2 

72.2 

90.  2 

no.  2 

132.2 

156.  2 

30 

31 

0.3 

2-3 

6.3 

12 

4 

20.4 

30.  4     42.  5     56.  5 

72.5 

90.  6 

no.  6 

132.6 

156.7 

31 

32 

0.3 

2.4 

6.4 

12 

5 

20.  6 

30.  6     42.  7     56.  8 

72.8 

90.9 

III.O 

133-0 

157-1 

32 

33 

0.3 

2.4 

f-I 

12 

6 

20.  7 

30.8     42.9     57.0 

73-1 

91.  2 

III. 3 

133-4 

157-5 

34 

0.3 

2-5 

6.6 

12 

7 

20.9 

31.0     43.1      57.3 

73-4 

91-5 

III. 7 

133-8 

157-9 

34 

35 
36 

0-3 
0.4 

2-5 
2.6" 

6.7 
6.8 

12 

8 

21.0 

31.2     43.3     57.5 
31-4     43-6     57-8 

73-7 
74.0 

91.8 

112.  0 

134.2 

158-3 

35 

13 

0 

21.2 

92.  2 

1 12. 4 

134.6 

158.8 

'36  " 

H 

0.4 

2.6 

6.8 

13 

I 

21.3 

31.5     43-8     58.0 

74-3 

92.5 

112.  7 

134-9 

159.2 

37 

3« 

0.4 

2.7 

6.9 

13 

2 

21-5 

31.7     44.0     58.3 

74-5 

92.8 

113.  I 

135-3 

159.6 

38 

39 

0.4 

2.7 

7.0 

13 

3 

21.6 

31.9     44.2     58.5 

74.8 

93-1 

1 13- 4 

135-7 

160.  0 

39 

40 

0.4 

2.8 

7-1 

13 

4 

21.8 

32.1     44.4     58.8 

75-1 

93-4 

113-8 

136.  I 

160. 4 

40 

4' 

0.  5 

2.8 

2.  9 

7.2 
7.3 

13 

6 

21.9 

32. 3     44-  7 

59.0 

59-3 

75-4 

75-7 

93-8 

114.  I 

136.5 

1.60.9 

41 

42 

0-5 

13 

7 

22.  I 

32-  5     44-9 

94.  I 

"4-5 

136.9 

161.3 

42 

43 

0-5 

2.9 

7-4 

13 

8 

22.  2 

32.  7     45.  I      59.  5 

76.0 

94-4 

1 14.  8 

137-3 

161.  7 

43 

44 

0-5 

3-0 

7-5 

13 

9 

22.4 

32.9     45-3     59-8 

76.3 

94-7 

115.2 

137-7 

162.  I 

44 

45 

0.6 

3-1 

7.6 

14 

I 

22.  6 

Si.  I     45.  6     60.  I 

76.6 

95-1 

,15.6 

138.  I 

162.  6 

45 

46 

0.6 

3-1 

7-7 

14 

2 

22.7 

3i-  3     45-  8     60.  3 

76.9 

95-4 

115.9 

138-5 

163.0 

46 

47 
48 

0.6 
0.6 

3-2 
3-2 

7-7 
7.8 

14 

3 

22.9 

33-  4_   46^o_  J>o.^ 

77.1 

95  7 

116.3 
1x6.6" 

138.8 
139.2 

163.4 
163.8 

47 
48 

14 

4 

23.0 

33.  6     46.  2     60. 8 

77.4 

96.0 

49 

0.7 

2,-?, 

7-9 

14 

6 

23.2 

33.8     46.5     61.  I 

77-7 

96.4 

117.0 

139.6 

164.  3 

49 

50 

0.7 

3-4 

8.0 

14 

7 

23-4 

34.0     46.7     61.4 

78.0 

96.7 

117.4 

140.  0 

164.7 

50 

51 

0.7 

3-4 

8.1 

14 

8 

23-5 

34.2     46.9     61.6 

78.3 

97.0 

117.7 

140.4 

165.  I 

51 

52 

0.8 

3-5 

8.2 

15 

0 

23-7 

34.4     47.2     61.9 

78.6 

97-4 

118.  I 

140.8 

165.6 

52 

53 
54 

0.8 
0.8" 

3-5 
3-6" 

8.3 

"8.4' 

15 

I 

23.8 

34.  6     47. 4 

62.1 

78-9  1 
79.2 

97-7 

118. 4 

141.  2 

166.  0 

53 

IS 

2 

24.  0 

34.  8  1  47.  6 

62.4 

98.0 

118.8 

141.  6 

166.4 

54 

55 

0.  S 

3-7 

^•5 

15 

3 

24.  2 

35.0  1  47.8 

62.  7 

79-5 

98.3 

119.  2 

142.0 

166.8 

55 

55 

0.9 

^■l 

8.6 

15 

5 

24-3 

35.  2     48.  I   1  62.  9 

79.8 

98.7 

119- 5 

142.4 

167-3 

56 

57 

0.9 

3-8 

^•7 

15 

6 

24-5 

35.4     48.3  1  63.2 

80.  I 

99.0 

1 19.  9 

142.8 

167.7 

57 

5S 

0.9 

3-9 

8.8 

15 

7 

24.7 

35.  6     48.  5     63.  5 

80.4 

99-3 

120.3 

143-2 

168.  I 

58 

59 

I.O 

0' 

3-9 

r 

8.9 

15 

9 

24.8 

35.8     48.  8  j  63.  7 

80.  7 

99-7 
9' 

120.  6 
10' 

143-6  1 

11'     • 

168.6 
12' 

59 

2' 

r 

4' 

5'     6'  '  r 

8^ 

Page  324 

TABLE  28  A. 

For  finding 

the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

A  = 

=  ist  correction.     Argument,  the  star's  hour  angle  (or  24''  - 

the  star's  hour  angle).                                    1 

tn. 

01^ 

V^ 

21 

V' 

4h 

Si^ 

0  1     II       II 

0    1       II        II 

0   1      II        II 

0  1     II       II 

0  1     II       II 

0    '       "         n 

m.  1 

o 

— I  20    0. 0 

—I  17  16.5 

— 1    9  17.1   ,„     —05634.4  __  „ 

-040   0.3 

— 0  20  42.  5           60 

20    2 

I 

19  59- 9-    '\ 

I7II.0  5 

5 

9    6.6    °-^ 

56  19-6  , 

1-0 

4.9 

5.0 

39  42.  2 

2 

20  22.  7         ■        59 

2 

0         .1 

19  59-8      2 

17    5-5    \ 

S 

f56-o;:-; 

56    4-  7 

3924.0 

■3 

20  2.0^^    58 

3 

19  59-  6      - 

1659.8- 

7 

8  45-  3-  10  7         55  49-  7  ; 
834-6'°-^         55  34-7 

39    5-  7  ,8 

0 
■3 

1941-7  30.     57 

4 

19  59-3 

1654-1 

7 

3847-4 

J 

19  21.4           56 

\ 

-I  1958.9    -^ 
1958.4    -6 

-I  1648.3    I 
1642.4    ^ 

8 
9 

-I  823.8 ;°-« -055 19.6 ; 
812.9  ,;l     55  4.4 , 

5.1 

5-2 

S  .  2 

-038  29.1;^ 

38 10-  7 : 

3 
4 
4 

20.  T 
— 0   19      I.  I            3     55 

?^                                       20.4                  *^ 

'^40-7,0.     54 

7 

19  57-8     •; 

1636.4    g 

J 

8    1.9  XI  I         5449.2  ^ 

37  52- 2- ^g 

5 

18  20.  3- ,0.,' 53 

8 

•  / 

19  57- I      8 

1630-3     6 

J 

750.8  „:^     543.3.9, 

37  33-8  ,8 

5 

1759-9-30.4   52 

9 

1956-3 

16  24.  2 

3 

7  39-7 

-^  728.5  :;•; 

54  IS-  6 

J     J 

S-4 
5.5 
5.6 
S.6 
5-6 

3715-3 

6 
6 

17  39- 5 

51 
50 

10 

—I  19  55.4     "^ 

-I   16  17.9     6 
16  II. 6    ° 

16    5.1-  ^ 
1558-6    g 

—054    3-I-' 

-°  36  56-  7  ,8 

~°^l'l-\  --5 

II 

12 
13 

19  54-  5  Z 
1953-4  ,., 
1952-3   X  , 

5 

6 

r?:8:::: 

^54-4   „.5 

53  47-  7  , 
5332-1. 
53  i6.  5- , 

36  38-  1  J 

3^  "^-  §  '8 
36    0.8  ^g 

6 
7 
7 

•6  58.6,„. 
16  17- 6- ,0.5 

49 
48 

47 
46 

14 

1951.0 

15  52.0 

6  42.  9 

53    0.9 

35  42. 0. 

' 

15  57-  I 

IS 

—I  19  49-7  \'l 

—I   1545-3-    6 
1538-6     ^ 

7 

,                II. 6 
~'     i^^-l   "-7 

— 0  52  45-  2 

5-7 
5-8 
5.8 

5-9 
6.0 

6.0 
6.1 

f,     T 

-0  35  23.  3  18 

8 
8 

^    ^    20 .  s 

-0  15  36-  6  ,„.6 

45 

16 

1948-2     1 

7 

5229.4 

35    4.  5  ,8 

8 

15  i6-o-,„.s 

44 

17 

1946.8  ;-^ 

1531-7     6 

9 

6  7.8-;;:8 

52  13-6  , 

34  45.  6-  ,8 

Q 

14  55-5  20.6 

43 

18 

19 

19  45-2  ,\^ 
19  43-  5 

•      1524-8 
15  17-7 

9 

I 

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7 
0 

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42 
41 
40 

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-°  '3  53-  7  :::, 
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0 

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38 

22 

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2  .  Z 

19  33-  7 

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n^ 

10'" 

91,            i            8" 

7" 

6" 

J 

Change  the  sign  to  +  when  the  argument  is  found  at  the  bottom. 


TABLE  28B.                                                [Page  325 

V 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

B  = 

the  2d  correction.    This  correction  is  always  additive. 

Star's 

Star's  altitude. 

Star's 

hour 
angle. 

— 

hour 
angle. 

10° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

h.  m. 

II 

// 

II 

// 

// 

II 

II 

II 

II 

II 

k.  m. 

o      0 

0.0 

0.0 

0.0 

0. 0      1   0. 0 

0.0 

0. 0       i    0. 0 

0.0 

0.0 

12      0 

10 

0.0 

0 

0. 0 

0 

0.0 

.0 

0.0 

•°  i   0. 0 

.0 

0.0 

0 

0.0 

°i     0.0 

0 

0.0 

0 

0.0 

0 

II    qo 

20 

0.  I 

1 

0. 1 

I 

0. 1 

.1 

0. 1 

'     0.1 

I 

0. 1- 

I 

0. 1. 

'       0.2 

2 

0.2 

2 

0.  2 

2 

40 

T 

I 

7 

2 

7 

7 

2 

7 

V 

7 

30 
40 

50 
I     0 

0.  2 

0-3 
0.5 
0.6. 
0.9 

I 
2 
2 

2 

0.2. 
0.4. 
0.7 

I.O 

2 
3 

3 
3 

0.3 
0.5 
0.7. 

1. 1 

1.4. 

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2 
3 
4 

0.3 
0.5 
0.8 

1. 1 

2 
3 
3 

4 

0.3 

0.  8. 
1.2 

2 
3 

4 
4 

0.6 
0.9 

1-3 
1-7 

3 
3 
4 

4 

0.3. 
0.6 
0.9. 
1.4 
1.8 

0.4 

3         0.6- 

4     1.0 
r  1.4 

3 
4 
4 

5 

0.4 
0.7 

I.O- 

1-5 

3 
3 
5 

S 

0.4 
0.7 
1. 1 
1.6 

3 
4 

s 

5 

30 

20 

10 

0 

10 

I-3- 

1-5 

1.6 

2.0 

2. 1 

10  50 

20 

I.I- 

3 

I.  7. 

4 

1.9 

s 

2.0 

5 

2.1 

5 

2.2- 

6 
6 

2.4 

6      "-5 

0 
6 

7 

8 

2.6 

6 

2.8 

7 

40 

30      1.4 

40  !    I.  8 

J 
4 

2.  2 
2.7 

5 

2.3 
2.9 

4 

6 

2.5 
3.0- 

6 
5 

2.7 
3-2 

0 
5 

2.8 

3-4 

3-0 
3.6  • 

1  3.8 

3-3 
4.0 

7 
7 
8 
8 

3-5 
4.2 

7 

30 
20 

50    ;    2.  I 

3 
4 

3 

3-2 

5 
5 
6 
6 
6 

3-4 

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6 

3.(> 

7      3-9 

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4.1 

7 
7 

7 
8 
8 
8 

4-3 

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4.8 

5-0- 

9 
9 

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4.0 

4.6 

4.3 
4.9 

6        4-5 

1      5-2 

7 
8 

4.8 
5-5- 

5-1 

I   5-^ 

8 
8 

5-6 

6:5 

9 

5-9 

6.8- 

0 

ID       2.8 

4.3 

5-9 

8 
8 
8 

6.2 

9  50 

20 

3-2 

4 

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5-3 

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S.6 

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t).3 

6.7 

7.0- 

7.4  ^ 

y 

7.8 ; 

40 

30 

3.6- 

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5-5 

S-9 

6.3 

7 

6.7 

1 
8 
8 
8 

7 
8 
8 
8 

7-1 

7-5 

^•9\ 

y 

8.4  ' 

8.8  ' 

30 

40 

4.1 

6.2 

7 
6 

7 

6 

6.6 

1 

7.0- 

1 

8 
7 
8 

7-5 

7-9- 

8.4 

y 

8.9  ' 

9-3  . 

y 

9.8 ; 

20 

50 

3    0 

4-5 
4-9 

4 
4 

4 

6.8 

7-5 
8.1 

7-3 
8.0 

8.7 

■J 
7 

7 

7.8 
8.5 

«.3 
9.1 

9.8- 

8.8 
9.6_ 
10.4 

y 

8 
8 

9-3 
10.2 

II. 0  ■ 

9 

9 

8 

9.8 
10.  7 

y 
9 

9 

10. 
II. 

I' 

3^ 

0 
0 

10.8 ' 

II.  8-' 

0 

I 

10 
0 

10 

S-3- 

9-3 

II. 6 

12. 

12.  Q    ' 

8  50 

20 

30 

40 

5.« 
6.2 
6.6 

4 
4 

8.8 

9-4 
10.  0 

6 
6 
6 
6 

6 

9-4 
10.  I 
10.7 

7 

7 
6 

10.  0 
10.7. 
II. 4. 

7 
7 
7 

10.  6- 
II. 4 
12.  2 

II-3 
12.  I 

12.9 

y 

8 
8 
8 

II. 9 

12.8 
13.6 

y 
9 

8 

12.6  ' 

13-5 
14.4 

0 

9 
9 
8 

13-2 

14.2  ^ 
15.  I. 

y 
0 

9 

13-9    1 
14.9 

15-9  , 

u 
0 
0 

40 

30 
20 

50 

7.0 

10.6 

II. 4 

6 

6 
6 
5 
4 

5 
3 

4 

12.  I 

/ 

12.9 

7 

13-7 

14-5 

y 

8 
7 

15.2. 

16.  o- 

y 

16.9 

10 

4     0 

7.4 

4 
3 

II. 2 

12.0 

12.8 

; 

13-6 

7 
6 
6 
S 

5 
4 

4 

14.4 

1 
7 

15.2. 

16. 1 

y 

8 

16.9 

y 
8 

17.8 
18.6- 

y 

8 
8 
7 
7 
7 
5 

5 

0 

10 

7-7- 

II. 8 

12.6 

13-4 

6 
6 
6 
5 
4 
4 

4 

14-3 

15-1 

16.0  • 

16.9 

17.7- 

7  50 

20 

30 
40 

50 
5    0 

8.  i 
8.4 
8.7 
9.0 
9.2 

4 

3 
3 
3 
2 

2 

12.3 
12.8 
13.2 
13.6 
14.0 

I4-T 

b 
5 
4 
4 
4 

3 

13.1- 

13-7 
14.  I 
14.6 
14.9 

15-3 

14.0 
14.6 

15- I 

15-5 
15-9 

i6.y 

14.9 

15-5 
16.  0 

16.5 
16.9 

16.4 

17. 0 

17-5 
17.9. 

18.3 

7 
6 
6 
5 
4 

4 

16.  7 

17-3  ■ 
17.9- ■ 
18.5  • 
19.0 

7 
6 
6 

6 
5 

17.6 
18.3 
18.9 
19.5 
20.0 

7 
7 
6 
6 
5 
4 

18.5 

19-3 
19.9 

20.  5 
21. 1 

8 
6 
6 
6 

4 

19-5 
20.2 
20.9 
21.6 
22.  I 
22.6 

40 

30 

20 

10 

0 

10 

q.4 

17-3 

19.4  ■ 

4 

20.4 

21.  s 

6  50 

20 

9.6 

14.5 

^ 

15-5 

16.6 

3 

17.6 

3 

18.  6- 

3 

19.7  ■ 

3 

20.8 

4 

21.9 

4 

23.0 

4 

40 

30 

9-  7 

14.7 

•2 

15-7 

16.8 

17.8 

18.9 

3 

20.0  ■ 

3 

21. 1 

3 

22.2 

3 

23-3 

J 

30 

40 
6    0 

9.8 
9.8- 

0 
0 

14.8- 
14.9 
15.0 

I 
I 
I 

15-9 
16.0 
16.0 

I 
0 

16.9 
17.0 
17. 1 

'       18.0 
^      18.  I 
'      18.  I 

1 

0 

19.  I 

19.  2 
19.2 

I 
0 

20.2  • 

20.3  • 
20.3  • 

I 
0 

21.3 
21.4 
21.4 

I 
0 

22.4 
22.  5 
22.6 

I 
I 

23-5 
23-7 
23-7 

2 
0 

20 

10 

6    0 

TABLE  28C. 

C  =  the  3d  ccnection. 

Hor.  Arg.,  the  star's  declination.    Vert.  Arg.,  B  =:  the  2d  correction. 

B. 

88°  39' 

88°  W 

88°  41'             1 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

30" 

40" 

50" 

0"    !    10" 

20" 

// 

//     1 

//     1         // 

II 

// 

II 

II 

II 

II 

II 

//         II 

II 

0 

0.0 

0.  0          0.  0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0. 0  '     0. 0 

0.  0 

10 

+0.2 

+0.  I      +0.  I   ;  -(- 

-0.  0 

0.0 

—0.0 

— 0.  I 

— 0.  I 

—0  2 

— 0.  2 

—0. 2-   —0. 3 

-0-3 

20 

0.3 

0.  2-           0.  2 

0.  I 

0. 0 

0.  I 

0.2 

0.  2- 

0-3 

0.4 

0.  5         0. 6 

0.7 

30 

0.5 

0.  4    1         0.  2- 

0.  I 

0.0 

0. 1 

0.2- 

0.4 

0.5 

0.6 

0.7 

0.9 

I.  0 

40 

0.7 

0.5             0.3 

0.2 

0.0 

—0.2 

'        0.3 

0.5 

0.7 

0.8 

I.  0 

1.2 

1-3 

50 

+0.8 

-fo.  6     -|-o.  4 

4 

-0.  2 

0.0 

+0.2 

—0.4 

—0.6 

—0.8 

— 1.0 

—  1.2     —1.4 

—  1-7 

Note. — Below  15°  B  is  nearly  proportional  to  the  altitude. 


Page  326]                                                 TABLE  28B. 

For  finding  the  Latitude  of  a 

place  by  Altitudes  of  Polaris. 

B  =  the  2d  correction.    This  correction  is  always  additive. 

Star's 

Star's  altitude. 

Star's 

hour 
angle. 

hour 
angle. 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

h.   VI. 

// 

// 

// 

II 

II 

// 

II 

II 

// 

II 

h.  m. 

0     0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

12     0 

.1 

10 

CO-  ■ 

CO- 

CO- 

CO- 

0. 1 

0. 1    ■ 

0.  I    ■ 

0. 1 

0, 1    ■ 

0. 1    ■ 

II  50 

_   .1 

.1 

20 

0.  2    ■ 

0.  2 

0.2 

0.2 

0. 2 

0.2    ■ 

0.  2 

0.  2* 

0.3    ■ 

0.3   ■ 

40 

30 
40 

I      0 

0.4    ■ 
0.7.  ■ 
I.  2 
1-7    ■ 

2 
3 
5 
5 

5 

0.4 
0.8 
1.2 
1-7 
2.3. 

.2 
4 
•  4 
.5 
.6 

0-5 
o.i 

1. 1 

I.? 

i 
3 

5 
5 

7 

0.5 
0.9 

1-3 
1.9 
2.6 

i 

4 

4 
6 

7 

0.5    ■ 
0.9   • 

1.4. : 
2.0 

i 

5 
5 

7 

°-5  :^ 
0. 9 

2. 1     ' 

i.o    -5 

2.2        ^ 

0.6 
1.0 

1.6 

2.2- 

3 
4 
6 
6 

8 

0.6     -3 
I.O-    -4 
1.6     ■' 
2.3     ■' 

0.6     -3 

2.4  7 
3.3  -^ 

30 

20 

10 

0 

10 

2.2.  • 

2.5 

2.7  • 

2.8     -7       2.9     -7 

3-0 

3.2     ■' 

10  50 

20 

30 
40 

50 
2       0 

2.9    • 
3.6-  • 
4.4.  ■ 

5-3    ■ 
6.2    • 

7 

7 

9 
9 
0 

3-0 

3-8 

4-7 

5-5- 

6.5 

7.5' 

•7 
.8 

■9 
9 

•9 
0 

3.2 
4.0 

4.9 

5-8, 

6.8' 

7.9' 

7 
8 

9 
9 
0 

I 

3.3 
4.2 

6.1  ' 

7-1  ' 
8.2' 

7 

9 
9 
0 
0 

I 

3.5  : 
6.3"° 

7-4 '•' 
8.6 '•  = 

3.6 
4-5 
5-5 
6.6 

7-7' 
8.9 

.0 

■9 
.0 
.  I 
.  I 

.2 

3-S 

4-7 
5-S 
6.g 
8.1 

•  y 

■  9 

I .  I 

I  I 

1 .2 

1 .2 

3.9, 
4.9, 
6.0' 

7-  I-' 
8.4' 

9.7' 

y 
0 

I 
2 
2 

3 

4.1      -^ 
10.  I    -4 

9.1       4 
10.5  -4 

40 

30 
20 

10 

0 

10 

7.2- 

9.3 

950 

20 

8.2'- 

u 

8.6' 

9.0 

9.4' 

9.8'-^ 

10.  2 

■3 

10.6-3 

II. 0  ' 

3 

II. 5  -4 

11.  9  '4 

40 

30 
40 

50 

9.2;- 
10.3    • 
II-3- 

0 
I 
0 

9-7[ 
10.8' 

0 
I 
I 

10.  I  ' 

11.  2-' 
12.4  ' 

I 
I 

10.  5.' 
II. 8  ' 
13.0  ' 

2 

2 
2 

11.0'=' 
12.3 '-3 

II. 5 
12.8 

14.1 

•3     ii.9.'-3 

■'    13-3 '"^ 

•3  4.7:-^ 

12.4' 
13.9  , 
15-3  , 

4 
5 
4 

12.9-4 
14.4;  J 

19.0-5 

'3-4;:^ 
16.6 '-^ 

30 
20 

10 

3     0 

12.4^- 

1 
I 

13.0^ 
14.  I-^ 

I 

13.6' 
14.8' 

2 

14.2 
15.5  ' 

3 

14.8  '-3 
16.  I  ^-3 

15.5 
16.8 

•+      16.  I   '-4 
t-3      17.5  '^ 

16.8' 
18.2  ' 

4 

18.  I  '-5 

19.7-6 

0 
8  50 

10 

13.  s^- 

20 

14.6'- 

I 

IS.  3' 

16.  0  ' 

2 

16.7^ 

17.4"^ 

18.2 

■4      18.9  '4 

19.7' 

i 

20.5  -5 

21.3-6 

40 

30 

1S.6.- 

° 

16.4' 

17.  I   ' 

1 

17.9' 

18.  7  '-3 

19-5 

•3     20.3-4 

21.  I 

4 

22.  0  -5 

22.8-5 

30 

40 

16.7'- 

1 

17- S^ 

18.3^ 

19.  I 

'9-9  ;•! 

20.8 

'•3     21.6-3 

22.5  ^ 

4 

23-4  :-4 

24.3''^ 

20 

50 

I7.7'- 

0 

18.  s^ 

19.4  ' 

I 

20.  2  ' 

21. 1  '•" 

22.0 

t.2 

22.9     '3 

23.9  , 

4 

24.8-4 

25.8  -5 

10 

4    0 

18.  6-  • 

9 
0 

19.5^ 
20.  5  ^ 

.0 

20.4 
21.4^ 

21.3  ' 
22.4^ 

I 

22.3"' 

23.4-' 

23.2 
24.  3- 

r .  I 

H.2'-3 
25.4-- 

25.  2 
26.4  ' 

3 
2 

26.2  '4 

27.2  ''4 
28.5  -3 

0 

ID 

19.6  ^• 

"z-5-:i 

750 

20 

20.4    • 

8 

21.4 

•9 

22.4' 

23.4' 

24.4"° 

25.4 

26.5   -' 

27.6  ' 

28.7  -^ 

29.8  -3 

40 

30 

21.  2 

b 

22.2 

.0 

.8 

23.2- 

9 

24.3 

9 
8 
8 

e 

6 

25.3.  'i 

26.4'°    27.5  ^■° 

28.6-' 

0 

29.8-' 

31.0;- 

30 

40 

22.  0 

8 
6 
6 

S 

23.0 

24.1 

8 

25.1 

26.2  • 
27. 0 
27.7  -7 

28.3  -^ 

27.3    'l    28.5"! 

29.  6  ^ 

30.8-° 

32.0-° 

20 

50 

5    0 

22.  6 

23.  2 

23.7 
24-3 
24.8 

•V 
.6 

■5 

24.8 
25.4 
26.0 

y 

6 
6 

25.9 
26.  5. 

28.2    -9 
28.9    -7 

^•5    •' 

29.3 
30.1 

.8 
,     -9 

30.5 
31-3 

9 
8 

7 

31.7  -^ 

32.6     -9 

33-3    -^ 

33.0'° 

33-8    • 
14.6    • 
35.2    -^ 

10 
0 

6  50 

10 

23-7 

27.  I 

30./ 

32.0 

20 

24.  I 

4 

25.3 

■b 

26.4 

4 

27.6 

b 

28.8     -5 

30.0     -5 

31-3  •: 

32.5 

b 

33.8    • 

40 

30 

24.4. 

i 

25.6 

■i 

26.8 

4 

28.0 

4 

29.  2     "■* 

30.4     ■' 

31.7  ■' 

33.0 

b 

34.3    'I 

35.6-4 

30 

40 

24.7 

i 

2c;.  8. 

27.0 

28.2 

29.5     'I 

30-7       , 

32.0  -3 

33-3 

3 

34-6    -3 

36.0      -4 

20 

.  50 

24.8 

26.0 

27.  2 

28.4 

29.6     • 

30-9     \ 

32-2  •: 

33-5 

34.8    ■ 

36.2  •; 

10 

6    0 

24.9    -^ 

26.0-  •" 

27.2      '"^ 

28.5    •' 

29.7     " 

31.0    " 

32.2  ■ 

33.6    ■' 

34-9    ■ 

36.3 

6    0 

TABLl 

i   28C. 

C  =  the  3d  correction.    Hot.  Arg.,  the  star's  c 

leclination.    Vert.  Arg.,  B  =  the  2d  correction.                              1 

B. 

88°  39^ 

88°  40^ 

88°  4r             1 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

// 

// 

II 

II 

II 

// 

// 

II 

II 

II 

// 

/f 

II 

II 

0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.  ( 

) 

0. 0  1     0. 0 

0.0 

10 

-f-o.  2 

+0.1 

+0.1 

+0.0 

0.0 

—0.0 

— 0.  I 

—0.  I 

—0.2 

— 0. ; 

J 

—0    2- 

-0.3 

—0.3 

20 

0-3 

0.  2- 

0.  2 

0.  I 

0.0 

0. 1 

0.2 

0.  2- 

0.3 

0.4  '       0.5 

0.6 

0.7 

30 

0-5 

i         0.4 

0.  2- 

0.  I 

0.0 

0. 1 

0.2' 

0.4 

0.5 

0.  ( 

5 

0.7 

0.9 

1.0 

40 

0.7 

i         0.5 

0.3 

0.  2 

0.0 

— 0.2 

0.3 

0.5 

0.7 

0.5 

i 

1.0 

1.2 

1.3 

50 

+0.8  •  -fo.  6 

+0.  4    '    -fo.  2 

0.0 

-f-O.  2        - 

-0.4 

—0.6 

—0.8 

— 1.( 

3 

—  I.  2    j    — 1.4 

-1.7 

Note.— Below  15°  B  is  nearly  proportional  to  the  altitude. 


TABLE  28  B.                                                [Page 

327 

V 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 
B  =  the  2d  correction.    This  correction  is  always  additive. 

Star's 

star's  altitude. 

Star's 

hour 
angle. 

hour 

34° 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

angle. 

h.  m. 

// 

II 

// 

// 

// 

II 

/; 

" 

// 

;/ 

h.  in. 

O      O 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0. 0          0. 0 

0.  0 

12     0 

lO 

0. 1    ■ 

• 

0.1    ■' 

0. 1 

1 

0.1    •' 

0. 1    ■ 

■     0.1    •' 

O.I    •' 

0.1    ■'     0.1    •' 

O.I     •' 

II  50 

20 

0-3    ■ 

■i 

0.3    " 

0-3 

2 

°-3  •! 

0-3   ■ 

\      °-3    1 

0.4     -l 

0.4   -^     0.4   1 

0.4     ■' 

40 

30 

0.6    • 

i 

0.7  •: 

0.7 

4 

°-7 :6 

2.0  -7 

2.8    -^ 

3-8 ;° 

0.7   • 

°-8    ■ 

0.8     • 

0.8   1     0.9   • 

0.  9     -5 

30 

40 
50 

I       0 

10 

1. 1    ■ 

1.8    ■ 

2-5    ■ 
3-4/ 

b 
7 

7 

9 

^•2 1 

2.6 

3-5    ■' 

1.2 

1.9 
2.7 

3- 7; 

S 
7 
8 

0 

1-3    ■ 
2.0 

2.9   • 
3.9.:- 

1.4 

'    3-0  ■' 

'•4 : 
2.2 

3.1  ■' 

'•5     , 
2-3,.o 
3-3 

'•5    '., 
2-4, .0 
3-4 

4-5-!-! 

1.6    ■^ 
2.4    •« 
3  5"' 
4-7'-^ 

20 

10 

0 

10  50 

4-4  ;■; 

20 

4.4 

4.6' 

.  1 

4.7.' 

4-9 '■' 

5- ' 

,  !    5-3  /, 

5-5 1 

5-7    1      5-9    • 

6.  I  ^-4 

40 

30 

5-5  ,' 

5-7  ' 

.  1 

S.9: 

6.  2  '-3 

6.4'" 

3  1    6.  6 '3 

^■9 1 

7-^   I;  7-4  1 

7.6 '0 

30 

40 

6.  7    ■ 

7.0  ' 

•3 

7-2- 

3 

7-5:1 

7.8    ■ 

♦  \    8.1  '-5 

«-4 : 

10. 0 

^•7  1    9-0  ! 

9-3:1 
II.  1  '^ 

20 

50 

8.0 

i 

8.s' 

•  3 

8.6-' 

4 

9-0    1 

9-3  / 

\'    9-6:1 

7--^. 
^3-  I, .8 

'  18.7"' 
^20.6"^ 

3                    ,    2.0 

'     22.  6 

I    24-  6  ,  ^ 

10.3.    8    10.7    -^ 

10 

2       0 

9.4 

4 

5 
5 
6 
6 
6 
6 

7 
6 
g 

9.8* 
12.  9 

•  b 

5 
.6 

10.  I 

I 

b 
6 

6 

10.5    '^ 
12.  i-'-^ 

'3-8-:-8 

10.9    ■ 
12.  6' • 

14-4 '■ 

13-5"' 
'5-4^: 

12.  I  '•** 

12.6  '-^ 

13.0^9 

15.02° 
17.  I  2-^ 

0 

10 

20 

10.9  '" 
12.4  '■ 

II. 7 
13-3 

14.0'-^ 
16. 0^° 

H-5"' 
16.5.^° 

950 
40 

30 
40 

50 

3    0 

14.  0 

I5-6;- 

17.  2     • 

18.8  • 

20.  5 

14-5  ! 
16.2" 

17. 8-; 
19.6 

21.8' 

.6 
•7 
•7 
■7 
■  7 

15-0  J 
16.8' 

18.5; 
20.3 

22.  I  ^ 

8 

7 

8 
8 

'5-6 : 

'7-4, .8 
21.  0 
22.9;-^ 
24-7     8 
'^•5    ■ 

16.2  '• 
18.0 '• 

'9-9" 
21.8 

23-  7  \' 

^7-4;;: 
^9-4,.„ 

2^-4..o 
23-4 

25-5": 

i8.o^-° 

2.0 

20.  o- 

2.2 

22.  2 

2. 1 

24.3 

26-^4  !1 

18.6^' 

20.  8^-^ 
2  1 

^^•9-..2 
25.  I- 

27.3!-! 

^9-3!1 
21.52-2 

23.8  2-3 

26.  o-^-^ 

30 

20 
10 
0 
850" 

ID 

28.32-3 

20 

22.  I  J 

23. 0 ' 

■  y 

.6 

23-  8 ; 

y 

25.6   ■ 

'    26.  5 '-9 

27-  5    ■ 

28-5:1 

29.5    • 

30.  6  2-3 

40 

30 

23- 7  X 

6 

24.  6  ' 

25-5 , 

/ 

27- 5  ^ 

I    ^8.5,:: 
7    30- 4, .8 

29-5::: 

^o.  6 
•^     ,  2.0 

^''^Ir 

32-8:, 

30 

40 

25-3  , 

5 
4 

4 

26.  2  ' 

g 

27.  2 

28.2  ^-^ 

29-3  I 

3i-4-,.8 

32-6,9    33- 7.,.o 

34-9-,., 

20 

50 

26.8 

27.8' 

28.9  \ 

29- 9!'^ 

3i-Oi 

32-2, 

\    33-  9     ' 

35-6  :-^ 

33- 3, .8 

34- 5, .9    35-8,, 

i''-''..^ 

10 

4    0 

28.2-' 

29.3  ' 

30-  8 ; 

.5 

30-4 

31-9, 

5 

3i.6'-7 
33-1  :1 

32.7,. 
34-3, 

3^-9x.6 

38-2,., 

37-7 
39-6:1 

39-  I 

4-°:i 

0 

ID 

29.6  ' 

750 

20 

30-9-' 

4 

32. 1 , 

■3 

2,Z-i  ^ 

34.6    • 

35-8-/ 

2'39-9-,1 

38- 5, .5 

39-9,., 

41-3, .6 

42-8,^ 

40 

30 

32-2^ 

33-  4  , 

•3 

34-^1 

3 

35-9,1 
37-2,1 

37-2-,. 

40-0,1    41. 4, .5:42.9,. 5 

44-5,. 

30 

40 

33- 3  I 

34-5  , 

35-8 

38.5, 

4i-4,.'!42.9,.3    44-4, .3 

46-0,1 

20 

50 

34-3 

g 

37-3     6 
37.9     , 

3^-9, 

38- 3:-: 

39-7,. 

0       4I-I     X.I 

42-6,.,    44-2,.,    45- 7, .a 

47-4,  ^ 

10 

5    0 

35- I- 
35-9 

8 
6 

37-9 
38.7 

8 

39-3     g 
40.  I    • 

40.7 
41.6 

42.2 

;  43-1 1 

43-/ 

45-3 
''•«    46.3^-8 

40.9 

48.6 
49.6-; 
50-5    1 

0 
6  50 

10 

44-  / 

47-9':° 

20 

36.  S 

39- 3- 

1 

40.8    -l 

42-3 

43-9    •' 

45.  4.  -  1  47-  I    .6  '  48-  8    .6 

40 

30 

37- 0 

3 

38.4    •' 

39-9 

5 

41-4     ^ 

42.9 

.1    44-5      . 

46.  I     ^47-7     ,    49-  4     , 
4^-§    '      48.2    1    49-9    1 

51-2  ; 

30 

40 

37-4 

4 

38.8    -^ 

40-3 

4 

41-8    1 

43-3 

44-9    1 

51-7  . 

20 

50 

37.6 

39- 0     , 

40-5 

42.0     ^ 

43-5- 

45-1    • 

46-8    .'    48. 5    .' 

50-2    ;; 

52-0   { 

10 

6    0 

37.7    ■' 

39- I 

40.  6 

,42.1 

43-6    "    45-2 

46. 9         48. 5 

50-3 

52.1  • 

6    0 

TABLE  28  C. 

C  —  the  3d  con 

rection.    Hor.  Arg.,  the  star's  declination.    Vert.  Arg.,  B  =  the  second  correction. 

B. 

88°  39 

/ 

88°  40' 

88°  iV            1 

20" 

30" 

4 

0" 

50 

// 

0" 

10" 

20" 

30" 

40" 

60" 

0" 

10" 

20" 

;/ 

// 

II 

// 

; 

/ 

// 

II 

II 

II 

II 

II 

// 

'' 

// 

0 

0.0 

0.0 

0.0          0 

.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

ID 

+0.  2 

+0.1 

+ 

0.  I      -j-o 

.0 

0.0 

— 0,0 

— 0.  I 

— 0.  I 

—0.2 

— 0.  2 

— 0.  2- 

— 0.  3 

—0.3 

20 

0-3 

0.2 

0. 2          0 

.  I 

0.0 

0.  I 

0.2 

0.  2- 

0.3 

0.4 

0-5 

0.6 

0.7 

30 

0-5 

0.4 

0. 2.         0 

.  I 

0. 0 

0.  I 

0.  2- 

0.4 

0.5 

0.6 

0.7 

0.9 

1.0 

40 

0.7 

0.5 

0. 3         0 

.2 

0.0 

— 0.2 

0.3 

0.5 

0.7 

0.8 

1.0 

1.2 

1-3 

50 

+0.8  j  +0.6 

4 

0.4     +0 

.2  1  0. 0 

+0.2 

—0.4 

—0.6 

—0.8 

—  I.O 

—1.2 

—1-4 

—1-7 

Page  328 

TABLE  28B. 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

B  =  the  2d  correction.    This  correction  is  always  additive. 

Star's 

Star's  altitude. 

Star's 

hour 
angle. 

hour 
angle. 

44° 

45° 

46° 

4r 

48° 

49° 

50° 

51° 

52° 

h.  m. 

II 

II 

// 

.'/ 

// 

II 

II 

// 

// 

h.   m. 

o    o 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

12      0 

lO 

0.1    ■' 

0.1    ■' 

0.1    •' 

0.1  •' 

0.1-  •' 

0.1    ■' 

0.1    -^ 

0.1    ■' 

0.1    -^ 

II  50 

20 

0.4    -l 

O.Q      ^ 

1.6    -7 

0.4    ■] 

0.4      -3        0.4-     -3 

°-5    1 

°-5    1 

°-5    1 

°-5  :: 

1.2        ' 
2.1      -9 

°-5  :: 

1.2      ^ 
2.2    '■" 

40 

30 
40 

?:?■  - 

1.7    ■'       1.8    -^ 

'■'       8 
1.9 

1-9 

1. 1    • 

2.0    '9 

30 

20 

.0 

r       .q 

'        1.0                           n      1.0 

^   1.0 

I.I 

I .  I 

I .  I 

I  .2 

50 
1     0 

3-6 

.  I 
•  3 

2.6      ^ 

3.7^-' 

^•7x.2 

3-9 

~5.2    "3 

2.6 

1.2 
4.0 

5.4  '-i 

2.9 
4.2-^ 

3.0 

1.3 

4.3 

"5.8  -5 

^6.0-5 

^-  ■•: 

3-4  ,  , 

4.8  '•* 

6.5    -7 

10 
0 

10 

4.9  ' 

5.o-"3 

5.6'-^ 

6.2    '^ 

10    50 

20 

6.3  "^ 

6.5  '-^ 

6.8  '-^ 

7.0  'i 

7.3  " 

7.5  '-^ 

7.8  ^-^ 

8.1   ^-9 

8.4    '-9 

40 

30 
40 

7.9  '■' 
9.6  '■■' 

8-^ :: 

10. 0 

8.5  '-o^ 
.^  1.8 
10.3 

6    0    1.8 

10:7  '-^ 

9.1  "'i    9.4  "' 
II.  I  ^■°,  11.5  '" 

9.8  -° 
11.9"^ 

10.  I    -° 
12.3'" 

10.5    -' 
12.8-3 

30 
20 

50 
2     0 

II.  s  "-^ 

•^  2.0 
13-5 
15.6  =•' 

17.7-"' 

II.9  '9 
14.0  -^ 

12.3 

14.5^-^ 
16.7  ^-^ 

19.0   "-3 

12.8^-' 

'7-3::: 

19.  7-  ^ 

13.2  ==-^  1  13.7^-^ 

15.5"^  lii' 

14.2  -3 
16.6 --^ 

14.7'-' 
17.2   "S 

17.9"' 

10 
0 

"9^50 
40 

10 
20 

16. 1  ^-^ 
18.4  "3 

17.9  "*     18.  5."^-^'  19.2  ^■° 
20.4  "^  21.  I  ^-^  21.9  ^-^ 

s?- 

20.6  -7 
23.5"^ 

30 
40 
50 

20.0    ''' 

22.3   ^-3 

24.6^-3 
^        2. /I 

20.7  ==-3 
23.  i  ^-^ 

25- 5, .J 

21.4  ^-^ 

23.9"' 
26.4^-5 

22.2  '^ 

^4.7:j 

27.3  ,.6 

23.0  ^-^ 
25.6==-' 

28.3  '•' 
"^2.7 

-3.8:;^     24.7:: 
26.5.          27.5 

•^     2.7              '      -^     2.0 

29.3   ,.8      30.  4, .9 

25.6  -9 
28.5"^ 

31.5   '^ 
J      ->   3.0 

26.5  3° 

29.5 ., 

32.6  ^ 

30 
20 
10 

3    0 

27.0 

•3 

27.9     '^ 

28.9       ^ 

29.9- 
32.6  ^l 

35- :1 
37.7  -\ 

31.0     7 

33- 7:-^ 

32.1      „     33-3 
34.9^-       36.2-9 

34.5 
"37.5^-: 

35.7  ^ 

0 

10 

29-3  I 

31-4  :-^ 

38.93- 

8  50 

20 
30 

31.  6- ^-^ 

33. 9- :-^ 

32.8  ^-^ 

35.x.!-! 

3^-4  l\ 

36-4  •     37. 7.:-!:  39.1:^ 
39.0 1'l'..  40.4   ^  41.9   0 

40.5   ^ 

43-4  :-^ 

42.0  3' 

45- o'-; 

40 
30 

40 

50 

4    0 

36.2 "" 

38.4: 

40.4- 

.2 
.0 

.0 

37-. 
39.' 
41.  c 

]- 
2.2 

-2.0 

38.8  '^■'^ 

41.1^-3 

43-4  ^-^ 

40.2  ^-s 
42.6  ''•'^ 
44.9"' 

41.6  "-^ 
44.1 "' 
46.5"' 

43- }  ; 

45-7  2.5 
48.2     ^ 

To76^-* 

44-  7  : 

47- 3-, .6 
49.9 

I2.4-5 

46.3  ^-^ 

49-  n 
51.7    ^ 

54-3:! 

38.0  3° 

50.9"' 

53.6^-! 

20 

10 

0 

ID 

42. 4  " 

43- S 

45-5  :•: 

47.1  "! 

48.x  ==-3 

56-2-:l 

7  50 

20 
30 

46. 0      I 
47.6^-! 

45-9  : 

47-  7  ,  6 

47-5::; 

49. 4  J ; 

49.2  ^-^     51.0  ^-^  !  52.8  "" 

li.i-^  52.9-:-°  4.8-:-° 

54.7      ' 
56.8-^ 

56.7     '^ 

58.9  r: 

58.  7    -^ 
61.0-3 

40 
30 

40 

49.3  •! 

51. 1 

52.9  ;-^  54.8  \-i  56.7  :-!^  58.8  r: 

60.9  ■° 

63.1  -' 
66.7  '-^ 

20 

50 

5    0 

49.1  I 
50.3 

0 
.2 

.1 

50.5 
52. 

-I.I 

52.6  '-5 

54.0'-'^ 

54-5  \\  56.4  ,:5 

55.9  -^57.9   ^ 

57.  I  "N  59.1  "^ 

58- 4.::^ 

60.0 
61.  3- ^-3 

60.5. '' 
^     ■^  1.6 
62.  I 

63.4.^3 

62.7  '•** 
64.4^-^ 
65.7.:-^ 

10 
0 

10 

51-4' 

53.: 

'55-  X  :•: 

68.  I- '-4 

6  50 

20 

52.3   :l 

54.2-° 

56.1  -°     58.1  -°     60.2  '-I  62.3  -°!  64.6  •- 

56.9  -^  58.9  -'i  61.0  -l  63.2   9;  65.4  •! 

66.9'- 

69.3.;-: 

40 

30 

53- 0    'l 

54-9    -l 

67.8    • 

70.3  "! 

30 

40 

53-5    • 

55.4    • 

57.4    ■      59.4    -fl  61.6    -^ 

63.8  •" 

66.1     ■' 

68.5     • 

71.0      -7 

20 

50 

53-8    • 

55.7.   'I 

57.7    -^     59-8    -^1  61.9    -3 

64.1       -3 

66.4      -3 

68.8.   -3 

71.4      -^ 

10 

6    0 

53-9    " 

55.9-    " 

57.8    ■    1  59.9    ■      62.0    • 

64.3  " 

66.6    -^ 

69.0    -^ 

71.5 

6    0 

TABLE  28C. 

C  =  the  3d  corr 

ection.    Hor.  Arg.,  the  star's  declination.    Vert.  Arg.,  B  =  the  2d  correc 

tion. 

B. 

88°  39^ 

88°  40^ 

88°  iV            1 

20" 

30" 

40" 

60" 

0" 

10" 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

// 

// 

II 

/ 

II 

// 

II 

II 

II 

II 

II 

// 

II 

II 

30 

+0.5 

+0.4 

+0. 

2- 

+0.1 

0.0 

— 0  I 

— 0.  2- 

—0.4 

-o.S 

— i 

0.6 

— 0, 

7 

—0.9 

—1.0 

40 

0.7 

0.5 

0. 

3 

0.2 

0.0 

0.2 

0.3 

0.5 

0.7 

0.8 

I. 

D 

1. 1- 

1.3 

50 

0.8 

0.6 

0. 

4 

0.2 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

I. 

2 

1.4 

1.6- 

60 

I.O 

0.7. 

0. 

5 

0.  2 

0.0 

0.  2- 

0.5 

0.7. 

1.0 

1.2 

I. 

5 

1.7 

2.0 

70 

I.  2 

0.9 

0. 

6 

0.3 

0.0 

0.3 

0.6 

0.9 

1.2 

1.4. 

I. 

7 

2.0 

2.3 

80 

+  1-3 

+  1.0 

+0. 

7 

+0.4 

0.0 

-0.4 

-0.7 

— 1.0 

-1.3 

— 

1.6. 

—2. 

0 

—2.3 

—2.6 

TABLE  28B.                                                [Page  329 

For 

finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

B  =  the  2C 

correction.     This  correc 
Star's  altitude 

.ion  is  always  additive.                                                           1 

Star's 

, 

Star's 

hour 
angle. 

hour 
angle. 

53° 

54° 

55° 

56° 

5r 

58° 

59° 

60° 

h.   m. 

/      II 

/     // 

;         // 

/     // 

/   // 

'     II 

/     II 

/       u 

h.  in. 

o     o 

0   0.0 

0  0.0 

0      0.0 

0   0.0 

0  0.0 

0   0. 0         0   0. 0 

0    0.0 

12     0 

10 

0.1    ■' 

O.I-  •' 

O.I-  -' 

0.2   -^ 

0.2  -^ 

0. 2   -^  ,       0.2   -^ 

0.2  -^ 

11  50 
40 
30 
20 
10 

20 

30 
40 

50 

0.6     -5 

1-3    •' 
2.2    -^ 

3-5"' 
^  -"  I  .  ? 

0.6     -5 

1-3    •' 

2.3  •" 
3.6 '3 

0.6    -5 

1.4 

^    I.O 

2.4 

^    7  '-3 
->-  '   1.6 

0.6    l 

1.4   • 
2.5"' 

3-9:.i 

0.6-  -5 

0.  7    'o  .        0.  7    -5 

1.5      -8               1.6      -9 

2.7"^          2.8'-^ 

4--:ii   4.3.:-^ 

0.7  ■' 

1.6.    -9 

2.9 '1 

4-5:- 

I     0 

5-f 

) 

0    6.9.-« 

5-3 
0    7.2^-9 

5-5- 
07.  5  -° 

5.8  '- 

6.0 

I 

6.2  *-^ 

6.5 

0 
10  50 

40 

10 

0    6.  ; 

0    7.8-° 

0    8. 1  - 

0   8.4-= 

0    8.7.-3 

20 

^.T^"" 

9-°:-: 

9.3"' 

9.7^^ 

10.  I  -3 

10.  4.-^^ 

10.9-5 

11.3"' 

30 

40 

50 

2      0 

10.  i 

15-^ 

18.5 

2-3 

2.6 

*  2.7 

2.9 

11.3^-3 

13.7"'* 

19.  2 

II. 7 
14.2 
17.0 
19.9 

2-4 

.2.5 
2.8 
2.9 

3-1 

12.1^ 

14.8" 
17.6.- 
20.  7  ^ 

4 
7 
8 
1 

2 

12.6-5 

.5.4"' 
18.3-9 
21.53-2 

024.  8  3-3 

13-  I  '■ 
16.0- 

19.  I  3- 
22.3.3- 

9 
I 

3 

4 

13.6-7 
16.  6  3° 
19.8  3-2 

23.  2  3-4 
"026.83-6 

14.2-9 
17.3'" 

20.  6  3-3 

24.  2  3-6 

0  27.  9  3-7 

30 

20 

10 

0 

10 

0  21.4 

0  22.2  3° 

023.0 

023.9  3- 

025.33- 

9  50 

20 

24. 4  r" 

25.33-: 

26.  2  3-2 

27.2  3-3 

28.33-5 

35-5  3-R 
39.3    ■ 

29.43-° 

30- 6  3-8 

31.83-9 

40 

30 

"7-5  3" 

28.53-2 

29.6  3-^ 

30.73-^ 

33- '    -g 
36-9    ■' 

34.4.3-^ 

35- 9!-^ 

30 

40 

30-6    • 

31.83-3 

33- of: 

34-2  3-^ 

37.8     -^ 

3«-4:-! 

40.  0  4-                20 

50 

33-«    • 

35- If 

36.4  -^ 

40.  8  3-9 

42-4:° 

44.  2  ■^'^             ID 
48.4^=^               0 

_3_  °_ 
10 

37.13-3 
040.33-2 

38.4.3-3 
041.83-4 

39- 9'-' 
043.43-5 

41.43- 

'a 

43.0  3-7 
046.83-8 

44.7'' 

46.5^" 

045.0  3- 

048.63  9  ,   050.54-0 

052.54-2 

850 

20 

43- 5^-: 

45.13-3 

46.8  3-4 

48.63"  : 

50.5  3-7 

57-73-, 

52.  5  3-9  j       54.6  4-' 
56.  P-^          58.53-9 

56.8  4-2 

40 

30 

46.7    -^ 

48-4  • 

50.23  + 

52.13-5 

I    0.94-' 

30 

40 

49.7    •" 

51.63-2 

53-5    • 

55-6  3- 

I     0.0  3-7  I    I     2.4  3-9 

I    4.9^-° 

20 

50 

52.73° 

54-  7  f : 

56.  7.3-^ 

58.9  r 

I      1.23-5 

I    3.63-^ 

I    6.13-7 

1    8.8  3-9 

10 

4    0 

55.6 

z.g 

2-7 

__57.7^-° 

59.8 

3-0 

I     2.  I  3- 

0 

I    4.5^-^ 

I    7.0.3- 

4 
3 

I    9.7^' 

I  13.1-3-4 

I    12.6  3-8 

0 

7  50 

10 

05^-3 

I    0.5-8 

I    3.1--^ 
I    5.6-5 

I    7.9"' 

I    2.8 

I     5.2  3- 

I  7.7  3•^ 

I   10.3  3- 

1    16.1   3-5 

20 
30 
40 

I    0.92° 

I    3- 3!'* 
I    5.5^- 

I    5-5  "I 
I  10.4.-* 

I     8.0-9 
I   10.7-7 
113.1"'^ 

I  I0.6--9 
-3.4::^ 

I   16.  0 

I   13.43-' 
I   16.3-9 
I   18.9.-^ 

1 16.43-3 
1 19.4'° 

122.7-7 

1    19.5  3--' 
I   22.6  3-' 

125-4" 

40 

30 
20 

50 
S    0 

I    7.4 
I    9.2 

1.9 
1.8 

1-5 

T              I.        ^      2.0 

'    9- 9, .8 
I  II.  7 

1 14.4 

I  16.  o.'-^ 

115.3" 
-"   -'  2.0 

I  18.9'-^ 

I   18.3-3 
•^  2.0 
120.3 

I  22.  0  '-7 

I  21.3-4 

123.4^-; 
125.2-8 

124.6-5 
1  26.  7."' 
1  28.6-9 

,215-'^ 

130.3"^ 
1  32.2-° 

10 

0 

6  50 

10 

I  10.  7 

I  13-3"' 

20 

111.9;- 

I  14.6^-3 

117.4"^ 

I  20.3  '^•^ 

123.4^-4 

1 26.7-5 

130.2-6 

I  33-9 ''^ 

40 

30 

I  12.9'° 

I  15.6^-° 

118.4- 

I    19.  2 

121.4-^ 

124.6- 
125.4     • 

127.9"^ 

I   31.4'! 

'35.1':, 

30 

40 

I  13.6    -7 

I  16.3    -7 

I  22.2    -" 

128.7  -8  132.3  -l 

136.0    -? 

20 

50 

I  14.0     * 

I  16.  7    ■'' 

I    19.6      -^ 

I  22.  7   -5  > 

125.9     ■\ 

I  29.  2    -^     I  32.  8    -^  1  I  36. 6    • 

10 

6    0 

I  14.  I    ■ 

I  16.9    -^  1 

I    19.8     -^ 

I  22.  8    -' 

I  26.0    •       I  29. 4    -    j  I  33.0    -       1  36. 8    - 

6    0 

TABLE  28C. 

C  =  the  3d  correct! 

on.     Hor.  Arg  ,  the  star's  declination.    Vert.  Arg.,  B=the  2d  correction. 

B. 

88°  39' 

88°  40' 

88°  41'             |. 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

w.  " 

n 

/' 

II 

" 

// 

II 

II 

11 

II 

II 

// 

// 

II 

1     0 

+  1.0 

+0.7. 

+0.5 

+0.  2- 

0.0 

— 0.  2- 

-0.5 

—0.7. 

— 1.0 

—  1.2 

-I- 5 

—1-7 

—2.0 

10 

I.  2 

0.9 

0.6 

0-3 

0. 0        0. 3 

0.6 

0.9 

1.2 

1.4- 

1-7 

2.0 

2.3 

20 

1-3 

1.0 

0.7 

0.3 

0.0 

0.3 

0-7 

1.0 

1-3 

1-7 

2.0 

2.3 

2.6- 

30 

1-5 

I.  I 

0.7. 

0.4 

0.0 

0.4 

0.7. 

I.  I 

'•5 

1.9 

2. 2        2.6 

3-0 

40 

1-7 

I.  2. 

0.8 

0.4 

0. 0 

0.4 

0.8 

1.2. 

I.  7 

2. 1 

2.5. 

2.9 

2,-Z 

50 

1.8 

1.4 

0.9 

0-5 

0.0 

0.4. 

0.9 

1.4 

1.8 

2.3 

2.7 

3-2 

.3-6 

2     0 

+2.  0 

+  1-5 

+  1.0 

+0.5 

0.0 

—0.5 

— 1.0 

-1-5 

— 2.0 

—2.5 

-30 

-3-5 

—4.0 

Page  330 

TABLE   28D. 

1 

For  finding  the  Latitude  of  a  place 

;  by  Altitudes  of  Polaris.                                                1 

D  =  the  4th  correction.    (D  has  the  same  sign 

as  A  when  the  Dec 

.  <88° 

40',  the  opposite  sign  when  the  Dec.  >  88°  40'.)       1 

Vertical  Argument,  A  =  the  i 

St  correction.     Horizontal  Argument,  the  star's  declination.                                   1 

A. 

Declination,  88°  39^ 

88°  40^ 

Proportional  parts. 

20" 

•25" 

30" 

35" 

40" 

45" 

50" 

55" 

0" 

5" 

10" 

15" 

20" 

25" 

1" 

2" 

3" 

4" 

; 

« 

II 

// 

II 

II 

II 

II 

II 

# 

II 

// 

II 

II 

II 

// 

II 

II 

* 

n 

0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.  0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

2 

I.O 

0.9 

0.7. 

0.6 

0-5 

0.4 

0.  2- 

0.  I 

0.0 

0.  I 

0.  2- 

0.4 

0.5 

0.6 

0.0 

0.  o- 

O.'I 

0.  I 

4 

2.0 

1.7. 

1-5 

I.  2* 

1.0 

0.7. 

0.5 

0.  2- 

0.0 

0.2- 

0.5 

0.7. 

1.0 

I.  2. 

0.  o- 

0.  I 

0.  I- 

0.  2 

6 

3-0 

2.6 

2.2- 

1.9 

1-5 

I.  I 

0.7. 

0.4 

0. 0 

0.4 

0.7. 

I.  I 

1-5 

1-9 

0. 1 

0.  I. 

0.  2 

0-3 

*     8 

4-0,    3-5 

3-0 

2-5 

.2.0 

1-5 

I.  0 

0.5 

0. 0 

0-5 

1.0 

1-5 

2.0 

2-5 

0. 1 

0.2 

0.3 
0.4 

0.4 

10 

5-0 

4.4 

3-7- 

31 

2-5 

1.9 

1.2- 

O.b 

0. 0 

0.6 

1.2- 

1.9 

2-5 

.3-1 

0. 1 

0.  2- 

0.5 

12 

6.0 

5.2. 

4-5 

3-7- 

3-0 

2.  2- 

1-5 

0.7. 

0. 0 

0.7. 

1-5 

2.2- 

.3-0 

.3-7- 

0.  I. 

0-3 

0.4. 

o.b 

14 

7.0 

6.  I 

S-2- 

4.4 

3  5 

2.b 

1.7. 

0.9 

0. 0 

0.9 

1.7. 

2.b 

.3-5 

4.4 

0.  2 

0.3. 

0-5 

0.7 

*  16 

8.0 

7.0 

b.o 

5-0 

4.0 

3-0 

2.0 

I.  0 

0.0 

1.0 

2.0 

3-0 

4.0 

5-0 

0.  2 

0.4 

o.b 

0.8 

18 

9.0:    7.9 

6.7. 

5.6 

4-5 

3-4 

2.2- 

I.  I 

0.0 

I.  I 

2.2- 

.3-4 

4-5 

5.6 

0.  2 

0.4. 

0.7 

0.9 

20 

10.  0 

8.7. 

Z-5 

6.2. 

5-0 

.3-7- 

2-5 

I.  2- 

0. 0 

1.2- 

2-5 

.3-7- 

5-0 

b.2- 

0.  2- 

o.s 

0.7. 

I.  0 

22 

II. 0 

9.6 

8.2. 

b.9 

5-5 

4.1 

2.7- 

1.4 

0. 0 

1.4 

2.7. 

4.1 

.S-5 

b.9 

0.3 

0.5. 

0.8 

1. 1 

*  24 

12.0 

10.5 

9.0 

7-5 
8.1' 

b.o 
6.5 

4  5 

3-0 

1-5 

0.0 

I- 5 

30 

3-2- 

4.5 
4-9 

b.o. 
6.5 

7.5 
8.1 

0-3 
0.3 

o.b 
o.b- 

0.9 

I.O 

1.2 

26 

13.0    II. 4 

9.7. 

4.9 

3-2. 

1.6 

0.0 

1.6 

1-3 

28 

14.0    12.2. 

10.5 

8.7. 

7.0 

5-2- 

3-5 

1.7. 

0. 0 

1.7. 

.3-5!    5-2- 

7.0 

8.7. 

0.3. 

0.7 

I.O 

1.4 

.  30 

15.0    13.  I 

II. 2- 

9-4 

7.5 

5.6 

3-7- 

1.9 

0. 0 

1.9 

Z-1\   5-6 

7-5 

9-4 

0.4 

0.7. 

1. 1 

1-5 

32 

16.0 

14.9 

12.0 

10.  0 

8.0 

b.o 

4.0 

2.  0 

0.0 

2.0 

4.0 

b.o 

8.0 

10.  0 

0.4 

0.8 
0.8- 

I.  2 

1-3 

I.b 

34 

17.0 

12.7. 

10.6 

8.5 

6.4 

4.2. 

2. 1 

0.0 

2. 1 

4.2- 

6.4 

8.5 

10.6 

0.4 

1-7 

3^ 

18.0 

15- 7- 

13-5 

II. 2- 

9.0 

6.7. 

4-5 

2.2- 

0.0 

2.  2. 

4-5 

6.7. 

9.0 

II.  2- 

0.4. 

0.9 

I-.3- 

1.8 

3^ 

19.0 

16.6 

14.2- 

II. 9 

9-5 

7-1 

4.7. 

2.4 

0. 0 

2.4 

4.7.     7.1 

9-5 

II. 9 

0-5 

0.9. 

1-4 

1-9 

*  40 

20.0 

17-5 
18.4 

15.0 

15- 7- 

12.5 
13- I 

10. 0 

7-5 
7-9 

5-0 
5-2- 

2-5 
2.  6 

0. 0 

2.5 

5-0 
5-2. 

7.  5  1  10.  0 

12.5 

0-5 

I.O 

1-5 
1.6 

2.0 

42 

21.0 

10.5 

0. 0 

2.6 

7-9 

10.5 

13- I 

0.5 

I.O. 

2.  I 

44 

22.0 

19.2. 

16.  5 

13-  7- 

II. 0 

8.2- 

5-5 

2.7. 

0. 0 

2.7. 

5-5 

8.2- 

II.  0 

1.3-  7- 

O..S. 

I.  I 

I.b. 

2.  2 

4b 

23.0 

20. 1 

17.2. 

14.4 

"•5 

8.b 

5.7- 

2.9 

0.0 

2.9 

5-7- 

8.b 

II- 5 

14.4 

o.b 

I.I. 

I.  7 

2-3 

*'48 

24.  0 

21.0 

18.0 

15.0 

12.0 

9.0 

b.o 

3-0 

0. 0 
0.0 

3-0 

b.o 

9.0 

12.0 

15.0 

o.b 

1.2 

I.  8 

1-9 

2.4 

2.5 

50 

25.0 

21.  9 

18.7. 

15.6 

12.5 

9.4 

6.2- 

3-1 

3-1 

6.2-    9.4 

12.5 

IS.  6 

0.6 

I.  2. 

52 

26.  0   22.  7. 

19-5 

16.  2. 

13.0 

9.7. 

6.5 

3.2. 

0.0 

3.2. 

6.5 

9.7. 

13.0 

16.  2. 

o.b. 

1-3 

1.9. 

2.  b 

54 

27.0I23.6 

20.2- 

16.9 

1.3-5 

10.  I 

b.7. 

3-4 

0.0 

3-4 

6,7- 

10.  I 

13-5 

16.  9 

0.7 

1-3- 

2.0 

2.7 

*  5b 
58 

28.  0   24.  5 

21.  0 

17.5 

14.0 

10.5 

7.0 

3-5 

0.0 

3-5 
3^6 

7.0 

10.5 

14.0 

17-5 

0.7 

1.4 

2.  I 
2.  2 

2.8 

29.0   25.4 

21.7. 

18.  I 

14-5 

10.  9 

7.2- 

.3-6 

0.0 

7.2- 

10.9 

14-5 

18.  I 

0.7 

1.4. 

2.9 

60 

30.  0    26.  2- 

22.  5 

18.7. 

15.0 

II. 2. 

7-5 

3-7- 

0. 0 

1>-1- 

7-5 

II.  2- 

15-  o- 

18.7. 

0.7. 

1-5 

2.  2. 

3-0 

62 

31.0 

27.  I 

23.2- 

19.4 

15-5 

II. b 

7-7- 

3-9 

0. 0 

3-9 

7.7- 

II. b 

15-5 

19.4 

0.8 

I-5- 

2-3 

3-1 

*  64 

32.0 

28.0 

24.  0 

20.0 
20.6 

16.0 

12.  0 

8.0 

4.0 

0. 0 

4.0 

8.0 

12.  0 

16.0 

20.  0 

0.8 

i.b 
i76- 

2.4 

2-5 

3-2 

3-3 

66 

33- 0 

28.9 

24.7. 

16.5 

12.4 

8.2. 

4.1 

0.0 

4.1 

8.2- 

12.4 

16.5 

20.  b 

0.8 

68 

34.0 

29.7. 

25-5 

21.  2. 

17.0 

12.7. 

8.5 

4.2- 

0.0 

4.2. 

8.5 

12.7. 

17.0 

21.  2. 

0.8- 

1-7 

2.5- 

3-4 

70 

35- 0 

30.6 

26.  2.    21.  9 

17-5 

1.3- I 

8.7. 

4.4 

0. 0 

4.4 

8.7. 

1.3- I 

17-5 

21.  9 

0.9 

1.7. 

2.b 

3-5 

*  72 

36.0 

31-5 

27.0 

22.  5 

18.0 

13-5 

9.0 

4-5 

0. 0 

4-5 

9.0 

13- 5 

18.0 

22.5 

0.9 

1.8 

2.7 

2.8 

3-6 
3-7 

74 

37.0 

32.4 

27.7. 

23.1 

18.5 

1.3-9 

9.2- 

4.6 

0.0 

4.6 

9.2- 

1.3-9 

18.5 

23.1 

0.9 

1.8- 

76 

38.0 

33-2. 

28.  5 

23- 7- 

19.0 

14.2. 

9-5 

4-7- 

0.0 

4.7. 

9-5 

14.2- 

19.0 

23-7- 

0.9. 

1-9 

2.8 

3-8 

78 

39-  0   34-  I 

29.  2- 

24.4 

19.5 

14.  6 

9-7- 

4.9 

0. 0 

4-9 

9.7. 

14.  6 

19-5 

24.4 

1.0 

1.9. 

2.9 

3-9 

*  80 

40. 0  j  35,  0 

30.0 

25.0 

20.0 

15.0 

10. 0 

5-0 

0.0 

5.0 

10. 0 

15.0 

20.0 

25.0 

I.O 

2.0 

3-0 

4.0 

Pr 

oportio 

nal  parts. 

// 

II 

II 

II 

II 

II 

II 

II 

II 

II 

// 

II 

II 

II 

0  20 

0.2 

0.  I 

0.  I 

0. 1 

0. 1 

0.  I 

0.0 

0.  0 

0.0 

0.0 

0.0 

0.  I 

0.  I 

0.  I 

0  40 

0-3 

0-3 

0.2. 

0.2 

0.  2 

0.  I 

0.  I 

0.  0 

0.0 

0.0 

0. 1 

0.  I 

0.2 

0.2 

I     0 

0-5 

0.4 

0.4 

0-3 

0.2. 

0.2 

0.  I 

0.  I 

0.0 

0.  I 

0. 1 

0.2 

0.  2- 

0-3 

I  20 

0.7 

0.6 

o-  5 

0.4 

0-3 

0.  2- 

0.  2 

0.  I 

0.0 

0. 1 

0.  2- 

0.  2- 

0.3 

0.4 

I  40 

0.8 

0.7 

0.6 

0.5 

0.4 

0-3 

0.2 

0.  I 

0. 0 

0.  I 

0.2 

0-3 

0.4 

0.5 

2     0 

I.  0 

0.9 

0.  7.J    0.  6 

0-5 

0.4 

0.  2- 

0.  I 

0. 0 

0.  I 

0.  2 

0.4 

o.s 

O.b 

Note.— The  numbers  in  the  columns  and  lines  marked  *  are  exact. 


TABLE  28D. 

Page  331 

* 

For  finding  the  Latitude  of  a  place  by 

Altitudes  of  Polaris,                                             1 

D  = 

the  4th  ( 

:orrection.    (D  has  the  same  sign  as  A  when  the  Dec.  <  88°  40',  the  opposite  sign  when  the  Dec.  >88''  40'.) 
Vertical  Argument,  A  =  the  1st  correction.    Horizontal  Argument,  the  star's  declination. 

A. 

Declination,  88°  40'. 

88°  iV 

• 

Proportional  parts.         1 

30" 

35" 

40" 

45" 

50" 

55" 

0" 

5" 

10" 

15" 

20" 

1" 

2" 

3" 

4" 

/ 

// 

/' 

* 

II 

// 

// 

II 

# 

II 

II 

// 

* 
11 

// 

// 

// 

* 
,1 

o 

0.0 

0. 0  !     0. 0 

0.0 

0.0 

0.0 

0. 0 

0,0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

2 

0.7. 

0.9   1      I.O 

I.  I 

I.  2. 

1.4 

1. 5      1.6 

I   7. 

1.9 

2.0 

0.0 

0.  0- 

0.  I  !  0.  I    1 

4 

1-5 

1.7. 

2.0 

2.2. 

2.5 

2.8 

3-0 

3.2. 

3-5 

3.7. 

4.0 

0.  0- 

0,  I 

0. 1- 

0.2 

6 

2.  2. 

2.6 

3-0 

3-4 

3-  7-      4.  I 

4.5 

4.8 

5.2. 

5-6 

6.0 

0.  I 

0,  I. 

0.2 

0.3 

*     8 

3-0 

3-5 

4.0 

4-5 
5.6 

5-0 

5-5 

6.0 

6.5 

7.0 

7.5 

8.0 

0. 1 

0.  I 

0.  2  1  0.  3 

0.4 

0-5 

10 

3-7- 

4.4 

5-0 

6.2. 

6.9 

7-5 

8.1 

8.7. 

9-4 

10.  0 

0.  2.    0. 4 

12 

4.5 

5-2- 

6.0 

b.7. 

7.5       8-3 

9.  0  1    9.  7. 

10.5 

"•3 

12.  0 

0.  I. 

0.  3     0. 4. 

0.6 

H 

5-2. 

6.1 

7.0 

7.9 

8.7. 

9.6 

10,5     II.  4 

12.3 

13- I 

14.0 

0.  2 

0. 3. 1  0.  5 

0.7 

*  i6 

iS 

6.0 

6.7. 

7.0 

8.0 

9.0 

10. 0 

II. 0 

12.0     13.0 

14.0 

15.0 

16.0 

18.0 

0.2 

0. 4  !  0.  6 

0.8 

7.9  i    9.0 

10. 1 

II.  2. 

12.4 

13.5  '  14.6 

15.8 

16.9 

0.  2 

0.  4.    0.  7 

0.9 

20 

7-5 

8. 7. ;  10.0 

II. 2. 

12.  5 

13.8 

15.0 

16.3 

17-5 

18.8 

20.0 

0.  2. 

0.  5     0.  7. 

I.  0 

22 

8.2. 

9.6    1 1.0 

12.4 

»3-  7- 

15.  I 

16.  5 

17.8 

19-3 

20.6 

22.0 

0-3 

0.5.    9.8      I.I     1 

*    24 

9.0 

10.5    12.0 

J3j.5_ 
14.6 

15.0 

16.  5 

18.0 

21. 1 

21.0 

22.5 

24.0 

0.3 

0.  6  1  0.  9 

1.2 

26 

9.7. 

II. 4    13.0 

16.2. 

17.9 

19.5 

22.8 

24.4 

26.0 

0.3 

0. 6-     1.0 

1-3 

28 

10.5 

12.2.    14.0 

15-7. 

17.5 

19.3 

21.0     22.8 

24-5 

26.  3 

28.0 

0.3. 

0.  7      1.0. 

1.4 

30 

II.  2- 

13. 1    15.0 

16.9 

•18.7. 

20.6 

22.  5 

24.4 

26.3 

28.1 

30.0 

0.4    1    0.  7.       1.  I 

1-5 

-    32 

12.0 

14.0 

16.0 

18.0 
19.  I 

20.0 
21.2, 

22.0 

24.0 

26.0 

28.0 

30.0 

32.0 

0.4 

0.8  1  1.2 

1.6 

34 

12.7. 

14.9 

17.0 

23.4 

25-5 

27.6 

29.8 

31.9 

34- 0 

0.4 

0.8-     1.3 

1-7 

^v 

13-5 

15.7. 

18.0 

20.  2* 

22.5 

24.8 

27.0 

39-3 

31-5 

33-8 

36.0 

0.4. 

0.9     1.3. 

1.8 

3« 

14.2. 

16. 6      19.0 

21.4 

23-7. 

26.  I 

28.5 

30.8 

33-3 

35-6 

38.0 

0.  5        0.  9.       1.4 

1.9 

*  40 

15.0 

17.5    :    20.0 

22.  5 
23.6 

25.0 

27-5 

30.0 

32.5 
34-1 

35- 0 
36.8 

37.5 
39-4 

40.0 
42.0 

0.5 

1.015 

2.0 

42 

15- 7- 

18.4 

21.0 

26.  2. 

28.9 

31-5 

0.  S 

1.0. 

1.6 

2. 1 

44 

lb.  5 

19.  2- 

22.0 

24.7. 

27.5 

30.3 

33-0  j  35-8 

38.5 

41.3 

44.0 

0.  s. 

1. 1 

1.6. 

2.2 

46 

17.2. 

20.  I 

23.0 

25-9 

28.7. 

31-6 

34-5  i  37.4 

40.3 

43.1 

46.  0 

0.  b 

I.  I. 

1.7 

2.3 

'  48 

18.0 

21.  0 

24.0 

27,0 

30.0 

33- 0 

36.0     39.0 

42.0 

45.0 

48.0 
50.  0 

0.6 
0.6 

I.  2 

1.8 

2.4 
2.5 

50 

18.7. 

21.9 

25.0 

28.  I 

31.2. 

34-4 

37-  5  1  40. 6 

43-8 

46.9 

1.2. 

1.9 

52 

19-5 

22.  7.      26.  0 

29.2- 

32.5 

35-8 

39- 0  1  42.3 

45-5 

48.8 

52.  0 

0.6. 

1-3 

1.9. 

2.6 

54 

20.  2. 

23.  6  1  27.  0 

30-4 

33-  7- 

37-1 

40.  5  !  43.  8 

47-3 

50.6 

54.0 

0.7 

1.3.    2,0 

2.7 

*  56 

21.0 

24. 5  !  28. 0 

31-5 

35- 0 

38.5 
39-9 

41- 0  !  45-5 

49.0 
50.8 

52.5 
54.4 

56.0 
58.0 

0.7 
0.7 

1.4     2. 1 

1.4.    2.2 

2.8 
2.9 

58 

21.7. 

25.4  '  29.0 

32.6 

36.2- 

43-  5  i  47- 1 

60 

22.5 

26.  2-  ,    30.  0 

33- 7- 

37-5 

41.3 

45.0 

48.8 

52.5 

56.3 

60.  0 

0.7. 

I.  5     2. 2. 

3.0 

62 

23.2- 

27.1     1    31.0 

34-9 

38.  7. 

42.  6 

46.5  '  50.4 

54-3 

58.1 

62.0 

0.8 

1.5. 

2.3 

3-  I 

'  64 
66^ 

24.0 
24.7. 

28.  0       32.  0 

36.0 
.S7.I 

40.0 

44.0 

48. 0  ,  52.  0 

56.0 

60.0 

64.0 
66.0^ 

0.8 
0  8 

1.6 
1.6- 

2.4 
2.5 

3-2 

3-3 

28.  9        33.  0 

41.2- 

45-4 

49-5 

.53.6 

57.8 

61.9 

68 

25  5 

29.7.      34.0 

38.2- 

42.5 

46.8 

51.0 

55-2 

59-5 

63.8. 

68.0 

0.8-     1.7  '  2.  5 

3.4 

70 

26.  2. 

30-6  1  35- 0 

39-4 

43- 7- 

48.1 

.S2.5 

56.8 

61.  3 

65.6 

70.0 

0.9 

1.7-1  26 

3-5 

*   72 

27.0 

31-5  i  36.0 

40.5 

45- 0 

49-5 

54- 0 

58.5 

63.0 

67.5 

72.0 

0.9 

1.8- 

2.7 

2.8 

3-6 
3-7 

74 

27.7. 

32.4  1  37- 0 

41.6 

46.2- 

50-9 

55-5 

60. 1 

64.7 

69.4 

74.0 

0.9 

76 

28.5 

33.  2.  i  38. 0 

42.7. 

47.5 

52.3 

57.0 

(1.7 

66.5 

71.2. 

76.0 

0.9. 

1.9 

2.8 

.3.8 

78 

29.  2. 

34-1 

39.0 

43-9 

48.7. 

53-6 

58.5     63.4 

68.2. 

73-1 

78.0 

1.0 

1.9. 

2.9 

3-9 

'  80 

30.0 

35- 0 

40.  0 

45.0 

50.0 

55- 0 

60. 0     65. 0 

70.0 

75- 0 

80.0 

1.0 

2.0 

3.0 

4.0 

Proportional  parts. 

// 

II 

II 

II 

II 

II 

// 

II 

ii 

//    1      // 

0  20 

0.  I 

0. 1 

0.  I 

0.  I 

0.  2 

0.  2 

0.  2. 

0.3 

0.3 

0.3  ;     0.3 

0  40 

0.2. 

0-3 

0.3 

0.4 

0.4 

0.5 

0-5 

0.6 

0.6 

0.  6  1     0.  7 

I     0 

0.4 

0.4 

0.5 

0.6 

0.6 

0.7 

0.  7.      0. 8 

0.9 

0.9        1.0 

I  20 

0.5 

0.6 

0.7 

0.7. 

0.8 

0.9 

1.0 

1. 1 

1.2 

1.2 

1.3 

I  40 

0.6 

0.7 

0.8 

0.9 

1.0 

I.  I 

I.  2. 

I-3- 

I  5 

1.6 

1.7 

2     0 

0.7. 

0.9 

1.0 

I.  I 

1.2- 

1.4 

1.5       1.6 

1.7. 

1.9 

2  0 

Note.— The  numbers  in  the  columns  and  lines  marked  *  are  exact. 


1 


Page  332j 

TABLE 

29. 

Mean  Reduced  Refraction  for  Lunars. 

Barometer  30  Inches.    Fahrenheit's  Thermometer  50*. 

Apparent  al- 

Reduced re- 

Diff. to 

Apparent  al- 

Reduced re- 

Apparent al- 

Reduced re- 

Apparent al- 

Reduced re- 

titude. 

fraction. 

i'. 

titude. 

fraction. 

titude. 

fraction. 

titude. 

fraction. 

o     / 

/       // 

// 

0      / 

1        II 

0     ' 

/       /< 

0     / 

/        // 

5    o 

9  54-2 

1.6 

10     0 

5  24.1 

15     0 

3  41.7 

27     0 

2     7-8 

5 

9  46.3 

1-5 

5 

5  21.6 

10 

3  39-4 

27  30 

2    5-7 

lO 

938.6 

1-5 

10 

5  19-2 

20 

3  37.1 

28     0 

23-7 

15 

9  31-0 

1-5 

15 

5  1(3.8 

30 

3  34-9 

28  30 

2     1. 7 

20 

9  23.7 

1.4 

20 

5  14-4 

40 

3  32.7 

29     0 

I  59-8 

25 

9  16.5 

1.4 

25 

5  12. 1 

50 

3  30-6 

29  30 

I  58.0 

5  30 

9    9.5 

1.4 

10  30 

5    9-8 

16     0 

328.5 

30     0 

I  56.2 

35 

9    2.  7 

1-3 

35 

5     7-5 

10 

3  26.5 

30  30 

I  54.5 

40 

8  56.0 

1-3 

40 

5    5-3 

20 

3  24.5 

31      0 

I  52.8 

45 

8  49-5 

1-3 

45 

5    3-1 

30 

3  22.6 

31   30 

I  51.2 

50 

8  43-1 

1.2 

50 

5    0.9 

40 

3  ^2-7 

32     0 

I  49-7 

55 

836.9 

1.2 

55 

4  58.8 

50 

3  18.8 

32  30 

I  48.2 

6    0 

8  30.9 

1.2 

II    0 

4  56.7 

17  0 

3  16.9 

33    0 

I  46.7 

5 

8  24.9 

1.2 

5 

4  54-6 

10 

3  15- 1 

33  30 

I  45-3 

10 

8  19. 1 

1. 1 

10 

4  52.5 

20 

3  13-4 

34    0 

I  44.0 

15 

8  13.4 

I.  I 

15 

4  50-5 

30 

3  "-6 

34  30 

I  42.7 

20 

8     7.8 

I.  I 

20 

4  48.5 

40 

3    9-9 

35    0 

I  41.4 

25 

8    2,4 

1. 1 

25 

4  46.  6 

50 

3     8.2 

35  30 

I  40.2 

6  30 

7  57-0 

I.O 

II  30 

4  44-6 

18  0 

3    6.6 

36    0 

I  39.0 

35 

7  51-8 

I.O 

35 

4  42.7 

10 

■3    5-0 

36  30 

I  37.8 

40 

7  46.7 

1.0 

40 

4  40.  8 

20 

3    3-4 

7>1    0 

I  36.7 

45 

7  41-7 

I.O 

45 

4  38-9 

30 

3     1-8 

37  30 

I  35-6 

50 

7  36-7 

I.O 

50 

4  37-1 

40 

■i    o-l 

38    0 

I  34-5 

55 

7  31-9 

0.9 

55 

4  35-3 

50 

2  58.8 

3830 

I  33.5 

7    0 

7  27.2 

0.9 

12    0 

4  33-5 

19    0 

2  57-3 

39    0 

I  32.5 

5 

7  22.6 

0.9 

5 

4  31-7 

10 

2  55-9 

39  30 

I  31-5 

10 

7  18.0 

0.9 

10 

4  3<^-o 

20 

2  54-4 

40    0 

I  30.6 

15 

7  13-6 

0.9 

15 

428.3 

30 

2  53- 0 

40  30 

I  29.6 

20 

7    9.2 

0.9 

20 

4  26.6 

40 

2  51.6 

41     0 

I  28.7 

25 

7    4.9 

0.8 

25 

4  24.9 

50 

2  50.3 

41  30 

I  27.8 

7  30 

7    0.8 

0.8 

12  30 

4  23.2 

20      0 

2  49.0 

42     0 

I  27.0 

35 

6  56.6 

0.8 

35 

4  21.6 

10 

2  47.6 

42  30 

I  26.  2 

40 

6  52.6 

0.8 

40 

4  20.0 

20 

2  46.4 

43    0 

I  25.4 

45 

6  48.6 

0.8 

45 

4  18.4 

30 

2  45-1 

43  30 

I  24.6 

50 

6  44.  8 

0.8 

50 

4  16.8 

40» 

2  43-8 

44    0 

I  23.8 

55 

6  40.9 

0.7 

55 

4  15-2 

50 

2  42.6 

44  30 

I  23.1 

8    0 

6  37.2 

0.7 

13    0 

4  13-7 

21     0 

2  41.4 

45     0 

I  22.  4 

5 

6  33-5 

0.7 

5 

4  12.2 

10 

2  40.2 

46    0 

I  21.  0 

10 

6  29.9 

0.7 

10 

4  10.7 

20 

2  39.0 

47    0 

I  19.6 

15 

6  26.3 

0.7 

15 

4    9.2 

30 

2  37.9 

48    0 

I  18.4 

20 

6  22.8 

0.7 

20 

4     7.7 

40 

2  36.7 

49    0 

I  17.2 

25 

6  19.4 

0.7 

25 

4     6.3 

50 

2  35.6 

50    0 

I  16.0 

8  30 

6  16.0 

0.7 

13  30 

4    4.8 

22     0 

2  34-5 

51     0 

I  15.0 

35 

6  12.  7 

0.6 

35 

4    3-4 

10 

2  33-4 

52    0 

I  13.9 

40 

6    9.5 

0.6 

40 

4    2.0 

20 

2  32.4 

53    0 

I  13.0 

45 

6    6.3 

0.6 

45 

4    0. 6 

30 

.    2  31.3 

54    0 

I  12.0 

50 

6    3.1 

0.6 

50 

3  59-3 

40 

2  30-3 

55    0 

I  II.  I 

55 

6    0.0 

0.6 

55 

3  57-9 

50 

2  29.2 

56    0 

I  10.3 

9    0 

5  57.0 

0.6 

14    0 

3  56.6 

23     0 

2  28.2 

57    0 

I    9-5 

5 

5  54.0 

0.6 

5 

3  55-3 

20 

2  26.3 

58    0 

I    8.7 

10 

5  51- I 

0.6 

10 

3  54- 0 

40 

2  24.4 

59    0 

I     8.0 

15 

5  48.2 

0.6 

15 

3  52.7 

24    0 

2  22.5 

60    0 

I     7-3 

20 

5  45-3 

0.6 

20 

3  51-4 

20 

2  20.  7 

62    0 

I     6.0 

25 

5  42.5 

0-5 

25 

3  50-1 

40 

2  18.9 

64    0 

I    4.9 

9  30 

5  39-8 

o.s 

14  30 

3  48.9 

25     0 

2  17.2 

66    0 

I    3-8 
I     2.9 

35 

5  37.0 

0-5 

35 

3  47-6 

20 

2  15-5 

68    0 

40 

5  34-4 

o-S 

40 

3  46.4 

40 

2  13-9 

70    0 

I     2.0 

45 

5  31.7 

0.5 

45 

3  45-2 

26     0 

2  12.3 

73    0 

I       I.O 

50 

5  29.2 

0-5 

50 

3  44-0 

20 

2  10.8 

76    0 

I     0. 1 

55 
10    0 

5  26.6 

0-5 

55 

3  42.8 

40 

2    9.3 

80    0 

0  59.2 

5  24.1 

15    0 

3  41.7 

27    0 

2    7.8 

90    0 

0  58-  3 

TABLE  30                  [Page  333 

^ 

Log.  A. 

Logs.  A, 

B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App 

alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                          1 

41' 

42' 

43' 

44/   45/ 

46' 

4r 

48' 

49' 

50' 

51' 

52' 

53' 

54' 

55' 

50  0' 

.0288  0295 

0301 

0308   0315   0321   0328 

0335  !  0341 

0348 

0355  0361  !  0368 

2 

.0286  0293  0299 

0306   0313  ,  0319  0326  0333  '  0339   0346 

0352  0359  0366 

4 

.0284  0291  0297 

0304  03 1 1   0317  0324  0330  0337  1  0344 

0350  1  0357  0363 

6 

.0282  0289 

0296 

0302   0309   0315   0322 

0328  ,  0335  j  0341 

0348  0354  0361 

8 

.0281  0287 

0294 

0300  0307  0313   0320 

0326  1  0333 

0339 

^346^ 

0344 

0352 
0350 

0359 

5  10 

.0279  0285  '  0292 

0298   0305   03 1 1   0318  0324  0331 

0337 

0356 

12 

.0277  0284  !  0290 

0296   0303   0309   0316   0322  ;  0329   0335 

0341  0348  0354 

14 

.0275   0282   0288 

0295   0301   0307   0314 

0320 

0327 

0333 

0339  0346  0352 

16 

.0274  0280  1  0286 

0293   0299   0306   0312 

0318 

0325 

0331 

0337  0344  0350 

18 

.0272  j  0278   0285 

0291   0297   0304   0310 

0316 

0323 

0329 

0335  0341  0348 

5  20 

.0270  0277   0283 

0289  1  0296   0302  :  0308 

0314 

0321 

0327 

0333  1  0339  0346 

22 

.0269   0275   0281 

0288  1  0294    0300    0306  ;  0313 

0319 

0325 

0331  0337  0344 

24 

.0267  0273   0280 

0286  '  0292  0298  0304  03 1 1 

0317 

0323 

0329  0335  0341 

26 

.0265   0272   0278 

0284  j  0290  0296  0303 

0309 

0315 

0321 

0327  i  0333  0339 

0346 

28 

.0264  0270   0276 

0282  1  0289 

0295  0301 
0293  0299 

0307 

0313 

0319 

0325 

0331  0337 
0329  0335 

0344 
0342 

5  30 

.0262  0268   0275 

0281  0287 

0305 

031 1 

0317 

0323 

32 

.0261   0267   0273 

0279  '  0285  0291  0297  0303  '  0309 

0315 

0321  !  0327  0334 

0340 

34 

.0259  0265   0271 

0277  02S3  0290  0296  i  0302  0308 

0314 

0320 

0326  1  0332 

0338 

3S 

.0258  0264   0270 

0276  1  0282  0288  0294  0300 

0306 

0312 

0318 

0324  0330 

033(> 

3« 

0262   0268 

0274 

0280  I  0286  1  0292  0298 

0304 

^310 
0308 

0316 

0322  0328 

0334 

5  40 

0261   0267 

0273 

0279  0285  1  0290  !  0296 

0302 

0314 

0320  '  0326 

0332 

42 

0259   0265 

0271 

0277  0283  0289 

0295 

0301 

0306 

0312    0318  0324 

0330 

44 

0258   0264 

0270  !  0275  1  0281  '   0287 

0293  •  0299  0305 

031 1    0316  0322 

0328 

46 

0256   0262 

0268 

0274 

0280  !  02S6 

0291  0297 

0303 

0309  :  0315  :  0320 

0326 

48 

0255   0261 

0267 

0272 

0278  0284 

0290  0296 

0301 

0307 

0313  0319 
031 1  0317 

0324 

5  50 

0253   0259 

0265 

0271  1  0277  !  0282 

0288  0294 

0300 

0305 

0323  1    1 

52 

0252   0258 

0264 

0269   0275   0281   0287  1  0292 

0298 

0304    0309  0315 

0321 

54 

0251   0256 

0262  1  0268  i  0274  0279   0285  '  0291 

0296 

0302  0308  0313 

0319 

5^ 

0249   0255 

0261 

0266   0272   0278   0283  1  0289  '  0295 

0300  0306  0312 

0317 

5^ 

0248   0254 

0259 

0265   0271   0276 

0282 

0287  0293 

0299  0304  0310 

0316 

6  0 

0247   0252 

0258 

0263  '  0269  !  0275 

0280 

0286  0291 

0297  I  0303  0308 

0314 

2 

0245   0251 

0256 

0262  0268  i  0273 

0279 

0284  0290 

0295  ;  0301  i  0307 

0312 

4 

0244   0249 

0255  0261  0266  0272  I  0277  1  0283  °288 

0294   0299  0305 

0310 

6 

0243   0248 

0254  0259  0265  0270  !  0276  0281  0287 

0292    0298  0303 

0309 

8 

0241   0247 

0252 

0258  0263  1  0269  0274  j  0280  0285 
0256  0262  i  0267  1  0273  1  ^278  0284 

0291 

0296  0302 

0307 

6  10 

0240   0246 

0251 

0289 

0295  030° 

0306 

12 

0239   0244 

0250  0255  0261  0266  1  0271  1  0277  0282 

0288  1  0293 '  0299 

0304 

14 

0237   0243 

0248  0254  0259  0265  '  0270  '  0275  0281 

0286  '  0292  !  0297 

0302 

16 

0236   0242 

0247  ,  0252  ,  0258  0263 

0269  i  0274  j  0279  !  0285  .  0290  ;  0295 

0301 

18 

0235   0240 

0246 

0251  1  0257  1  0262 

0267  0273  ;  0278 

0283  0289 

0294  0299 
0292  0298 

6  20 

0234   0239 

0245 

0250  0255  \   0261 

0266  1  0271  1  0276 

0282 

b287 

22 

0233   0238 

0243 

0249  0254  '  0259  0264 

0270  0275 

0280 

0286 

029 1  0296 

24 

i  0231   0237 

0242  :  0247  !  0253  0258  1  0263 

0268  0274 

0279 

0284 

0289  0295 

26 

0236 

0241  '  0246  0251  0257  0262 

0267  0272 

0277 

0283 

0288  0293 

28 

0234 

0240  '0245  0250  0255  i  °26o  1  0266  0271 

0276 

0281 

0286  1  0292  1  0297 

6  30 

0233 

0238  0244  1  0249  0254  1  0259 

0264  1  0270 

0275  0280 

0285  0290  0295 

32 

0232 

0237  1  0242  0248  0253  0258 

0263  0268 

0273  0278 

0284  02S9  0294 

^ 

0231 

0236  '  0241  _  0246  0251  0257 

0262  0267 

0272  0277 

0282  0287  '  0292 

^v 

0230 

0235 

0240 

0245  ;  0250  0255 

0260  0266 

0271  0276 

0281  ;  0286  1  0291 

3« 

0229 

0234 

0239 

0244  ;  0249  j  0254 

0259  0264 

0269 

0274 
0273 

0279  ,  0284   0290 
0278   0283  "0288" 

6  40 

0227 

0232 

0238  0243  0248  0253 

0258 

0263 

0268 

42 

0226 

0231 

0236  0241   0246  0252 

0257 

0262 

0267  0272 

0277  1  0282   0287 

44 

0225 

0230 

0235  i  0240  0245  1  0250 

0255  0260 

0265  0270 

0275  '  0280   0285 

46 

0224 

0229 

0234  0239  0244  ,  0249 

0254  0259 

0264  0269 

0274   0279   0284 

48 

0223 

0228 

0233  '  0238  0243  0248 

0253  0258 

0263 

0268 

0273  '  0278  1  0283 

6  50 

0222 

0227 

0232  0237 

0242  1  0247 

0252  0257 

0262 

0266 

0271  1  0276   0281 

52 

0221 

0226 

0231   0236 

0241   0246 

0250  0255 

0260  0265  0270  0275  °28o 

54 

0220 

0225 

0230  0235 

0239  0244 

0249  0254 

0259  0264  0269  0274  0279 

56 

0219 

0224 

0229  0233 

0238  0243 

0248  0253 

0258  0263  :  0267  0272  :  0277 

58 

0218 

0223 

0227  0232 

0237  0242  0247  0252  0257  0261 1 0266  0271 '  0276 

7  0 

0217 

0222 

0226 

0231 

0236 1 0241   0246  0251   0255  j  0260 ,  0265  i  0270  0275 

Page  334]                   TABLE  30. 

Log  A. 
Logs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App. 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                         1 

44/ 

45' 

46' 

iV 

48' 

49' 

50' 

51' 

52' 

53' 

54' 

55' 

56' 

sr 

•f  0' 

3 

6 

9 
12 

.0222 

.0220 
.0218 
.0217 
.0215 

0226 

0225 
0223 
0222 
0220 

0231 
0230 
0228  1 
0226 
0225 

0236 
0234 
0233 

0231 

0230 

0241 
0239 
0238 
0236 
0234 

0246 
0244 
0242 
0241 
0239 

0251 
0249 
0247 
0245 
0244 

0255 
0254 
0252 
0250 
0248 

0260 
0258 
0257 

0255  i 
0253  i 

0265 
0263 
0261 
0260 
0258 

0270 

0268 
0266 
0264 
0262 

0275 
0273 
0271 
0269 
0267 

7  15 
18 

21 

24 

27 

.0214 
.0213 
.0211 
.0210 
.0208 

0219 
0217 
0216 
0214 
0213 

0223  0228 
0222  0226 
0220  0225 
0219  0223 
0217  0222 

0233 
0231 
0230 
0228 
0227 

0237 
0236 
0234 
0233 
0231 

0242 
0240 
0239 
0237 
0236 

0247  0251 
0245  0250 
0243  0248 
0242  0246 
0240  0245 

0256 
0254 

0253 
0251 
0249 

0261 
0259 

0257 

0255 
0254 

0265 
0263 
0262 
0260 
0258 

7  30 

36 
39 
42 

.0207 
.0206 
.0204 
.0203 
.0202 

021 1 
0210 
0209 
0207 
0206 

0216 
0215 
0213 
0212 
0210 

0220 
0219 
0218 
0216 
0215 

0225 
0224 
0222 
0221 
0219 

0230 
0228 
0227 
0225 
0224 

0234 
0232 
0231 
0229 
0228 

0239 
0237 

0235 
0234 

0232 

0243 
0241 
0240 
C238 
0237 

0248 
0246 
0244 
0243 
0241 

0252 
0250 
0249 
0247 
0246 
02^ 
0242 
0241 
0239 
^38 
0236 

0235 
0233 
0232 

_023I 

0229 

0228 
0226 

0225 

0224 

0257 
0255 

0253 
0252 

0250 

7  45 
48 

51 

54 
57 

.0200 
.0199 
.0198 
.0196 
.0195 

0205 
0203 
0202 
0201 
0200 

0209 
0208 
0206 
0205 
0204 

0213 

0212 
021 1 
0209 
0208 

0218 
0216 
0215 
0214 
0212 

0222 
0221 
0219 
0218 
0217 

0227 
0225 
0224 
0222 
0221 

0231 
0229 
0228 
0227 
0225 

0235 
0234 

0232 

0231 

0229 

0240 
0238 
0237 

0235 
_°234_ 
0232 
0231 
0229 
0228 
0227 

0248 

0247 

0245 
0244 

0242 

0249 
0248 
0246 

8  0 

3 
6 

9 
12 

.0194 
.0193 
.0192 

0198 
0197 
0196 

0195 
0193 

0192 
0191 
0190 
0189 
0188 

0203  I  0207 
0201  0206 
0200  0204 
0199  0203 
0198  0202 

02 1 1 
0210 
0208 
0207 
0206 

0215 
0214 
0213 
021 1 
0210 

0219 
0218 
0217 
0215 
0214 

0224 
0222 
0221 
0220 
0218 

0228 
0227 
0225 
0224 
0222 

0241 
0239 
0238 
0236 
0235 

0245 
0243 
0242 
0240 
0239 

«  15 
18 

21 

24 
27 

0196 

0195 
0194 

0193 
0192 

0201 

0199 

0198 

0197 

0196 

0205 
0203 
0202 
0201 
0200 

0209 
0207 
0206 
0205 
0204 

0213 
0212 
0210 
0209 
0208 

0217  1  0221 
0217  0220 
0214  0218 
0213  0217 
0212  0216 

0225 
0224 
0222 
0221 
0220 

0233 
0232 

0231 
0229 
0228 

0237 

0236 

0235 

0233 
0232 

8  30 

36 

39 
42 

0187 
0186 
0184 
0183 
0182 

0191 
0190 
oi88 
0187 
0186 

0195 
0193 

0192 
0I9I 
0190 

0199 
0197 
0196 

0195 
0194 

0203 
0201 
0200 
0199 
0198 

0207 
0205 
0204 
0203 
0202 

0211  0215 
0209  0213 
0208  0212 

0207  !   O2II 
0206     0210 

0219 
0217 
0216 
0215 
0214 

0223 
0221 
0220 
0219 
0217 

0226 
0225 
0224 
0223 
0221 
0220 
0219 
0218 
0216 
0215 

0230 
0229 
0228 
0226 
0225 

«45 
48 

51 
54 

57 

0181 
0180 
0179 
0178 
0177 

0185 
0184 
0183 
0182 
0181 

0189 

0188 
0187 
0186 
0185 

0184 

0183 
0182 
0I8I 
0180 

0193 
0192 
0191 
0190 
0189 
0188 
0186 
0185 
0184 
0183 

0197 
0196 

0195 
0193 

0192 

0201 
0200 
0198 
0197 
0196 

0205 

0203 
0202 
0201 
0200 

0208 

0207 
0206 
0205 
0204 

0212 
021 1 
0210 
0209 
0208 

0216 
0215 
0214 
0212 
02 1 1 

0224 
0223 
0221 
0220 
0219 

9  0 

i 

9 
12 

0176 

0175 
0174 

0173 

0172 

0180 
0179 
0178 
0177 
0176 

0191 
0190 
0189 
0188 
0187 

0195 
0194 
0193 
0192 
0191 

0199 
0198 
0197 
0196 
0194 

0203 
0201 
0200 
0199 
0198 

0206 
0205 
0204 
0203 
0202 

0210 
0209 
0208 
0207 
0206 

0214 
0213 
021 1 
0210 
0209 

0218 
0216 
0215 
0214 
0213 

9  15 

18 

21 
24 
27 

0171 
0170 
0170 

0175 
0174 

0173 
0172 

0171 

0179 
0178 
0177 
0176 

0175 

0182 
0181 
0180 
0179 
0179 
0178 
0177 
0176 
0175 
0174 

0186  0190  0193  0197 
0185  0189  0192  0196 
0184  0188  0191  0195 
0183  1  0187  0190  0194 
0182  0186  0189  0193 

0201 
0200 
0199 
0198 
0196 

0204 

0203 

0202 
0201 
0200 

0208 
0207 
0206 
0205 
0204 
"0203 
0201 
0200 
0199 
0198 

0212 
021 1 
0209 
0208 
0207 

9  30 

36 

39 
42 

0170 
0170 
0169 
0168 
0167 

0174 
0173 

0172 
0171 
0170 

0181 
0180 
0179 
0178 
0177 

0185 
0184 
0183 
0182 
0181 

0188 
0187 
0186 
0185 
0184 

0192 
0191 
0190 
0189 
0188 

0195 
0194 
0193 
0192 
0191 

0199 
0198 
0197 
0196 

0195 

0206 
0205 
0204 
0203 
0202 

9  45 
48 

51 
54 

57 

• 

0166 
0165 
0164 
0163 
0163 

0169 
0169 

,  0168 
0167 
0166 

0173 
0172 
0171 
0170 
0169 

1  0176 

j  0176 

0175 
0174 

0173 

0180 
0179 
0178 
0177 
0176 

0183 
0182 
0182 
OI8I 
0180 

0187 
0186 
0185 
0184 
0183 

0190 
0189 
0188 
0187 
0186 

0194 
0193 
0192 
OI91 
0190 

0197 
0196 
0195 
0194 
0193 

0201 
0200 
0199 
0198 
0197 

0203 
0202 
0201 
0200 

10  0 

0162 

j  0165 

0169 

0172 

0175  0179  0182 

0186 

0189 

0192 

0196  j  0199 

TABLE  30. 

Page  335 

%. 

Log.  A. 

Logs.  A,  B 

,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of 

moon. 

46' 

4r 

48' 

49' 

50' 

51'   52' 

53' 

54' 

55' 

56' 

57' 

58' 

lO'^  o' 

.0162 

0165 

0169 

0172 

0175 

0179  0182 

0186  ' 

0189 

0192 

0196 

0199 

S 

.0160 

0164 

0167 

0171 

0174 

0177  0181 

0184 

0187 

0191 

0194 

0197 

lO 

.0159 

0162 

0166 

0169 

0172 

0176  0179 

01S2 

0186 

0189 

0192 

0196 

15 

.0158 

0161 

0164 

0168 

0171 

0174  0178 

0181 

0184 

0187 

0191 

0194 

20 

.0156 

0160 

0163 

0166 

0170 

0173  0176 

0179 

0183 

0186 

0189 

0192 

25 

•0155 

0158 

0162 

0165 

0168 

0171  0175 

0178 

0181 

0184 

0188 

0191 

10  30 

.0154 

0157 

0160 

0164 

0167 

0170  }  0173 

0177 

0180 

0183 

0186 

0189 

35 

•0153 

0156 

0159 

0162 

0166 

0169  '  0172 

0175 

0178 

0181 

0185 

0188 

40 

.0151 

0155 

0158 

0161 

0164 

0167  1  0171 

0174 

0177 

0180 

0183 

0186 

45 

.0150 

0153 

0157 

0160 

0163 

0166  :  0169 

0172 

0175 

0179 

0182 

0185 

50 

.0149 

0152 

0155 

0158 

0162 

0165 

0168 

0171 

0174 

0177 

0180 

0183 

55 

.0148 

0151 

0154 

0157 

0160 

0163 

0167 

0170 

0173 

0176 

0179 

0182 

II  0 

.0147 

0150 

0153 

0156 

0159 

0162 

0165 

0168 

0171 

0174 

0177 

0181 

5 

.0146 

0149 

0152 

0155 

0158 

oi6i  i  0164 

0167 

0170 

0173 

0176 

0179 

10 

0148 

0151 

0154 

0157 

0160 

0163 

0166 

0169 

0172 

0175 

0178 

15 

0146 

0149 

0152 

0155 

0158 

0161 

0164 

0167 

0170 

0173 

0176 

20 

0145 

0148 

0151 

0154 

0157 

0160 

0163 

0166 

0169 

0172 

0175 

25 

0144 

0)47 

0150 

0153 

0156 

01 5r 

0159 
0158 

0162 

0165 

0168 

0171 

0174 

II  30 

0143 

0146 

0149 

0x52 

0161 

0164 

0167 

0170 

0172 

35 

0142 

0145 

0148 

0151 

0154 

0157 

0160 

0162 

0165 

0168 

0171 

40 

0141 

0144 

0147 

0150 

0153 

0156 

0158 

0161 

0164 

0167 

0170 

45 

0140 

0143 

0146 

0149 

0151 

0154 

0157 

oibo 

0163 

0166 

0169 

50 

0139 

0142 

0145 

0148 

0150 

0153 

0156 

0159 

0162 

0165 

0167 

55 

oi3« 

0141 

0144 

0146 

0149 

0152 

0155 

0158 
0157 

0161 

0163 

0166 

12  0 

0137 

0140 

0143 

0145 

0148  0151 

0154 

0159 

0162 

0165 

5 

0136 

0139 

0142 

0144 

0147  0150 

0153 

0156 

0158 

0161 

0164 

10 

0^35 

0138 

0141 

0143 

0146 

0149 

0152 

0154 

0157 

0160 

0163 

15 

0134 

0137 

0140 

0142 

0145 

0148 

0151 

0153 

0156 

0159 

0162 

20 

0133 

0136 

0139 

0141 

0144 

0147 

0150 

0152 

0155 

0158 

0160 

25 

0132 

0135 

0138 

0140 

0143 

0146 

0148 

0151 

0154 
0153 

0157 

0159 

12  30 

0131 

0134 

0137 

0139 

0142 

0145 

0147 

0150 

0155 

0158 

35 

0130 

0133 

0136 

0138 

0141 

0144 

0146 

0149 

0152 

0154 

0157 

40 

0129 

0132 

0135 

0137 

0140 

0143 

0145 

0148 

0151 

0153 

0156 

45 

0129 

0131 

0134 

0136 

0139 

0142 

0144 

0147 

0150 

0152 

0155 

0158 

>o 

0128 

0130 

0133 

0136 

0138 

0141 

0143 

0146 

0149 

0151 

0154 

0156 

55 

0127 

0129 

0132 

0135 

0137 

0140 

0142 

0145 

0148 

0150 

0153 

0155 

13  0 

0126 

0129 

0131 

0134 

0136 

0139 

0141 

0144 

0147 

0149 

0152 

0154 

5 

0125 

0128 

0130 

0133 

0135 

0138 

0141 

0143 

0146 

0148 

0151 

0153 

ID 

0124 

0127 

0129 

0132 

0135 

0137 

0140 

0142 

0145 

0147 

0150 

0152 

15 

0123 

0126 

0129 

0131 

0134 

0136 

0139 

0141 

0144 

0146 

0149 

0151 

20 

0123 

0125 

0128 

0130 

0133 

013s 

0138 

0140 

0143 

0145 

0148 

0150 

25 

0122 

0124 

0127 

0129 

0132 

0134 

0137 

0139 
0138 

0142 
0141 

0144 

0147 

0149 

13  30 

0121 

0124 

0126 

0129 

0131 

0133 

0136 

0143 

0146 

0148 

35 

0120 

0123 

0125 

0128 

0130 

0133 

0135 

0138 

0140 

0142 

0145 

0147 

40 

0120 

0122 

0124 

0127 

0129 

0132 

0134 

0137 

0139 

0142 

0144 

0146 

45 

0121 

0124 

0126 

0128 

0131 

0133 

0136 

0138 

0141 

0143 

0145 

50 

0120 

0123 

0125 

0128 

0130 

0132 

0135 

0137 

0140 

0142 

0145 

55 

0120 

0122 

0124 

0127 
0126 

0129 
0128 

0132 

0134 

0136 

0139 

0141 

0144 

14  0 

0119 

0121 

0124 

0131 

0133 

0136 

0138 

0140 

0143 

5 

0118 

0121 

0123 

0125 

0128 

0130 

0132 

0135 

0137 

0139 

0142 

ID 

0117 

0120 

0122 

0124 

0127 

0129 

0132 

0134 

0136 

01^9 

0141 

15 

01 1 7 

01 19 

0121 

0124 

0126 

0128 

0131 

0133 

0135 

0138 

0140 

20 

0116 

01 18 

0121 

0123 

0125 

0128 

0130 

0132 

0135 

0137 

0139 

25 

0115 

0118 

0120 

0122 

0124 

0127 

0129 

0131 
0131 

0134 

0136 

0138 

14  30 

01 14 

0117 

0119 

0121 

0124 

0126 

0128 

0133 

0135 

0137 

35 

0114 

0116 

0118 

0121 1 0123 

0125 

0128 

0130 

0132 

0134 

0137 

40 

0113 

0115 

0118 

0120  0122 

0124 

0127 

0129 

0131 

0134 

0136 

45 

0112 

0115 

0117 

0119  0121 

0124 

0126 

0128 

0130 

0133 

0135 

50 

0112 

01 14 

0116 

0118 

OI2I 

0123 

0125 

0127 

0130 

0132 

0134 

55 

OIII 

0113 
[  0113 

0116 

0118 

0120 

0122 

0124 

0127 

0129 

0131 

0133 

»5  0  1 

Olio 

0115 

0117 

OII9 

0121 

0124 

0126 

0128 

0130 

0133 

•• 

1 

Page  336 

TABLE  30. 

Log.  A. 

Logs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance.                1 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of 

moon. 

48' 

49' 

50' 

51' 

52' 

53' 

54' 

55' 

56' 

57' 

58' 

59' 

150  0' 

.0110 

0113 

0115 

0117 

0119 

0121 

0124 

0126 

0128 

0130 

0133 

10 

.0109 

cm 

0113 

0116 

0118 

0120 

0122 

0124 

0127 

0129 

0131 

20 

.0108  Olio 

0112 

01 14 

0116 

0119 

0I2I 

0123 

0125 

0127 

0129 

30 

.0107  i  0109 

cm 

0113 

0115 

0117 

OII9 

0I2I 

0124 

0126 

0128 

40 

.0105 

0107 

Olio 

0112 

0114 

0116 

01 18 
OII7 

0120 

0122 

0124 

0126 

.0104 

0106 

0108 

Olio 

0112 

0115 

OII9 

0121 

0123 

0125 

16   0 

.0103 

0105 

0107 

0109 

OIII 

0113 

OII5 

OII7 

0119 

0121 

0124 

10 

.0102 

0104 

0106 

0108 

Olio 

0112 

01 14 

OI16 

0118 

0120 

0122 

20 

.0101 

0103 

0105 

0107 

0109 

OIII 

OII3 

OII5 

0117 

0119 

0121 

30 
40 

.0100 
.0098 

0102 

0103 

0105 

0107 

0109 

OIII 

OII3 

0115 

0117 

0119 

0100 

0102 

0104 

0106 

0108 

Olio 

OII2 

0114 

0116 

0118 

50 

.0097  0099 

OIOI 

0103 

0105 

0107 

0109 

OIII 

0113 

0115 

0117 

17  0 

.0096  1  0098 

0100 

0102 

0104 

0106 

0108 

OIIO 

0112 

0114 

0116 

10 

.0095   0097 

0099 

OIOI 

0103 

0105 

0107 

0109 

OIIO 

0112 

0114 

20 

.0094  0096 

0098 

0100 

0102 

0104 

0106 

0107 

0109 

OIII 

0113 

30 

0095 

0097 

0099 

OIOI 

0103 

0104 

0106 

0108 

OIIO 

0112 

40 

0094 

0096 

0098 

0100 

OIOI 

0103 

0105 

0107 

0109 

OIII 

50 

0093 

0095 

0097 

0099 

0100 

0102 

0104 

0106 

0108 

0109 

18   0 

0092 

0094 

0096 

0098 

0099 

OIOI 

0103 

0105 

0107 

0108 

10 

0091 

0093 

0095 

0097 

0098 

0100 
0099 

0102 

0104 

0105 

0107 

0109 

20 

0090 

0092 

0094 

0096 

0097 

OIOI 

0103 

0104 

0106 

0108 

30 

0089 

0091 

0093 

0095 

0096 

0098 

0100 

0102 

0103 

0105 

0107 

40 

0088 

0090 

0092 

OC94 

0095 

0097 

0099 

OIOI 

0102 

0104 

0106 

50 

0088 

0089 

0091 

0093 

0094 

0096 

0098 

0099 

OIOI 

0103 

0105 

19  0 

0087 
0086 

0088 
0087 

0090 
0089 

0092 

0093 

0095 

0097 

0098 

0100 

0102 

OIOI 

0104 

10 

0091 

0092 

0094 

0096 

0098 

0099 

0103 

20 

0085 

0087 

0088 

0090 

0092 

0093 

0095 

0097 

0098 

OIOO 

0102 

30 

0084 

0086 

0087 

0089 

0091 

0092 

0094 

0096 

0097 

0099 

OIOI 

40 

0083 

0085 

00S7 

0088 

0090 

0091 

0093 

0095 

0096 

0098 

OIOO 

50 

0082 

0084 

0086 
0085 

0087 

0086 

0089 

0088 

0090 

0092 

0094 

0095 

0097 

0099 

20  0 

0082 

0083 

0090 

0091 

0093 

0094 

0096 

0098 

10 

0081 

1082 

0084 

0086 

0087 

0089 

0090 

0092 

0093 

0095 

0097 

20 

0080 

Ov,82 

0083 

0085 

0086 

0088 

0089 

0091 

0093 

0094 

0096 

30 

0079 

0081 

0082 

0084 

0086 

0087 

0089 

0090 

0092 

0093 

0095 

40 

0079 
0078 

0080 

0082 

0083 

008; 

0086 

0088 
0087 

0089 

0091 

0092 
0091 

0094 

50 

OO71) 

0081 

0082 

0084 

0085 

0088 

0090 

0093 

21   0 

0077 

0079 

0080 

0082 

0083 

0085 

0086 

0088 

0089 

0091 

0092 

10 

0076 

0078   0079 

0081 

0082 

0084 

0085 

0087 

0088 

0090 

0091 

20 

0076 

0077 

0079 

0080 

0082 

0083 

0085 

0086 

0087 

0089 

0090 

30 

0075 

0076 

0078 

0079 

0081 

0082 

0084 

0085 
0084 

0087 

0088 

0090 

40 

0074 

0076 

0077 

0079 

0080 

0082 

0083 

0086 

0087 

0089 

50 

0074 

0075 

0076 

0078 

0079 

0081 

0082 

0084 

0085 

0086 

0088 

22   0 

0073 

0074 

0076 

0077 

0079 

0080 

0081 

0083 

0084 

0086 

0087 

10 

0072 

0074 

0075 

0076 

0078 

0079 

0081 

0082 

0083 

0085 

0086 

20 

0072 

_oo73_ 
0072 

0074 
0074 

0076 

"0075 

_oo77 
0076 

0079 
0078 

0080 

^079 

ooSi 
0081 

0083 
0082 

0084 
0083 

0086 

30 

0071 

0085 

40 

0070 

0072 

0073 

0074 

0076 

0077 

0079 

0080 

0081 

0083 

0084 

50 

0070 

0071 

0072 

0074 

0075 

0076 

0078 

0079 

0081 

0082 

0083 

23  0 

0069 

0070 

0072 

0073 

0074 

0076 

0077 

0078 

0080 

0081 

0082 

10 

\  0068 

0070 

0071 

0072 

0074 

0075 
0074 

0076 
0076 

0078 
0077^ 

0079 

0080 

0082 

20 

0068 

0069 

0070 

0072 

0073 

0078 

0080 

0081 

30 

0067 

0069 

0070 

0071 

0072 

0074 

0075 

0076 

0078 

0079 

0080 

40 

0067 

0068 

0069 

0071 

0072 

0073 

0074 

0076 

0077 

0078 

0080 

50 

0066 

0067 

0069 

0070 

0071 

0073 

0074 

0075 

0076 

0078 

0079 

24   0 

0067 

0068 

0067 

0069 
0069 

0071 
0070 

0072 

0073 

0074 

0076 

^075" 

0077 

0076 

0078 

10 

0066 

0071 

0073 

0074 

0078 

20 

0066  0067 

0068 

0069 

0071 

0072 

0073 

C074 

0076 

0077 

30 

0065 

0066 

0068 

0069 

0070 

0071 

0072 

0074 

0075 

0076 

40 

0065 

0066 

0067 

0068 

0069 

0071 

0072 

0073 

0074 

0076 

SO 

0064 

0065 
0065 

0066 
0066 

0068 

0069 

0070 
0069 

0071 
0071 

0072 

0074 

0075 

25  0 

0063 

0067 

0068 

0072 

0073 

0074 

TABLE  30.                   [Page  337 
Log.  A. 
Logs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

Aim-. 

alt,  lit 

lllOOU. 

25  '  0' 
20 
40 

20   0 
20 
40^ 

27  0 

20 
40 

28  0 
20 
40 

29  0 
20 

40 

30  0 
20 

4.) 

31  0 

20 

Reduced  parallax  and  refraction  of  moon.                          1 

50' 

51' 

52' 

53' 

54' 

55' 

56' 

5V 

58' 

59' 

«©' 

.0063 
.  0062 
.  0061 
.  0060 
.0059 

0065 
0064 
0062 
0061 
0060 

0066  0067  0068 
0065  0066  0067 
0064  0065  0066 
0063  0064  0065 
0062  0063  0064 

0069  0071 
0068  0069 
0067  0068 
0066  0067 
0065  0066 

0072 
0071 
0069 
0068 
0067 

0073 
0072 
0071 
0069 
0068 

0074 
0073 
0072 
0071 
0069 

.  0058  0059 
.0057  0058 
.0056  0057 
•  0055  0057 
.  0055  0056 

0061  0062  0063 
0060  0061  0062 
0059  0060  0061 
0058  0059  0060 
0057  ,  0058  0059 

0064  0065 
0063  0064 
0062  0063 
0061  0062 
0060  0061 

0066  0067 
0065  0066 
0064  0065 
0063  0064 
0062  0063 

0068 
0067 
0066 
0065 
0064 

.0054 

•  0053 

•  0052 

•  0051 
.  0050 
.  0050 
.0049 
.  0048 
.0047 
.0047 

0055  • 
0054 

0053 
0052 
0051 
0051 
0050 
0049 
0048 
0047 
0047 
0046 
0045 
0045 
0044 

0056 

0055 
0054 

0053 
0052 

0051 
0051 
0050 
0049 
0048 

0057  0058  0059  ,  0060 
0056  0057  i  0058  0059 
0055  0056  0057  0058 
0054  0055  0056  0057 
0053  '  0054  1  0055  ,  0056 

0061  0062  0063 
0060  0061  0062 
0059  0060  0061 
0058  0059  0060 
0057  0058  j  0059 

0052  '  0053  ;  0054   0055 
0052   0052   0053   0054 
0051   0052   0053   0053 
0050   0051   0052   0053 
0049   0050  '  0051  '   0052 

0056  0057 
0055  0056 
0054  0055 
0053  0054 
0053  0054 
0052  0053 
0051  0052 
0050  0051 
0049  0050 
0049  0049 

0058 
0057 
0056 

0055 
0054 

0055 

40 

3^  0 
20 
40 

20 

40 

34  0 
20 
40 

.  0046 
.0045 
.0044 
.0044 
•  0043 
.  0042 
.  0042 
.  0041 
.  0040 
.  0040 

0048  0048  0049  0050 
0047  0048  0048  0049 
0046  0047  1  0048  0049 
0045  0046  0047  0048 
0045  '  0045  0046  0047 

0051 

0050 

0049 

0049 

0048 

0047" 

0046 

0046 

0045 

0044 

0054 

0053 
0052 

0051 

0050 

0054 
0054 

0053 
0052 

0051 

0050 

0050 

0049 

0048 

0047 

0043  1  0044 

0043  ;  0043 
0042    0043 
0041    0042 
0041    0041 
0040    004'! 
0039  j  0.140 
0039  1  0039 
0038    0039 
0038    0038 

0037  0038  : 
0036   0037 
0036  1  0037 
0035  '  0036  ! 
0035  '  0035  1 

0045  i  0046 
0044   0045 
0043  i  0044 
0043   0043 
0042   0043 

0046 
0045 
0045 
0044 
0044 
0043 
0042 
0042 
0041 
0040 
0C40 
0039 
0039 
0038 
0037 

0048 
0047 
0046 
0046 
0045 

0049 

0048 

0047 

0047 

0046 

0045^ 

0044 

0044 

0043 

0042 

0050 
0049 
0048 
0047 
0047 

35  0 
20 

40 

36  0 
20 
40 

37  0 
20 
40 

j8  o_ 
20 
40 

39  0 
20 
40 

.0039 
.0039 
.  0038 
.0037 
■  003  7_ 
,  0036 
.  0036 
•0035 
.0035 
.0034 

0041   0042 
0041   0042 
0040   0041 
0040   0040 
0039   0040 

0044 
0043 
0042 
0042 
0041 
0040 
0040 
0039 
0039 
0038 

0044 
0044 
0043 
0042 
0042 

0046  0047 
0045  0046 
0044  0045 
0044  0044 
0043  0044 

0038   0039 
0038   0038 
0037   0038 
9037   0037 
0036   0037 

0041 
0040 
0040 
0039 
0039 

0042 
0041 
0040 
0040 
^039 

0039 
0038 
0037 
0037 
0036 

0042 
0042 
0041 
0040 
0040 

0043 
0042 
0042 
0041 
0040 

.0034  i  0034 

.0033  0034 

'   0033 

0033 
j  0032 

0035  !  0036  0036 
0034  i  0035  0036 
0034  j  0034  0035 
"033  '  0034  0035 
0033  0033  "034 
0032  0033  0033 
0032  0032  0033  ' 
0031  0032  0032 
0031  0031  0032 
0030  1  0031  0031 

0037 
0036 
0036 

0035 
0035 

0037 
0037 
0036 
0036 
0035 

0038 
0037 
0037 
0036 
0036 

0039 
0039 
0038 
0037 
0037 

0040 
0039 
0039 
0038 
0037 
0037 
0036 
0036 

0035 
0035 

40  0 

20 

4'T 

41  0 
20 
40" 

42  0 
20 
40 

43  0 

0032 
i  0031 

'   0031 

0030 

1  0030 

0034  0035 
0034  0034 
0033  0034 
0033  0033 
0032  0033 

^035 
0035 
0034 
0034 
0033 

0033 
0032 

0032 

0031 

0031 

0036 
0035 

0035 
0034 

_oo34 

0033 
0033 
0032 
0032 
0031 

0036 
0036 
0035 
0035 
0034 

0029 
0029 
0029 
0028 
0028 

0030  0030  0031  0032  0032 
0029  0030  0031  0031  0032 
C029  0030  0030  0031  0031 
0029  0029  0030  0030  0031 
0028  0029  0029  0030  0030 

0034  0034 
0033  0034 
0033  0033 
0032  0033 
0032  0032 

20 

40 

44  0 

4u 

45  " 

0027 
0027 
0026 
0026 
0026 

0028  0028  0029  0029 
0027  0028  0028  0029 
0027  0027  0028  0028 
0026  0027  0027  0028 
0026  0026  0027  0027 

0030 
0029 
0029 
0028 
0028 

0030 
0030 
0029 
0029 
0028 

0031 
0030 
0030 
0029 
0029 

0031 
0031 
0030 
0030 
0029 

0032 
0031 
0031 
0030 
0030 
0029 

0025 

0026 

0026 

0027 

0027 

0027 

0028 

0028 

0029 

22    B 


Page  338 

TABLE  30. 

Log.  A. 

Logs 

3.  A,  B, 

C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance.               1 

App. 
alt.  of 
moon. 

45"  o' 

Reduced  parallax  and  refraction  of  moon.                          1 

51' 

.0025 

52' 

53' 

54^ 

55^ 

56' 

sr 

58' 

59' 

60' 

0026 

0026 

0027 

0027 

0027 

0028  1  0028 

0029 

0029 

3° 

.  0025 

0025 

0025 

0026 

0026 

0027 

0027  0028  0028 

0028 

46  0 

.0024 

0024 

0025 

0025 

0026 

0026 

0027  0027 

0027 

0028 

30 

.0023 

0024 

0024 

0025 

0025 

0026 

0026  0026 

0027 

0027 

47  0 

.0023 

0023 
0023 

0024 

0024 

0025 

0025 
0024 

0025 
0025 

0026 

0026 

0026 

0  3° 

.0022 

0023 

0024 

0024 

0025 

0025 

0026 

48  0 

.0022 

0022 

0023 

0023 

0023 

0024 

0024  0024 

0025 

0025 

30 

.0021 

0022 

0022 

0022 

0023 

0023 

0024  0024 

0024 

0025 

49  0 

.0021 

0021 

0022 

0022 

0022 

0023 

0023   !   0023 

0024 

0024 

30 

.  0020 

0021 

0021 

0021 

0022 

0022 

0022  0023 

0023 
0023 

0023 
0023 

50  0 

.0020 

0020 

0020 

0021 

'0021 

0022 

0022  0022 

30 

.0019 

0020 

0020 

0020 

0021 

0021 

0021  0022  0022 

0022 

51  0 

.0019 

0019 

0020 

0020 

0020 

0020 

0021  0021  !  0021 

0022 

30 

.0018 

0019 

0019 

0019 

0020 

0020 

0020   0021  1  0021 

0021 

52  0 

.0018 

0018 
0018 

0019 

0019 

0019 

0019 

0020  0020 

0020 
0020 

0021 

30 

.0018 

0018 

0018 

0019 

0019 

0019  1  0020 

■  0020 

53  0 

.  0017 

0017 

0018 

0018 

0018 

0018 

0019  1  0019  0019 

0020 

30 

.0017 

0017 

0017 

0017 

0018  i  0018 

0018  :  0019  !  0019 

0019 

54  0 

.0016 

0016 

0017 

0017 

0017  0018 

0018  j  0018  0018 

0019  i 

30 

.  0016 

0016 

0016 

0017 

0017  0017 

0017  ,  0018  0018 

0018 
0018 

55  0 

.0015 

0016 

0016 

0016 

0016  1  0017 

0017  0017  0017 

30 

.  0015 

0015 

0015 

0016 

0016  1  0016 

0016  0017  1  0017 

0017 

56  0 

.0015 

0015 

0015 

0015 

0016  0016 

0016  0016 

0017 

0017 

30 

.0014 

0014 

0015 

0015 

0015  0015 

0016  '  0016 

0016 

0016 

1 
1 

57  0 

.0014 

0014 
0014 

0014 

0015 

0015  0015 

0015  ;  0015 

0016 

0016 
0015 

'        1 

0  30 

.0014 

0014 

0014 

0014  0015 

0015  0015 

0015 

i    1 

58  0 

.0013 

0013 

0014 

0014 

0014  0014 

0014  0015 

0015  :  0015 

30 

.0013 

0013 

0013 

0013 

0014  0014 

0014  0014 

0014  '  0015 

59  0 

.0012 

0013 

0013 

0013 

0013  0013 

0014  0014 

0014   0014 

30 

.0012 

0012 

0012 

0013 

0013  0013 

0013  0013  0014  0014 

60 

.0012 

0012 

0012 

0012 

0013  0013 

0013  0013  0013  0013 

61 

.0011 

001 1 

001 1 

0012 

0012  0012 

0012  0012  '\   0012  j  0013 

62 

.0011 

001 1 

001 1 

001 1 

001 1  001 1 

001  I  ■  0012  ;  0012  j  0012 

63 

.0010 

0010 

0010 

0010 

001 1  001 1 

001 1   001 1  i  001 1  1  001 1 

64 

.  0009 

0010 

0010 

0010 

0010  0010 

0010 
0010 

0010  0010 

001 1 

65 

0009 

0009 

0009 

0009 

0009  0009 

0010  0010 

0010 

■  66 

.0008 

0008 

0009 

0009 

0009  :  0009 

0009  0009  1  0009 

0009 

67 

.  0008 

0008 

0008 

0008 

0008  ;  0008 

0008  0009  ]  0009 

0009 

68 

.0007 

0007 

0008 

0008 

0008  j  0008 

0008  0008  '\   0008 

0008 

69 

.0007 

0007 
0007 

0007 

0007 

0007  0007 
0007  0007 

0007 
0007 

0008 

0008 

0008 

70 

.0007 

0007 

0007 

0007  0007 

0007 

71 

.0006 

0006 

0006 

0006 

0006  0006 

0007  0007  0007 

0007 

72 

.  0006 

0006 

0006 

0006 

0006  0006 

0006  0006  0006  0006 

n 

.  0005 

0005 

0006 

0006 

0006  0006 

0006  0006  0006  0006 

74 
75 

.0005 
.0005 

0005 

0005 

0005 
0005 

0005  1  0005 
0005  0005 

0005  0005  0005 

0006 

0005 

0005 

0005  0005  0005 

0005 

76 

.0004 

0005 

0005 

0005 

0005  0005 

0005  0005  0005 

0005 

77 

.0004 

0004 

0004 

0004 

0004  0004 

0004  0004  0004  0004 

7« 

.  0004 

0004 

0004 

0004 

0004 

0004 

0004  :  0004  0004  :  0004 

79 

.  0004 

0004 

0004 
0004 

0004 
0004 

0004 
0004 

0004 
0004 

0004  0004  1  0004  1  0004 
0004  0004  0004  0004 

80 

.0004 

0004 

81 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  0003 

0003   0003 

82 

.0003 

0003 

0003 

0003 

0003  0003 

0003  0003 

0003   0003 

v3 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  0003 

0003   0003 

84 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  0003  0003  0003 

85 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  1  0003  0003 

0003 

86 

.  0003 

0003 

0003 

0003 

0003 

0003 

0003  0003  1  0003 

0003 

87 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  '  0003  ;  0003  0003 

88 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  0Q03  0003  0003 

89 

.0003 

0003 

0003  - 

0003 

0003 

0003 

0003  0003 

0003   0003 

90 

.0003 

0003 

0003 

0003 

0003 

0003 

0003  0003 

0003  0003  ! 

TABLE  30.                                               [Page  339 
>                                                                     Log.  B. 

I.,ogs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

.\pp.alt. 

cil  sun 

or  star. 

5' '  0' 

lO 
20 

3° 
40 

50 

0    0 

20 

40 
7     >' 

Reduced  refraction  and  parallax  of  sun  or  star. 

«'  0'' 

0'  30^' 

10^^ 

r  30'^ 

2^0^^ 

r  w 

3^0^^ 

r  m'' 

4/9// 

4^  30^' 

S'd'' 

5^  30^^ 

- 

- 

9. 9976 

9. 9970 
9. 9972 

9-  9974 

20 
40 

8     0 
20 
40 

9. 9981 

9. 9982 
9. 9982 
9- 9983 

9. 9977 

9. 9978 

9. 9979 

9. 9980 

9. 9981 

9-  9975 
9- 9976 
9.9977 

9- 9978 
9-  9979 

9     0 
20 
40 

10 

II 

9- 9992 

9- 9989 
9- 9991 

9. 9986 
9. 9986 
9.  9987 
9.9988 
9.  9989 

9- 9984 
9- 9985 
9-  9985 
9.  9986 
9.  9987 

9. 9982 
9- 9983 
9-  9983 
9. 9984 
9. 9986 

9. 9980 
9.9981 
9. 9982 
9. 9982 
9.  9984 

12 

13 
14 

15 
16 

9.  9997 
9-  9997 

9-  9995 
9- 9995 
9- 9996 
9. 9996 

9-  9993 
9- 9994 
9- 9994 
9- 9995 
9-  9995 

9. 9992  9. 9990 
9. 9992  i  9. 9991 

9-  9993    9- 9992 
9-  9994  '  9-  9993 
9.  9994    9. 9993 

9-  9989 
9- 9990 
9- 9991 
9- 9992 
9-  9993 

9-  9987 
9- 9989 
9. 9990 

9-  9991 

9.  9986 
9-  9987 

18 
20 

25 
30 
50 

0.  0001 

0. 0001 
0. 0001 

0. 0000 
0. 0000 
0. 0001 
0. 0001 

9. 9990 

9-  9999 
0. 0000 
0. 0000 
0. 0001 

9.  9998 
9.  9998 

9-  9999 
0. 0000 

0.  0001 

9.9997  9.9996 

9.9998  9.9997 

9. 9999  9. 9998 
0.  0000   9.  9999 
0.  0001 

9-  9995 
9- 9996 
9. 9998 

9- 9995 
9-  9996 

go 

0.  0001  j  0.  0002  '  0.  0002   0.  0002 

1              1              1 

App.  alt. 
of  sun 
or  star. 

5  0' 
10 
20 

30 
40 

50 

6  0 
20 
40 

7  0 
20 
40 

8  0 
20 
40 

9  0 
20 
40 

10 
II 
12 

13 
14 

15 
16 

18 

20 

25 
30 
50 

Reduced  refraction  and  parallax  of  sun  or  star.                                                             1 

6'0'^ 

6^30^' 

9-9951 
9- 9953 
9-  9954 

9- 9956 
9-9957 

r  30^' 

9- 9947 
9-  9949 
9-9951 

9- 9952 
9- 9954 

S'O'' 

8^30^^;  9^0'' 

9^30^^ 

9- 9933 
'9-9935 
9-9937 
9-  9939 
9. 9941 

10^  0^^ 

10^  30^' 

11^  0^^ 

11^  30^' 

9-  9959 
9. 9960 

9. 9944 
9.  9946 

9- 9948 
9- 9949 
9-9951 

9-  9940 
9- 9942 
9-9944 
9. 9946 
9. 9948 

9. 9937 
9- 9939 
9- 9941 
9- 9943 
9.9944 

9- 9946 
9. 9948 

9-9951 
9-  9953 
9.  9956 

9- 9929 
9- 9932 

9- 9934 
9.  9936 

9-  9938 

9. 9926 
9. 9928 
9-9931 
9-  9933 
9-  9935 
9-  9937 
9- 9939 

9.  9922 

9-  9925 
9.9927 
9.  9929 
9.  9932 

9.9919 
9.9921 
9. 9924 

9- 9965  '  9- 9962   g.ggsS  9-9955   9-9952 
9.9966  9.9963   9.9960  9.9957  9.9954 
9.9968  9.9965   9.9962   9.9959  9-9956 
9.9969:9.9967  9. 9964  9.9961    9.9959 
9.997119.9958  9.9966  9.9963   9.9961 

9- 9949 
9-9951 
9- 9954 
9-  9956 
9- 9958 

9-  9943 
9- 9945 
9- 9948 
9-9951 
9-  9953 

9-  9940 
9- 9942 
9-  9945 
9.  9948 

9.9972  9.9970 
9.9974  9-9971 
9-9975   9-9973 
9.9976   9.9974 

9-9977,9-9975 
9.9978   9.  9976 

9- 9979   9- 9977 

9.9980  9.997^ 

9.9981  9-9979 
9.  9983 '9.  9981 

9-9968  9.9965 
9.9969  9.9967 

9.9971  9.9968 

9.9972  g.9970 
9-9973   9-9971 

9-  0963 

9-  9965 
9. 9966 

9.  9968 

9.  9960 
9.  9962 
9-  9964 

9.  9958 

9- 9974 

9-  9975 
9.  9976 

9-9977 

9. 9972 

9-  9985 



,0 

! 


Page  340]                                               TABLE  30. 

Log.  C. 
Logs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App.alt. 
of  sun 
or  star. 

Reduced  refraction  and  parallax  of  sun  or  star.                                                            1 

0^0'^ 

0^  m'' 

10^^ 

1^  30'^ 

2^0'^ 

r  m'' 

3^0^' 

3^  30^^ 

4/0^/ 

4'  W' 

5'0'' 

5'  30" 

5^  0' 
20 
40 

6    0 
20 

9-  9969 
9-  9970 
9-  9972 
9-9975 
9-  9978 
9.9981 

40 
.9 

ID 

9.  9988 

9.  9984 
9.  9986 

9. 9980 
9. 9982 
9. 9984 

9-  9974 
9- 9978 
9.  9980 
9.  9982 

II 
12 

14 
15 

9. 9995 

9-  9993 
9- 9994 
9- 9994 

9-  9990 
9.9991 

9-  9992 
9-  9993 
9-  9993 

9- 9994 
9.  9994 

9.  9994 

9-  9995 
9.9996 

9.  9997 

9-  9989 

9- 9990 
9.9991 

9.9991 

9-  9992 

9-  9993 
9-  9993 
9- 9994 
9. 9994 
9.  9996 

9.  9987 
9. 9988 

9-  9989 
9. 9990 

9-9991 

9. 9986 

9-  9987 
9.  9988 
9.  9989 
9. 9990 

9- 9984 

9-  9985 

9-  9987 
9. 9988 

9.  9989 

9. 9982 
9- 9984 
9-  9985 

16 

17 
18 
20 

25 

9.  9998 
9. 9999 

9. 9997 

9. 9998 
9.  9998 

9. 9996 
9.  9996 
9. 9996 
9.  9997 
9^9998 
9. 9998 
9-  9999 
9-  9999 

9-  9995 
9-  9995 
9.  9995 

9-  9996 
9. 9997 

9-  9998 
9.  9999 

9- 9992 
9.  9992 

9-  9993 
9-  9993 

9.  9990 
9-9991 

30 
40 

50 
90 

O. GOOO 
O.  0000 

0. 0000  i  9. 9999 
0. 0000  9. 9999 
0. 0000  0. 0000 
0. 0000  0. 0000 

9. 9999 
9.  9999 
9. 9999 
0. 0000 

A  pp.  alt. 
of  sun 
or  star 

5^  0' 
20 
40 

6    0 
20 

40 

7 
8 

9 
10 

Reduced  refraction  and  parallax  of  sun  or  star. 

60'^ 

9. 9962 
9. 9964 
9.  9966 
9.9968 
9.  9969 

9-  9973 
9.  9976 

9.  9979 

9.9981 

9.  9983 

6'  30'^ 

J/Q'/ 

r3o^^ 

8^0^^ 

8^  30'^ 

ro'^ 

9'30  " 

9-9931 
9-  9936 
9-  9939 
9-  9943 
9- 9946 

10^  0'' 

10' 30'' 

9. 9924 
9. 9929 

9-  9933 
9-  9937 

11' 0' 

9. 9920 

9-  9925 
9.  9930 

11' 30"! 

9.9916 
9. 9922 

9. 9956 
9. 9959 
9.9961 
9.  9963 

9.  9949 
9-  9953 
9- 9955 
9.  9958 

9.  9960 

9. 9946 
9. 9949 
9-9952 

9-9955 
9-9957 

9. 9942 
9-  9946 
9. 9949 
9-  9952 
9- 9955 

9-  9938 
9-  9942 
9-  9946 
9-  9949 
9-  9952 

9- 9954 
9-  9956 
9. 9962 

9-  9935 

9-  9939 

9-  9943 
9.  9946 

9.  9949 

9-9951 
9-  9954 
9. 9960 

9- 9927 
9-  9932 
9- 9936 
9-  9940 
9-  9943 

9-  9965 
9. 9967 
9.9971 

9-  9974 
9.9977 

9. 9962 
9.  9964 
9.  9969 
9.  9972 
9-  9975 

9. 9960 
9. 9962 
9.  9966 
9. 9970 

9-9957 
9-  9959 
9- 9964 
9.  9968 

9-  9949 
9-9951 

9.  9946 

II 

12 

13 
14 
'5 

9. 9979 

16 

17 
18 
20 

25 

30 
40 

50 
90 

TABLE  30. 

Page  341 

V 

Log. 

D. 

Logs.  A, 

B,  C,  and  D,  for 

computing  the  First  Correction  of  the  Lunar  Distance.               1 

.\pp 
alt.  of 
moon. 

Reduced  parallax 

and  refraction  of  moon. 

1 

4r 

42^ 

43^ 

44/ 

45^ 

46' 

iV 

48' 

49' 

50' 

51' 

52' 

53'  54' 

55' 

5-"'  o' 

.0283 

0290 

0296 

0303 

0310 

0316 

0323 

0329 

0336 

0343 

0349 

0356 

0362  0369 

.0280 

0287 

0293 

0300 

0307 

0313 

0320 

0326 

0333 

0339 

0346 

0352 

0359  0365  '     1 

6 

.0277 

0284 

0291 

0297 

0304 

0310 

0317 

0323 

0330 

0336 

0342  I  0349 

0355  0362 

9 

.0275 

0281 

0288 

0294 

0301 

0307 

0313 

0320 

0326 

0333 

0339  !  0345 

0352  0358 

12 

.0272 

0279 

0285 

0291 

0298 

0304 

0310 

0317 

0323 

0330 

0336  :  0342 

0349  0355 

5  15 

.0270 

0276 

0282 

0289 

0295 

0301 

0308 

0314 

0320 

0326 

0333  0339 

0345  0351 

i8 

.0267 

0273 

0280 

0286 

0292 

0298 

0305 

0311 

0317 

0323 

0330  0336 

0342  0348 

21 

.0264 

0271 

0277 

0283 

02S9 

0296 

0302 

0308 

0314 

0320 

0327 

0333 

0339  0345 

-4 

.0262 

0268 

0274 

0281 

02S7 

0293 

0299 

0305 

031 1 

0317 

0324 

0330 

0336  0342 

27 

.0260 

0266 

0272 

0278 

0284 

0290 

0296 

0302 

0308 

0314 

0321 

0327 
0324 

0333  0339 

5  30 

.0257 

0263 

0269 

0275 

0282 

0288 

0294 

0300 

0306 

0312 

0318 

0330  0336 

33 

.0255 

0261 

0267 

0273 

0279 

0285 

0291 

0297 

0303 

0309 

0315 

0321 

0327  0333 

^6 

•0253 

0259 

0265 

0271 

0276 

0282 

0288 

0294 

0300 

0306 

0312  0318 

0324  0330 

39 

0256 

0262 

0268 

0274 

0280 

0286 

0292 

0298 

0303 

0309  i  0315 

0321  0327 

42 

0254 

0260 

0266 
0263 

0272 

0277 

0283 

0289 

0295 

0301 

0306  0312 

0318  0324 

5  45 

0252 

0258 

0269 

0275 

0281 

0287 

0292 

0298 

0304  0310 

0315  0321 

48 

0250 

0255 

0261 

0267 

0273 

0278 

0284 

0290 

0295 

0301  0307 

0313  0318 

51 

0247 

0253 

0259 

0265 

0270 

0276 

0282 

0287 

0293 

0299  0304 

0310  0316 

54 

0245 

0251 

0257 

0262 

0268 

0274 

0279 

0285 

0290 

0296  0302 

0307  0313 

57 

0243 

0249 

0254 

0260 

0266 

0271 

0277 

0282 

0288 

0294 

0299 

0305  (0310 

6  0 

0241 

0247 

0252 

0258 

0263 

0269 

0275 

0280 

0286 

0291 

0297 

0302  0308 

^ 
J 

0239 

0245 

0250 

0256 

0261 

0267 

0272 

0278 

0283 

0289 

0294 

0300  0305 

6 

0237 

0243 

0248 

0254 

0259 

Q265 

0270 

0275 

0281 

0286 

0292 

0297  0302 

9 

0235 

0241 

0246 

0252 

0257 

0262 

0268 

0273 

0279 

0284 

0289 

0295  0300 

12 

0233 

0239 

0244 

0249 

0255 

0260 

0266 

0271 

0276 

0282 

0287 

0292  0298 

6  15 

0231 

0237 

0242 

0247 

0253 

0258 

0263 

0269 

0274 

0279 

0285 

0290  0295 

18 

0230 

0235 

0240 

0245 

0251 

0256 

0261 

0267 

0272 

0277 

0282 

0288  0293 

21 

0228 

0233 

0238 

0243 

0249 

0254 

0259 

0264 

0270 

0275  0280 

0285  0290  t 

24 

0226 

0231 

0236 

0242 

0247 

0252 

0257 

0262 

0267 

0273 

0278 

0283  0288 

27 

0229 

0234 
0233 

0240 
07.38 

0245 

0250 

0255 

0260 

0265 

0271 

0276 

0281  0286  0291 

6  30 

0227 

0243 

0248 

0253 

0258 

0263 

0268 

0274 

0279  0284 

0289  1 

33 

0226 

0231 

0236 

0241 

(  246 

0251 

0256 

0261 

0266 

0271 

0276  0281 

0287  1 

^.6 

0224 

0229 

0234 

0239 

0244 

0249 

0254 

0259 

0264  0269 

0274  0279  1  0284 

39 

0222 

0227 

0232 

0237 

0242 

0247 

0252 

0257 

0262  0267 

0272  :  0277  0282 

42 

0220 

0225 

0230 

0235 

0240 

0245 

0250 

0255 

0260  ;  0265 

0270  :  0275  1  0280 

6  45 

0219 

0224 

0229 

0234 

0239 

0244 

0248  0253 

0258 

0263 

0268  :  0273  I  0278 

48 

0217 

0222 

0227 

0232 

0237 

0242 

0247 

0251 

0256 

0261 

0266  :  0271  0276 

51 

0216 

0220 

0225 

0230 

0235 

0240 

0245 

0250 

0254 

0259 

0264  0269 

0274  1 

54 

0214 

0219 

0224 

0228 

0233 

0238 

0243 

0248 

0253 

0257 

0262  1  0267 

0272  1 

57 

0212 

0217 

0222 

0227 

0232 

0236 

0241 

0246 

0251 

0255 

0260  ;  0265  j  0270  1 

7  0 

02 1 1 

0216 

0220 

0225 

0230 

0235 

0239 

0244 

0249 

0254 

0258 

0263 

0268 

0209 

0214 

0219 

0223 

0228 

0233 

0238 

0242 

0247 

0252 

0256 

0261 

0266 

6 

0208 

0212 

0217 

0222 

0227 

0231 

0236 

0241 

0245   0250 

0255  !  0259 

0264 

9 

02 1 1 

0216 

0220 

0225 

0230 

0234 

0239 

0243   0248 

0253  i  0257  1  0262 

12 

0209 

0214 

0219 

0223 

0228 

0232 

0237 

0242   0246 

0251  0255  0260 

7  J5 

0208 

0212 

0217 

0222 

0226 

0231 

0235 

0240   0245 

0249  0254  0258 

18 

1. 

0206 

02 1 1 

0216 

0220 

0225 

0229 

0234 

0238   0243 

0247  0252  I  0256 

21 

0205 

0209 

0214 

0219 

0223 

0228 

0232 

0237   0241 

0246  0250  1  0255 

24 

0204 

0208 

0213 

0217 

0222 

0226 

0230 

0235   0239 

0244  0248  0253 

27 
7  30 

0202 

0207 

0211 

C2l6 

0220 

0224 

0229 

0233   0238 

0242  0247  025 1 

0201 

0205 

0210 

0214 

0218 

0223 

0227 

0232   0236 

0241  0245 

0249 

33 

0199 

0204 

0208 

0213 

0217 

0221 

0226 

0230   0234 

0239  0243 

0248 

36 

0198 

0202 

0207 

02 1 1 

0215 

0220 

0224 

0229   0233 

0237  0242 

0246 

39 

0197 

0201 

0205 

0210 

0214 

0218 

0223 

0227  ;  0231 

0236  0240  0244  1 

42 

0195 

0200 

0204 

0208 

0213 

0217 

0221 

0225  0230 

0234  0238 

0243 

7  45 

0194 

0198 

0203 

0207 

021 1 

0215 

0220 

0224  0228 

0232  1  0237 

0241 

48 

0193 

0197 

0201 

0205 

0210 

0214 

0218 

0222  i  0227 

0231  0235 

0239 

51 

0191 

0196 

0200 

0204 

0208 

0213 

0217 

0221  0225 

0229  0234 

0238 

54 

0190 

0194 

0198 

0203 

0207 

021 1 

0215 

0219  0224 

0228  0232 

0236 

57 

0189 

0193 

0197 

0201 

0206 

0210 

0214 

0218  0222 

0226  0230 

0235 

8  0 

0188 

0192 

0196 

0200 

0204 

0208 

0212 

0217  0221 

0225  0229  1  0233  1 

Page  342] 

TABLE 

3°- 

Log.  D 

Logs.  A,  B, 

C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance.                1 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  1 

noon.                           1 

45' 

46' 

iV 

48' 

49' 

50' 

51' 

52' 

53' 

54' 

55' 

56' 

57' 

58' 

8°  O' 

.0192 

0196 

0200 

0204 

0208 

0212 

0217 

0221 

0225 

0229 

0233 

0237 

5 

.  0190 

0194 

0198 

0202 

0206 

0210 

0214 

0218 

0222 

0227 

0231  0235 

lO 

.0188 

0192 

0196 

0200 

0204 

0208 

0212 

0216 

0220 

0224 

0228  0232 

15 

.0186 

0190 

0194 

0198 

0202 

0206 

0210 

0214 

0218 

0222 

0226  0230 

20 

.0184 

0188 

0192 

0196 

0200 

0204 

0207 

0211 

0215 

0219 

0223  0227 

o  ^5 

.0182 

0186 

0190 

0194 

0197 

0201 

0205 

0209 

0213 

0217 

0221  0225 

8  30 

.0180 

0184 

0188 

0192 

0195 

0199 

0203 

0207 

02 II 

0215 

02x9  0223 

35 

.0178 

0182 

0186 

0190 

0193 

0197 

0201 

0205 

0209 

0213  0216  0220 

40 

.0176 

0180 

0184 

0188 

0191 

0195 

0199 

0203 

0207 

02X0  1  0214  !  0218 

45 
50 

.0174 
.0173 

0178 
0176 

0182 

0186 

0189 

0193 

0197 

0201 

0205 

0208 

02x2  02x6 

0180 

0184 

0188 

0191 

0195 

0199 

0202 

0206 

02x0  0214 

55 

.  0171 

017s 

0178 

0182 

0186 

0189 

0193 

0197 

0200 

0204 

0208  0212 

9  0 

.0169 

0173 

0177 

0180 

0184 

0188 

0191 

0195 

0198 

0202 

0206  0209 

5 

.0167 

0171 

0175 

0178 

0182 

0186 

0189 

0193 

0197 

0200  0204  '  0207 

10 
15 

.0166 

0169 

0173 

0177 

0180 

0184 

0187 

0191 

0195 

0198 

0202  0205 

.0164 

0x68 

0I7I 

0175 

0179 

0182 

0186 

0189 

0193 

0196 

0200  0203 

20 

.0163 

0166 

0170 

0173 

0177 

0180 

0184 

0187 

0191 

0194  1  0X98  !  020X 

25 

.0161 

0165 

0168 

0172 

0175 

0179 

0182 

0186 

0189 

0193   0196  i  0199 

9  30 

0163 

0166 

0170 

0173 

0177 

0180 

0184 

0187 

0x91 

0194  [  0x98 

35 

0161 

0165 

0163 

0168 
0167 

0172 

0175 

0179 

0182 

0185 

0189 

0x92 

0196 

40 

0160 

0170 

0174 

0177 

0180 

0184 

0187 

0x91 

0194 

45 

0158 

0162 

0165 

0169 

0172 

0175 

0179 

0182 

0X85 

0x89  1  0192 

0195 

50 

0157 

0160 

0164 

0167 

0170  1  0174 

0177 

0180 

0184  !  0187  1  0190 

0194 

55 

0156 

0159 

0162 

0165 

0169  0172 

0175 

0179 

0182 

0185  0189 

0192 

10  0 

0154 

0157 

0156 

0161 

0164 

0167 

0171 

0174 

0177 

0180 

0184  0187 

0190 

5 

0153 

0159 

0162 

0166 

0169 

0172 

0175 

0x79 

0182  0185 

0188 

10 

0151 

0155 

0158 

0161 

0164  0167 

0171 

0174 

0x77 

0x80  0183 

0x87 

15 

0150 

0153 

0156 

0160 

0163 

0166 

0169 

0172 

0x75  0179  0182 

0x85 

20 

0149 

0152 

0155 

0158 

0161 

0164 

0168 

0171 

0174   0177  :  0180 

0183 

25 

0147 

0150 

0154 

0T57 

0160 

0163 

0166 

0169 

0172  |oi75  0179 

0x82 

10  30 

0146 

0149 

0152 

0155 

0158 

0162 

0165 

0168 

017X  0x74  !  0x77 

0x80 

35 

0145 

0148 

0151 

0154 

0157  0160 

0163 

0166 

0169  1  0172  :  0175 

0x79 

40 

0143 

0147 

0150 

0153 

0156  0159 

0162 

0165 

0168  0x71  :  0x74 

0x77 

45 

0142 

0145 

0148 

0151 

0154  1  0157 

0160 

Q163 

0x66  0x69  0x72 

0175 

50 

55 

,0141 

0144 

0147 

0150 
0149 

0153  1  0156 

0159 

0162 

0x65  0168  0171 

0x74 

0140 

0143 

0146 

0152  1  0155 

0158 

0161 

0x64  0167  ■  0170 

0x72 

1 1  0 

0139 

0142 

0145 

0147 

0150  !  0153 

0156 

0159 

0x62  0165  :  0168 

0x71 

5 

0137 

0140 

0143 

0146 

0149  0152 

0155 

0158 

ox6x  0164  0167 

0170 

10 

0139 

0142 

0145 

0148  0151 

0154 

0157 

0159  •  0162  1  0165 

0x68 

15 

0138 

0141 

0144 

0147  0150 

0152 

0155 

0158  1  ox6x  ;  0164 

0x67 

20 

0137 

0140 

0143 

0145  0148 

0151 

0154 

0157  0160  0163 

0x65 

25 

* 

0136 

0139 

0141 

0144  !  0147 

0150 

0153 

0x56  0x58  0161 

0x64 

II  30 

013s 

0137 

0140 

0143   0146 

0149 

0151 

0154  0157  0160 

0163 

35 

0133 

0136 

0139 

0142  1  0145 

0147 

0150 

0153  ;  0156  {0159 

0161 

40 

0132 

0135 

0138 

OI41   0143 

0146 

0149 

0152  0x54  0x57 

0160 

45 

0I3I 

0134 

0137 

0140  1   0142 

0145 

0148 

0x50  0153  0156 

0x59 

50 

0130 

0133 

0136 

0138  !  OI41 

0144 

0x47 

0149  0152  0155 

0157 

55 

0129 

0132 

0135 

0137  1  0140 

0143 

0145 

0148^0151  0153 

0x56 

12  0 

0128 

0131 

0134 

0136  !  0139 

0142 

0144 

0147  0150  0x52 

0155 

5 

0127 

oi3o_ 
0129 

0132 
0131 

0135 
0134 

0138 

0140 

0143 

0x46  0148  j  0x51 

0x54 

10 

0126 

0137 

0139 

0x42 

0x45  0147  '  015° 

0x52 

' 

15 

0125 

0128 

0130 

0133  1  0136 

0138 

0x41 

0143  °'46  0149 

0151 

20 

0124 

0127 

0129 

0132   0135 

0137 

0140 

0142  0145  0147 

0150 

25 

0123 

0126 

0128 

013I  1  0133 

0136 

0139 

0x41  1  0144  0146 

0149 

12  30 

0122 

0125 

0127 

0130   0132 

0135 

0138 

0140  0x43  0145 

0148 
0147 

35 

OI2I 

0124 

0126 

0129 

0131 

0134 

0136 

0139  '  014X  0144 

40 

0120 

0123 

0125 

0128 

0130 

0133 

0135 

0138  1  0x40  0143 

0x45 

45 

OII9 

0122 

0124 

0127  '   0129 

0132 

0134 

0137  '  0139  0142 

0x44 

0x47 

50 

OI18 

0121 

0123 

0126  1  0128 

0131 

0133 

01:56  ,  0138  0141 

0143 

0146 

55 

OI18 

0120 

0123 

0125   0127 

0130 

0x32 

0135 

0137  j  0140 

0142 

0145 

13  0 

OII7 

0119 

0122 

0124 

0126 

0129 

0131 

0134 

0136  0139 

0X4X 

0143 

TABLE  30.                    [Page  343 

Log.  D. 
Logs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

.\pp. 
alt.  ot 
moon. 

if  0' 
10 

20 

30 
40 

50 

14  0 
10 
20 

30 
40 

50 

15  0 
10 

20 

Reduced  parallax  and  refraction  of  moon.                           1 

iV       48'   49' 

50'   51' 

52'   53' 

54'   55' 

56' 

57' 

58' 

59' 

.0117 
•  0115 
.0113 
.0112 

1 
0119  j  0122 
0117  0120 
0116  0118 
0114  0116 
0112  !  0114 

0124 

G122 

GI2G 
OII9 
GII7 

OII5 
GII3 
0II2 
GIIO 
GIG9 

G126 
0125 
0123 
0121 
G119 

1 

0129  0131 
0127  0129 
G125  0127 
G123  0125 
0121  0124 

0134  G136  i  G139 
G132  G134  G137 
G130  \   G132  G134 
G128  G13G  G132 
G126  0128  i  G131 

GI4I 

GI39 
GI37 

0135 
0133 

0143 
G141 

G139 

0137 

013s 

GUI  0113 
0109  j  GUI 
GIG7  ;  Giio 
0106  0108 
0104  gig6 

0117 
0116 
G114 
G112 

GUI 

OI2G   bl22 
01x8   0120 
GI16   OI18 
OII4   OII7 
OII3   GII5 

G124  j  G126  0129 
0122  0125  G127 
G121  G123  0125 
G119  G121  0123 
G117  G119  G121 

GI3I 
GI29 

GI27 

0125 

GI23 

0133 
G131 

0129 

0127 

G126 

0103  GIG5 
Gioi  0103 
0100  0102 

GG99   GIOI 

GG97  0099 

0107  j  0109 
0106   0108 
0104  !  0106 
0103   0105 
OIGI   0103 

GUI  1  G113 

GIIO   GII2 
0108   01 10 
0107   0109 
0105   0107 

0104  j  oig6 

0102  {  GIG4 
OIGI   0103 
G099   OIOI 

0098   01  GO 

G115  G118 
G114  0116 
G112  :  0114 
GUI   GI13 

GIO9   GUI 

0120 
G118 
G116 
G115 
G113 

0122 
GI20 
GI18 
OII7 
OII5 

0124 
G122 

OI2G 
OII9 
OII7 

30 
40 

16  0 
10 

G096  0098 
G094  0096 
0093  0095 
0092  0094 
0091  0093 

OIGO   OIG2 
0098  1  0100 
0097  ,  0099 
0096  1  0098 
0094   0096 

gig8. 

gig6 

G105 

0103 

G102 

0100 

0099 

0098 

G096 

0095 

GIIO 

oig8 
0107 
0105 
0104 

GI02 
OIGI 
GIOO 
0098 
0097 

G112 

GIIO 

gig8 
GI07 
gig6 

OII3 
GII2 
GIIG 
0109 
GI07 

GII5 
GII4 
OII2 
GUI 
GIG9 

20: 

30 
40 

SO 
17  0  1 

G089 
0088 
0087 
0086 
0085 

0091  i  0093  [   0095 
0090  •  0092  0094 
0089  .  0091  0092 
0088  0089  ]   0091 
0087  1  0088  j  0090 

GG97   GO99 
GO96   GO97 
0094   GO96 
0093  ,  0095 
GO92   0093 

0104 
.  0103 

OIGI 
GIOO 
0099 

gig6 

0105 
GIG3 
0102 
GIOO 

gig8 
gig6 
0105 
GIG4 

GIG2 

10 

20 

30 
40 

50 

0084 
|oo83 

G085 
0084 
0083 
0082 
G081 

0087  i  0089 
G086  j  0088 
0085  ]  0086 
0084   0085 
0083   0084 

0091    GO92 
0089   0091 
0088   0090 
0087   0089 
0086   0087 

0085  ;  gg86 
G083  j  G084 
0080  1  0082 
0078  0080 
0076  0078 

0094 
0093 
0091 
0090 
0089 

GG96  i  0097 
0094   0096 

0093  ;  0095 
0092   0094 
0091   GG92 

GG99 
0098 
0096 
0095 
0094 

GIGI 
GG99 
GO98 
0097 
GG96 

18  0 
20 
40 

19  0 
20 

0080 
0078 

GO  76 
0074 
0072 

0082  ;  0083 
0079  1  0081 
0077   0079 
0075   0077 
0073   0075 

gg88  1  G09G  ]  0091 
G086  G087  :  0089 
00S3  0085  0087 
0081  0083  :  0084 

0079   0081  :  0082 

0G93 
0090 
G088 
0686 
0084 

GG94 
GG92 
OO9G 
0087 
0085 

GG93 
G091 
0089 
gg86 

40 

20  0 
20 
40 

21  0 

0070 
G068 
G067 
0065 
GG63 

0072  0073  !  °°74  °°7^  1  °°77 
0070  1  0071  0073  j  GG74  0075 
0068  ';  0069  '  0071  ;  0072  0073 
0066  0068  G069  0070  0072 
0065  0066  0067  ;  0068  0070 

0079 

GG77 

0075 

GO  73 
0071 

go8g 
0078 
0076 
GO  74 

GO  72 

og8i  j  0083 
0079  0081 
G077  0079 
0075  0077 
0074  0075 

0084 
0082 
0080 
0078 
0076 

20 

40 

22  0 

20 

40 

G062 

gg6o 

0059 
0057 

G056 

G063 
0061 
0060 
0058 
0057 

0064  ;   0065     0067 

G063    0064  :  0065 
0061  0062  :  0063 
0059  ,  0061  0062 
0058  1  0059  ;  0060 

0068 

0066 
0065 
0063 
0061 

GG69 
G067 
0066 
0064 
0062 

G07G 
0069 
0067 
0065 
0064 

GO  72 
0070, 

gg68 
0066 
0065 

0073 
GG7I 
GO69 
0068 

gg66 

0074 
0072 
0070 
0069 
0067 

23  0 

20 
40 

24  0 
20 

0054 

0053 
0052 
OG50 

0055 
G054 

0053 
0051 

0050 

0057  0058  !  G059  i  gg6g 
0055  0056  0057  G058 
0054  0055  '  °°5^  °°57 
0052  0053  0054  1  0055 
0051  0052  0053  0054 

0061 
G059 
G058 
0056 

0055 

0062 
og6g 

GGS9 

0057 

0056 
0054 

0053 

G052 
0050 
G049 

0063 
0061 
gg6g 
0058 
0057 

0064 
0063 
og6i 
G059 
0058 

0065 
0064 
0062 
0060 
0059 

40 

25  0 
20 

40 

26  0 

0049 
G047 
0046 
GG45 
0G44 

0050  0051  ;  OG52  0053 
0048  0G49  1  0050  0051 
0047  0048  G049  ;  0050 
G046  0047  0048  1  0049 
0G45  G046  0046  0047 

0053 
0052 
0051 
G049 
GG48 

0055 
0054 

0053 
0051 
0050 

0056 
0055 

0053 
G052 

G051 

0057 
0056 
0054 

0053 
0052 

20 
40 
27  0 
20 
40 

GG43 
004 1 
0040 
G039 
0038 

0043  °044  °°45 
0042  0043  °°44 
0041  0042  0043 
0040  0041   0042 
0039  G040  0040 

GG46 

GG4S 

0044 
GG42 
OG4I 

0047 
G046 
0G44 
0043 
GG42 

0048 
G046 

0045 
0044 
0043 

G048 

0047 
qp46 

0045 
0043 

G049 
GG48 

GG47 

G045 

GG44 

0050 
0049 
0047 
0046 
0045 

28  0 

G037 

0038  G039  GG39  004G 

G041 

GG42 

0042  0043 

0044 

Page  344]                    TABLE  30. 

Log.  D. 
Logs.  A,  B,  C,  and  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App. 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                          1 

50^ 

51^ 

52'    53' 

54' 

55' 

56' 

51' 

58' 

59' 

60' 

28°  0' 

30 

29  0 

30 

30  0 

0.0037 
0. 0036 
0. 0034 
0. 0033 
0.0031 

1      1      1 

1  0. 0038  ■  0. 0039  !  0.  0039 
0. 0036  0. 0037  0.  0038 
0.  0035  1  0.  0035  !  0. 0036 
c.  0033  0.  0034  0.  0035 
0.  0032  0.  0032  0.  0033 

0. 0040 
0. 0038 
0.0037 
0. 0035 
0. 0034 

0. 0041 
0. 0039 
0.0037 
0. 0036 
0. 0034 

0. 0042 
0. 0040 
0. 0038 
0. 0036 
0. 0035 

0. 0042 
0. 0040 
0. 0039 
0. 0037 
0. 0035 

0. 0043 
0. 0041 
0. 0039 
0. 0038 
0. 0036 

0.0044 
0. 0042 
0. 0040 
0. 0038 
0. 0037 

30 

31  0 

30 

32  0 

30 

0. 0030 
0. 0028 
0.0027 
0.  0026 
0. 0024 

;  0.  0030  1  0.  0031 

0.  0029  1  0.  0029 

0.  0028   0.  0028 
0. 0026  1  0.  0027 
0.  0025   0.  0025 

0. 0024  ■  0.  0024 

0.  0022   0.  0023 
0.0021  1  0.0022 
0.  0020  !  0.  0020 
0.  0019  1  0.  0019 

0.0031 
0.  0030 
0.  0029 
0.0027 
0.  0026 

0. 0032 
0. 003 1 
0. 0029 
0. 0028 
0. 0026 

0. 0033 
0. 0031 
0. 0030 
0. 0028 
0. 0027 

0. 0033 
0. 0032 
0. 0030 
0. 0029 
0.0027 

0. 0034 
0. 0032 
0. 003 1 
0.  0029 
0. 0028 

0. 0034 
0. 0033 
0. 003 1 
0. 0030 
0. 0028 
0. 0027 
0. 0025 
0. 0024 
0. 0023 
0.0021 
0. 0020 
0.0019 
0. 0018 
0. 0016 
0.0015 

0. 0035 
0. 0033 
0. 0032 
0. 0030 
0. 0029 

0. 0032 
0.0031 
0. 0029 

33  0 
30 

34  0 
30 

35  0 

/^° 

36  0 

30 

37  0 
30 

0. 0023 
0. 0022 
0. 0021 
0. 0020 
0.0018 

0.  0025 
0.  0023 
0.  0022 
0.  002 1 
0.  0020 

0. 0025 
0. 0024 
0. 0022 
0.0021 
0. 0020 

0. 0025 
0. 0024 
0. 0023 
0. 0022 
0. 0020 

0. 0026 
0. 0025 
0. 0023 
0. 0022 
0.  002 1 

0. 0026 
0. 0025 
0. 0024 
0. 0022 
0.0021 

0. 0027 
0. 0026 
0. 0024 
0. 0023 
0. 0022 

0. 0028 
0. 0026 
0. 0025 
0. 0023 
0. 0022 

0.0017  0.0018  0.0018  0.0018 
0.0016  I  0.0017  0.0017  0.0017 
0.0015  0.0016  \  0.0016  0.0016 
0.0014  0.0014  0.0015  0.0015 
0.0013  0.0013  '  0.0014  0.0014 

0. 0019 
0. 0018 
0.0016 
0.0015 
0. 0014 

0. 0019 
0.0018 
0.0017 
0.0016 
0. 0014 

0. 0019 
0.0018 
0. 0017 
0.0016 
0. 0015 

0. 0020 
0. 0019 
0.0017 
0.  0016 
0.0015 

0. 0020 
0. 0019 
0.  0018 
0.0017 
0.0015 

0.0021 
0. 0019 
0. 0018 
0.  0017 
0. 0016 

38  0 
30 

39  0 
30 

40 

0.0012 

0.  OOII 

0. 0010 

0.0012   0.0013 

0. OOII  j  0.0012 

0.  0010   0.  OOII 
0.  0009   0.  0010 
0.  0008   0.  0009 

0. 0013 
0.  0012 

0.  OOII 

0.  0010 
0.  0009 

0. 0013 
0.0012 
0. 001 1 
0. 0010 
0. 0009 

0. 0013 
0. 0012 

0.  OOII 

0.  00  lO 
0.  0009 

0, 0014 
0. 0012 

0.  OOII 

0.  0010 
0.  0009 

0. 0014 
0.0013 
0. 0012 
0.  0010 
0. 0009 

0. 0014 
0. 0013 
0. 0012 

0.  OOII 

0.  0010 

0. 0014 
0.0013 
0. 0012 

0.  OOII 

0. 0010 

0.0014 
0.  0013 
0.0012 

0.  OOII 

0.  0010 

41 
42 

43 
44 
45 

0.  0007   0.  0007 

0.  0005  1  0.  0005 
0.  0003  0.  0003 
0.  0001  ;  0.  0001 
0.  0000  1  0.  0000 

0.  0007 
0.  0005 
0.  0003 
0.  0001 
0.  0000 

0. 0007 
0. 0005 
0. 0003 
0. 0001 
0. 0000 

0. 0007 
0. 0005 
0.  0003 
0. 0001 
0. 0000 

0. 0007 
0. 0005 
0.  0003 
0.  0001 
0.  0000 

0. 0007 
0. 0005 
0. 0003 
0. 0002 
0. 0000 

0. 0007 
0. 0005 
0. 0003 
0.  0002 
0. 0000 

0. 0008 
0.  0005 
0. 0003 
0. 0002 
0. 0000 

0.  0008 
0.  0006 
0.  0004 
0.  0002 
0.  0000 

46 

47 
48 

49 
50 

9.9998  :  9.9998 
9.9997  9.9997 
9.9995  9.9995 
9.  9994  •  9.  9994 
9.  9992  9.  9992 

9.  9998 
9.  9997 

9-  9995 
9-  9994 
9. 9992 

9. 9998  9. 9998 
9-  9997  9-  9996 
9-  9995  9-  9995 
9-  9993  9-  9993 
9-  9992  9-  9992 

9.  9998 
9-  9996 
9-  9995 
9-  9993 
9.  9992 

9.  9990 

9-  9989 
9.  9988 
9.  9086 
9-  9985 

9-  9998  9-  9998 
9.9996  9-9996 
9-9995  9-9995 
9-9993  9-9993 
9.9992  9.9991 

9.  9998 
9.  9996 
9.  9994 

9-  9993 
9.  9991 

9.  9998 
9-  9996 
9-  9994 
9-  9993 
9-  9991 

51 
52 
53 
54 
55 

9.  9991 
9.  9990 
9.  9989 
9.  9988 
9.  9986 
9.9085 
9.  9984 

9-  9983 
9. 9982 
9.  9981 

9.  9991 
9.  9990 
9. 9988 
9. 9987 
9.  9986 
9.  9985 
9. 9984 
9.  9983 
9.  9982 
9. 9981 
9  9980 

9-  9979 
9.  9978 

9- 9977 
9-9977 

9.9991  9.9991  9-9990 

9-  9990  9-  9989  9-  99S9 
9. 9988  9. 9988  9. 9988 
9.9987  j  9.9987  1  9.9987 
9.  9986  1  9.  9986  !  9.  9985 

9.9990  9.9990  9.9990 
9.  9989  9.  9989  9.  9988 
9.9987  9.9987  9.9987 
9.  9986  9.  9986  9.  9986 
9-9985  9- 9984  i  9- 9984 

9-  9990 
9.  9988 
9.  9987 
9.  9985 
9.  9984 

56 

9-  9985 
9- 9984 
9-  9983 
9.9981  ; 

9^9980  [ 

9. 9980 

9-9979 
9.9978 

9-9977 
9.9976 

9.9984  1  9.9984 

9-9983  i  9-9983 
9.  9982  !  9.  9982 
9.  9981  :  9.9981 
9.  9980   9.  9980 

9.  9984 

9-  9983 
9.  9982 
9.  9980 

9-  9979 
9-  9978 
9-  9977 
9-  9976 
9-  9976 
9-  9975 
9- 9974 
9-  9973 
9-  9972 
9-  9972 
9.9971 

9.  9970 
9.  9969 
9.  9968 
9.  9967 
9.  9966 
9.  9964 

9-  9984 
9.  9982 
9.  9981 
9.  9980 
9.  9979 
9.  9978 
9.  9977 
9.  9976 

9-  9975 
9-  9974 

9-  9973 
9-  9973 
9.  9972 

9.9971 
9.  9970 
9. 9969 
9.  9968 
9.  9967 
9.  9966 
9.  9965 
9. 9964 

9.  9983 
9.  9982 
9.  9981 
9.  9980 
9.  9979 
9.  9978 

9-  9977 
9-  9976 

9-  9975 
9.  9974 

9.  9983 
9.  9982 
9.  9981 

9-  9979 
9-  9978 

9-  9983 
9.  9981 
9.  9980 

9-  9979 
9.  9978 

61 
62 

63 
64 

65 

9.  9980 

9.9979 
9. 9979 
9-9978 
9.  9977 

9.  9976 
9. 9976 

9-  9975 
9- 9974 
9.  9974 

9.  9979 
9.  9978 
9.9977 

9- 9976 
9.  9976 

9.  9979 

9-9978 

9-9977 
9.  9976 

9-  9975 
9.  9974 
9-  9974 
9-  9973 
9-  9972 
9-  9972 

9. 9977 

9-  9976 

9.  9975 
9.  9974 

9-  9973 

9-  9977 
9.  9976 

9-  9975 
9-  9974 
9.  9972 

66 

67 
68 
69 
70 

9.9976  9.9975  :  9.9975 

9-  9975  9-  9975  9-  9974 
9.  9974  9.  9974  9.  9973 

9-  9974  9-  9973  9-  9973 
9-9973  9-9973  9-9972 

9-  9973  9-  9973  i  9-  9972 
9.9972  9.  9972  '  9.  9971 
9.9971  9.9971  ,9-9970 
9.9971  9.9970  9.9970 
9.9970  9.9969^9.9069 

72 
74 
76 

9.  9972 
9.9971 
9.9971 
9.  9970 
9.  9969 

9.9972  9.9971  1 
9.9971  9.9970 

^-9970 ;  9-9969 

9.9969  9-9969 
9.  9969  9.  9968 

9-  9971  I  9-  9970 
9.9970  ;  9.9969 
9.  9969  [   9.  9968 

9. 9968  ;  9. 9967 
9. 9967  9. 9967 

9.  9969 
9.  9968 
9.  9966 
9.  9966 
9.  9965 
9.9963 

9.  9968 
9.  9967 
9.  9966 

9-  9965 
9.  9964 

9. 9968 
9.  9966 

9-  9965 
9.  9964 
9.  9964 

90 

9.  9968 

9.9967  9.9966 

9. 9966  9. 9965 

9-  9963 

9.  9962 

TABLE  31.                                               [Page  345 

Second  Correction  of  the  Lunar  Distance. 

Appar- 
ent dis- 
tance. 

Sub. 
15^'   0' 

30 

16  0 

30 

17  0 

First  correction  of  distance. 

Appar- 
ent dis- 
tance. 

Add. 

r 

r 

w 

12' 

14' 

16' 

18'  1  20' 

21' 

22' 

23' 

24' 

25' 

26' 

2r 

28' 

II 

26 

25 
24 

23 
22 

■  1 

0 
0 
0 
0 
0 

11 

2 
2 

II 

3 

\ 

3 
3 

II 

5 
5 
4 
4 
4 

II 

6 
6 
6 
6 
6 

II 

8 
8 

8 
8 

7 

II 
10 
10 
10 
9 

II 

13 
13 
12 
12 
II 

'; 

14 
14 
13 
13 
13 

II 

16 

15 
15 

14 

II 

17 
17 
16 
16 

15 

II 

19 
18 
18 

17 
16 

II 

20 
20 

19 

18 
18 

II 

22 
21 
21 
20 
19 

II 
24 

23 
22 

21 

21 

30 

18  0 

30 

19  0 

30 

20  0 
21 

22 

23 
24 

11 

27 

28 
29 

0 

0 
0 
0 

0 
0 
0 
0 
0 
0 
0 
0 

0 

0 

0 

— 

3 

3 

3 

3 
2 

4 

4 
4 
4 
4 

5 
5 
5 
5 
5 

7 
7 
7 
6 
6 

9 
9 

8 
8 
8 

II 
II 
10 

ID 
ID 

12 
12 
12 
II 
II 

13 
13 
13 
12 
12 

15 
14 
14 
13 
13 

16 

15 
15 
15 
14 

17 

17 
16 
16 
15 

19 
18 
i8 
17 
17 

20 
20 

19 
18 
18 

22 
21 
20 

20 
19 

2 
2 
2 

2 
2 

3 
3 
3 
3 
3 

5 
4 
4 
4 
4 

6 
6 
6 

5 

5 

8 

7 
7 

ID 
9 
9 

8 

8 

II 

ID 

ID 

9 

9 

12 
II 

10 
10 

9 

13 
12 

II 

II 

ID 

14 
13 
12 
12 
II 
II 
10 
10 
9 
9 

15 
14 
14 

13 
12 

16 
15 
IS 
14 
13 

17 

17 
16 

15 

14 

19 
18 

17 
16 

15 

2 
2 
2 
2 

2 

3 

3 
2 

2 

2 

4 
4 
3 
3 
3 

5 
5 
4 
4 
4 

6 

5 
5 

7 
7 

7 

7 
6 

8 
8 
8 

\ 

9 

9 
8 

8 

8 

10 

9 
9 
9 
8 

12 
II 
II 
10 
10 

13 
12 

12 

II 

II 

14 

13 

12 

12 
II 

15 

14 
13 

13 

12 

30 

31 

32 

34 

35 
36 
37 
38 
39 

0 

0 

o- 

0 

0 

2 

2 
2 
2 
2 
2 

3 
3 
3 
3 
3 

4 
4 
4 
3 
3 

5 
5 
5 
4 
4 

6 
6 
6 

5 
5 

7 
6 
6 
6 
6 

7 

7 
7 
7 
6 

8 
8 

7 
7 
7 

i 

8 
8 

7 

9 
9 
9 
8 

8 

10 

ID 

9 
9 
9 

II 
II 

10 

ID 

9 

12 
II 
II 
II 

10 

0 

0 

0 

0 
0 

2 
2 
2 
2 
2 

2 
2 

2 
2 
2 

3 
3 
3 
3 
3 

4 
4 
4 
4 
3 

5 

5 
5 
4 
4 

5 
5 
5 
5 
5 

6 
6 
6 
5 

5 

7 
6 
6 
6 
6 

7 

7 
7 
6 

6 

8 
8 

7 
7 
7 

8 
8 
8 
8 
7 

9 

9 

8 
8 
8 

10 
9 
9 
9 
8 

40 

42 

44 
46 

48 

0 
0 

0 
0 

0 

0 
0 
0 
0 

0 
0 
0 
0 
0 

2 

2 
2 
2 
2 
2 

3 
2 

2 
2 
2 

3 
3 
3 
3 
3 

4 
4 
4 
3 
3 

5 
4 
4 
4 
3 

5 

5 
4 
4 
4 

6 

5 
5 
4 
4 

6 
6 

5 
5 
5 

7 
6 
6 
5 
5 

7 
7 
6 
6 

5 

8 
7 

7 
6 
6 

5 
5 
5 
4 
4 

8 
8 

7 
7 
6 

6 
5 
5 
5 
4 

140° 

138 

136 

134 

132 

130 
128 
126 
124 
122 

50 

52 

56 
58 

0 

0 

0 

0 

0 

^ 

2 
2 
2 
2 

2 
2 
2 
2 
2 

3 
3 
3 
2 
2 

3 

3 

3 

3 
2 

4 
3 
3 
3 
3 

4 
4 
3 
3 
3 

4 
4 
4 
3 
3 

5 
4 
4 
4 
3 

5 
5 
4 
4 
4 

60 
62 

64 

66 

68 

70" 

74 

78 

82 

86 

90 

Appar- 
ent dis- 
tance. 

0 

0 

0 

0 

0 

0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

2 

2 

2 
2 
2 
2 
I 

2 
2 
2 
2 
2 

2 
2 
2 
2 
2 

3 
2 
2 
2 
2 

3 
3 
2 

2 
2 

3 
3 
3 
2 

2 

3 
3 
3 
3 
2 

4 
3 
3 
3 
3 

4 
4 
3 
3 
3 

120 
118 
116 
114 
112 

0 

0 

0 

0 
0 

0 
0 

0 
0 

0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

0 
0 
0 
0 

0 
0 
0 

0 
0 

I 
I 
I 
0 
0 

I 
I 

I 
I 
0 

2 
I 
I 
I 
0 

2 
I 
I 
I 
0 

2 
I 

I 
I 
0 

2 
2 
I 

I 
0 

2 
2 

I 
I 
0 

2 
2 
I 
I 
0 

2 
2 

I 
I 
0 

IIO 

106 

102 

98 

94 

0 

0 

V 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

90 

10' 

12' 

14' 

16' 

18' 

20' 

21' 

22' 

23' 

24' 

25' 

26' 

27' 

28' 

Appar- 
ent dis- 
tance. 

First  correction  of  distance. 

Page  346] 

TABLE  3 

I. 

Second  Correction  0 

f  the  Lunar  Distance. 

Appar- 

First correction  of  distance 

. 

Appar- 

ent dis- 

ent dis- 

tance. 

29^ 

30' 

31' 

32' 

33' 

34' 

35' 

36' 

3r 

38' 

39' 

40' 

41' 

42' 

43' 

44' 

tance. 

Sub. 

II 

II 

II 

ii 

// 

11 

// 

11 

II 

II 

II 

II 

II 

II 

II 

II 

Add. 

150  0' 

27 

29 

33 

33 

35 

38 

40 

42 

45 

47 

50 

52 

55 

57 

60 

63 

30 

26 

28 

32 

32 

34 

3(> 

39 

41 

43 

45 

48 

50 

53 

^^ 

58 

61 

16  0 

2b 

27 

31 

31 

33 

35 

37 

39 

42 

44 

4b 

49 

51 

54 

5(> 

59 

30 

25 

27 

30 

30 

32 

34 

3^' 

38 

40 

43 

45 

47 

50 

52 

54 

57 

17  0 

24 

2b 

29 

29 

31 

33 

35 

37 

39 

41 

43 

46 

48 

50 

53 

55 

,  30 

23 

25 

28 

28 

30 

32 

34 

36 

38 

40 

42 

44 

47 

49 

51 

54 

18  0 

23 

24 

28 

28 

29 

31 

33 

35 

37 

39 

41 

43 

45 

47 

50 

52 

30 

22 

23 

27 

27 

28 

30 

32 

34 

2,^ 

38 

40 

42 

44 

46 

48 

50 

19  0 

21 

23 

2b 

2b 

28 

29 

31 

33 

35 

37 

39 

41 

43 

45 

47 

49 

30 

21 

22 

25 

25 

27 

28 

30 

32 

34 

3b 

37 

39 

41 

43 

4b 

48 

20 

20 

22 

25 

25 

26 

28 

29 

31 

33 

35 

36. 

38 

40 

42 

44 

46 

21 

19 

20 

23 

23 

25 

2b 

28 

29 

31 

33 

35 

?,^ 

38 

40 

42 

44 

22 

18 

19 

22 

22 

24 

25 

26 

28 

30 

31 

33 

35 

36 

38 

40 

42 

23 

17 

19 

21 

21 

22 

24 

25 

27 

28 

3e 

31 

33 

35 

30 

38 

40 

24 

lb 
16 

18 

20 

20 

21 

23 

24 

25 

27 

28 

30 

31 

33 

35 

3b 

38 

25 

17 

19 

19 

20 

22 

23 

24 

26 

27 

28 

30 

31 

33 

35 

36 

26 

IS 

lb 

18 

18 

19 

21 

22 

23 

25 

26 

27 

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FABLE  3 

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Appar- 
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tance. 

First  c 

orrecti 

on  of  d 

istance. 

tance. 

Page  348]                                               TABLE  32. 

For  finding  the  Correction  of  the  Lunar  Distance  for  the  Contraction  of  the  Moon's  Semi-diameter. 

TABLE  32A.— GIVING  THE  ARGUMENT  FOR  TABLE  32B. 

Red. 

Apparent  altitude  of  moon. 

P.  and 

R.  of 

moon. 

5° 
65 

5i° 

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Whole  cor- 
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4 

5 

b 

7 

8 

9 

10 

II 

12 

14 

15 

lb 

17 

18 

19 

20 

21 

23 

25 

27 

52 

I     2 

3 
3 

4 
4 

5 
6 

6 

7 

8 
8 

9 
9 

10 
10 

II 
II 

12 
12 

n 
13 

14 
15 

15 
lb 

lb 

17 

17 
18 

18 
19 

19 

21 

22 

24 

2b 

53 

I     2 

20 

21 

22 

25 

27 

54 

2 

3 

5 

6 

7 

8 

9 

10 

12 

13 

14 

15 

lb 

17 

19 

20 

21 

22 

23 

2b 

55 

2,4 

5 

6 

7 

8 

10 

II 

12 

13 

15 

lb 

17 

18 

19 

21 

22 

5^^ 

3!4 

5 

6 

8 

9 

10 

II 

13 

14 

15 

lb 

57 

'4 

1          1 

5 

7 

When  the  nearest  limb  is  observed,  subtract  this  correction ;  when  the/ari/iesi,  add. 


TABLE  S3. 

Page  349  1 

For 

finding  the  Correction  of  the  Lunar  Distance  for  the  Contraction  of  the  Sun's  Semi-diameter.             1 

TABLE  33A.-GIVING  THE  ARGUMENT  FOR  TABLE  33B. 

Red.  P. 

Apparent  altitude  of  sun. 

and  R. 
of  sun. 

5° 

5i° 

6° 

U° 

r 

U° 

8° 

8r 

9° 

9i° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

n° 

18° 

20° 

25° 

30° 

40° 

50° 

jO  0" 

22 

18 

30 

30 

34 

24 

29 

2       0 

i  35 

37 

42 

46 

46 

30 

40       42    !    44 

47 

53 

59 

3    0 

30 

-  — 

— 

44 

46 

49  !  51     53 

57 

45 

48 

51 

54 

57 

60 

62 

67 

4     0 

45 

49 

52 

55 

59 

62 

65 

68 

30 

47 

49 

51    55 

59 

63 

bb 

70 

5    0 

47 

50 

52 

54 

57,61 

66  1  70 

74 

30 
6    0 

— 

49 

47 

52 

50 

55 

52 
57 

55 

57 

60 

62   67 

72 

60 

63 

66 

68 

74 

30 

50 

53 

S^' 

59 

62 

^S 

68 

71 

74 

7    0 

51 

54 

5« 

61 

64 

67 

70 

74 

30 

55 

5« 

62 

65 

69 

72 

75 

8    0 

55 

59 

62 

66 

70 

73 

77 

30 

59 

63 

66 

70 

74 

78 

9    0 

62 

6b 

70 

74 

79 

30 

6b 

70 

74 

79 

10    0 

69 

74 

7« 

II     0 

73 

77 

76 

81 

30 

80 

TABLE  33B.— CONTRACTION  OF  SUN'S  SEMI-DIAMETER.                                                  1 

^  Whole  cor- 
rection of 
;        sun. 

Argument  =  number  from  Table  33A.                                                                    1 

20 

24  28 1 32 

36 

40 '44 

46 

48 

50 

52 

54 

56 

58 

60 

62 

64 

66 

68 

110 

n 

H    76 

78 

//        ;/ 

II 

// 

II 

// 

// 

// 

// 

// 

// 

// 

;/ 

II 

II 

II 

II 

II 

// 

II 

//      // 

II 

0     0 

0 

0        0 

0     0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

o 

0 

0  I    0 

0 

I      0 

I 

I         I 

I 

I 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0      0 

0 

2      0 

2 

2 

2 

2 

2 

2 

2 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I       I 

I 

30 

3 

3 

3 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

I 

I 

3    0 

1 



4 

4 
5 

4 

5 

3 
5 

3 
4 

31    3 

3 

3 

3 

3 

3 

2 

3 

2 

2 

2 

2 

2 

3 

2 
3 

30 

4!   4 

4 

4 

4 

4 

1 

3 

3 

3 

3 

4    0 

7 

6 

6 

b 

6     5 

5 

5 

5 

5 

5 

4 

4 

4 

4 

4 

4 

4 

20 

7 

7 

7 

7 

6 

b 

6 

6 

5 

5 

5 

5 

5 

5 

5 

4 

4 

40 

9 

8 

8 

8 

7 

7 

7 

7 

b 

b 

6 

6 

6 

5 

5 

5 

5 

5    0 

10 

9 

9 

9 

8 

8 

8 

8 

7 

7 

7 

7 

6 

6 

b 

6 

b 

20 

II 

ID 

10 

9 

9 

9       9 

8 

8 

8 

8 

7 

7 

7 

7 

7 

40 

12 

12 

II 

II 

ID 

10      10 

9 

9 

9 

9 

8 

8 

^  8 

8 

7 

6    0 

13 

12 

12 

12 

II      II 

10   :    10 

10 

10 

9 

9 

9 

9 

8 

20 

14 

14 

13 

13 

12      12 

12       II 

II 

II 

10 

10 

10 

10 

9 

40 
7    0 

lb 

18 

15    15 

14 

14      13 

13       13 

12 
13 

12 
13 

II      II 

13  i  12 

II 

II 

10 

17    16 

16 

15      15 

14       14 

12 

12 

II 

20 

19    18    17 

17      16 

16       15       15 

14 

14     13     ^3 

13 

12 

40 

20 

19 

18      18 

17       17 

16 

16 

15     15 

14 

14 

14 

8    0 

21 

21 

20      19 

19       18 

17 

17 

lb 

lb 

lb 

15 

15 

20 

22     21 

20       20 

20 

18 

18 

17 

17 
18 

lb 

lb 

40 

23     23 

22       21 

20 

19      19 

18 

17 

9    0 

24       23       22 

21 

21       20      20       19 

19 

20 

25  f  24 

23 

22        22 

21     21 

20 

40 

1  25 

^5  , 

24       23 

23  j  22 

22 

10    0 

26  1 

26       25 

24  [  24 
26     25 

23 
25 

20 

28       27 

40 

28 

28 

27 

26 

II     0 

1 

1 

29 

28 

20 

30 

Stibtract  this  correction  from  the  distance. 


Page  350 

TABLE  34. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

Q'' 

V 

2'' 

3^^ 

4// 

5'' 

6'^ 

^// 

8^^ 

r^ 

0          /           // 

O''   0'"     o^ 

0. 0000 

0.  3010 

0. 4771 

0.6021 

0. 6990 

0.  7782 

0.8451 

0.9031 

0. 9542 

o 

lO 

1 .  0000 

I.  0414 

1.0792 

I- "39 

I.  1461 

1. 1761 

I. 2041 

I.  2304 

1.2553 

1.2788 

0 

20 

I.  3010 

1.3222 

1-3424 

I. 3617 

1.3802 

1-3979 

1. 4150 

1.4314 

1.4472 

1. 4624 

o 

30 

1. 4771 

1-4914 

1-5051 

1-5185 

1-5315 

I- 5441 

1-5563 

I.  5682 

1.5798 

1-59" 

0 

40 

I . O02 I 

I. 6128 

1.6232 

1-6335 

1-6435 

1.6532 

1.6628 

I.  6721 

1. 6812 

I . 6902 

o 

SO 

I . 6990 

I.  7076 

I.  7160 

I-  7243 

I-  7324 

I.  7404 

I.  7482 

1.  7559 

1.  7634 

I.  7709 

O       I 

0 

I.  7782 

I.  7853 

I.  7924 

I-  7993 

1.8062 

I.  8129 

1.8195 

I.  8261 

1.8325 

1.8388 

10 

1-8451 

1-8513 

1-8573 

1-8633 

1.8692 

1.8751 

1.8808 

I.  8865 

1 . 892 1 

1.8976 

20 

1-9031 

I . 9085 

I.  9138 

1.9191 

1-9243 

1.9294 

1-9345 

1-9395 

1.9445 

1.9494 

30 

1.9542 

1.9589 

1.9638 

1.9685  •■  I.  9731 

1-9777 

1.9823 

1.9868 

1.9912 

1.9956 

40 

2.  0000 

2-  0043 

2. 0086 

2.  0128 

2.0170 

2.  02I2 

2-0253 

2. 0294 

2. 0334 

2.0374 

so 

2.  0414 
2.  0792 

2-  0453 
2. 0828 

2. 0492 
2. 0864 

2.0531 

2. 0569 

2.  0607 

2.  0645 

2. 0682 

2.0719 

2.0755 

O      2 

0 

2.  0899 

2. 0934 

2.  0969 

2.  1004 

2. 1038 

2. 1072 

2.  1 106 

2 

10 

2.  1 139 

2- "73 

2. 1206 

2.  1239 

2.  1271 

2.  1303 

2-  1335 

2.  i3<^7 

2. 1399 

2.  1430 

2 

20 

2. 1461 

2.  1492 

2- 1523 

2-1553 

2.  1584 

2.  1614 

2.  1644 

2.  1673 

2.1703 

2.1732 

2 

30 

2.  1 761 

2.  1790 

2. 1818 

2.  1847 

2-  1875 

2.  1903 

2-  1931 

2. 1959 

2. 1987 

2.  2014 

2 

40 

2. 2041 

2. 2068 

2-  2095 

2.  2122 

2.2148 

2.2175 

2.  2201 

2.2227 

2.  2253 

2.  2279 

2 

50 

2.  2304 

2-  2553 

2.  2330 

2.  2355 

2.  2380 

2. 2405 

2.  2430 

2.  2455 

2. 2480 

2. 2504 

2.  2529 

o    3 

0 

2-2577 

2.  2601 

2.  2625 

2.  2648 

2.  2672 

2.  2695 

2.2718 

2. 2742 

2. 2765 

3 

10 

2.  2788 

2.2810 

2.  2833 

2.  2856 

2.  2878 

2.  290c 

2.  2923 

2.  2945 

2. 2967 

2.  2989 

3 

20 

2.3010 

2- 3032 

2-  3054 

2-  3075 

2. 3096 

2.3I18 

2.3139 

2.3160 

2.3181 

2.3201 

3 

30 

2.  3222 

2-  3243 

2.  3263 

2-  3284 

2-  3304 

2.  3324 

2-  3345 

2. 3365 

2.  3385 

2.  3404 

3 

40 

2.  ^424 

2.3444 

2- 3464 

2. 3483 

2- 3502 

2-3522 

2-3541 

2.  3560 

2.3579 

2. 3598 

3 

50 

2.3617 
2.  3802 

2-  3636 
2.  3820 

2-  3655 
2-3838 

2. 3674 

2, 3692 

2.37II 

2.3729 

2.  3747 

2. 3766 

2.  3784 

o    4 

0 

2.  3856 

2. 3874 

2.  3892 

2.  3909 

2.3927 

2.  3945 

2.  3962 

4 

ID 

2.3979 

2-3997 

2.4014 

2.4031 

2. 4048 

2- 4065 

2. 4082 

2. 4099 

2.4116 

2.4133 

4 

20 

2.4150 

2.4166 

2.4183 

2. 4200 

2.4216     2.4232 

2.  4249 

2. 4265 

2.4281 

2. 4298 

4 

30 

2-4314 

2-  4330 

2.  4346 

2-  4362 

2-4378 

2-  4393 

2.4409 

2.  4425 

2.4440 

2. 4456 

4 

40 

2.  4472 

2. 4487 

2-  4502 

2.4518 

2-4533 

2. 4548 

2.  4564 

2.4579 

2.4594 

2. 4609 

4 

.5o_ 
0 

2.  4624 
"^2.4771 

2.  4639 

2-  4654 

2. 4669 

2-  4683 

2.  4698 

2-4713 

2.  4728 

2.  4742 

2.4757 

o    5 

2. 4786 

2.  4800 

2. 4814 

2. 4829 

2.  4843 

2.4857 

2.4871 

2. 4886 

2. 4900 

■     5 

10 

2.4914 

2.  4928 

2.  4942 

2-  4955 

2. 4969 

2-  4983 

2. 4997 

2.  501 1 

2.  5024 

2.  5038 

5 

20 

2-5051 

2.  5065 

2-  5079 

2-  5092 

2.5105     2.5119 

2-5132 

2-5145 

2.5159 

2.5172 

5 

30 

2-5185 

2.5198 

2. 52II 

2.  5224 

2-5237  ;  2.5250 

2.  5263 

2.5276 

2. 5289 

2. 5302 

5 

40 

2-53'5 

2-  5328 

2-  5340 

2.  5353 

2- 5366  1  2. 5378 

2-5391 

2.  5403 

2.5416 

2. 5428 

5 

50 

2-  5441 

2.  5453 
2-  5575 

2.  5465 

2. 5478 

2. 5490 

2.  5502 
"2. 5623 

2-5514 
2.  5635 

2.5527 

2.5539 

2-5551 

o    6 

0 

2-  5563 

2.5587 

2.  5599 

2.  5611 

2. 5647 

2.  5658 

2.  5670 

6 

10 

2.  56S2 

2. 5694 

2.5705    1    2.5717    ,    2.5729    !    2.5740 

2.5752 

2-5763 

2.5775 

2.5786 

6 

20 

2-5798 

2.  5809 

2.5821     ,    2.5832    i    2.5843    i    2.5855 

2.  5866 

2-5877 

2. 5888 

2.  5899 

6 

30 

2. 5911 

2. 5922 

2-5933  ;  2-5944     2.5955  1  2.5966 

2-5977 

2.  5988 

2. 5999 

2.  6010 

6 

40 

2. 6021 

2.6031 

2.  6042  1  2.  6053 

2.  6064  ,  2.  6075 

2.  6085 

2.  6096 

2.6107 

2.  6117 

6 

50 
0 

2.6128 
2.  6232 

2.6138 
2.  6243 

2.6149 

2.6160 

2.6170 

2.6180 

2.  6191 

2.  6201 

2.6212 

2.  6222 

o    7 

2.  6253 

2. 6263 

2. 6274 

2.  6284 

2. 6294 

2.  6304 

2.6314 

2. 6325 

7 

10 

2-6335 

2.  6345 

2-  6355 

2.  6365 

2-6375 

2-  6385 

2-  6395 

2.  6405 

2.6415 

2.  6425 

7 

20 

2-6435 

2.6444 

2.  6454  I  2.  6464 

2.  6474     2. 6484 

2-  6493 

2-  6503 

2.6513 

2.  6522 

7 

30 

2-6532 

2-  6542 

2.6551   1  2.6561 

2.6571     2.6580 

2.  6590 

2-  6599 

2.  6609 

2.6618 

7 

40 

2.  6628 

2.6637 

2.  6646  ,  2.  6656 

2. 6665     2. 6675 

2.  6684 

2-  6693 

2.  6702 

2.6712 

7 

50 

2.6721 

2. 6730 

2.  6739 

2. 6749 

2. 6758  i  2.  6767 

2.6776 
2.  6866 

2.  6785 
2-  6875 

2.  6794 

2.  6803 

0    8 

0 

2.6812 

2.6821 

2.  6830 

2-  6839 

2.6848  ;  2.6857 

2.  6S84 

2.  6893 

8 

10 

2.  6902 

2.  691 1 

2. 6920    ;    2. 6928 

2.6937     2.6946 

2-  6955 

2.  6964 

2.  6972  i  2.  6981     1 

8 

20 

2.  6990 

2.  6998 

2.  7007       2.  7016 

2.  7034     2.  7033 

2.  7042 

2.  7050 

2.  7059 

2.  7067 

8 

30 

2.  7076 

2.  7084 

2.  7093        2.  7101 

2. 7110     2.7118 

2.  7126 

2-  7135 

2.  7143 

2.7152 

8 

40 

2.  7160 

2.  7168 

2.7177       2.7185 

2.  7193     2.  7202 

2.  7210 

2.  7218 

2.  7226 

2.  7235 

8 

50 

2-  7243 

2.7251 

2.  7259  ;  2.  7267 

2.  7275      2.  7284 

2.  7292 

2.  7300 

2.  7308 

2.  7316 

0    9 

0 

2.  7324 

2-  7332 

2.  7340       2.  7348 

2.  7356 

2.  7364 

2.  7372 

2.  7380 

2.  7388 

2.  7396 

9 

10 

2.  7404 

2.  7412 

2-  7419       2.  7427 

2-  7435 

2-  7443 

2.7451 

2-  7459 

2.7466     2.7474    1 

9 

20 

2.  7482 

2-  7490 

2.  7497 

2.  7505 

2.7513     2.7520 

2.  7528 

2-  7536 

2.  7543 

2-7551 

9 

30 

2.  7559 

2.  7566 

2.  7574 

2.  7582 

2.  7589     2.  7597 

2.  7604 

2.  7612 

2.7619 

2.  7627 

9 

40 

2-  7634 

2.  7642 

2.  7649 

2-  7657 

2.  7664     2.  7672 

2-  7679 

2.  7686 

2.  7694 

2.  7701 

9 

50 

2.  7709 

2.7716 

2-  7723 

2-7731 

2.  7738   ;   2.  7745 

2.  7752 

2.  7760 

2.  7767 

2.  7774 

TABLE  34.                   [Page  351 

» 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

W 

V 

V 

%" 

4// 

W 

%" 

\" 

8^^ 

W' 

0"  10"' 

II 
OS 

2.  7782 

2.  7789 

\ 
2.  7796  :  2.  7803 

2.  7810 

2.  7818 

2.  7825 

2.  7832 

2.  7839 

2.  7846 

lO 

10 

2.  7S53 

2.  7860  2.  7868  2.  7875 

2.  7882 

2.  7889 

2.  7396  2.  7903 

2.  7910 

2.7917 

lO 

20 

2.  7924 

2.  7931  2.  7938  2.  7945 

2.  7952 

2.  7959 

2.  7966  2.  7973 

2.  7980 

2.  7987 

lO 

30 

2.  7993 

2.8000  2.8007  2.8014 

2.  8021 

2. 8028 

2.  8035  2.  8041 

2. S048 

2.  8055 

lO 

40 

2.  8062 

2.8069  '•   2.8075  2.8082 

2.  8089 

2. 8096 

2.8X02 

2.  8109 

2. 81 16 

2.8122 

lO 

_5o 

2.  8129 

2.8136  1  2.8142  2.8149 

2.8156 

2.8162 

2.8169 

2.8176 
2. 8241 

2.8182  2.8189  1 

O   II 

0 

2.  8195 

2,8202  :  2.8209   2.8215 

2.  8222 

2.  8228 

2.8235 

2. 8248 

2.  8254 

II 

10 

2.8261 

2.8267   2.8274   2.8280 

2.8287 

2.  8293 

2.  8299 

2. 8306 

2.8312 

2.8319 

II 

20 

2.  8325 

2.8331   2.8338   2.8344 

2.8351 

2.8357 

2. 8363 

2.8370 

2. 8376 

2. 8382 

1 1 

3'' 

2.  8388 

2. 8395   2. 8401    2. 8407 

2.  8414 

2.  8420 

2.  8426 

2. 8432 

2. 8439 

2.  8445 

II 

40 

2.8451 

2.8457  i  2.8463   2.8470 

2.  8476 

2. 8482 

2.  8488 

2. 8494 

2. 8500 

2.  8506 

II 

50  , 

2.8513 

2.8519 

2. 8525 

2.8585 

2.8531 

2.8537 

2.  8543 

2.8549 
2.  8609 

2.8555 
2.8615 

2. 8561 

2.  8567 

O   12 

0 

2.8573 

2. 8579 

2.8591 

2.8597 

2. 8603 

2.8621 

2. 8627 

12 

10 

2.  8633 

2.8639   2.8645   2.8651 

2.8657 

2. 8663 

2.  8669 

2.  S675 

2. 8681 

2.  8686 

12 

20 

2. 8692 

2. 8698   2.  8704   2. 8710 

2.8716 

2. 8722 

2.8727 

2. 8733 

2. 8739 

2-  8745 

12 

30 

2.8751 

2.8756  ■  2.8762   2.8768 

2. 8774 

2.  8779 

2.  8785 

2.  8791 

2. 8797 

2. 8802 

12 

40 

2. 8808 

2.8814  j  2.  S820   2.8825 

2.8831 

2.  8837 

2.  8842 

2. 8848 

2. 8854 

2.  8859 

12 

50 

2.  8865 

2.8871   2.8876  1  2.8882 

2.  8887 

2.  8893 

2. 8899 

2.  8904 

2. 8910 

2.8915 
2.8971 

o  13 

0 

2.  8921 

2. 8927  [  2.  8932   2. 8938 

2.  8943 

2.  8949 

2.  8954 

2. 8960 

2".896y 

13 

10 

2.  8976 

2. 8982  !  2.  8987  1  2. 8993 

2.  S998 

2. 9004 

2.  9009 

2.9015 

2. 9020 

2. 9025 

13 

20 

2.9031 

2.  9036  1  2. 9042  '  2.  9047 

2. 9053 

2. 9058 

2.  9063 

2. 9069 

2. 9074 

2. 9079 

13 

30 

2. 9085 

2. 9090   2.  9096   2. 9IOI 

2.9106 

2.9112 

2.9II7 

2.9122 

2.9128 

2.9133 

13 

40 

2.9138 

2.9143   2.9149   2.9154 

2.9159 

2.9165 

2.9170 

2.9175 

2.  9180 

2.9186 

13 

50 

2.  9I9I 

2.  9196   2.  9201 

2. 9206 
2.9258 

2.  9212 

2.9217 

2.  9222 

2.9227 

2.9232 
2. 9284 

2.9238  _ 

2. 9289 

0  14 

0 

"2:92^ 

2.  9248   2.  9253 

2.  9263 

2. 9269 

~2."9274 

2. 9279 

14 

ID 

2.  9294 

2. 9299   2.  9304   2. 9309 

2.9315 

2.  9320 

2.9325 

2. 9330 

2.  9335 

2. 9340 

14 

20 

2. 9345 

2.9350  j  2.9355 

2. 9360 

2. 9365 

2.9370 

2.9375 

2. 9380 

2.  9385 

2.  9390 

14 

30 

2. 9395 

2.  9400   2.  9405 

2. 9410 

2.9415 

2.  9420 

2.  9425 

2. 9430 

2.  9435 

2.  9440 

14 

40 

2.9445 

2.9450  1  2.9455 

2. 9460 

2.  9465 

2.  9469 

2.  9474 

2. 9479 

2.  9484 

2. 9489 

14 

50 

2. 9494 

2. 9499 

2. 9504 

2. 9509 

2.9513 

2.9518 

2.9523 

2.9528 

2. 9533 
2.9581 

2.  9538 
2.  9586 

0  15 

0 

2.9542 

2.  9547 

2.9552  2.9557 

2. 9562 

2. 9566 

2.9571 

2.9576 

15 

10 

2. 9590 

2. 9595  1  2. 9600 

2.  9605 

2.  9609 

2.9614 

2.9619 

2. 9624 

2. 9628 

2.  9633 

15 

20 

2.  9638 

2.9643  1  2.9647 

2. 9652 

2.9657 

2. 9661 

2.  9666 

2.9671 

2. 9675 

2. 9680 

15 

30 

2.  9685 

2. 9689  :  2. 9694   2. 9699 

2.  9703 

2. 9708 

2.9715   2.9717 

2.  9722 

2.9727 

15 

40 

2.9731 

2.9736  '  2.9741   2.9745 

2.9750 

2.  9754 

2.9759 

2-  9763 

2.9768 

2.9773 

15 

50 

2.9777 

2.  9782 

2.9786 

2. 9791 

2.  9795 

2. 9800 
2.9845" 

2.  9805 

2. 9809 

2.  9814 

2.9818 
2.  9863 

0  16 

0 

2. 9823 

2.  9827 

2. 9832 

2. 9836 

2.  9841 

2. 9850 

2.9854^ 

'2.9859 

16 

10 

2. 9868 

2.  9872 

2.9877  2.9881 

2.  9886 

2. 9890 

2. 9894 

2. 9899 

2.  9903 

2.  9908 

16 

20 

2.9912 

2.9917 

2.9921  2.9926 

2. 9930 

2. 9934 

2.  9939 

2. 9943 

2. 9948 

2.  9952 

16 

30 

2. 9956 

2.  9961  ;  2.  9965   2.  9969 

2.  9974 

2. 9978 

2. 9983 

2- 9987 

2.  9991 

2. 9996 

16 

40 

3. 0000 

3. 0004 

3.0009  :  3.0013 

3.0017 

3. 0022 

3. 0026 

3. 0030 

3-  0035 

3- oo^9 

16 

50 

3. 0043 
3. 0086 

3.0048 

3.  0052 

3- 0056 
3. 0099 

3. 0060 
3.0103 

3-  0065 

3. 0069 

3- 0073 

-3-  0077 
3. 0120 

3. 0082 
3.0124^ 

0  17 

0 

3.  0090 

3-  0095 

3.0107 

3.OIII 

3.  0116 

17 

10 

3.0128 

3.0133  :  3.0137   3.0141 

3.0145 

3.0149 

3-0154 

3.0158 

3.  0162 

3.  0166 

17 

20 

3.0170 

3.0175    3.0179   3.0183 

3.0187 

3.0191 

3-0195 

3.0199 

3.  0204 

3.  0208 

17 

30 

3.0212 

3.0216   3.0220  !  3.0224 

3.  0228 

3.  0233 

3-0237 

3.0241 

3.  0245 

3-  0249 

17 

40 

3.  0253 

3.0257  3.0261  '  3.0265 

3.  0269 

3. 0273 

3.0278 

3. 0282 

3.  0286 

3. 0290 

17 

50 

3.  0294 

3.  0298 
3- 0338 

3-  0302  3.  0306 

3-0310 
3. 0350 

3.0314 
3-  0354 

3.0318 
3.  0358 

3. 0322 
3- 0362 

3- 0326 
3- 0366 

3- 0330 
3- 0370 

0  18 

0 

3- 0334 

3.0342  3.0346 

18 

10 

3.0374 

3.0378  3.0382  3.0386 

3-  0390 

3. 0394 

3-  0398 

3.  0402 

3.  0406 

3.0410 

18 

20 

3.0414 

3. 0418  3. 0422  3. 0426 

3.  0430 

3. 0434 

3- 0438 

3.0441 

3-  0445 

3.0449 

18 

30 

3-  0453 

3-0457  3.0461   3.0465 

3. 0469 

3-  0473 

3-  0477 

3.0481 

3.  0484 

3.  0488 

18 

40 

3. 0492 

3.0496  3.0500  3.0504 

3. 0508 

3.0512 

3.0515 

3.0519 

3-  0523 

3.0527 

18 

jo^ 

3.0531 

3.0535  3.0538  3-0542 

3. 0546 

3-0550 
3.0588 

3.0554 
3. 0592 

3.0558 
3. 0596 

3-0561 
3-0599 

3.o565__ 
3. 0603 

0  19 

0 

3- 0569 

3.0573  i  3-0577  3-0580 

3.  0584 

19 

10 

3  0607 

3. 0611  3.0615  3.0618 

3.  0622 

3. 0626 

3. 0630 

3-  0633 

3.0637 

3.0641 

19 

20 

3. 0645 

3.0648  3.0652  3.0656 

3.  0660 

3.  0663 

3. 0667 

3.0671   3.0674 

3.0678 

19 

30 

3.  0682 

3. 0686  3. 0689  3.  0693 

3.  0697 

3.  0700 

3- 0704 

3.0708  3.  07 1 1 

3-0715 

19 

40 

3.0719 

3. 0722  3. 0726  3.  0730 

3-  0734 

3.0737 

3-0741 

3.  0745  3.  0748 

3-  "752 

19 

50 

3.0755 

3-  0759  3-  0763  3-  0766 

3-  0770 

3-0774 

3.0777 

3.0781  1  3.0785 

^.  0788 

Page  352 

TABLE  34. 

• 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0'^ 

V 

2'' 

3'^ 

4// 

5'' 

6^' 

V' 

S'' 

9'' 

0     /     // 

O"  20"i  O^ 

3. 0792 

3-  0795 

3-  0799 

3. 0803 

3.  0806 

3.0810 

3-0813 

3-0817 

3.0821 

3. 0824 

20 

10 

3. 0828 

3-0831 

3-  0835 

3-  0839 

3- 0842 

3. 0846 

3-  0849 

3-  0853 

3.  0856  '  3.  0860  1 

20 

20 

3. 0864 

3. 0867 

3.0871 

3-  0874 

3-  0878 

3.0881 

3.0885 

3.  0888 

3.0892  1  3.0896  1 

20 

30 

3. 0899 

3-  0903 

3. 0906 

3.0910 

3-0913 

3-0917 

3. 0920 

3-  0924 

3.0927 

3-  0931 

20 

40 

3- 0934 

3-  0938 

3- 0941 

3-  0945 

3-  0948 

3-  0952 

3-  0955 

3- 0959 

3. 0962 

3.  0966 

20 

50 

3.0969 

_3-_2973 
3. 1007 

3. 0976 

3.  0980 

3-  0983 

3.0986 

3- 0990 

3-  0993 

3-0997 

3.  1000 

0   21 

0 

3. 1004 

3.  lOII 

3.  1014 

3. 1017 

3.  1021 

3- 1024 

3.  1028 

3-  1031 

3-  1035 

21 

10 

3-  1038 

3-  1041 

3-  1045 

3- 1048 

3-  1052 

3-  1055 

3-  1059 

3. 1062 

3-  1065 

3- 1069 

;    21 

20 

3.  1072 

3-  1075 

3-  1079 

3. 1082 

3. 1086 

3- 1089 

3. 1092 

3-  1096 

3-  1099 

3-1103 

'    21 

30 

3.1106 

3.  1 109 

3-1113 

3-  "16 

3.1119 

3- "23 

3.  1126 

3.1129 

3-1133 

3-1136 

21 

40 

3-  1 139 

3- "43 

3.  1146 

3- "49 

3- "53 

3- "56 

3- "59 

3-1163 

3.  1166 

3- "69 

21 

50 

3-II73 

3.  1 1 76 
3-  1209 

3- "79 
3.  1212 

3- "83 
3.  1216 

3.1186 
3.  1219 

3.1189 
3.  1222 

3- "93 
3-  1225 

3^1196 

3-1199 

3. 1202 

0  22 

0 

3.  1206 

3.  1229 

3-  1232 

3-  1235 

22 

10 

3-  1239 

3-  1242 

3-  1245 

3- 1248 

3-  1252 

3-  1255 

3-  1258 

3.  1261 

3-  1265 

3.  1268 

22 

20 

3. 1271 

3-  1274 

3- 1278 

3.  1281 

3. 1284 

3.  1287 

3- 1290 

3-  1294 

3- 1297 

3-  1300 

22 

30 

3-  1303 

3-  1307 

3-1310 

3-1313 

3-1316 

3-1319 

3-  1323 

3-  1326 

3-  1329 

3-1332 

22 

40 

3-  1335 

3-  1339 

3-  1342 

3-  1345 

3- 1348 

3-1351 

3-  1355 

3-  1358 

3-  1361 

3-  1364 

22 

50 

3-  1367 

3-  1370 

3- 1374 

_3-_L377 

3-  1380 
3.  141 1 

3-  1383 

3-  1386 

3-  1389 

3-  1392 

3-  1396 

0  23 

0 

3-  1399 

3-  1402 

3-  1405 

3-  1408 

3-  1414 

3.  1418 

3-  1421 

3- 1424 

3.  1427 

23 

10 

3-  1430 

3-  1433 

3-  1436 

3.1440 

3-  1443 

3- 1446 

3-1449 

3-  1452 

3-  1455 

3-  1458 

23 

20 

3.  1461 

3-  1464 

3- 1467 

3-  1471 

3-  1474 

3-  1477 

3-  1480 

3-  1483 

3-  i486 

3-  1489 

23 

30 

3-  1492 

3-  1495 

3- 1498 

3-  1501 

3-  1504 

3-  1508 

3-15" 

3-1514 

3-1517 

3-1520. 

23 

40 

3-  1523 

3-  1526 

3-  1529 

3-  1532 

3-  1535 

3- 1538 

3-  1541 

3-1544 

3- 1547 

3-  1550 

23 

50 

3-  1553 

3-  1556 

3-1587 

3-  1559 

3- 1562 

3-  1565 

3- 1569 
3- 1599 

3-1572 

3-  1575 

3- 1578 

J-  1 58 1 

0  24 

0 

3-  1584 

3-  J  590 

3-  1593 

3-  1596 

3.  1602 

3-  1605 

3.  1608 

3-  16" 

24 

10 

3-1614 

3. 1617 

3.  1620 

3-  1623 

3.  1626 

3-  1629 

3-  1632 

3-  1635 

3-  1638 

3-  1641 

24 

20 

3.  1644 

3- 1647 

3-  1649 

3-  1652 

3-  1655 

3-  1658 

3.  1661 

3-  1664 

3- 1667 

3- 1670 

24 

30 

3-  1673 

3-  1676 

3-  1679 

3.  1682 

3-  1685 

3.  1688 

3-  1691 

3-  1694 

3-  1697 

3-  1 700 

24 

4^ 

3-1703 

3.1706 

3.1708 

3.17" 

3- '714 

3-1717 

3. 1720 

3-1723 

3.1726 

3-1729 

24 

J_'L. 

3-1732 

3-  1735 
3-1764 

3-  1738 

3-1741 

3-1744 

3-1746 

3-1749 

3-1752 

3-1755 

3-1758 

0  25 

0 

3.  1 761 

3.1767 

3.1770 

3-1772 

3-1775 

3-1778 

3-1781 

3-1784 

3-  1787 

25 

10 

3-  1790 

3-1793 

3-1796 

3-  1798 

3. 1801 

3-  1804 

3-  1807 

3.1810 

3-1813 

3.1816 

25 

20 

3.1818 

3-  1821 

3-  1824 

3-  1827 

3-  1830 

3-  1833 

3- 1836 

3-  1838 

3-  1841 

3-  1844 

25 

30 

3-  1847 

3-  1850 

3-  1853 

3- 1855 

3-  1858 

3.  1861 

3-  1864 

3- 1867 

3.  1870 

3-  1872 

25 

40 

3-  1875 

3-  1878 

3. i88i 

3- 1884 

3.  1886 

3-  1889 

3-  1892 

3-  1895 

3.  1898 

3- 1901 

25 

50 

3-  1903 

3-  1906 

3-  1909 

3. 1912 

3-1915 

3-1917 

3-  1920 

3-  1923 

3- 1926 

3-  1928 

0  26 

0 

3-  1931 

3-  1934 

3-  1937  3-  1940 

3-  1942 

3-  1945 

3-  1948 

3-  1951 

3-  1953 

3-  1956 

26 

10 

3-  1959 

3-  1962 

3. 1965  3. 1967 

3-  1970 

3-  1973 

3- 1976 

3- 1978 

3. 1981 

3- 1984 

26 

20 

3-  1987 

3-  1989 

3-  1992  1  3-  1995 

3-  1998 

3. 2000 

3- 2003 

3. 2006 

3.  2009 

3.2011 

26 

30 

3.2014 

3-2017 

3.2019 

3.  2022 

3-  2025 

3.  2028 

3- 2030 

3-  2033 

3.  2036 

3- 2038 

26 

40 

3.2041 

3.2044 

3- 2047 

3-  2049 

3- 2052 

3-  2055 

3-2057 

3. 2060 

3-  2063 

3.  2066 

26 

50 

3. 2068 

3.2071 

3-  2074 

3.  2076 

3-  2079 

3.  2082 

3-  2084 
3.2111 

3- 2087 

3.  2090 

3.  2092 

0  27 

0 

"  3-  2095" 

3. 2098 

3.  2101 

3.2103 

3.  2106 

3-2109 

3-2114 

3-2117 

3.2119 

27 

10 

3.  2122 

3-2125 

3.2127 

3.2130 

3-2133 

3-2135 

3-2138 

3.2140 

3-2143 

3.2146 

27 

20 

3.2148 

3-2151 

3-2154 

3-2156 

3-2159 

3.  2162 

3.2164 

3-2167 

3.2170 

3.2172 

27 

30 

3-2175 

3.2177 

3.  2I»0 

3-2183 

3-2185 

3.2188 

3.2191 

3-2193 

3.2196 

3.2198 

27 

40 

3.  2201 

3. 2204 

3.  2206 

3.  2209 

3.  2212 

3-2214 

3.2217 

3-2219 

3.  2222 

3-  2225 

27 

50 

3.2227 

3^230  3. 2232 

3-2235 

3- 2238 

3-  2240 

3i_2243 

3- 2245 

3-  2248 
3-  2274 

3- 2250 
^3.T276~ 

0  28 

0 

3-22S3 

3.2256  3. 2258  :  3. 2261 

3.  2263 

3.  2266 

3.  2269 

3.2271 

28 

10 

3.2279 

3. 2281  3. 2284  3. 2287 

3.  2289  1  3.  2292 

3-  2294 

3- 2297 

3- 2299 

3-  2302 

28 

20 

3-  2304 

3.2307  3.2310  3.2312 

3.2315  1  3.2317 

3- 2320 

3-  2322 

3-  2325 

3-2327 

28 

30 

3-  2330 

3-2333  '  3-2335  3-2338 

3.2340  I  3.2343 

3-  2345 

3-  2348 

3-  2350 

3-  2353 

28 

40 

3-2355 

3-  2358  i  3-  2360  '  3.  2363 

3-  2365 

3-  2368 

3- 2370 

3-2373 

3-  2375 

3-  2378 

28 

JO 

3-  2380 

3-  2383  3-  2385  1  3-  2388 

3-  2390 
3-2415 

3-  2393 
3.2418 

J- 2395 
3-  2420 

3- 2398 

3-  2400 

3-  2403 

0  29 

0 

3-  2405 

3.  2408  3.  2410 

3-2413 

3-  2423 

3-  2425 

3.  2428 

29 

10 

3-  2430 

3-2433 ;  3-2435 

3-  2438 

3.2440 

3-  2443 

3-  2445 

3-2448 

3-  2450 

3-  2453 

29 

20 

3-  2455 

3.2458  3.2460 

3-  2463 

3- 2465 

3- 2467 

3-  2470 

3-  2472 

3-  2475 

3-2477 

29 

30 

3- 2480 

3. 2482  3. 2485 

3. 2487 

3.  2490 

3.  2492 

3-  2494 

3- 2497 

3-  2499 

3.  2502 

29 

40 

3-  2504 

3-  2507 

3-  2509 

3-2512 

3-2514 

3-2516 

3-2519 

3-2521 

3-  2524 

3-  2526 

29 

50 

3-  2529 

3-2531 

3- 2533 

3- 2536 

3-2538 

3-  2541 

3. 2543 

3-  2545 

3-  2548 

3-2550 

TABLE  34. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 


[Page  353 


Arc. 


o'-  30"^    o^ 

30       ID 
30      20 


30      40 

^o    50^ 

o 

10 


31 

3' 


!l 


20 

30 
40 


31     50 


32  10 

32  20 

32  30 

32  40 

32  50 

33  o 
33  10 
33  20 
33  30 

33  40 
33_  50 

34  .  o 
34  10 
34  20 
34  30 

34  40 
34^  5o_ 

35  o 
35  lo 
35  20 
35  30 
35  40 
35  50 


o    36  o 

36  10 

36  20 

36  30 

36  40 

36  50 

o    37  o 

37  10 
37  20 
37  3" 

37  40 
37_Jo__ 

o      38         O 

^8  10 

38  20 

38  30 

38  40 

38  50 

o 

39  10 
39  20 
39  30 
39  40 
39  50 

23    B 


// 


o     39 


0 


3-  2553 

3-2577 
3.  2601 

3-  2625 

3- 2648 

3-  2672 

3-  2695 
3.2718 

3-2742 
3-  2765 
3- 2788 
3.  2810 
3-^833 
3- 2856 
3-  2878 
3. 2900 

3- 2923 
3-  2945 

3-  2967 
3. 2989 

3-3010 
3.  ^o-,2 
3- 


|// 


jNO-= 
3054 

3-  3075 

3- 3096 
3-3118 

3-3139 
3.3160 

3-31S1 
3.3201 

3.3222 

3-  3243 
3- 3263 
3- 3284 
3304 
3324 
3345 
3365 
33S5 
3-  3404 
3-  3424  - 
3- 3444 
3-  3464 
3-  3483 
3- 3502 
3-  3522 
3- 354' 
3- 3560 

3-3579 
3-  3598 
3-3617 
3-  3636 
3-  3655 
3-  3674 
3-  3692 
3- 37 1 1 
3-3729 
3-3747 


j- 3/ 
3-3 


50 


784 


3- 2555 
3-2579 
3-  2603 
3-  2627 
3-2651 
3. 2674 

3- 2697 
3-  2721 

3-2744 
3-2767 
3-  2790 
3-_28^3 
3- 2835 
3- 2858 
3. 2880 

3-  2903 
3-2925 
3- 2947  ^ 
3-  2969 
3- 2991 
3-3012 

3-  3034 
3-  3056 
3:  3077^ 

3-  3098 
3-3120 

3-3141 
3-  3162 
3-3183 
3- 3204 


3224 
3245 
3265 
3286 

3306 
3326 

3347 
3-  3367 
3- 3387 
3- 3406 
3-3426 
3-3446 


3-  2700 
3-  2723 
3-2746 
3-  2769 
3- 2792 
3-2815 
3.2838 
3.  2860 
3. 2882 

3- 2905 
3- 2927 
3i2949 
3- 2971 
3-  2993 
3-3015 
3- 3036 
3- 3058 
_3-J079_ 
3-3101 
3.3122 

3-3143 
3-3164 
^  3'85 
3206 

3226 

3247 
3267 
3288 

3308 
3328 

3349 


2702 
2725 
2749 
2772 

2794 
2817 

2840 
2862 
2885 
2907 
2929 

295J_ 
3-  2973 
3- 2995 
3-3017 
3-  3038 
3- 3060 
3-3081 


3- 3465 
3-  3485 
3-  3504 
3-3524 

3-  3562 

3- 3581 
3- 3600 
3-3619 
3638 
3057 
3675 
3694 


3- 
J- 

'3- 
3- 
J- 

3- 3768 
3-  3786 


3713 
3731 
3749 


-^ 

J 

t 
-^ 

3 
3 

3 

3-  3369 
3-  3389 
3- 3408 
5428 
5448 

5467 
5487 
5506 
5526 

5545 
3564 

3-  3583 
3-  3602 
3-3621 
3-  3640 

3-  3659 
.3:_3677 

3- 3696 
3-3714 
3-3733 
3-3751 
3-  3769 
3- 3788 


3-3103 

3-3124 

3-3145 
3-3166 

3-3187 
3- 3208 
3. 3228 

3-  3249 
3- 3269 
3- 3290 
3-3310 
3- 3330 


2704 

2728 

2751 
2774 

2797 
2819 

2842 
3-  2865 
3.2887 

3- 2909 
3-2931 
3-  2953 
3-2975 
3- 2997 
3-3019 
3- 3041 
3. 3062 

3^3084 

3-3105 
3-3126 

3-3147 
3-3168 

3-3189 
3^3210 

3-3230 
3251 
3272 
3292 


jj 


12 


3351 
3371 
3391 
3410 


3-  3585 
3-  3604 
3-  3623 
3-  3642 
3. 3660 

^•3^9 

3- 3698 
3-3716 
3-3735 
3-3753 
3-3771 
3-  3789 


r' 

3^' 

4// 

3-2558 

3-  2560 

3-  2562 

3-  2582 

3-  2584 

3-  2586 

3. 2605 

3*2608 

3.2610 

3. 2629 

3-  2632 

3-  2634 

3-  2653 

3.  2655  3.  2658 

3- 2676 

3.  2679  3-  2681 

;// 


3 

3 
3 

•»    T  T  ->  O 

J-  JJJ- 

3- 3353 
3-3373 
3- 3393 
3-3412 


6 


// 


3-  2565 " 
3-  2589 
3-  2613 
3- 2636 
3. 2660 
3-  2683 
3-2707 
3-  2730 
3-2753 
3-2776 

3-  2799 

2822 

2844 
2867 
2889 
291 1 

2934 
2956 
2978 
2999 
021 


3-  3043 
3-  3064 
3,3086 

3-  3107 
3-3128 

3-3149 

3-3170 

3-3191 
3.3212 

^  3233 
3253 
3274 
3294 
3314 
3334 


3-  3428 

3-  3430 

3- 3432 

3-  3448 

3-  3450 

3-3452 

3-  3467 

3-  3409 

3-  3471 

3- 3487 

3-  3489 

3-3491 

3- 3506 

3-  350S 

3-3510 

3- 3526 

3-3528 

3-  3530 

3- 3545 

3-  3-547 

3-  3549 

3-  3564 

3- 3566 

3-3568 

3- 3355 

J' 
3 

J 


3375 

3395 

3414 

3434 

3454_ 

3473 

3493 

3512 

3531 

3551 

3570 


3587 
3606 

3625 

3644 
3662 
3681 


3-3700 

3-371S 
3-3736 
3-  3755 
3-3773 
3-3791 


3-  3589 
3-  3608 
3-3627 
3-  3646 
3-  3664 
J-J683 

3-3701 

3-3720 
3-3738 
3-3757 
3-3775 
3-  3793 


3-2567 
3-  2591 
3-2615 
3- 2639 
3.  2662 
3.  2686 
3-  2709 
3- 2732 
3-2755 
3-2778 
3.  2801 
^^2824 

,3-2847 
3- 2869 
3- 2891 
3-2914 
3-  2936 
3-  2958 
3-  2980 
3-  3002 
3-  3023 
3- 3045 
3- 3066 
3-  3088 
3-3109 
3-3130 
3-3151 
3-3172 
3-3193 
3-3214 

3-  3235 
3-3255 
3-3276 
3- 3296 
3-3316 
3-3336 

3-3357 
3-  3377 
3- 3397 
3-3416 

3- 3436 
3-  3456 
3-  3475 
3-  3495 
3-3514 
3-  3533 
3-3553 
J- 3572 

3-  3591 
3- 361^ 
3-  '3629 
3-  3647 
3-  3666 
3-3685_ 

3- 3703 
3-3722 
3- 3740 
3-3758 
3-3777 
3-  3795 


r// 


3-2570 

2594 
2617 
2641 
2665 
2688 


3.2711 

3-  2735 
3-2758 
3.  2781 
3- 2804 
3. 2826 
3.2849 
3.2871 

3- 2894 
3- 2916 
3- 2938 
3.  2960 

3-  2982 
3- 3004 
3- 3025 
3- 3047 
3-  3069 
^,3090 

3-3"! 
3-3132 
3-3153 

3-3174 
3-3195 
3-3216 

3-  3237 
3-3257 
3-3278 
3- 3298 
3-3318 
3-3339 

3- 3359 
3-  3379 
3- 3398 
3- 3418 
3- 3438 
_3-  3458 

3- 
3- 
3- 
3- 
3' 
_3: 
3 
3- 
3- 
j- 
3- 
3- 
3- 
3- 
3- 
3- 
3- 
3- 


3477 
3497 
3516 
3535 

3555 
3574 

3593 
3612 

3630 
3649 
3668 
3687 


9 


// 


3-2572 
3-  2596 
3. 2620 

3-  2643 
3.  2667 
3. 2690 
3^2714 

3-2737 
3-  2760 

3-  2783 

3.  2806 

J.  2828 

""2851 

2874 
2896 

2918 

2940 
2962 

2984 
3006 
3028 

3049 
071 


3- 
3- 
3- 
3- 
3-j- 


3"3 
3134 
3156 
3176 

3197 
3218 


3-  3361 
3-3381 
3- 3400 
3- 3420 
3-3440 
3-  3460 


3-  3595 
3-3614 
3-  3632 
3-3651 
3-  3670 


3- 3092  3 


3-2574 
3- 2598 
3. 2622 
2646 
2669 
2693 
2716 
_  2739 
3-  2762 

3-  2785 
3.  2808 

3,12831 

3-  2853 
3-  2876 
3. 2898 
3. 2920 
3- 2942 
3-  2964 
3- 2986 
3. 3008 

3-  3030 
3-3051 
3-  3073 
3o_94 


3239 
3259 
3280 

3300 
3320 
3341 


3-3115 
3-3137 
3-3158 
3-3179 
3-3199 

J^3220 

3-  3241 

3-3261 

3-  3282 
3-  3302 
3-  3322 
3- 3343 


3479 
3499 
3518 
3537 
3556 
3576 


3- 3363 
3- 3383 
3-  3402 
3-  3422 
3-3442 
3-  3462 
3-  3481 
3-3501 
3-3520 

3-  3539 
3-3558 
3-3577 


3- 3596 
3-3615 
3-  3634 
3-  3653 
3- 3672 
3- 3690 


Page  354 

TABLE  34. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0' 

V 

2'' 

3^^ 

4// 

5'' 

6'^ 

V 

S'' 

-    1 

O     /      // 

oh  40'"  0^ 

3. 3802 

3-  3804 

3. 3806 

3.3808 

3-  3809 

3- 381 1 

3.3813 

3.3815 

3-3817 

3-3818   1 

40   10 

3-  3820 

3-  3822 

3-  3824 

3-  3826 

3 

.3827 

3-  3829 

3-  3831 

3 

•3833  1  3-3835 

3 

3836   ' 

40   20 

3-  3838 

3-  3840 

3-38/2 

3-  3844 

3 

-  3845  , 

.  3- 3847 

3- 3849 

3 

-3851  ;  3-3852 

■^ 
J 

3854 

40   30 

3-  3856 

3-  3858 

3.3810 

3-  3861 

3 

•  3863 

•3-3865 

3- 3867 

3 

•3869  1  3-3870 

3 

3872 

40   40 

3-  3874 

3-  3876 

3-3877 

3- 3879 

3 

.3881 

3-3883 

3-3885 

3 

.3886  I  3.3888 

3 

3890 

4050 

3-3892 

3-  3893 
3- 391 1 

3- 3895 

3-  3897 

3 

-3899 

3-3901 

3- 3902 

_3 

•3904  3-3906 

3 
3 

390  > 

-3925 

041   0 

3-  3909 

3-3913  !  3-3915 

3 

.3916 

3-3918 

3- 3920 

2 

.3922  i  3.3923 

41   IQ 

3-3927 

3-  3929 

3-3930  i  3-3932 

3 

-3934 

3-  3936 

3- 3938 

3 

-3939  '   3-3941 

3 

-  4943   1 

41   20 

3-  3945 

3-  3946 

3-3948  [  3.3950 

-> 

-3952 

3-  3953 

3-3955 

3 

-3957  3-3959 

3 

-  3960 

41   30 

3-  3962 

3-  3964 

3-3965  !  3-3967 

3 

-3969 

3-3971 

3-  3972 

3 

•  3974  3-  3976 

3 

•3978 

41   40 

3-  3979 

3-  3981 

3-  3983 

3- 3985 

1 

.3986 

3-3988 

3- 3990 

3 

.3992  1  3.3993 

•1 

-3995 

41  _5o_ 

0  42   0 

3- 3997 
3-4014 

3-  3998 
3.4016 

3. 4000 

3.  4002 

3 

.4004 
.4021 

3-  4005 

3- 4007 

3 
3 

.4009 
.4026 

3-  401 1 

3 

3 

.4012   I 
-4029 

'3-4017" 

3-4019 

3-  4023 

3-  4024 

3. 4028 

42  10 

3-  4031 

3-  4033 

3-  4035  3-  4036 

3 

•  4038 

3  4040 

3- 4041 

3 

•4043 

3-  4045 

-» 

J 

-  4047   : 

42  20 

3-  4048 

3-  4050 

3.4052  ;  3-4053 

3 

-4055 

3-4057 

3-  4059 

3 

.4060 

3.  4062 

3 

.  4064 

42  30 

3-  4065 

3- 4067 

3.4069   3.4071 

3 

4072 

3-  4074 

3-  4076 

3 

.4077 

3-  4079 

1 

J 

4081 

42  40 

3.  4082 

3.  4084 

3.4086  j  3-4087 

3 

4089 

3.4091  1  3.4093 

3 

.4094 

3. 4096 

3 

.  409S 

42  50 

3.  4099 

3.4101 
3.4118 

3.4103   3-4104 
3.4120  3.4121 

3 
3 

4106 
"4123" 

3.4108  1  3.4109 
3.4125  [3. 4126 

3 
3 

4111 

4128" 

3-4113 

3 
3 

4115 
-4131 

0  43   0 

3.  41 16 

3-4130 

43  JO 

3-4133 

3-4135 

3.4136   3.4138 

3 

4140 

3.4141  3.4143 

3 

4145 

3.4146 

3 

4148 

43  20 

3-4150 

3-4151 

3-4153   3-4155 

3 

4156 

3.4158  1  3.4160 

3 

4161 

3-4163 

3 

•  4165 

43  30 

3.4166 

3.4168 

3.4170   3.  41 71 

3 

4173 

3.4175  I  3.4176 

3 

4178 

3.4180 

3 

.4181 

43  40 

3-4183 

3-4185 

3.4186  3.4188 

3 

4190 

3-4191  :   3-4193 

3 

4195 

3.4196 

3 

.4198 

43  50  _ 

3-  4200 

3.4201 

3-  4203   3.  4205 

3 
3 

4206 
4223 

3.  4208  3.  4209 
3. 4224  3.  4226 

3 
3 

421 1 

422F 

3-4213 

3 

4214   j 

0  44   0 

3.4216 

3.4218 

3.4219   3.4221 

3- 4229 

.3 

4231 

44  10 

3-  4232 

3-  4234 

3.4236   3.4237 

3 

4239 

3-4241 

3-  4242 

3 

4244 

3-  4246 

3 

4247 

44  20 

3-  4249 

3-4250 

3.4252   3.4254 

1 

4255 

3-4257 

3-  4259 

'> 

J 

4260 

3-  4262 

3 

42<)3 

44  30 

3-  4265 

3- 4267 

3.4268   3-4270 

•> 

0 

4272 

3-4273 

3-  4275 

3 

4276 

3-4278 

T 

J 

4280 

44  40 

3.4281 

3-  4283 

3.  4285   3.  4286 

-> 

4288 

3-  4289 

3-4291 

3 

4293 

3-  42^4 

3 

4296 

44  50  _ 
0  45   0 

3.  4298 
3-43H 

3-  4299 
3-4315 

3-4301 
3-4317 

3-  4302  3 

4304 

3-  4306  3-  4307 

3 
3 

4309 
4325 

3-4310 

3 

4312 

4328    j 

3-4318  3 

4320 

3-  4322 

3-  4323 

3-  4326  3 

45  10 

3-  4330 

3-4331 

3- 4333  3- 4334  3 

4336 

3-  4338 

3-  4339 

3 

4341 

3- 434  2  :  3 

434 1    ' 

45  20 

3-  4346 

3-  4347 

3-  4349  3-  4350 

3 

4352 

3-  4354 

3-  4355 

3 

4357 

3-4j58  3 

4360 

45  30 

3-  4362 

3-  4363 

3-4365   3-4366 

3 

4368 

3-  4370 

3-4371 

3 

4373 

3-4374  3 

4376 

45  40 

3-4378 

3-4379 

3.43S1   3.4382  3 

4384 

3-  4385 

3- 4387 

3 

4389 

3-4390  3 

4392 

45  50  _ 
0  46   0 

3-  4393 
3.4409 

3-  4395 
3-44" 

3-4396  3-4398  3 
3.4412  3.4414  3 

4400 
44"i5" 

3.  4401 
3-4417 

3-  4403 
3-4419 

3 
3 

4404 

3-4406  3 
3-4422  ,  3 

440S 
4423 

4420 

46  10 

3-4425 

3-4426 

3. 4428  3. 4429  3 

4431 

3-4433  !  3-4434 

3 

4436 

3-4437  1  3 

4439 

46  20 

3.4440 

3-4442 

3. 4444  3- 4445 

3 

4447 

3.4448  :  3.4450 

3 

4451 

3-4453  1  3 

4454 

46  30 

3-4456 

3-4458 

3-  4459  3-  4461 

3 

4462 

3-4464  '  3-4465 

3 

4467 

3-44(>8  3 

4470 

46  40 

3-  4472 

3-4473 

3-4475  ,  3-4476 

3 

4478 

3-4479  3-4481  ,  3 

4482 

3-4484 

3 

4486 

46  so 

3-4487 

3-  4489 

3-4490 
3-  4506 

3- 4492 

J_ 

4493 

3-  4495 

3-4496  3 
3-4512  I  3 

4498 

3-  4499 

3 
3 

4501 
4516 

0  47   0 

3-4502 

3-  4504 

3-4507 

■J 

3 

4509 

3-4510 

4513 

3-4515 

47  10 

3-4518 

3-4519 

3.4521   3-4522 

3 

4524 

3.4526  3.4527  1  3 

4529 

3-4530 

3 

4532 

47  20 

3-4533 

3-  4535 

3-4536  3-4538 

3 

4539 

3.4541  3.4542  1  3 

4544 

3-4545  i  3 

4547 

47  30 

3-4548 

3-4550 

3-4551   3-4553 

3 

4555 

3-4556  '  3-4558  !  3 

4559 

3-4561 

3 

4562 

47  40 

3-  4564 

3-  4565 

3-4567  3-4568 

3 

4570 

3-4571   3-4573  '  3 

4574 

3- 4576 

3 

4577 

47  50_ 
0  48   0 

3-4579 

3- 4580 

3.  4582  3.  4583 

.3 

4585, 

3-4586  3-4588  3 

4589_ 

3-_459i . 
3. 4606 

3 

3 

4592 
4607 

3-4594   3-4595  3-4597  3-4598 

3 

4600 

3.4601  3.4603  3 

4604 

48  10 

3-  4609 

3.  4610 

3.4612  3.4613  3 

4615 

3.4616  3.4618  3 

4619 

3.4621 

3 

4622 

48  20 

3-  4624 

3.4625  3.4627  3.4628  3 

4630 

3.4631   3-4633  '  3 

4634 

3-  4636 

3 

4637 

48  30 

3-  4639 

3.4640  3.4642  3.4643  3 

4645 

3. 4646  3. 4648  3 

4649 

3-4651 

3 

4652 

48  40 

3-4654 

3-4655  3-4657  3-4658  3 

4660 

3.4661   3.4663  3 

4664 

3. 4666 

3 

4667    , 

48  50  _ 

0  49   0 

3.  4669 
3.46S3 

3.4670-  3.4672 
3. 4685  3. 46S6 

3-4673  3 

4675  3. 4676 

3- 467S  3 
3-  4692  3 

4679 
4694 

3.4681   3 
3-  4695  3 

4682   1 

3-4688  3 

4689 

3.4691 

4697 

49  10 

3-  4698 

3.4700  3.4701   3.4703 

3 

4704 

3.4706  3.4707  :  3 

4709 

3-4710  3 

4711  ■ 

49  20 

3-4713 

3.4714  3.4716  :  3-4717 

3 

4719 

3.4720  j  3.4722  1  3 

4723 

3-  4725  3 

4726 

49  30 

3-  4728 

3-4729  3-4730  3-4732 

3- 

4733 

3-4735  '   3-4736  3 

4738 

3-  4739 

3 

4741 

49  40 

3.4742   3.4744  :  3-4745  3-4747 

3 

4748  3-4749  1  3-4751  ,  3 

4752 

3-4754 

3 

4755 

49  50 

3-4757  '  3-4758  '   3-4760 

3-4761 

3-4763  3-4764  '  3-4765  3-4767 

3-4768 

3-4770  1  j 

TABLE  34. 

[Page  355 

% 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0  ' 

V 

2^^ 

3'^ 

4// 

5'' 

g// 

V 

8^' 

r^ 

0     /      // 

o''  50"'  0*" 

3-4771 

3-  4773 

3-  4774 

3-  4776 

3-4777  3-4778  '  3-4780 

3-4781 

3-  4783 

3-  4784 

50   10 

3-4786 

3-4787 

3-  4789 

3-  4790 

3-4791   3.4793  3-4794 

3-  4796 

3-4797  3-4799 

50   20 

3.  4S00 

3-  4802 

3-  4803 

3- 4804 

3.4806  3.4807  3.4809  ;  3.4810 

3.4812  3.4813 

50   30 

3-4814 

3-4816 

3-4817 

3-4819 

3-  4820 

3.4822  3.4823  1  3.4824 

3.  4826  3. 4827 

50   40 

3-  4S29 

3-  4830 

3-  4832 

3- 4833 

3-  4834 

3.4836  3.4837  ■  3.4839 

3.  4840  3.  4842 

50   50 

3- 4843 

3-4844 
3-  4859 

3-  4846 
3.  4860 

3-  4847 
3. 4861 

3.4849  3.4850  3.4852  3.4853 

3. 4854  3-  4856 

0   51    0 

3-4857 

3-4863 

3.4864  3.4866  3.4867 

3.4869  1  3.4870 

51   10 

3-4871 

3-4873 

3- 4874 

3-4876 

3-4877 

3.4878  3.4880  3.4881 

3.  4883  3.  4884 

51   20 

3. 48S6 

3- 48S7 

3.  4888 

3-  4890 

3.4891   3.4S93  3.4894  3.4895 

3.  4897  3-  4898 

51   30 

3-  4900 

3-4901 

3. 4902 

3- 4904 

3-  4905 

3-4907  3-4908 

3-  4909 

3-49"   3-4912 

51   40 

3-4914 

3-4915 

3-4916 

3.4918 

3-4919 

3-4921  ;  3-4922 

3-  4923 

3-  4925  3-  4926 

51   50 

3,4928 

3-4929 
3- 4943 

3-  4930 
3-4944 

3- 4932 
3-  4946 

3-  4933 
3-  4947 

3i4935  1  3-4936_ 

3-  4937 

3-4939  3-  4940 
3-  4953   3-  4954 

0   52    0 

3-  4942 

3.4949  3.4950  '  3-4951 

52   10 

3-4955 

3-4957 

3-  4958 

3- 4960 

3-4961 

3.4962  '  3.4964  3-4965 

3-4967  1  3-4968 

52  20 

3-  49^59 

3-4971 

3-4972 

3-  4973 

3-4975 

3-4976  ,  3-4978  3-4979 

3.4980  :  3.4982 

52  30 

3- 4983 

3-  4984 

3- 4986 

3- 4987 

3-  4989 

3-4990  ,  3-4991  ;  3-4993 

3-4994  :  3-4995 

52  40 

3- 4997 

3- 4998 

3- 5000 

3- 5001 

3-  5002 

3- 5004  ,   3- 5005  3- 5006 

3- 5008  3. 5009 

52  50 

3.5011 

3-5012 

3-5013 
3- 5027 

3-5015  3-5016 
3. 5028  3. 5030 

3-5017  3-5019  1  J.  5020 
3-5031   3-5032  !  3-5034 

3. 5022  3. 5023 

3-5035  !  3-5037 

0  53   0 

3-  5024 

3.  5026 

53  I" 

3- 5038 

3-  5039 

3-  5041 

3- 5042  3- 5043 

3-5045  3-5046  3-5047 

3-5049  ,  3-5050 

53  20 

3-5051 

3-  5053 

3- 5054 

3.5056  3.5057 

3-5058  :  3-5060  ;  3.5061 

3-5062  ;  3.5064 

53  30 

3-  5065 

3. 5066 

3-  5068 

3- 5069  3- 5070 

3.5072  3.5073  1  3.5075 

3-5076  1  3-5077 

53  40 

3-  5079 

3. 50S0 

3- 5081 

3- 5083  3- 5084 

3- 5085  3- 5087  ;  3- 5088 

3-5089  1  3-5091 

.53_  50 

3- 5092 

3- 5093 

3-  5095 

3- 5096  3- 5097  3- 5999 

3-5100 
3-5113 

3-5101 

3-5103  1  3-5104 

0  54   0 

3-5105 

3-5107 

3.5108  3-5109  3-5111   3- 5112 

3-5"5 

3-5116  1  3.5117 

54  10 

3-5119 

3-5120 

3.5122  3.5123  3.5124  3.5126  3.5127  :  3.5128 

3-5130  1  3-5131 

54  20 

3-5132 

3-5134 

3-5135 

3-5136  3-5138  3-5139  3-5140  :  3-5141 

3-5143  :  3-5144 

54  30 

3- 5 '45 

3- 5147 

3-5148 

3-5H9  3-5151   3-5152  3-5153  :  3-5155 

3-5156  '  3-5157 

54  40 

3-5159 

3-5160 

3.5161   3-5163  i  3-5164  3-5165  1  3-5167  1  3-5168 

3-5169    3-5171 

54  50  • 

3-5172 

3-5173 

3-5175  3-5176  !  3-5177  3-5179  '   3-5180  1  3.5181 

3-5183 

3-5196 

3-5184 

0  55   0 

"  3-5185 

3.5186 

3.5188  3.5189  !  3.5190  3.5192 

3-5193 

3-5194 

3-5197  1 

55  10 

3-5198 

3-  5200 

3.5201   3.5202  3.5204  3.5205 

3- 5206 

3- 5207 

3-5209  1  3-5210 

55  20 

3-5211 

3-5213 

3.5214  3.5215  ,  3.5217  3.5218 

3-5219 

3.5221 

3-5222  i  3.5223 

55  30 

3- 5224 

3- 5226 

3-5227 

3.5228  j  3.5230  3.5231 

3- 5232 

3- 5234 

3-5235  1  3-5236 

55  40 

3-5237 

3- 5239 

3- 5240 

3. 5241  3. 5243  3. 5244 

3-  5245 

3- 5247 

3.5248  !  3.5249 

55  50 

3-5250 

3- 5252 

3- 5253 

3-  5254 

3.5256  3.5257 

3.  5258  3.  5260 

3-5261  3-5262 

0  56   0 

3-5263 

3- 5265 

3- 5266 

3-  5267 

3-5269  3-5270 

3-5271  1  3-5272 

3-  5274 

3-5275 

56   ID 

3-5276 

3-5278 

3-5279 

3.5280  3.5281   3.5283 

3.5284  1  3.5285 

3-  5287 

3- 5288 

t;6  20 

3- 5289 

3- 5290 

3- 5292 

3-5293  1  3-5294 

3- 5296 

3- 5297  ;  3- 5298 

3- 5299 

3-5301 

56  30 

3-  5302 

3-  5303 

3-  5305 

3- 5306  3- 5307 

3- 5308 

3-5310  !  3-53" 

3-5312 

3-53H 

56  40 

3-5315 

3-5316 

3-5317 

3-5319  3-5320 

3-5321 

3-5322  :  3.5324 

3-  5325 

3- 5326 

56  50 

3- 5328 

3- 5329 

3-5330  3-5331  3-5333 
3- 5343  3- 5344  '   3- 5345 

3- 5334 

3- 5335  3- 5336 

3- 5338  1  3- 5339 

0  57   0 

^  3-  5340 

3-  5342 

3-  5347 

3- 5348 

3- 5349 

3-5350  i  3-5352 

57  10 

3- 5353 

3-5354 

3-5355  3-5357  3-5358 

3- 5359 

3-  5361 

3- 5362 

3-  5363  3-  5364 

57  20 

3-  5366 

3-5367 

3- 5368  3- 5369  3- 5371 

3-5372 

3-  5373 

3- 5374 

3-5376 

3-5377 

57  30 

3-  5378 

3-5379 

3- 5381   3- 5382  3- 5383 

3- 5384 

3- 5386 

3-5387 

3- 5388 

3- 5390 

57  40 

3-5391 

3- 5392 

3- 5393  3- 5395  3- 5396 

3-  5397 

3- 5398 

3- 5400 

3-  5401 

3-  5402 

57  50 

3-  5403 

3-  5405 

3.5406  3.5407  3.5408  3.5410 

3-54" 

3-5412 

3-5413 

3-5415 

0  58   0 

3-5416 

3-5417 

3-5418 

3. 5420  3. 5421  3. 5422 

3-  5423  3-  5425 

3-  5426 

3- 5427 

58  10 

3-  5428 

3-  5429 

3-5431 

3- 5432  3- 5433  3- 5434 

3- 5436  j  3- 5437 

3-5438  1  3-5439 

58  20 

3-  5441 

3-5442 

3-5443   3-5444  3-5446  3.5447 

3- 5448  3- 5449 

3-5451  1  3-5452 

58  30 

3-  5453 

3-  545  ; 

3-  5456 

3-5457  3-5458  3-5459 

3. 5460  3. 5462 

3-5463  i  3-5464 

58  40 

3-  5465 

3-  5467 

3-  5468 

3- 5469  3- 5470  3- 5472 

3- 5473  3- 5474 

3-  5475  3-  5477 

58  50 

3-  5478 

3-  5479 
3-  5491 

3-  5480 
3-  5492 

3.5481   3-5483  3-5484 

3-5485  :  3-5486 

3.5488  3.5489 

0  59   0 

3-  5490 

3- 5494  3- 5495 

3- 5496 

3- 5497  i  3- 5499 

3-5500  1  3-5501 

59  10 

3-  5502 

3- 5504 

3-  5505 

3- 5506  3- 5507 

3-  5508 

3-5510  3-55" 

3.5512  3.5513 

59  20 

3-55J4 

3-5516 

3-55'7 

3-5518 

3-5519 

3-5521 

3.5522  '  3.5523 

3- 5524 

3-5525 

59  30 

3- 5527 

3-5528 

3-  5529 

3- 5530 

3- 5532 

3-5533 

3-5534  3-5535 

3- 5536 

3- 5538 

59  40 

3-  5539 

3-  5540 

3-5541 

3- 5542 

3-5544 

3- 5545 

3- 5546  3-  5547 

3-  5549 

3-5550 

59  50 

3-5551 

3-5552 

3-5553 

3-5555 

3-  5556 

3-5557 

3-5558  3-5559 

3-5561 

3-  5562 

il 

Page  356 

TABLE  34. 

1 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

1 

Arc. 

0'' 

V' 

r' 

3'^ 

3- 5567 

4// 
3-  5568 

5'' 

6'' 

V 

S'' 

r^ 

// 

OS 

3-  5563 

3- 5564 

3-  5565 

3-  5569 

3-5570 

3-5571 

3-5573 

3-5574 

O 

lO 

5575 

1 

0 

5576 

3-5577 

3-5579 

3-  5580 

-» 

J 

5581 

3 

5582 

3 

5583 

3 

5585 

3 

5586 

O 

20 

3 

55''^7 

3 

5588 

3- 5589 

3-5591 

3- 5592 

3 

5593 

3 

5594 

3 

5595 

3 

5597 

3 

5598 

O 

3° 

-1 

5599 

3 

5600 

3- 5601 

3-  5603 

3-  5604 

3 

5605 

3 

56.6 

3 

5607 

3 

5609 

3 

5bio 

0 

40 

3 

561 1 

5612 

3-5613 

3-5615 

3-5616 

3 

5^' 7 

3 

5618 

3 

5619 

3 

5621 

-> 

5622 

1 

O 

50 

■> 

J 

5623 
5635 

3 
3 

5624 

3-  5625 

3.  5626 
Y.S638 

3-  5628 
3-  5640 

1 

5629 

3 

5630 

3 
3 

5631 
5643 

3 
3 

J632 
5644 

3 

3 

5634 
5645 

I   I 

0 

-1 

5636 

3- 5637 

3 

5641 

3 

5642 

10 

3 

5647 

3 

5648 

3- 5649 

3-  5650 

3-5651 

3 

5653 

3 

5654 

3 

5655 

3 

5656 

3 

5657 

20 

3 

5658 

3 

5660 

3-  5661 

3-  5662 

3-  5603 

1 

5664 

3 

5666 

3 

5667 

3 

5668 

1 
3 

5^-69 

30 

3 

5670 

3 

5671 

3-  5673 

3-  5674 

3-5675 

3 

5676 

3 

5677 

■7 

3 

5678 

3 

5680 

3 

5681 

40 

3 

5682 

5683 

3. 5684 

3-  5686 

3-5687 

3 

568S 

3 

5689 

3 

5690 

3 

5691 

3 

5693 

50 

■T 

5694 

3 

5695 
5707 

3-  5696 

3- 5697 

3- 5698 
3-5710 

3 
3 

5700 
5711 

3 
3 

5701 
5712 

3 
3 

5702 
5714 

3 

5703 

_3 
3 

5704 
5716 

I   2 

0 

3 

5705 

3-  5708 

3-5709 

3 

5715 

2 

10 

3 

5717 

3 

5718 

3-5719 

3-5721 

3-5722 

3 

5723 

3 

5724 

3 

5725 

3 

5726 

3 

5728 

2 

20 

3 

5729 

3 

5730 

3-5731 

3-  5732 

3-5733 

3 

5735 

3 

5736 

3 

5737 

3 

5738 

3 

5739 

2 

30 

3 

5740 

3 

5741 

3-  5742 

3-5744 

3-5745 

3 

5746 

0 

J 

5747 

3 

5748 

3 

5750 

3 

575' 

2 

40 

3 

5752 

3 

5753 

3-5754 

3-5755 

3-5756 

3 

5758 

5759 

-1 

3 

5760 

3 

5761 

3 

5762 

2 

50 

3 

5763 

3 

5765 

3- 5766 

3-5767 

3-5778 

3-5768 
3- 5780 

3 

5769 

3 
3 

5770 
5782 

3 
3 

5771 
5783 

3 
3 

5773 
5784 

3 
3 

5774 
5785  " 

I   3 

0 

3 

5775 

3 

5776 

3-5777 

3 

5781 

3 

10 

■^ 
3 

5786 

3 

5788 

3-  5789 

3-  5790 

3-5791 

3 

5792 

3 

5793 

3 

5794 

3 

5796 

3 

5797 

3 

20 

^ 

J 

5798 

3 

5799 

3. 5800 

3.  5801 

3-  5802 

3 

5804 

3 

5805 

3 

5806 

3 

5807 

3 

5808 

3 

30 

1 

5809 

3 

5810 

3.5812  3.5813 

3-5814 

3 

5815 

3 

5816 

3 

5817 

3 

5818 

3 

5819 

3 

40 

5821 

3 

5822 

3. 5823  '  3. 5824  1  3. 5825 

3 

5826 

3 

5827 

3 

5829 

3 

5830 

3 

5S31 

3 

50 

5832 

-> 

3 

5833 

3-  5834  3-  5835 

3- 5837 

3 

5838 

3 
3 

5839 
5850 

3 
3 

5840 
5851 

3 
3 

5841 

5852 

J 

3 

5842 
5853 

I  4 

0 

0 
J 

5843 

5844 

3- 5846  ;  3- 5847 

3-5848 

3 

5849 

4 

10 

3 

5855 

3 

5856 

3-5857  i  3-5858  1  3-5859 

3 

5860 

3 

5861 

3 

5862 

3 

5864 

3 

•58('5 

4 

20 

^ 
J 

5866 

3 

5867 

3. 5868  1  3. 5869  I  3- 5870 

3 

5871 

3 

5873 

3 

5874 

3 

5875 

3 

5876 

4 

30 

3 

5S77 

3 

5878 

3-  5879 : 3-  5880  3-  5882 

3 

5883 

3 

5884 

3 

5885 

3 

5886 

3 

5887 

4 

40 

-1 

5888 

3 

5889 

3.5891  1  3.5892  I  3.5893 

3 

5894 

3 

5895 

3 

5896 

3 

5897 

3 

5898 

4 

50 

_  3 

5899 

3 

5901 

3- 5902 

3-  5903 
3-  5914 

3- 5904 
3-5915 

3 

-y 

3 

5905 
5916 

3 
3 

5906 

3 

5907 

3 

5908 

3 

5910 

I  5 

0 

n 

J 

591 1 

3 

5912 

3-5913 

•5917 

3 

5918 

3 

5920 

3 

5921 

5 

10 

3 

5922 

3 

5923 

3- 5924 

3-  5925 

3- 5926 

3 

5927 

3 

5928 

3 

5930 

3 

5931 

3 

5932 

5 

20 

3 

5933 

3 

5934 

3-  5935 

3-  5936 

3- 5937 

3 

5938 

3 

5940 

t 

3 

5941 

1 

3 

5942 

3 

5943 

5 

30 

-> 

J 

5944 

3 

5945 

3- 5946  3- 5947  3- 5948 

5949 

3 

5951 

3 

5952 

3 

5953 

3 

-5954- 

5 

40 

3 

5955 

3 

5956 

3-5957  3-5958  ,  3-5959  ,  3 

5960 

3 

5962 

3 

5963 

5964 

3 

•5965 

5 

50 

3 
3 

5966 

3 

5967 

3- 5968 

3-5969  I  3-5970 
3- 5980  !  3. 5981 

3 
3 

5971 
5982" 

3 
3 

5973 
5984 

3 
3 

5974 
5985 

3 
3 

5975 
5986 

3 
3 

5976 
5987 

I  6 

0 

5977 

3 

5978 

3-  5979 

6 

10 

0 
^ 

5988 

3 

5989 

3- 5990  3. 5991  3. 5992 

3 

5993 

3 

5994 

3 

5996 

3 

5997 

3 

5998 

6 

20 

3 

5999 

3 

6000 

3.  6001  1  3. 6002  3.  6003 

3 

6004 

3 

6005 

3 

6006 

3 

6008 

3 

6009 

6 

30 

3 

6010 

3 

601 1 

3.6012  3.6013  ;  3.6014  i  3 

6015 

3 

6016 

3 

6017 

3 

6018 

3 

6020 

6 

40 

6021 

3 

6022 

3.6023  3.6024  3.6025  3 

6026 

3 

6027 

3 

6028 

3 

6029 

3 

.6030 

6 

50 

-> 

J 

6031 

3 

6033 
6043 

3^6c534_  _3^6o35_ 
3. 6044  3. 6046 

3-  6036 

3 

6037 

3 

6038 

3 

6039 

3 

6040 

3 

.  6041 

I  7 

0 

3 

6042 

3 

3-  6047 

3 

6048 

3 

6049 

3 

6050 

3 

605 1 

3 

"6052  ^ 

7 

10 

3 

6^53 

3 

6054 

3-  6055  3-  6056 

3- 6057 

3 

6058 

3 

6060 

3 

6061 

3 

6062 

3 

.6063 

7 

20 

^ 
J 

6064 

3 

6065 

3. 6066  3. 6067 

3.  6068 

0 
0 

6069 

3 

6070 

3 

6071 

•^ 

J 

6072 

3 

.6073 

7 

30 

3 

6075 

3 

6076 

3.6077   :   3.6078 

3- 6079 

3 

6080 

3 

6081 

3 

6082 

3 

6083 

3 

.6084 

7 

40 

3 

6085 

3 

6086 

3.6087   '   3.6088 

3.  6090 

3 

6091 

3 

6092 

3 

6093 

3 

6094 

3 

6095 

7 

50 

3 

6096 

3 

6097 

3.6098      3.6099 

3.6100 

3 

6101 

3 

6102 

3 

6103^ 

3 
3 

6104 
61 15 

3 

3 

6106 
6116^ 

I  8 

0 

3 

6107 

3 

6108 

3.6109      3.  6IIO 

3.6111 

3 

6112 

3 

6113 

3 

61 14 

8 

10 

3 

6117 

3 

6118 

3.  6119  !  3.  6120  3.  6121 

3 

6123 

3 

6124 

3 

6125 

3 

6126 

3 

6127 

8 

20 

^ 
J 

6128 

1 

0 

6129 

3.6130  ■  3.6131   3.6132 

3 

6133  !  3 

6134 

3 

6135 

3 

6136 

3 

^'H 

8 

30 

3 

6138 

1 

6139 

3.6141   3.6142  ,  3.6143 

3 

6144  i  3 

6145 

3 

6146 

3 

6147 

3 

6148 

8 

40 

0 
0 

6149 

^ 

J 

6150 

3.6151   3.6152  3.6153 

3 

6154  3 

6155 

3 

6156 

3 

6157 

3 

6158 

8 

50 

3 

6160 

3 

6161 

3.6162  ■  3.6163  1  3.6164 

3 

6165  1  3 

6166 

3 

6167 

3 

6168 

3 

6169 

I  9 

0 

3 

6170 

3 

6171 

3.6172  1  3.6173 

3-6174 

3 

6175 

3 

6176 

3 

6177 

3 

6178 

3 

6T79~ 

9 

10 

6180 

3 

6182 

3.6183  \   3.6184 

3-6185 

3 

6186 

3 

6187 

3 

6188 

3 

6189 

3 

6190 

9 

20 

6191 

•^ 
J 

6192 

3.6193  ■  3.6194 

3-6195 

3 

6196 

3 

6197 

3 

6198 

3 

6199  1  3 

6200 

9 

30 

3 

6201 

3 

6202 

3-  <J203  3.  6204 

3. 6206 

3 

6207  '  3 

6208 

3 

6209  1  3 

6210  '  3 

621 1 

9 

40 

3 

6212 

3 

6213 

3.6214  :  3.6215 

3.6216 

3 

6217  3 

6218 

3 

6219  I  3 

6220 

3 

6221 

9 

50 

3.  6222 

3.  6223 

3. 6224  3. 6225 

3.  6226 

3. 6227  '  3. 6228 

3.  6229 

3-6230 

3-6231 

TABLE  34.                   [Page  357 

Logarithms  of  Small  Arcs  in  Space  or  time. 

Arc. 

d' 

V 

2'' 

3^^ 

4// 

5'' 

6'' 

V 

8'^ 

9^'   1 

0   /   // 

10   10 

10   20 

10  30 

10   40 
10   50 

3-  6232 
3-  6243 
3-  6253 
3-  6263 
3.6274 
3-  6284 

3- 6234 
3.6244 

3- 6254 
3.  6264 

3-6275 
3.  6285 

3-  6235 

3-  6245 

3-  6255 
3.6265 

3. 6276 

3. 6286 

3-  6236 

3- 6246 
3- 6256 
3. 6266 
3.6277 
3-6287 

3- 6237 
3-  6247 
3-6257 
3.  6268 
3.6278 
3.  6288 

3. 6238 
3. 6248 
3-  6258 
3.  6269 

3- 6279 
3.  6289 

-1 

3- 
3- 
3- 

3- 

6239 
6249 

6259 
6270 
6280 
6290 

3 
0 
3 
3 
3 
3 
3- 
3 
3 
3 
3 
3 

6240 
6250 
6260 
6271 
6281 
6291 

3 

3 
3 
3 
3- 

6241 
6251 
6261 
6272 
6282 
6292 

3- 
3- 
3 

-> 

3 
3 

6242 
6252 
6262 
6273 
6283 
6293 

I   II    0 

II   10 
II   20 
II   30 
II   40 
II   50 

3.  6294 
3-  6304 
3-6314 
3-  6325 
3-  6335 
3-  6345 

3-  6295 
3-  6305 
3-6315 
3-  6326 
3-  6336 
3-  6346 

3. 6296 
3.  6306 
3-6316 
3-6327 
3-  6337 
3-  6347 

3- 6297 
3-  6307 
3-6317 
3.  6328 
3-6338 
3-6348 

3.  6298  3.  6299 

3.6308 : 3.6309 
3.6318 , 3.6320 

3-6329 '  3-6330 
3-6339 ;  3-6340 
3. 6349  3. 6350 

3 
3 
3 
3 
3 
3 

6300 
6310 
6321 

6331 
6341 
6351 

6301   3 

631 1   3 
6322  3 

6332  1  3 
6342  3 
6352  !  3 

6302 
6312 
6323 
6333 
6343 
6353 

3 
3 
3 
3 
3 
3 

6303 

6313 
6324 

6334 
6344 
6354 

I   12    0 
12   10 
12   20 
12   30 
12   40 
12   50 

3-6355 
3-  6365 
3-6375 
3-  6385 
3-  6395 
3-  6405 

3-6356  3-6357 
3.6366  ,  3.6367 

3-6376  i  3-6377 
3.6386  3.6387 

3-6396  3-6397 
3.  6406  3.  6407 

3-  6358 
3- 6368 
3-6378 
3-  6388 
3-6398 
3.  6408 

3-  6359  3-  6360 
3-6369 , 3-6370 
3-  6379  3-  6380 
3.6389  3.6390 
3-6399  3-6400 
3.6409  3.6410 

3 

3 
3 
3- 
3 

6361 

6371 
6381 
6391 
6401 
641 1 

3 
3 
3 
3 
3 
3 

6362  3 
6372  3 
6382  3 
6392  3 
6402  1  3 
6412  :  3 

6363 

6373 

6383 

6393 
6403 

6413 

1 

3 

3 
3 
3 

6364 

6374 
6384 

6394 
6404 

6414 

I  13   0 

13   10 
13   20 

13   30 
13   40 
13   50 

3.6415  i  3.6416  j  3.6417 
3.6425   3.6426  :  3.6427 
3.6435   3-6436  1  3-6437 
3.6444   3-6445  ,  3-6446 

3.6454    3-6455 : 3-6456 

3.6464   3.6465  1  3.6466 

3.6418  1  3.6419  ,  3.6420 
3.6428  3.6429  ^  3.6430 
3.6437  3.6438  3.6439 
3. 6447  3. 6448  3. 6449 
3.6457  3.6458  3.6459 
3.6467  3.6468  !  3.6469 

3- 
3 
3 
3 
3 
3 

6421  1  3 

6431   3 
6440  3 
6450  3 
6460  I  3 

6470  3 

6422  '  3 
6432  3 
6441  ,  3 

6461  3 
6471   3 

6423  '  3 
6433  3 
6442  3 
6452  3 
6462  1  3 

6472  ;  3 

6424 
6434 
6443 
6453 
6463 
6473 

I   14    0 
14   10 

14  20 

14  30 
14  40 

14  50 

3- 6474   3- 6475 
3. 6484   3. 6485 

3.  6493   3-  6494 
3-  6503   3-  6504 
3.6513   3.6514 
3.6522   3.6523 

3-  6476 
3.  6486 

3-  6495 
3-  6505 
3-6515 
3- 6524 

3.6477  3.6478 
3.6487  3-6488 
3.6496  j  3.6497 
3. 6506  ,  3. 6507 
3.6516  3.6517 
3.6525  !  3.6526 

3- 6479  3 
3-  6488  3 
3-6498  1  3 
3-  6508  1  3 
3-6518  :  3 
3-6527  3 

6480 
6489 

6499 
6509 

6519 
6528 

3 

■~* 

3 
3 
3 

3 

64S1   3 
6490  3 
6500  3 

6510  3 
6520  3 

6529  3 

6482 
6491 
6501 
651 1 
6521 
6530 

3 
3 
3 
3 
3 

6483 
6492 
6502 
6512 
6521 
6531 

I  15   0 

15   10 
15  20 

15   30 
15  40 
15   50 

3. 6532   3.  6533 
3.  6542   3.  6543 

3-6551   3-6552 
3.6561   3.6562 

3-6571   3-6572 
3.6580   3.65S1 

3-  6534 
3-6544 
3-6553 
3-  6563 

3-6572 
3-  65S2 

3-6535  ,  3-6536  3-6537  3 

3-6545  ;  3-6546    3-6547    3 

3-6554  ,  3-6555  3-6556  3 
3- 6564  :  3- 6565  i  3- 6566  3 

3-6573  3-6574  3-6575  3 
3.6583  3.6584  3.6585  3 

6538 
6548 
6557 
6567 
6<;76 
6586 

3 
3 
3 
3 
3 
3 

6539 
6549 
6558 
6568 

6577 
6587 

3 

3 
3 
3 
3 
3 

6540  1  3 
6549  '  3 
6559    3 

6569  !  3 

6578  3 
6588  3 

6541 
6550 
6560 

6570 
6579 
6589 

I  16   0 
16  10 
16  20 
16  30 
16  40 
16  50 

3.6590   3.6591  1  3.6592 
3-  6599   3.  6600  3.  6601 
3.6609   3.6610  3.  661 1 
3.6618   3.6619  3.6620 
3.  6628   •:;.  6629  3.  6629 
3.6637   3.6638  3.6639 

3-6593  i  3-6593  3-6594  1  3 
3.  6602  3.  6603  3.  6604  1  3 

3.  661 1    3.6612  i  3.6613  ;  3 
3.6621    3.6622   3.6623   3 
3.6630   3.6631    3.6632   3 

3. 6640  3. 6641  3. 6642  3 

6595 
6605 
6614 
6624 

6633 
6643 

3 

3 
3 
3 
3 
3 

6596 
6606 
6615 
6625 

6634 
6644 

3 
3 
3 
3 
3 
3 

6597  !  3 
6607  3 
6616  3 
6626  '  3 

6635  3 
6645  3 

6598 
6608 
6617 
6627 
6636 
6645 

I  17   0 

17  10 

17   20 

17   30 
17   40 

17   50 

3.  6646 
3.  6656 
3.  6665 

3-  6675 
3.  6684 

3-  6693 

3. 6647  3. 6648 
3.6657  3.6658 
3. 6666  3. 6667 
3.  6675  3-  6676 
3.6685  3.6686 
3.  6694  3.  6695 

3.  6649  3. 6650 
3.  6659  3.  6660 
3.  6668  3.  6669 
3. 6677  3. 6678 
3. 6687  3. 6688 
3. 6696  3. 6697 

3-6651 
3.  6660 

3-  6670 
3.  6679 
3.  6689 
3.  6698 

3 
3 
3 

3 
3 

6652 
6661 
6671 
6680 
6689 
6699 

3 
3 
3 
3 
3 
3 

6653 
6662 
6672 
6681 
6690 
6700 

3 

3 
3 
3 
3 
3 

6654 
6663 
6673 
6682 
6691 
6701 

3 
3 
3 
3 
3 
3 

6655 
6664 

6674 
6683 
6692 
6702 

I   18  .  0 

18  10 

18   20 
18   30 
18   40 

18  50 
I   19    0 

19  10 
19   20 
19   30 
19   40 
19   50 

3. 6702 
3.6712 
3-6721 
3-  6730 
3-  6739 
3-  6749 

3-  6703  3-  6704 
3.6713  3.6714 
3.  6722  3.  6723 

3-6731   3-6732 
3.  6740  3.  6741 
3.6750  .  3.6750 

3-  6705 
3-6715 
3-  6724 
3-6733 
3-  6742 
3-6751 

3.6706  3.6707  3 
3.6715  3.6716  3 
3-6725  3-6726  3 

3-6734  3-6735  3 
3. 6743  3. 6744  3 
3.6752  3.6753  3 

6708 
6717 
6727 
6736 
6745 
6754 

3 
3 
3 
3 

-» 

3 

6709 
6718 
6727 
6737 
6746 
6755 

3 
3 
3 

J 

3 

6710  :  3 

6719  3 
6728  3 

6738  3 
6747  3 
6756  i  3 

6711 
6720 
6729 

6738 
6748 

6757 

3.6758   3.6759  ^  3.6760 
3.  6767   3.  6768  3.  6769 
3.6776   3.6777  3-6778 
3.6785   3.6786  3.6787 
3.  6794   3.  6795  3.  6796 

3.  6803   ;     3.  6804      3.  6805 

3.6761 
3.6770 

3-6779 
3-  6788 

3- 6797 
3. 6806 

1 

3.6761   3.6762 
3.6771   3.6772 
3. 6780  3. 6781 
3. 6789  3. 6790 
3-6798 1 3-6799 

3.6807  !  3.6808 

3 

3 
3 
3 
3 

6763 
6772 

6782 

6791 

.6800 

.6809 

3 
3 
3 
3 
3 
3 

6764 
6773 
6782 

6792 

6801 

.6810 

3 

3 
3 
3 
3 
3 

6765  i  3 
6774  3 
6783  3 
6792  3 
.6802  3 
.68ji   3 

6766 

6775 

6784 

6793 

.6802 

.6812 

Page  358]                   TABLE  34. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0'' 

V 

2'^ 

r' 

4// 

5- 

6^^ 

;// 

8^^ 

9''      1 

0  /   // 

jh  20'"  O"^ 
20   10 
20   20 
20   30 
20   40 
20   50 

3 
3 

3 
0 
3 
3 

6812 

6821 
6830 
6839 
6848 

6857 

3 
3 
3 
3 
3 
3 

6813 
6822 
6831 
6840 
6849 
6858 

3 

3 
3 
3 
3 
3 

6814 
6823 
6832 
6841 
6850 
6859 

3 
3 

I 

3 
3 

6815 
6824 

6833 
6842 

6851 

6860 

3 
3 
3 
3 
3 
3 

6816 
6825 
6834 

6843 
6852 
0861 

3 
3 

J 

-» 

3 
3 
3 
3 
3 
3 
3 

6817 
6826 

6835 
6844 

6853 
6862 

3 

-> 

3 
3 
3 
3 

6818 

6827 
6836 
6845 
6854 
6863 

3 
3 
3 
0 
3 
3 

6819 
6828 

6837 
6846 

6855 
6864 

3 
3 

6820 
6829 
6838 

6847 
6856 
6865 

3 

3 
3 
3 
3 

6821 
6830 
6839 
6846 

6857 
6865 

"6874 
6883 
6892 
6901 
6910 
6919 

I   21    0 
21   10 
21   20 
21   30 
21   40 
21   50 

■-> 

3 

3 
3 
3 
3 
3 
3 
3 

-1 

3 
3 

6866 

6875 
68S4 
6893 
6902 
691 1 

3 
3 
3 
3 

6867 
6876 
6885 
6894 
6903 
6912 

3 
3 
3 
3 
3 
3 

6868 
6877 
6886 
689s 
6904 
6913 

3 
3 
3 
3 
3 
3 

6869 
6878 
6887 
6896 
6905 
6913 

3 
J 
3 
3 
3 
3 

6870 
6879 
6888 
6897 
6906 
6914 

6871 
6880 
6889 
6898 
6906 
6915 

3 
3 
3 

-> 

0 
0 

6872 
6881 
6890 
6898 
6907 
6916 

3 

3 
3 
J 
3 

6873 
6882 
6S90 
6899 
6908 
6917 

3 

-7 

3 
3 
3 
3 
3 

6874 
6882 
6891 
6900 
6909 
6918 

3 
3 
3 
3 
3 
3 

I   22    0 
22   10 
22   20 
22   30 
22   40 
22   50 

6920 
6928 

6937 
6946 

6955 
6964 

3 

3 
3 
3 
3 

6921 

6929 
6938 
6947 
6956 
6964 

3 
3 
3 
3 
3 
3 

6921 
6930 

6939 
6948 

6957 
6965 

3 
3 
3 
3 
3 
3 

6922 
6931 
6940 
6949 

6957 
6966 

3 
3 
3 
3 
3 

6923  3 
6932  3 

6941  3 
6950  3 

6958  3 
6967  3 

6924 

6933 
6942 
6950 

6959 
6968 

3 

3 
3 
3 

6925 
6934 
6943 
6951 
6960 
6969 

3 
3 
3 
3 
3 

3 
3 
3 
3 
3 

6926 
6935 

6943 
6952 

6961 

6970 

3 

3 
3 
3 
3 

6927 
6936 
6944 

6953 
6962 
6971 

3 
3 
3 
3 
3 
3 

6928 
6936 

6945 
6954 
6963 
6971 

I  23   0 
'   23   10 

23   20 

23   30 
23   40 

23   50 

3 
3 
3 
3 

-> 

3 
3 

-7 

3 
3 
3 
3 

6972 
6981 
6990 
6998 
7007 
7016 

-> 

3 
3 

3 
3 
3 
3 
3 
3 
3 

6973  3 
6982  3 

6991   3 

6999  3 
7008  3 

7017  3 
7025  3 
7034  3 
7042  3 

7051  :  3 

7060  !  3 
7068  1  3 

6974 
6983 
6991 
7000 
7009 
7017 

3 
3 
3 

3 
3 

6975 
6984 
6992 
7001 
7010 
7018 

3 
3 
3 
3 
3 
3 

6976  3 
6984  3 

6993  3 
7002  3 

7010  3 
7019  3 

6977 
6985 
6994 
7003 
701 1 
7020 

3 
3 
3 
3 

6978 
6986 

6995 
7004 
7012 
7021 

6978 
6987 
6996 
7004 

7013 
7022 

-> 

3 
3 
3 
3 
3 

6979 
6988 
6997 
7005 
7014 
7023 

3 

3 
3 
3 
3 

6980 
6989 
6998 
7006 
7015 
7023 

I   24    0 
24   10 
24   20 

24   30 
24   40 
24   50 

7024 

7033 
7042 

7050 

7059 
7067 

7026 

7035 
7043 
7052 

7060 
7069 

3 
-) 

3 

■-» 

3 
3 

7027 

7035 
7044 

7053 
7061 
7070 

3 
3 
J 
3 
3 
3 

.7028  3 
7036  :  3 
7045  :  3 
7054  3 
7062  3 

7071   3 

7029 

7037 
7046 

7054 
7063 
7071 

3 

3 
3 
3 
3 
3 

7029 
7038 
7047 

7055 
7064 
7072 

3 
3 
3 
3 
3 

7030 

7039 
7048 
7056 
7065 

7073 

3 
3 
3 
3 
3 
3 

7031 
7040 
7048 

7057 
7065 

7074 

3 

-> 
■-> 

3 
3 
3 

7032 
7041 
7049 

7058 
7066 

7075 

I   25    0 
25   10 
25   20 
25   30 
25   40 
25   50 

3 
3 
3 

3 

7076 
7084 

7093 
7101 
7110 
7118 

3 

3 
3 

3 

7077  !  3 

7085  :  3 

7094  !  3 
7102  j  3 
7110  1  3 

7119  t  3 

7077 
7086 
7094 
7103 
7111 
7120 

3 
3 
3 
3 
3 
3 

7078 
7087 

7095 
7104 
7112 
7121 

3 
3 

•7 

3 
3 
3 
3 

7079  ■  3 
7088  3 

7096  j  3 

7105  3 

7113  3 
7121  1  3 

7080 
7088 
7097 
7105 
7114 
7122 

3 
3 
3 
3 
3 
3 

7081 
7089 
7098 
7106 

7"5 
7123 

3 
3 
3 
3 
3 
3 

7082 
7090 
7099 
7107 
7116 
7124 

3 
3 
3 
3 
3 
3 

7083 
7091 
7099 
7108 
7116 
7125 

3 

3 
3 
3 
3 

7083 
7092 
7100 
7109 
7117 
7126 

I   26    0 
26   10 
26   20 
26   30 
26   40 
26   50 

3 
3 

■-» 

J 
3 

7126 
7135 

7143 

7152 

7160 
7168 

3 
3 
3 
3 
3 
3 

7127  i  3 
7136  3 
7144  3 

7153  3 
7161   3 
7169  3 

7128 
7137 
7145 

7153 
7162 
7170 

3 

3 
3 
3 
3 
3 

7129 

7137 
7146 

7154 
7163 
7171 

3 

3 
3 
3 

I 

7130 
7138 
7147 

7155 
7163 

7172 

3 
3 
3 
3 
3 
3 

7131 
7139 
7147 
7156 
7164 

7173 

3 
3 
3 
3 

i 

7132 
7140 
7148 
7157 
7165 
7173 

3 
3 
3 
3 
3 
3 

7132 
7141 

7149 
7158 
7166 

7174 

3 
3 
3 
3 
3 
3 

7133 
7142 
7150 

7159 
7167 

7175 

3 
3 
3 

3 
3 

7134 
7142 

7151 
7159 
7168 
7176 

I   27    0 
27   10 
27   20 

27   30 
27   40 
27   50 

3 
3 
3 
3 
3 
3 

7177 
7185 

7193 
7202 

7210 

7218 

1 

3 
3 

3 
3 

7178 
7186 

7194 
7202 
72 1 1 
7219 

3 
3 
3 
3 
3 
3 
3 

3 

3 
3 
3 

7178 

7187 

7195 
7203 
7212 
7220 

3 
3 
3 
3 
3 
3 

7179 
7188 
7196 
7204 
7212 
7221 

3 
3 
3 
3 
3 
3 

7180 
7188 
7197 
7205 

7213 
7221 

3 
3 
3 
3 
3 
3 

7181 

7189 

7197 
7206 

7214 

7222 

3 
3 
3 
3 
3 
3 

7182 
7190 
7198 
7207 

7215 
7223 

3 
3 
3 

3 
3 

7183  1  3 
7191  I  3 
7199  1  3 
7207  j  3 
7216  1  3 
7224  I  3 

7183 
7192 
7200 
7208 
7216 
7225 

-> 

J 

3 

"» 

3 
3 
3 

7184 
7192 
7201 
7209 
7217 
7226 

I   28    0 
28   10 
28   20 
28   30 
28   40 
28   50 

3 
3 
3 

J 

3 

-» 

7226 
7235 

7243 
7251 

7259 
7267 

7275 
7284 
7292 
7300 
7308 
7316 

3 
J) 
3 

3 
3 

7227 

7235 
7244 
7252 
7260 
7268 

7228 
7236 
7244 

7253 
7261 
7269 

3 
3 
3 
3 
3 
3 

7229 
7237 
7245 
7253 
7262 
7270 

3 
3 
3 
3 
3 
3 

7230  ,  3 
7238  1  3 
7246  :  3 
7254  3 
7262  3 
7271  :  3 

7230  ;  3 
7239  3 
7247  3 
7255  3 
7263  3 
7271  3 

7231 
7239 
7248 
7256 
7264 
7272 

3 
3 
3 
3 
3 
3 

7232  I  3 
7240  ]  3 
7248  ;  3 
7257  3 
7265  ,  3 
7273  1  3 

7233 
7241 

7249 

7257 
7266 
7274 

3 
3 
3 

3 
3 
3 
3 
3 
3 
3 
3 

7234 
7242 
7250 

7266 
7275 

7283 
7291 

7299 
7307 
7315 
7323 

I  29   0 
29  10 
29  20 

29  30 

29  40 
29  50 

-> 

3 
3 

•> 

3 

3 

J 

3 

7276 
7284 
7292 

7301 
7309 
7317 

3 
3 

3 
3 
3 

3 

7277 
7285 

7293 
7301 
7309 

7317 

3 
3 
3 
3 
3 
3 

7278 
7286 
7294 
7302 
7310 
7318 

3 

3 
3 
3 
3 

7279 
7287 

7295 
7303 
73" 
7319 

3 
3 
3 
3 
3 
3 

7279 
7288 
7296 

7304 
7312 
7320 

3 

3 
J 
3 
3 

7280  3 
7288  3 
7297  3 
7305  ;  3 
7313  3 
7321  j  3 

7281 
7289 
7297 
7305 
7313 
7322 

3 
3 
3 
3 
3 
3 

7282 
7290 
7298 
7306 

7314 

7322 

TABLE  34.                                               [Page  359 
»                                     Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0^^ 

V 

"r' 

3^' 

4// 

5'^ 

6^' 

r^ 

%'' 

%''      1 

0      1       II 

30       10 
30      20 

30      30 
30      40 

30      50 

3 
3 
3 
3 

-> 

0 

7324 
7332 
7340 
7348 
7356 
7364 

3 

J 

J) 

0 

7325 
7333 
7341 
7349 

7357 
7365 

3 

■> 
■> 

-> 

3 
J) 
3 
3 

J 

3 

7326 

7334 
7342 
7350 
7358 
7366 

7374 
7381 
7389 
7397 
7405 
7413 

3 

-% 

J 

3 
3 

-> 

j> 
3 
3 
3 
3 
3 
3 

7326 
7334 
7342 
7350 

7358 
7366 

3-  7327 
3-  7335 
3-  7343 
3-7351 
3-  7359 
3- 7367 

3 
3 
3 
3 
3 
3 

7328 
7336 
7344 
7352 
7360 
73(^8 

7376 
7384 
7392 
7400 
7408 
7415 
7423 
7431 
7439 
7447 
7455 
7462 

3 

3 
3 
J 

"> 

3 
3 

3 
J 
3 
3 
3 
3 
3 
3 
3 
3 
3 

7329 

7337 
7345 
7353 
13('^ 
7369 

3 

3 

3 
3 
3 

7330 
7338 
7346 
7354 
7362 

7370 

3-  7330 
3-  7338 
3-  7346 
3-  7354 
3-  7362 
3-  7370 

3 

■> 

3 
3 
3 

7331 
7339 
7347 
7355 
7363 
7371 

I      31         0 

31       10 
31       20 
31       30 
31      40 
31      50 

3 

J 

J) 

3 

7372 
7380 
7388 
7396 
7404 
7412 

3 
3 

3 
3 

7373 
7381 
7389 
7397 
7404 
7412 

7374 
7382 
7390 
7398 
7406 

7414 

3.  7375 
3-  7383 
3-  7391 
3-  7399 
3-  7407 
3-  7415 

3 

3 

3 
3 
3 

7377 
7385 

7393 
7400 
7408 
7416 

3 

3 
3 
3 

-> 

3 

7377  !  3- 7378 

7385  '  3-  7386 

7393     3-7394 
7401  !  3.  7402 

7409 ;  3-  7410 

7417  '  3-7418 

-» 

3 

7379 
7387 
7395 
7403 
741 1 

7419 

I       32         0 
32      10 

32       20 
32      30 
32       40 
32       50 

3 
3 
3 
3 

J 

3 

7419 

7427 
7435 
7443 
7451 
7459 

1 

3 
3 

3 
3 

-» 

-> 
3 

■-> 

3 

7420 
7428 

7436 
7444 
7452 
7459 
7467 

7475 
7483 
7490 
7498 
7506 

7514 
7521 

7529 
7537 
7544 
7552 
7560 
7567 

7575 
7582 
7590 
7597 

1 

J 

-> 

t 

J 

-> 

J 
3 
3 

3 

-1 

3 
3 

3 

3 

J 

3 
3 

3 
0 

7421 
7429 
7437 
7444 
7452 
7460 

3 

3 

3 
3 
3 

-y 

3 
3 
3 

7422  j  3.7423  !  3 

7430  1  3-  7430     3 

7437  \  3-  7438     3 

7445     3-  7446  ;  3 

7453     3-  7454     3 
7461  i  3. 7462     3 

7424 

7432 
7440 

7448 

7455 
7463 

3 
3 

~> 
■-> 

3 
3 

7425 
7433 
7441 

7448 

7456 
7464 

3-  7426     3 
3-  7434  1  3 
3-  7441      3 
3-  7449     3 
3-  7457     3 
3-  7465  i  3 

7426 

7434 
7442 

7450 
7458 
7466 

I     33      0 
33     10 
33    20 
33    30 
33    40 
33    50 

3 

J 
J 

3 
3 

7466 

7474 
7482 
7490 
7497 
7505 

7468 
7476 
7483 
7491 
7499 
7507 

7514 
7522 
7530 
7537 
7545 
7553 
7560 
7568 
7575 
7583 
7591 
7598 

7469 
7476 

7484 
7492 
7500 

7507 

3-  7469 
3-  7477 
3-  7485 
3-  7493 
3-  7500 
3-  7508 

3 
3 
3 
3 
3 
3 

7470 

7478 
7486 

7493 
7501 
7509 

3 
3 

3 

3 

7471     3 
7479     3 
7487     3 
7494     3 
7502     3 
7510     3 

7472 
7480 

7487 
7495 
7503 
7510 

3-  7473  1  3 
3-  7480     3 
3-  7488     3 
3-  7496  ,  3 

3-  7504 : 3 

3-75"  1  3 

7473 
7481 
7489 

7497 
7504 
7512 

I     34      0 
34     10 
34    20 
34    30 
34    40 
34     50 

3 
3 

-> 

3 

7513 
7520 

7528 

7536 

7543 

7551 

-1 

3 
3 
3 

3 

J 

3 

3 
3 

3 
3 
3 
3 
3 

3 
3 

3 

7515  1  3-  7516 
7523     3-  7524 
7530  '  3- 7531 
7538  ;  3- 7539 
7546     3- 7547 
7553  I  3-  7554 

3 
3 
3 
3 
3 
3 

7517 
7524 
7532 
7540 
7547 
7555 

3 

3 
3 
3 
3 
3 

7517 
7525 
7533 
7540 
7548 
7556 

3 

3 
3 
3 

7518 
7526 
7534 
7541 
7549 
7556 

3-7519 
3-  7527 
3-  7534 
3-  7542 
3-  7550 
3-  7557 

3 

-» 

3 
3 
3 
3 

7520 
7527 
7535 
7543 
7550 
7558 

I     35      0 
35     10 
35     20 
35    30 
35    40 
35     50 

3 
3 
3 
.  J) 
3 
3 

7559 
7566 

7574 

7582 

7589 
7597 

7561 
7569 
7576 
7584 
7591 
7599 

3-  7562 
3-  7569 
3-  7577 
3-  7585 
3-  7592 
3.  7600 

3 
3 
3 
3 
3 
3 

7563 
7570 
7578 
7585 

7593 
7600 

3 
3 
3 
3 
3 
3 

7563 
7571 
7579 
7586 

7594 
7601 

3 
3 
3 
3 
3 
3 

7564 !  3-  7565 

7572  '  3-  7572 
7579  1  3-  7580 
7587  \  3- 7588 
7594     3-  7595 
7602     3. 7603 

3 

3 

3 
3 
3 

7566 

7573 
7581 

7588 
7596 
7603 

I     36      0 
36     10 
36    20 

36    30 
36    40 

36    50 

3 
3 
3 
3 

3 

7604      3 
7612      3 

7619      3 
7627      3 

7634  1    3 
7642  !    3 

7605 

7613 
7620 
7628 

7635 
7643 

3 

-> 
-> 

3 

•-» 

3 

7606 

7613 
7621 
7628 
7636 

7643 

3 

^ 

3 
3 
3 
3 

-> 

3 
3 
3 
3 

7606 
7614 
7622 
7629 

7637 
7644 

3.  7607 

3-  7615 
3.  7622 

3-  7630 

3- 7637 

3-  7645 

3 
3 
3 
3 
3 
3 

7608 
7616 
7623 
7631 
7638 
7645 

3 

3 

3 
3 
3 

7609     3 
7616     3 
7624     3 

7631      3 

7639  j.3 
7646  !  3 

7609 
7617 
7625 
7632 
7640 
7647 

3-  7610 
3.  7618 

3-  7625 
3-  7633 
3-  7640 
3-  7648 

3 
3 
3 
3 
3 
3 

761 1 
7619 
7626 

7634 
7641 
7648 

I     37      0 
37     10 
37     20 
37    30 
37    40 
37    50 

3 

3 
3 
3 
3 

7649      3 
7657      3 
7664  j    3 

7672       3 

7679  1    3 
7686  1    3 

7650 

7657 
7665 
7672 
7680 
7687 

3 

J 

3 
3 

7651 
7658 
7666 

7673 
7681 

7688 

7651 
7659 
7666 
7674 
7681 
7689 

3-  7652     3 
3. 7660     3 

3-  7667  i  3 
3-  7675     3 
3-  7682     3 
3-  7689  1  3 

7^|3 
7660 

7668 

7675 
7683 

7690 

3 

3 
3 
3 

7654  i  3 
7661      3 
7669     3 
7676     3 

7683  i  3 
7691  '  3 

7654 
7662 
7669 
7677 
7684 
7692 

^-  7^|5 
3-  7663 
3-  7670 
3- 7677 
3-  7685 
3-  7692 

3 
3 
3 
3 
3 
3 

7656 
7663 
7671 
7678 
7686 
7693 

I     38      0 
38     10 
38    20 

38    30 
38    40 

38    50 

3 

-> 
'I 

7694  ■    3 
7701       3 
7709      3 
7716       3 
7723       3 
7731       3 

7695 

7702 

7709 

7717 
7724 
7731 

J 

3 
3 

3 

■> 

7695 
7703 
7710 

7717 
7725 
7732 

3 

-> 

3 
3 

-> 

3 

7696  J  3. 7697     3 

7703     3- 7704     3 
7711     3. 7711     3 
7718     3.7719     3 
7725  1  3.  7726     3 
7733  i  3-  7733     3 

7697 

7705 
7712 
7720 
7727 
7734 

3 
3 
3 
3 
3 
3 

7698     3 
7706     3 

7713     3 
7720     3 
7728  j  3 
7735  •  3 

7699 
7706 

7714 
7721 

7728 
7736 

3-  7700  ,  3 
3-  7707  ,  3 
3-  7714     3 
3.7722  1  3 

3-  7729     3 
3-  7736     3 

7700 
7708 

7715 
7722 

7730 
7737 

I     39      0 

39     10 
39     20 
39     30 
39    40 
39     50 

3 

J 

-> 
J 

3 

7738       3 
7745       3 
7752       3 
7760      3 

7767       3 
7774      3 

7739 
7746 

7753 
7760 
7768 

7775 

3 
J 

J) 

7739 

7747 

7754 
7761 

7768 

7776 

3 
3 
3 
3 
3 
3 

7740 
7747 

7755 
7762 
7769 
7776 

3-'  7741 
3-  7748 
3-  7755 
3-  7763 
3-  7770 
3-  7777 

3 
3 
3 
3 
3 
3 

7742 

7749 
7756 
7763 
7771 
7778 

3 
3 
3 
3 
3 
3 

7742 
7750 

•nsi 
7764 
7771 
7779 

3 
3 
3 
3 
3 
3 

7743 
7750 
7758 
7765 
7772 
7779 

3-  7744 
3-7751 
3.  7758 
3-  7766 
3-  7773 
3-  7780 

3 
3 

3 
3 
3 

7744 

7752 

7759 
7766 

7774 
7781 

Page  1 

360] 

TABLE  34. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

y 

Arc. 

W 

v 

%" 

3-  7784 

4// 

h" 

^" 

V 

8^^ 

%" 

0             / 

ill  40" 

'      OS 

3-  7782 

3. 7782 

3-  7783 

3-  7784  3-  7785 

3-  7786 

3-  7787 

3-  7787 

3-  7788 

40 

10 

3-  7789 

3-  7789 

3-  7790 

3-  7791  !  3 

7792    3 

7792  i  3 

7793 

3 

7794 

7795  !  3-  7795    1 

40 

20 

3-  7796 

3-  7797  t  3-  7797 

3-  7798  ;  3 

7799     3 

7800    :    3 

7800 

^ 
0 

7801 

J 

7802  1  3.  7802    1 

40 

30 

3-  7803 

3-  7804 

3-  7805 

3-  7805 

3 

7806     3 

7S07     3 

7807 

3 

7808 

3 

7309 

3.  7810 

40 

40 

3-  7810 

3.7811 

3-  7812 

3-  7813 

3 

7813  ,  3 

7S14  i  3 

7815 

3 

7815 

3 

7816 

3-7817 

40 

50 

3.7818 

3.  7818 

3-  7819 

3.  7820 

^ 

7820 

3 
3 

7821  t  3 
7828     3 

7822 

7829 

_3 

7823 

0 

J 

7823 
7830 

3-  7824 
3-  7831 

I    41 

0 

3-  7825 

3-  7825 

3-  7826 

3-  7827 

1 

7828 

-> 

J 

7830     3 

41 

10 

3-  7832 

3-  7833 

3-  7833 

3-  7834 

3 

7835     3 

7835     3 

7836 

7837     3 

7838  i  3-  7838    1 

41 

20 

3-  7839 

3-  7840  i  3-  7840 

3-  7841 

3 

7842     3 

7843     3 

7843 

7844     3 

7845 

3-  7845 

41 

30 

3.  7846 

3-  7S47  1  3-  7848 

3-  7848  1  3 

7849     3 

7850     3 

7850 

0 

7851 

T 
J 

7852 

3-  7853 

41 

40 

3-  7853 

3-  7854  '  3-  7855 

3-  7855 

t 

J 

7856     3 

7857     3 

7858 

0 

J 

7858 

0 

7859 

3-  7860 

41 

50 

3.  7860  , 

3.  7861 

3.  7S62 

3-  7863 
3-  7870 

--> 

3 

7863  ,  3 

7864 

3 
3 

7865 
7872 

3 

7865 
7872 

3 

7866 

3-  7867 

I   42 

0 

3-  7868  i 

3.  7868 

3-  7869 

7870  1  3 

7871 

3 

7873" 

3-  7874 

42 

ID 

3-  7875 

3-  7875 

3.  7876 

3-  7877 

7877     3 

7878     3 

7879 

3 

7880 

7880 

3.  7881 

42 

20 

3.  7882 

3-  7882 

3-  7883 

3-  7884  I  3 

7885     3 

7885     3 

7886 

1 

J 

7887     3 

7887 

3-  7888 

42 

30 

3.  7889 

3-  7889 

3-  7890 

3-  7891      3 

7892     3 

7892     3 

7893 

'I 

0 

7894     3 

7894 

3-  7895 

42 

40 

3.  7896 

3. 7897 

3-  7897 

3-  7898 

3 

7899  ,  3 

7899     3 

7900 

3 

7901      3 

7901     3. 7902 

42 

50 

3-7903  1 

3-  7904 

3-  7904 

3-  7905 

j^ 

7906 

J, 
3 

7906     3 
7913     3 

7907 
7914 

3 

7908     3 
7915     3 

7908     3. 7909 
•  7916  1  3. 7916 

I     43 

0 

3-  7910 

3- 791 1      3- 791 1 

3-  7912 

-> 

J 

7913 

43 

10 

3-7917 

3.  7918     3.  7918 

3-  7919 

3 

7920     3 

7920     3 

7921 

•-> 

7922     3 

7923  1  3-  7923 

43 

20 

3-  7924 

3-  7925     3-  7925 

3.  7926 

3 

7927     3 

7927     3 

7928 

3 

7929     3 

7930  i  3-  7930 

43 

30 

3-7931 

3-  7932     3-  7932 

3-  7933 

•1 

7934     3 

7934     3 

7935 

3 

7936 

7937  i  3- 7937 

43 

40 

3-  7938 

3-  7939 

3-  7939 

3-  7940     3 

7941      3 

7941      3 

7942 

3 

7943 

3 

7943  \  3-  7944 

43 

50 

3-7945 

3-  7946 

3-  7946 
3-  7953 

3- 7947 

3 

7948 

3 
3 

7948  1  3 

7949 

3 
3 

7950 
7957 

3 

3 

7950  ;  3-7951 

7957  j  3-  7958 

I     44 

0 

3-  7952 

3-  7953 

3-  7954 

3 

7955 

7955     3 

7956 

44 

10 

3-  7959 

3-  7959 

3-  7960 

3-  7961 

-> 

7962     3 

7962     3 

7963 

7964 

3 

7964     3. 7965 

44 

20 

3-  7966 

3.  7966 

3-  7967 

3-  7968  i  3 

7969     3 

7969     3 

7970 

0 
0 

7971 

3 

7971  1  3-  7972 

44 

30 

3-7973 

3-  7973 

3-  7974 

3-  7975 

7975  ,  3 

7976     3 

7977 

-> 

7978 

1 

7978 

3-7979    1 

44 

40 

3-  7980 

3-  7980 

3-  7981 

.  3-  7982 

3 

7982  :  3 

7983  \  3 

7984 

3 

7984 

3 

7985 

3.7986 

44 

50 

3-  7987 

3-  7987 

3.  7988 
3-  7995 

3-  7989 

3 

7989 

3 

-^ 

7990  1  3 
7997  i  3 

7991 
7998 

7991 

.3 

7992  1  3.  7993 

I     45 

0 

3  7993 

3-  7994 

3-  7995 

3 

7996 

7998     3 

7999  1  3.  8000 

45 

10 

3. SoGO 

3.8001      3. 8002 

3.  8002 

1 

J 

8003     3 

8004     3 

8004 

1 

J 

8005 

•^ 
J 

8006     3. 8006 

45 

20 

3.8007 

3. 8008 

3-  8009 

3-  8009 

•1 

0 

8010     3 

801 1      3 

801 1 

3 

8012 

8013 

3-8013 

45 

30 

3-8014 

3-8015 

3-8015 

3.8016  1  3 

8017     3 

8017  ,  3 

8018 

3 

8019 

3 

8020 

3. 8020 

45 

40 

3.8021 

3. 8022 

3.  8022 

3.  8023 

3 

8024     3 

8024  ,  3 

8025 

3 

8026     3 

g026 

3-  8027 

45 

50 

3.8028  ; 

3. 8028 
3-  8035" 

3- 8029 
3-  8036 

3-  8030 
3-  8036 

3 
3 

8030  j  3 
8037    '3 

8031      3 

8032 
8039 

3 
3 

8033     3 
8039     3 

8033 

3-  8034 

I    46 

0 

3-8035 

8038 

3 

8040 

3.8041 

46 

10 

3.8041 

3.  8042 

3-  8043 

3-  8043 

3 

8044     3 

8045     3 

8045 

8046     3 

8047  ■  3. 8048 

46 

20 

3. 8048 

3.  8049  1  3.  8050 

3.  8050 

3 

8051      3 

8052     3 

8052 

8053 

3 

8054    3-8054 

46 

30 

3-  8055 

3.8056  I  3.8056 

3-8057 

3 

8058     3 

8058     3 

8059 

1 

8060 

3 

8060  '  3.  8061 

46 

40 

3  8062 

3.  8062 

3-  8063 

3-  8064 

3 

8065     3 

8065     3 

8066 

3 

8067 

1 

0 

8067 

3. 8068 

46 

_5°_ 

3.  8069 

3- 8069 

3-  8070 

3.  8071 

3 

8071 

3 

8072     3 
8079     3 

8073 
8079 

3 

8073 
8080 

3 
3 

8074 

3-  8075 

I     47 

0 

3-  8075 

3.8076  '  3.8077" 

3-8077  '  3 

8078" 

8081 

3.  8081 

47 

10 

3.  8082 

3.  8083     3.  8083 

3.  8084 

3 

8085  '  3 

8085     3 

8086 

3 

8087 

0 
J 

8088  1  3.8088  1 

47 

20 

3.  8089 

3. 8090     3.  8090 

3-  8091 

3 

8092     3 

8092     3 

8093 

3 

8094 

-1 

8094  1  3.8095   1 

47 

30 

3.  8096 

3.8096 !  3.8097 

3. 8098 

-1 

8098     3 

8099     3 

8099 

3 

8100 

3 

8I0I    3.8102 

47 

40 

3.8102 

3-8103 

3.  8104 

3.8104 

3 

8105  1  3 

8106     3 

8106 

3 

8107 

3 

8108    3.8108 

47 

50 

3-8109 

3.8110 

3.8110 
3.8iif 

3.8111 
3.8118 

3 

8112 
81 18 

J 

8112 

3 
3 

8113 
8120 

J 

8114 

3 

8114  !  3.8115 

I     48 

0 

3.8116 

3.8'ii"6 

3 

8119 

3 

8120     3 

8121  t  3.8122 

4f 

10 

3.S122 

3.8123  \  3.8124 

3-8124     3 

8125     5 

8126     3 

8126 

T 

0 

8127     3 

8128     3.8128 

48 

20 

3.8129 

3.S130     3.8130 

3-8131      3 

8132     3 

8132     3 

8133 

T 

J 

8'34     3 

8134     3-8135 

48 

30 

3-8136 

3-8136 !  3-8137 

3-8138 

3 

8138  1  3 

8139 : 3 

8140 

8140  1  3 

8141     3.8142 

48 

40 

3.8142 

3.8143   3.8144 

3.8144 

3 

8145  '  3 

8146   3 

8146 

•> 

8147     3 

8148     3.8148 

48 

50 

3-  8149 

3.8150   3.8150 

3-8151 

3 

8152  !  3 
8158  '  3 

8152   3 

81 5^     3 

8153 
8160 

3 

8154     3 

8154     3-8155 
8161     3.8162 

I     49 

0 

3.8156 

3.S156    :    3.S157 

3-8i58"i  3 

8160 

3 

49 

10 

3.8162 

3.  S163        3.8164 

3-8164  '  3 

8165    3 

8it.6     3 

8166 

•1 

8167 

3 

8168     3.8168 

49 

20 

3.  8169 

3.8170     3.  Si  70 

3-8171  !  3 

8172  !  3 

8172     3 

8173 

8174 

3 

Si 74  '  3.8175 

49 

30 

3.8176 

3.8176     3.S177 

3-8178 

-, 
J 

8178     3 

8179     3 

8 1  So 

-> 

81S0 

T 

J 

8181   i  3.8182 

49 

40 

3.8182 

3.8183  1  3.8184 

3.8184 

3 

8185 : 3 

8185     3 

S1S6 

3 

8187 

3 

8188 

3.8188 

49 

50 

3.8189 

3.8190 

3.8190 

3.8191 

3.8191     3.8192  ;  3.8193 

3-8193 

3-8194 

3-8195 

TABLE   34.                   [Page  361 

»- 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0'' 

V 

2''    3'^  f  4'^ 

5'' 
3-  8199 

6^^ 

V 

S'' 

9'' 
3. 8201 

3-  819s 

3-  8196 

3.8197  3.8197  3.8198 

3.8199 

3.  8200 

3. 8201 

50  10 

3.  8202 

3. 8203  3. 8203  e.  8204  3. 8205  3. 8205 

3. 8206 

3-  8207 

3- 8207 

3.  8208 

50   20 

3.  S209 

3.8209  3. 821Q  3. 8211  3. 8211  3.8212 

3-8213 

3.8213 

3.8214 

3.8214 

50   30, 

3.8215 

3.8216  3.8216  3.8217  3.8218  3.8218 

3.8219 

3.  8220  3.  8220 

3.8221 

50   40 

3.  8222 

3. 8222  3. 8223  3-  8224  3. 8224  '  3. 8225 

3.  8226 

3.8226  !  3. 8227 

3.8228 

^o_   50 

3.  8228 

3. 8229 

3.8230  3.8230  3-8231  1  3.8231 
3. 8236  3. 8237  3-  8237  j  3. 8238 

3. 8232 

3-  8233 

3-8233 

3-  8234 
3.  8241 

I   51    0 

3- 8235 

3.8235 

3.  8239 

3-  8239 

3.  8240 

51   10 

3.  8241 

3.  8242  '  3.  8243  3.  8243  3-  8244  !  3.  8245 

3.  8245 

3. 8246 

3.  8246 

3.  8247 

51   20 

3.  8248 

3.8248  3.8249  3.8.50  3.8250  j  3. 8251 

3.8252 

3.8252  1  3.8253 

3-  8254 

51   30 

3-  S254 

3.8255  3.8256  3.8256  3.8257,3.8258 

3.  S258 

3-8259  !  3.8259 

3. 8260  • 

51   40 

3.8261 

3.8261  3.8262  3.8263  3.8263 

3.  8264 

3.  8265 

3.8265  j  3.8266 

3-8267 

5L_5° 

3.  8267 

3.  8268  3. 8269  3. 8269  3. 8270 

3.  8270 

3-8271 

3.  8272 
3-  8278 

3.  8272 
"3-  8279 

3-  8273 
3.8280 

I  52   0 

3-  8274 

3-  8274 

3-  8275  3-  8276 

3-  8276 

3.'8277^ 

3-  8278 

52  10 

3.  8280 

3.8281 

3.  8281  3.  8282 

3.8283  3.8283 

3.  8284 

3.  8285 

3-  8285 

3.  8286 

52  20 

3.  8287 

3- 8287 

3.  8288  i  3.  8289 

3. 8289  3. 8290 

3.  8290 

3.8291  1  3.8292 

3. 8292 

52  30 

3-  8293 

3-  8294 

3.  8294  3.  8295 

3.  8296  3.  8296 

3.8297 

3.S298  i  3.8298 

3.  8299 

52  40 

3. 8299 

3.  8300 

3.  8301  3.  8301 

3-8302  ,  3.8303 

3- 8303 

3-  8304 

3-  8305 

3-  8305 

52  5" 
I  53   0 

3.  8306 

3.  8307 

3.8307  3.8308 

3.  8308  1  3.  8309 

3.8310 

3.8310 

3-8311 

3.8312 
3-8318 

3.8312 

3.8313 

3.8314  3.^3I4 

3-8315  3-8315 

3.8316 

3.8317" 

3-8317 

53  10 

3-8319 

3.8319 

3.8320  3.8321 

3.  8321   3.  8322 

3-  8323 

3-  8323 

3-  8324 

3-  8324 

53  20 

3-  8325 

3.  8326 

3.  8326  3.  8327 

3. 8328  :  3. 8328 

3.  8329 

3. 8330 

3.  8330 

3-8331 

53  30 

3-  8331 

3-  8332 

3-  8333  3.  8333 

3-  8334  3. 8335 

3-  8335 

3.  8336 

3- 8337 

3-8337 

53  40 

3-  8338 

3-  8338 

3.  8339  3-  8340 

3. 8340  ;  3- 8341 

3- 8342 

3-  8342 

3-  8343 

3-8344 

53  50 

3-8344 

3-  8345 

3.8345  3.8346 

3.8347  1  3.8347 

3.  8348 
3-  8354 

3-  8349 

3- 8349 

3-  8350 

I  54   0 

3.835r 

3-8351 

3.  8352  3.  8352 

3-  8353  '  3. 8354 

3-8355 

3-  8356 

3- 8356 

54  10 

3-8357 

3-  8358 

3-  8358  1  3-  S359 

3.8359  1  3-8360 

3.8361 

3-  8361  1  3-  8362 

3-  8363 

54  20 

3-  8363 

3-  8364 

3.  8365  3-  8365 

3.8366  3.S366 

3-8367 

3. 8368 !  3. 8308 

3- 8369 

54  30 

3-  8370 

3-8370 

3-8371  3-8371 

3- 8372  3-  8373 

3-8373 

3-  8374  i  3-  8375 

3-  8375 

54  40 

3-  8376 

3-8377 

3-8377  3.8378 

3-8378 : 3-8379 

3-  8380 

3. 8380  , 3. 8381 

3.  8382 

54  50 
I  55   0 

3-  8382 
3.8388 

3- 8383 

3. 8383 
3-  8390 

3. 8384 

3.8385  :  3.8385 

3-  8386 

3.8387 

3- 8387 

3-  8388 

3-  8389 

3-  8390 

3. 8391 

3-  8392 

■  3- 8392 

3-  8393 

3- 8394 

3-  8394 

55  10 

3-  8395 

3-  8395 

3. 8396  3. 8397 

3. 8397 

3-  8398 

3- 8399 

3- 8399 

3.  8400 

3.  8400 

55  20 

3.  8401 

3.  8402 

3. 8402  3. S403 

3. 8404 

3.  8404 

3- 8405 

3.8405  1  3.8406 

3. 8407 

55  30 

3.  8407 

3.  8408 

3.  8409  3.  8409 

3. 8410  1  3. 8410 

3.  841 1 

3.8412  3.8412 

3-8413 

55  40 

3.8414 

3.8414 

3.8415  3.8415 

3.8416  3.8417 

3-8417 

3.8418  3.8419 

3-  8419 

55  50 
I  56   0 

3.  8420 

3.  8420 

3.8421  1  3.8422 

3. 8422  3. 8423 

3.  8424 

3. 8424  3.  8425 

3.  8425 

3.  8426 

3-  8427 

3. 8427 

3.  8428 

3.8429  1  3.8429 

3-  8430 

3.  8430 

3-8431 

3- 8432 

56  10 

3-  8432 

3-  8433 

3-  8434 

3-  8434 

3.8435  '  3.8435 

3. 8436 

3- 8437 

3-  8437 

3- 8438 

56  20 

3-  8439 

3-  8439 

3.  8440 

3.8440 

3-  8441  3-  8442 

3.8442 

3-  8443 

3-  8444 

3.8444 

56  30 

3-8445 

3-  8445 

3.8446 

3.8447 

3.  8447  3.  8448 

3.8448 

3.8449 

3-  8450 

3- 8450 

56  40 

3-8451 

3-  8452 

3.  8452 

3-  8453 

3.8453  '  3.8454 

3-  8455 

3- 8455 

3.  8456 

3-8457 

56  50 

3-8457 

3-8458 
3. 8464 

3-  8458 
3-  8465 

3-  8459 
3.8465 

3. 8460 
1.8466^ 

3. 8460 

3.  8461 

3.  8462 

3.  8462 
3.8468 

3-8463  _ 
3-  8469 

I  57   0 

3-  8463 

3. 8466 

3. 8467 

3. 8468 

57  10 

3. 8470 

3- 8470 

3.8471 

3-  8471 

3.  8472 

3-  8473 

3-  8473 

3.  8474 

3-  8474 

3-  8475 

57  20 

3-8476 

3-  8476 

3-  8477 

3-  8478 

3.8478 

3-  8479 

3-  8479 

3.  8480 

3.  8481 

3.8481 

57  30 

3-  8482 

3- 8483 

3-  S483 

3-  8484 

3.8484 

3.  8485 

3.  8486 

3.  8486 

3. 8487 

3- 8487 

57  40 

3. 8488 

3.  8489 

3-  8489 

3-  8490 

3-  8491 

3.  8491 

3.  8492 

3-  8492 

3.  8493 

3. 8494 

57  50 
I  58   0 

3- 8494 
3-  8500 

3-  8495 
3.8501 

3.  8495 
3. 8502 

3.  8496 
3-  8502 

3- 8497 
3.  8503 

3.  8497 

3.8498 

3- 8499 

3-  8499 

3-  8500 

3.  8503 

3-  8504 

3.  8505 

3-  8505 

"378506"" 

58  10 

3.  8506 

3- 8507 

3. 8508 

3.  8508 

3-  8509 

3.8510 

3.8510 

3-8511 

3.8511 

3.85'2 

58  20 

3-8513 

3.8413 

3.8514 

3-8514 

3-8515 

3.8516 

3.8516 

3-8517 

3-8517 

3.8518 

58  30 

3-8519 

3-8519 

3.8520 

3-  8521 

3.8521 

3-  8522 

3.8522  3.8523 

3. 8524 

3-  8524 

58  40 

3-  8525 

3-  8525 

3.8526 

3.8527 

3-8527 

3-  8528 

3-8528  3.S529 

3.8530 

3-  8530 

58  50 

3-8531 

3-  8532 

3-  8532 

3-  8533 

3-  8533 

3-  8534 

3.  8535  3-  8535 

3.  8536 

3-  8536 

I  59   0 

'  3-8537 

3-8538  3.8538 

3.  8539 

3.  8539 

3-  8540 

3.8541   3.8541 

3-8542 

3.8542  j 
3-  8549 

59  10 

3-  8543 

3-  8544  3-  8544  3-  8545 

3-  8545 

3-  8546 

3.8547  3.8547 

3-  8548 

59  20 

3-  8549 

3.8550 

3-8550  3-8551 

3-  ^552 

3-  8552 

3-  8553  3-  8553 

3-8554 

3- 8555 

59  30 

3-8555 

3-  8556 

3-8556  3-8557  , 

3-8558 

3-8558 

3- 8559  3- 8559 

3. 8560 

3.8561 

59  40 

3-8561 

3.  8562 

3.8562  3.8563 

3-  8564 

3.  8564 

3.8565 

3.  8565 

3-  8566 

3.  8567 

59  50 

3-8567  i 

3.8568 

3.  8568  1  3.  8569  1 

3-8570 

3-  8570 

3-8571 

3.8572 

3-8572 

3-8573 

Page  362 

TABLE  34.                            1 

Logarithms  of  Small  Arcs  in  Space  or  Time.                      1 

Arc. 

0' 

V 

2'^ 

3^^ 

4// 

5'' 

6'' 

V' 

S'' 

9'^ 

O     /     // 

2U  0'"  0^ 

3-8573 

3-8574 

3-  8575 

3.8575 

3.8576 

3.8576 

3-8577 

3.8578 

3-8578 

3-8579 

0   10 

3-8579 

3. 8580 

3.8581 

3-^581 

3-f582 

3-f5«2 

3-8583 

3.8584 

3.8584  3.8585 

0   20 

3-8585 

3-  8586 

3- 8587 

3.8587 

3. 8588 

3.8588 

3-8589 

3-  8590 

3.8590  3.8591 

0   30 

3-8591 

3-  8592 

3-  8593 

3. 8593 

3. 8594  3. 8594 

3-  8595 

3-  8596 

3.8596  3-8597 

0   40 

3-8597 

3-  8598 

3-  8599 

3. 8599 

3.8600  3,8600 

3.  8601 

3.  8602 

3.8b02  3.8603 

0   50 

3.  8603 

3.  8604 

3. 8605 

3. 8605 
3. 861 1 

3.8606  3.8606 

3.8607  '  3.8608 
3.  8613  '  3786147 

3. 8608 
3.8614 

3. 8609 
3-8615 

2   I    0 

3.  8609 

3.8610 

3. 861 1 

3.8612  3.8612 

I   10 

3.8615 

3.8616 

3.8617 

3-8617 

3.8618 

3.8618 

3.  8619  3.  8620  3.  8620 

3.8621 

I   20 

3.8621 

3.  8622 

3.8623 

3.8623 

3.8624 

3. 8624 

3.8625  3.8625 

3.  8626 

3-  8627 

I   30 

3- 8627 

3.  8628 

3. 8628 

3.  8629 

3. 8630 

3. 8630 

3.8631  :  3.8631 

3.8632 

3-  8633 

I   40 

3-  8633 

3-  8634 

3. 8634 

3.«635 

3.8636 

3.8636 

3-  8637  :  3-  8637 

3-8638 

3.8639 

I  SO 

3-8639 

3.  8640 
3.  8646 

3. 8640 

3.  8641 

3. 8642 

3. 8642 
3:8648 

3.8643  3.8643 

3.8644 

3.  8645 

2   2    0 

3.  8645 

3. 8646 

3. 8647 

3.8647 

3. 8649 

3. 8649 

3. 8650 

3.8650 

2   10 

3.8651 

3-  8652 

3.8652 

3-  8653 

3.8653  I  3.8654 

3.8655 

3-  8655 

3.  8656 

3-8656 

2   20 

3-8657 

3-  8658 

3.  8658 

3-  8659 

3.8659  3.8660 

3.8661 

3.8661 

3.  8662 

3.  8662 

2   30 

3.8663 

3-  8663 

3.  8664 

3.  8665 

3.8665 

3.  8666 

3.  8666 

3. 8667 

3.8668  3.8668  1 

2   40 

3.  8669 

3-  8669 

3. 8670 

3-8671 

3-8671 

3.  8672 

3-  8672 

3-8673 

3.8673 

3.  8674 

2   50 

3-8675 

3-8675 
3.  868  f" 

3. 8676 
3.8682 

3.8676 
3.8682 

3.8677 

3.8678 

3.  8678 
3.8684 

3.8679 
3.8685 

3-  8679 
3-  8685 

3.  8680 
3.  8686  ' 

230 

3.8681 

3.8683' 

3.8684 

3  10 

3.  8686 

3- 8687 

3.  8688 

3.  8688 

3.8689  I  3.8689 

3.  8690 

3.8691 

3.  8691 

3.  8692 

3  20 

3.  8692 

3-  8693 

3.8693 

3-  8694 

3.  869s 

3-  8695 

3.8696  '  3.8696 

3-8697 

3.  8698 

3  30 

3. 8698 

3.  8699 

3.  8699 

3.  8700 

3.  8701 

3.  8701 

3.  8702 

3.8702 

3-  8703 

3-  8703 

3  40 

3-  8704 

3-  8705 

3-  8705 

3.8706 

3. 8706 

3.  8707 

3.  8708 

3.  8708 

3-  8709 

3.  8709 

3  50 

3.8710 

3.8710 

3.8711 

3.8712 

3.8712 

3.8713 

3-8713  '   3.8714 

3.8715  1  3.8715 

240 

3.8716 

3-8716 

3.8717 

3-8717 

3.8718 

3.8719 

3.8719 : 3.8720 

3.8720  1  3.8721 

4  10 

3.8722 

3-  8722 

3.  8723 

3.8723 

3.  8724 

3.  8724 

3.8725  !  3.8726 

3-8726  i  3.8727 

4  20 

3-8727 

3-  8728 

3.  8729 

3-  8729 

3-  8730 

3.  8730 

3-8731 !  3.8731 

3-8732 

3.8733 

4  30 

3-8733 

3-  8734 

3.  8734 

3.8735 

3.8736 

3.8736 

3-8737 

3-8737 

3-8738 

3-8738 

4  40 

3-  8739 

3-  8740 

3.  8740 

3-  8741 

3.  8741 

3.  8742 

3-  8742 

3-  8743 

3-8744 

3.8744 

4  50 

3-  8745 

3-  8745 

3-  8746 

3- 8747 

3.  8747 

3.8748 

3. 8748 

3-  8749 

3-  8749 

3.  8750 
3-8756 

250 

3-8751 

3-8751 

3^:8752 

3.8752 

3. 8753 

3-  8754 

3.8754 

3.8755 

3-  8755 

5  10 

3-  8756 

3-8757 

3.8758 

3.8758 

3-8759 

3-8759 

3.8760  3.8760 

3.8761 

3-  8762 

5  20 

3-  8762 

3-  8763 

3.8763 

3.8764 

3.8764 

3-8765 

3.  8766  !  3.  8766 

3.8767 

3.8767 

5  30 

3-  8768 

3.  8769 

3.8769 

3-  8770 

3-  8770 

3.8771 

3-8771 

3-8772 

3.8773 

3-8773 

5  40 

3-8774 

3-  8774 

3-  8775 

3-8775 

3.8776 

3.8777 

3-8777 

3-  8778 

3.8778 

3-8779 

5  50 

3-8779 

3.  8780 

3.8781 

3.8781 

3.  8782 
3:8788 

3.8782 
3.8788" 

3.8783  3.8783 

3.8784 

3.8785 

260 

3-  8785 

3.  8786 

3:8786 

3-8787 

3.8789  3.8789 

3.  8790 

3-  8790 

6  10 

3-8791 

3-  8792 

3-  8792 

3-8793 

3.  8793 

3.  8794 

3-8794  3-8795 

3.8796 

3-  8796 

6  20 

3-8797 

3-  8797 

3.8798 

3-8798 

3.  8799 

3.  8800 

3.8800  '  3.8801 

3.8801 

3.  8802 

6  30 

3.  8802 

3.  8803 

3.  8804 

3. 8804 

3-  8805 

3.  8805 

3.8806  ]  3.8806 

3. 8807 

3.  8808 

6  40 

3.  8808 

3. 8809 

3.  8809 

3.8810 

3.8810 

3.  881 1 

3.8812  j  3.8812 

3-8813 

3.8813 

6  50 

3.8814 

3.8814 

3.8815 

3.8816 

3.8816 

3.8817 

3.8817  1  3.8818 

3.8818 

3.  8819 

270 

3.  8^820 

3.  8820 

3.8821 

3.  8821 

3.  8822 

3.  8822 

3.8823  j  3.8824 

3-  8824 

3.8825 

7  10 

3-8825 

3.  8826 

3. 8826 

3.8827 

3. 8828 

3.  8828 

3.  8829  !  3.  8829 

3-  8830 

3.  8830 

7  20 

3-8831 

3-  8832 

3.8832 

3-  8833 

3.8833 

3.  8834 

3-  8834 

3-!!35 

3-^f35 

3.8836 

7  30 

3-  8837 

3-  8837 

3.8838 

3- 8838 

3.8839 

3-8839 

3.  8840 

3-^^^ 

3-  8841 

3.  8842 

7  40 

3.  8842 

3-  8843 

3.8843 

3.8844 

3.  8845 

3.8845 

3. 8846 

3. 8846  1  3. 8847 

3.8847 

7  50 

3.  8848 

3.  8849 

3.8849 

3.  8850 

3.  8850 
3.8856 

3.8851 
"3.8856 

3.8851  3.8852  i  3.8852 

3.8857  ;  3.8858  1  3.8858 

3-  8853 
3.8859 

280 

3-"88"54 

3-  8854 

3. 8855 

3-8855 

8  10 

3-  8S59 

3.  8860 

3. 8860 

3.  8861 

3. 8862 

3.  8862 

3.  8863  i  3.  8863  I  3.  8864 

3.8864 

8  20 

3.  8865 

3.  8865 

.3.  8866 

3.8867 

3.  8867 

3.  8868 

3.  8868 

3.8869  '   3.8869 

3-8870 

8  30 

3.8871 

3.8871 

3.  8872 

3.  8872 

3.8873 

3.8873 

3.8874 

3.8874  3.8875 

3.8876 

8  40 

3.  8876 

3-8877 

3.8877 

3.  8878 

3.8878 

3.8879 

3.  8880 

3.8880  3.8881 

3. 8881 

8  50 

3.  8882 

3.  8882 

3.8883 

3.  8883 

3.  8884 

3.8885 

3.  8885   3.  8886 

3.8886  !  3.8887  1 

290 

3-8887 

3.  8888 

3.8889 

3.8889 

3.  8890  3.  8890 

3.  8891  ,  3.  8891 

3.8892  i  3.8892  1 

9  10 

3-  8893 

3.  8894 

3.8894 

3.8895 

3.8895  3.8896 

3. 8896  1  3. 8897  1  3. 8897  '  3. 8898  1 

9  20 

3.  8899 

3.  8899 

3.  8900 

3, 8900 

3.  8901   3.  8901 

3.8902  ,  3.8903  ;  3.8903  :  3.8904  1 

9  30 

3.  S904 

3-  8905 

3-  8905 

3.  8906 

3. 8906  3. 8907 

3. 8908 

3.8908  3.8909  3-8909  1 

9  40 

3.8910 

3.  8910 

3.  891 1 

3.  891 1 

3.8912  3.8912 

3-8913 

3.8914  3.8914  3.8915  1 

9  50 

3-S915 

3.8916 

3.8916  1  3.8917 

3.8918  3.8918 

i 

3.8919  1  3.8919  3.8920  '  3.8920  1 

TABLE  34.                   [Page  363 

% 

Logarithm 

s  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0    /     // 

2h  lo"'  0'* 

0'' 

V 

r' 

d'' 

4// 

5'' 

6r 

r' 

S'' 

r^ 

3.8921 

3-  8922 

3. 8922 

3- 8923 

3-  8923 

3. 8924 

3-  8924 

3. 8925 

3-  8925 

3. 8926 

10   10 

3-^927 

3. 8927 

3. 8928 

3.  8928  j  3.  8929  1  3. 8929 

3-  8930 

3-  8930 

3-8931 

3-8932 

10   20 

3-  S932 

3-  8933 

3-  8933 

3-8934  i  3.8934  1  3-8935 

3-  8935 

3.8936 

3-8937 

3-8937 

10  30 

3-  -"^93^ 

3.  8938  3.  8939 

3-8939    3-8940  ;  3-8940 

3.8941  1  3.8941   3.8942 

3-8943 

10  40 

3-  S943 

3.  8944  3.  8944 

3-8945    3-8945    3-8946 

3.8946  3.8947  3.8948 

3-  8948 

10   50 

3.  8949 

3.  8949 

:  3-8950 
i  3.8955 

3-8950    3-8951 
I  3.  8956    3.  8956 

3.8951 

3-8952  !  3-8953 

3- 8953 
3- 8959 

3-  8954 
3-8959 

2   11    0 

3-  8954 

3- 8955 

3.8957 

3. 8958  1  3. 8958" 

II   10 

3.  S960 

3. 8960  3. 8961 

3.8961  1  3.8962  i  3.8963 

3-  8963   3-  8964   3-  8964 

3-  8965 

II   20 

3.  8965 

3.  8966  3.  8966 

3-8967  !  3-8967  3-8968  1  3.8969  !  3.8969  1  3.8970 

3-8970 

II   30 

3-  S971 

3.8971   3.8972 

3.8972   3.8973 

3.8974  3.S974  3.8975  ,  3.8975 

3-  8976 

II   40 

3. 8976 

3-8977 

3-8977 

3-  8978  ;  3-  8978 

3.8979  3.8980  ;  3.8980 

3-  8981 

3-8981 

II   50 

3.  8882 

3.  8982 

3-  8983 

3-  8983 
3- 8989" 

3-  8984 

3. 8985  I  3. 8985  !  3. 8986 

J.  8986 
3- 8992 

3- 8992 

2   12    0 

3. 8987 

3.8988" 

3. 8988 

3.8989  1  3.8990  !  3.8991  '  3.8991 

12   10 

3-  8993 

3-  8993 

3. 8994 

3-  8994  :  3-  8995  1 3-  8995  1 3-  8996 '  3-  8997 

3-8997 

3-  8998 

12   20 

3.  S998 

3.  8999 

3- 8999 

3.9000   3.9000   3.9001 

3.  9001  1  3.  9002 

3-  9003 

3- 9003 

12   30 

3.  9004 

3-  9004 

3-  9005 

3. 9005  !  3. 9006  !  3. 9006 

3.9007   3.9007 

3. 9008 

3-  9009 

12   40 

3.  9009 

3.9010 

3.  9010 

3.9011  1  3. 90II 

3.9012 

3.9012   3.9013 

3-9013 

3-  9014 

12   50 

3-9015 

3-9015 

3-  9016^ 

3.9016  3.9017 

3.9017 

3.9018   3.9018 

3.9019 

3.9019 

2   13    0 

3. 9020 

3.  9021 

3-  9021 

3. 9022 

3. 9022 

3^9023 

3.9023  I  3.9024 

3.  9024 

3-  9025 

13   10 

3-  9025 

3.  9026 

3.  9027 

3.9027 

3.9028  :  3.9028  j  3.9029  1  3.9029  ;  3.9030 

3- 9030 

13   20 

3-9031 

3-9031 

3-  9032 

3-  9033 

3-9033  ;  3-9034  ;  3-9034  3-9035 

3-  9035 

3-  9036 

13   30 

3-  9036 

3- 9037 

3- 9037 

3- 9038 

3-9038  <  3-9039 

3.9040  !  3.9040 

3-  9041 

3. 9041 

13   40 

3.  9042 

3- 9042 

3-  9043 

3- 9043 

3- 9044 

3.9044 

3.9045  !  3-9046 

3.  9046 

3- 9047 

13  5° 

3-  9047 

3- 9048 

3- 9048 

3.  9049 

3-  9049 

3- 9050 

_3-905o  :  3^9051 

3-9051 

3- 9052 

2  14   0 

3-  9053 

3-  9053 

3- 9054 

3-  9054 

3-9055  '  3-9055 

3.9056  :  3.9056 

3-9057 

3-9057 

14  10 

3-  9058 

3- 9058 

3-  9059 

3.  9060 

3.9060  3.9061  3.9061  3.9062  3.9062 

3-  9063 

14  20 

3-  9063 

3-  9064 

3.  9064 

3.  9065 

3.9066  .  3.9066 

3-9067  3-9067  3-9068 

3.  9068 

14  30 

3-  9069 

3.  9069 

3- 9070 

3.  9070 

3.9071  3.9071 

3.9072  3.9073  1  3.9073 

3- 9074 

14  40 

3-  9074 

3-  9075 

3- 9075 

3-  9076 

3-9076  ;  3-9077 

3. 9077 

3- 9078  3- 9078 

3- 9079 

14  50 

3-  9079 

3.  9080 
3-  9085 

3.9081 

3-  9081 

3.9082  1  3.9082 

3. 9083 

3-  9083  3.  9084 

3-  9084 

2  15   0 

3-  9085 

3. 9086 

3.  9086 

3.9087  1  3.9088 

3.9088  i  3.90S9  1  3.9089 

3-  9090 

15  10 

3.  9090 

3.9091 

3-  9091 

3- 9092 

3.9092   3.9093 

3.9093  1  3-9094  1  3-9094 

3- 9095 

15  20 

3.  9096 

3.  9096 

3- 9097 

3-  9097 

3.9098  i  3.9098 

3.9099  3.9099  3.9100 

3.9100 

15  30 

3.9101 

3.9101 

3.  9102 

3-9103 

3-9103   3-9104 

3.9104 

3.9105  3.9105 

3.9106 

15  40 

3.9106 

3.9107  3.9107 

3-  9108 

3-  9108 

3.9109 

3.9109 

3.9110 

3.9111 

3.9111 

15  50 

3.9112 

3.9112  3.9113 

3-9"3 
3.9118 

3.9114 
3.9II9 

3.9114 

3.9II5 

3.9115 

3.9116 

3.9116 

2  16   0 

3-9117 

3-9117 

3.9118 

3.9120 

3.9120 

3.9121  '  3.9121 

3.9122 

16  10 

3.9122 

3-9123 

3-9123 

3.9124 

3.9124 

3.9125 

3.9125  3.9126 

3.9126 

3.9127 

16  20 

3.9128 

3.9128 

3.9129 

3.9129 

3.9130 

3.9130 

3-9I3I 

3.9131 

3.9132 

3.9132 

16  30 

3- 9133 

3-9133 

3-9134 

3.9134 

3-9135 

3.9135 

3.9136 

3-9137 

3.9137 

3.9138 

16  40 

3-9138 

3-9139 

3-9139 

3-  9140 

3- 9140 

3.9I4I 

3.9I4I 

3.9142  3.9142 

3.9143 

16  50 

3-9143 

3- 9144 

3-9144 

3-9145 
3-9150 

3.9146 
3.9151 

3.9146 

3.9147  1  3-9147  !  3-9148 

3.9148 

2  17   0 

3-9149 

3-9149 

3-9150 

3-9I5I 

3-9152  \  3-9152  '  3-9153 

3.9153 

17  10 

3-9154 

3-9155 

3-9155 

3-9156 

3-9156  '  3-9157 

3-9157  !  3-9158  !  3-9158  ! 

3-9159 

17  20 

3-9159 

3.9160 

3.  9160 

3.9161 

3. 9161  3.9162 

3.9162  1  3.9163  3-9163 

3-9164 

17  30 

3-9165 

3-9165 

3.9166 

3.9166 

3.9167   3.9167  1  3.9168  1  3.9168  :    3.9169 

3.9169 

17  40 

3.9170 

3-9170 

3-9171 

3-9171 

3.9172   3.9172 

3-9173  i  3-9173 : 3-9174 

3-9175 

17  50 

3-9175 

3-9176 

3-9176 

3-9177 

3.9177  1 

3-9178 
3-9183 

3.9178  3.9179  3.9179 

3.9180 
3-9185 

2  18   0 

3.9180 

3-9181 

3.9181 

3.9182 

3.9182 

3.9183  ,  3.9184    3.9184 

18  10 

3.9186 

3.9186 

3-9187 

3-9187 

3.9188   3.9188 

3.9189  j  3.9189  1  3.9190 

3.9190 

18  20 

3-9191 

3-9191 

3.9192 

3.9192 

3.9193  '  3.9193 

3-9194  1  3-9194  !  3-9195 

3-9195 

18  30 

3.9196 

3-9197 

3-9197 

3-9198 

3.9198  '    3.9199   3.9199   3.9200  1  3.9200 

3.9201 

18  40 

3.9201 

3.  9202 

3.  9202 

3. 9203 

3-9203   3.9204  j  3.9204   3.9205   3.9205 

3-  9206 

18  50 

3.  9206 

3-  9207 

3. 9207 

3.9208  1 

3.9209   3.9209  1  3.9210   3.9210   3.9211 

3.  921 1 
3.9216 

2  19   0 

"3.9212 

3.9212  3.9213 

3.9213  1  3.9214  3.9214  j  3.9215  3.9215  3.9216 

19  10 

3-9217 

3.9217  3.9218 

3.9218  3.9219  3.9219  3.9220  3.9221  3.9221 

3- 9222 

19  20 

3.9222 

3-  9223  3-  9223 

3-  9224 

3.9224  ,    3.9225 

3.9225  3.9226  1  3.9226 

3-9227 

19  30 

3.9227 

3.  9228  3.  9228 

3- 9229 

3.9229   3.9230 

3.9230  3.9231  3.9231 

3-  9232 

19  40 

3-  9232 

3-  9233  3-  9233 

3.9234  3.9235  3.9235 

3-9236  ;  3-9236  i  3-9237 

3-9237 

19  50 

3.9238  1 

3-9238  3-9239 

3-9239  '  3-9240  '   3-9240  3-9241  i  3-9241  '  3-9242  ' 

3.  9242 

Page 

364] 

TABLE  34. 
Logarithms  of  Small  Arcs  in 

Space  or  Time. 

Arc. 

0'' 

• 

2'^ 

3^^ 

4// 

5'' 

1 

6'^ 

^// 

8^^     9'' 

0      /      // 

■2'>  20™  0* 

3-  9243 

3-  9243 

3. 9244 

3-9244 

3- 9245 

3-  9245 

3-  9246 

3. 9246 

3-9247  3-9247 

20 

10 

.9248 

3 

.9248 

3 

.9249 

3-  9250 

3-  9250 

3-9251 

3-9251 

3.9252  '  3-9252  !  3-9253  1 

20 

20 

3 

•9253 

n 

J 

-9254 

3 

•9254 

3-  9255 

3-  9255 

3.9256  3.9256 

3-9257  1  3-9257 

3-9258 

20 

30 

n 
0 

.9258 

3 

-9259 

3 

•9259 

3. 9260 

3.  9260 

3.9201  3.9261 

3.  92b2  1  3.  9202 

3-  9263 

20 

40 

0 

J 

.9263 

3 

.9264 

3 

.9264 

3-  9265 

3.  9265 

3. 9266  3. 9267 

3-  9267  3-  9268 

3.  9268 

20 

50 

3 

.9269 

3 

.9269 

3 

.9270 

3. 9270 

3.9271 

3.  9271  3.  9272 

3.  9272  3.  9273 

3-9273 

2   21 

0 

3 

.9274 

3 

.9274 

3 

.9275 

3-  9275 

3.  9276 

3.9276  3.9277 

3.9277  3.9278 

3-9278 

21 

10 

•^ 
J 

.9279 

3 

.9279 

3 

.9280 

3.  9280 

3.  9281 

3.9281  3.9282 

3.  9282  3.  9283 

3-  9283 

21 

20 

T 

J 

.9284 

3 

.9284 

3 

.9285 

3-  9285 

3.  9286 

3.9287  ■  3.92S7 

3.  9288  3.  9288 

3-  9289 

21 

30 

3 

9289 

3 

.9290 

3 

.9290 

3-  9291 

3.9291 

3.9292  3.9292 

3-9293  i  3-9293 

3-  9294 

21 

40 

3 

9294 

3 

9295 

3 

•9295 

3-  9296 

3-  9296 

3- 9297  3- 9297 

3- 9298 

3-  9298 

3-  9299 

21 

_5o_ 

_3 

9299^ 

3 

9300 

3 

9300 

3-  9301 

3-  9301 

3.  9302  3.  9302 

3-  9303 
3-  9308 

3-  9303 
3-  9308 

3- 9304 
3-  9309 

2   22 

0 

0 

J 

9304 

3 

9305 

3 

9305 

3- 9306 

3-  9306 

3-9307  1  3-9307 

22 

10 

3 

9309 

3 

9310 

1 

93" 

3- 931 1 

3-9312 

3-9312  ;  3-9313 

3-9313  1  3-9314 

3-9314 

22 

20 

0 

9315 

3 

9315 

3 

9316 

3-9316 

3-9317 

3-9317  ;  3-9318 

3-9318 

3-9319 

3-9319 

22 

30 

3 

9320 

3 

9320 

3 

9321 

3-9321 

3-  9322 

3-  9322 

3- 9323 

3-  9323 

3-  9324 

3-  9324 

22 

40 

3 

9325 

3 

9325 

3 

9326 

3-  9326 

3-9327 

3-9327 

3-  9328 

3-  9328 

3-  9329 

3. 9329 

22 

50  _ 

3 

9330 

3 

9330 

3 
3 

9331 
9336 

3-9331 

3-  9332 
3-  9337 

3-  9332 

3-  9333 

3-  9333 

3-  9334 

3-  9334 

2   23 

0 

3 

9335 

3 

9335 

3-  9336 

3-9337     3-933^ 

3-9338  !  3-9339 

3-  9339 

23 

10 

3 

9340 

3 

9340 

3 

9341 

3-  9341 

3-  9342 

3-9342  3-9343 

3-9343  i  3-9344 

3-9344 

23 

20 

9345 

3 

9345 

3 

9346 

3-  9346 

3- 9347 

3-9348  I  3-9348 

3-9349  i  3-9349 

3- 9350 

23 

30 

9350 

3 

9351 

3 

9351 

3-  9352 

3-  9352 

3-  9353  3-  9353 

3-  9354 

3-  9354 

3-  9355 

23 

40 

-> 

J 

9355 

3 

9356 

3 

9356 

3-9357 

3-9357 

3-  9358  3-  9358 

3-  9359 

3-  9359 

3.  9360 

23 

50 

_  3 

9360 

3 

9361 

0 

3 

9361 
9366 

3- 9362 
3- 9367 

3- 9362 

3-  9363  3-  9363 
3-9368  !  3-9368 

3-  9364 
3-  9369 

3-  9364 
3-  9369 

3-  9365 
3-  9370 

2   24 

0 

1 

J 

9365 

3 

9366 

3- 9367 

24 

10 

3 

9370 

3 

9371 

3 

9371 

3-9372  !  3-9372 

3-9373  '   3-9373 

3-9374  ;  3-9374 

3-9375 

24 

'20 

-> 

9375 

3 

9376 

3 

9376 

3-9377  3-9377 

3-9378  3-9378 

3-9379  ,  3-9379  :  3- 938o  | 

24 

30 

3 

9380 

3 

9381 

3 

9381 

3-  9382  3-  9382 

3-  9383 

3-9383 

3-  9384 

3-9384  3-9385  1 

24 

40 

3 

9385 

3 

9386 

3 

9386 

3-9387  3-9387 

3-  9388 

3-9388 

3-  9389 

3- 9389 

3-  9390 

24 

SO 

3 

9390 

3 

9391 

3 
3 

9391 

3-9392  1  3-9392 

3-  9393 

3-  9393 

_3_i_9394_ 

3-  9394 

3-  9395 

2   25 

0 

3 

9395 

3 

9396 

9396  3-9397  1  3-9397 

3-  9398  ,  3-  9398 

3-9399  ,  3-9399 

3-  9400 

25 

10 

3 

9400 

3- 

9401 

3 

9401 

3.9402  j  3.9402 

3-9403  !  3-9403 

3- 9404 

3-  9404 

3-  9405 

25 

20 

3 

9405 

3- 

9406 

3- 

9406 

3- 9407 

3- 9407 

3-9408  3.9408 

3-  9409 

3-  9409 

3.9410 

25 

30 

3- 

9410 

3- 

941 1 

3 

941 1 

3.9412 

3.9412 

3-9413  ,   3-9413 

3-9414 

3-9414 

3-9415 

25 

40 

3- 

9415 

3 

9416  1  3 

9416 

3-9417 

3-9417 

3.9418  i  3.9418 

3-9419 

3.9419  I  3.9420  1 

25 

50 

3- 

0- 

9420 

3 

9421  ,  3. 

_?42l_ 

3.  9422 

3.  9422 

3-9423  3-9423 

3-  9424  1  3-  9424  1  3-  9425  1 

2   26 

0 

9425 

3- 

9426  j  3. 

9426 

3-9427 

3-  9427 

3.9428  3.9428 

3-  9429 

3-9429  3-9430  1 

26 

10 

J- 

9430 

3- 

9430  !  3- 

9431 

3-9431  t  3-9432 

3.9432  ,  3.9433  3.9433 

3.9434  '  3-9434  1 

26 

20 

0- 

9435 

0 
J- 

9435  3- 

9436 

3-9436  3-9437 

3-9437  3-9438  1  3-9438  !  3-9439  3-9439  | 

26 

30 

J- 

9440 

3- 

9440 

3- 

9441 

3-9441 

3-9442 

3. 9442  3.  9443 

3-9443  ]  3-9444  3-9444  1 

26 

40 

J- 

9445 

3- 

9445 

3- 

9446 

3.  9446 

3- 9447 

3-9447  3-9448 

3-9448  3-9449  i  3-9449  | 

26 

50 

J- 

9450 
9455 

3- 

9450 
9455 

_3: 

945 1_ 
9456 

3-9451 

3-  9452 

_3-_9452  J-9453_ 

3-  9453 
3-  9458 

3-9454  1  3-9454 

2   27 

0 

J- 

3-  9456 

3- 9457 

3-9457  3-9458 

3-9459  3-9459 

27 

10 

J- 

9460 

3- 

9460  3. 

9461 

3.9461  j  3.9462 

3.9462  ,  3-9463 

3- 9463 

3.9464  ;  3.9464 

27 

20 

3- 

9465 

3- 

9465  3- 

9466 

3.9466  3.9466 

3.9467  1  3.9467 

3.  9468 

3.9468  1  3.9469 

27 

30 

3- 

9469 

3- 

9470  1  3- 

9470 

3.9471  '.   3.9471 

3-9472  3.9472 

3-  9473 

3-  9473  3-  9474 

27 

40 

3- 

9474 

3- 

9475  3- 

9475 

3-9476  j  3.9476 

3-9477  3-9477 

3-  9478 

3-  9478 

3-  9479 

27 

2   28 

50 

3- 

9479 
9484 

3- 
3- 

9480  3. 
9485  1  3- 

9480 

T48r 

3^9481 
3.9486 

3-  9481 

3-  9482  3-  9482 
3.9487  j  3.9487 

3-  9483 
3.9488' 

3-  9483 

3-  9484 

0 

J- 

3- 9486 

3-  9488 

3-  9489 

28 

10 

3- 

9489 

'1 

J- 

9490  ,  3- 

9490  3.9490  ,  3-9491 

3-9491 

3- 9492 

3-  9492 

3- 9493 

3-  9493 

28 

20 

3- 

9494 

3- 

9494  1  3- 

9495 

3-9495  3-9496 

3. 9496 

3- 9497 

3-9497 

3-  9498 

3-  9498 

28 

30 

3- 

9499 

3- 

9499  3- 

9500 

3- 9500  ,  3- 9501 

3-9501 

3-  9502 

3-  9502 

3- 9503  3- 9503 

28 

40 

0 

J- 

9504 

3- 

9504  3- 

9505 

3- 9505  3- 9506 

3.9506  3.9507  !  3.9507 

3-  9508  3-  9508 

28 

50 

3- 

9509 

3- 

9509 

3- 
3- 

9509 

3.9510  3.9510 

3.9511  3.9511  3-9512 
3-9516  3-9516  1  3-9517 

3.9512  3.9513 
3-9517  3-9518 

2   29 

0 

3' 

9513 

3- 

9514 

9514  ;  3-9515  3-9515 

29 

10 

3- 

9518 

3- 

9519  1  3- 

9519  3-9520  ,  3-9520 

3.9521  3.9521 

3-  9522 

3-9522  1  3-9523 

29 

20 

0 
J' 

9523 

3- 

9524  3- 

9524 

3-9525  I  3-9525 

3-9526  ;  3-9526 

3-  9526 

3-9527  1  3-9527 

29 

30 

J* 

9528 

J- 

9528  3- 

9529 

3-9529  3-9530 

3-9530  3.9531 

3-9531 

3-9532  3-9532 

29 

40 

0- 

9533 

3- 

9533  I  3- 

9534 

3-9534  3-9535 

3-9535  3-9536 

3-  9536 

3-9537 

3-9537 

29 

50 

3-953^ 

3-9538  '  3.9539  1  3.9539  !  3-9540 

3-  9540  3-  9540 

3-9541 

3-9541 

3-  9542 

TABLE  34.                                               [Page  365  1 

Arc 

V 

Logarithms  of  Small  Arcs  in  Space  or  Time.                                                           1 

0' 

V' 

2'' 

3^' 

4// 

5''           6'' 

^// 

8'' 

r^ 

0          /             // 

ill    jo">     o'' 

3-  9542 

3-9543 

3-  9543 

3-9544 

3-9544 

3-  9545     3-  9545 

3- 9546 

3-  9546 

3-  9547 

30 

10 

3-9547 

3-9548 

3-9548  1  3-9549     3-9549 

3-9550  ;  3-9550 

3-9551 

3- 9551 

3-9552 

30 

20 

3-9552 

3-9553 

3-9553  1  3-9554     3-9554 

3-  9554     3. 9555 

3-9555 

3- 9556 

3-9556 

30 

30 

3-9557 

3-9557 

3-9558  :  3-9558     3-9559 

3-9559     3-9560 

3-  9560 

3-9561 

3-9561 

30 

40 

3-  9562 

3-  9562 

3-9563  i  3-9563     3-9564 

3-9564  '  3-9565 

3-  9565 

3- 9566 

3-  9566 

30 

50 

3- 9566 

3-  9567 

3-9567  '  3-9568     3-9568 

3-9^%     3-9569 
3-9574  :  3-9574 

3-9570 

3-9570     3-9571     1 

2      31 

0 

3- 9571 

3-9572 

3-9572     3-9573  :  3-9573 

3-9575 

3-9575     3-9576    1 

31 

10 

3-9576 

3-9577 

;  3-9577  1  3-9578     3-9578 

3-9578     3-9579 

3-9579 

3-9580 

3-  9580 

31 

20 

3-9581 

3-9581 

3.9582     3.9582     3.9583 

3.9583  !  3-9584 

3-  9584 

3-9585 

3-  9585 

31 

30 

3.9586 

3-  9586 

3-  9587 

3-9587     3-9588 

3.9588  '  3.9589 

3-  9589 

3-  9589 

3-  9590 

31 

40 

3- 9590 

3-9591 

3-9591 

3-9592     3-9592 

3-9593  '  3-9593 

3-  9594 

3-  9594 

3-  9595 

31 

50 

3-9595 

3-9596 

3-9596 

3-9597     3-9597 
3. 9601     3.  9602 

3-  9598     3-  9598 

3-  9599 

_3-_9599_ 

3- 9599 
3- 9604 

2       32 

0 

3.  9600 

3. q6oo 

3- 9601 

3.9602  }  3.9603 

3.  9603 

3- 9604 

32 

10 

3- 9605 

3.  9605 

3.  9606 

3. 9606     3. 9607 

3.9607     3.9608 

3. 9608 

3-  9609 

3. 9609 

32 

20 

3.  9609 

3.9610 

3.9610 

3.  961 1     3. 961 1 

3.9612 

3.9612 

3-9613 

3-9613 

3.9614 

32 

30 

3.9614 

3-9615 

3-9615 

3.9616     3.9616 

3-9617 

3.9617 

3.9618 

3-9618 

3.9618 

32 

40 

3- 9619 

3.9619 

3.  9620 

3.9620     3.9621 

3.9621     3.9622 

3.  9622 

3- 9623 

3-  9623 

32 

_i°    _ 

3. 9624 

3.  9624 

3-  9625 

3.9625     3.9626 

3.9626     3.9627 

3-  9627 

3-  9627 

3. 9628 

2    33 

0 

3. 9628 

3- 9629 

3-  9629 

3.9630  i  3.9630 

3-  9631 

3-9631 

3- 9632 

3- 9632 

3- 9633 

33 

10 

3- 9633 

3-  9634 

3- 9634 

3-  9634  !  3-  9635 

3. 9635 

3.  9636 

3- 9636 

3-9637 

3-9637 

33 

20 

3-9638 

3-  9638 

3-  9639 

3-9639  !  3-9640 

3. 9640 

3-  9641 

3- 9641 

3- 9642 

3-  9642 

33 

30 

3.  9642 

3-  9643 

3- 9643 

3-9644  i  3-9644 

3-  9645 

3- 9645 

3- 9646 

3-  9646 

3- 9647 

33 

40 

3-  9647 

3- 9648 

3- 9648 

3.9649  I  3.9649 

3- 9650 

3- 9650 

3-9651 

3-9651 

3.9652 

33 

50 

3- 9652 

3-  9653 

3-  9653 

3-9653    3-9654 

3.9654  '  3.9655 

3-9655      3-9656 

3-  9656 

2    34 

0 

3-9657 

3-9657 

3-  9658 

3-  9658 

3.9658 

3- 9659     3-  9659 

3.  9660     3.  9660 

3.9661 

34 

10 

3.9661 

3-  9662 

3.  9662 

3-  9663 

3-  9663 

3- 9664     3- 9664 

3-  9665     3-  9665 

3-  9665 

34 

20 

3.  9666 

3. 9666 

3- 9667 

3-  9667 

3. 9668 

3. 9668     3.  9669 

3-  9669     3- 9670 

3-  9670 

34 

30 

3-9671 

3-9671 

3-  9672 

3.9672 

3-  9672 

3-  9673     3-  9673 

3. 9674     3- 9674 

3- 9675 

34 

40 

3-  9'' 75 

3-  9676 

3- 9676 

3-  9677 

3-9677 

3.9678  1  3.9678 

3-  9679 

3-  9679 

3.  9680 

34 

JO    _ 

3.  9680 

3- 9681 

3-  9681 

3-  9682 

3. 9682 

3.9682  !  3.9683 
3-9687     3-9688 

3-  9683 

3.  9684 

3- 9684 
3-  9689  ' 

2    35 

0 

3-9685^ 

3-  9685 

3.  9686 

3. 9686 

3-9687 

3.  9688  ,  3.  9689 

35 

10 

3- 9689 

3-  9690 

3- 9690 

3- 9691 

3- 9691 

3. 9692     3-  9692 

3-9693  :  3-9693 

3-  9^94 

35 

20 

3. 9694 

3- 9695 

3- 969; 

3- 9696 

3-  9696 

3.9696  j  3.9697 

3-9697 ;  3-9698 

3- 9698 

35 

30 

3-  9699 

3-  9699 

3-9700 

3.9700 

3-  9701 

3-9701  '  3.9702 

3.9702   3.9703 

3-  9703 

35 

40 

3-  9703 

3-  9704 

3-  9704 

3-  9705 

3- 9705 

3-  9706 

3- 9706 

3-9707  i  3-9707 

3.  9708 

35 

50 

3. 9708 

3-  9709 

3-  9709 

3-9710 
3-9714 

3-9710 

3-9710 

3-97" 
3-9716 

3-97"   !  3-9712 

3-9712 

^    36 

0 

3-9713 

3-9713 

3-9714 

3-  9715 

3-  9715 

3-9716 

3-9716 

3-9717 

36 

10 

3-9717 

3-9718 

3-9718 

3-9719 

3-9719 

3. 9720 

3-  9720 

3-9721 

3-9721 

3-9722 

36 

20 

3-  9722 

3-9722 

3-  9723 

3-9723 

3-  9724 

3. 9724 

3-  9725 

3-  9725 

3.9726 

3-9726 

36 

30 

3-9727 

3-9727 

3-9728 

3-9728 

3-9729 

3-9729     3-9729 

3-  9730 

3-  9730 

3-9731 

36 

40 

3-9731 

3-  9732 

3-9732 

3-9733 

3-9733 

3-9734  i  3.9734 

3-9735  :  3-9735 

3-  9735 

36 

50 

3-  9736 

3-  9736 

3-9737 

3-9737 

3.9738 

3.9738     3-9739  ' 

3-9739 

3- 9740 

3-  9740 

2    37 

0 

3-9741 

3-9741 

3-  9741 

3-  9742 

3-9742 

3-9743     3.9743     3-9744 

3- 9744 

3-  9745 

37 

10 

3-  9745 

3-  9746 

3-  9746 

3-  9746 

3-9747 

3-9747  1  3-9748     3.9748 

3-9749     3-9749    1 

37 

20 

3-9750 

3-9750 

3-9751 

3-9751 

3-9752 

3-9752  ;  3-9752     3-9753  .  3-9753 

3-  9754 

37 

30 

3-9754 

3-9755 

3-9755 

3-9756 

3-9756 

3-9757  1  3-9757 

3-9758  '  3-9758 

3-9758 

37 

40 

3-9759 

3-  9759 

3-  9760 

3.  9760 

3.9761 

J-  9761     ;    3-9762 

3.9762     3.9763 

3- 9763 

37 

50 

3-  9763 

3-  9764 

3-  9764 
3-  9769 

3-  9765 
3-  9769 

3-9765  I 
3.9770  t 

3.9766 

3- 9766 

3-9767  :  3-9767 

3- 9768 

2    38 

0 

3.9768 

3-  9769 

3.  9770 

3.9771      3.9771  1  3.9772 

3-9772 

38 

10 

3-9773 

3-9773 

3-  9774 

3-  9774 

3.9774 

3-9775  '  3-9775      3-9776  '  3-9776 

3-9777 

38 

20 

3-9777 

3-9778 

3-9778 

3-9779 

3-9779 

3-9779     3-9780     3-9780     3-9781 

3-9781 

3^ 

30 

3-  9782 

3-  9782 

3-9783  ' 

3-  9783 

3-  9784 

3-9784     3-9785     3-9785      3-9785      3-9786    1 

^4 

40 

3-  9786 

3-9787 

3-97S7 

3.9788 

3- 9788     3- 978Q     3- 97S9 

3-9790     3-9790 

3- 9790 

38 

50 

3.9791 

3-9791 

3.9792 

3-  9792 

3-  9793     3-  9793 

3- 9794 

3-9794  1  3-9795 

3-  9795 

2  39 

0 

3-9795 

3.9796 

3-  9796 

3-9797 

3-9797     3-9798 

3-  9798 

3-9799  '  3-9799 

3. 9800 

39 

10 

3.9800 

3. 9800 

3-9801 

3- 9801 

3. 9802     3. 9802     3. 9803 

3-9803  !  3-9804     3- 9*804    1 

39 

20 

3-  9805 

3- 9805 

3-  9805 

3.  9806 

3. 9806     3. 9807     3. 9807 

3.9808     3. 9S08     3. 9S09    1 

39 

30 

3.  9809 

3.9810 

3-9S10 

3.9810 

3.  981 1 

3. 981 1      3.9812     3.9812  1  3.9813     3.9813    1 

39 

40 

3.9814 

3.9814 

3-9815 

3-9815 

3-9815 

3.9816     3.9816 

3.9817     3.9817     3.9818 

39 

50 

3.9818 

3.9819 

3.9819 

3-9819 

3.  9820 

3.9820     3.9821 

3.9821      3.9822  1  3.9822 

Page  i 

366] 

TABLE  34. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

{i" 

\" 

V' 

%" 

4// 

5'^ 

6'^ 

v 

8'^ 

%" 

2''  40" 

1  OS 

3-  9823 

3-  9823 

3.  9824 

3. 9824 

3-  9825 

3.  9825 

3. 9825 

3-  9826 

3.9826 

3. 9827 

40 

10 

3-  9827 

3-  9828 

3-  9828 

3. 9829 

3. 9829 

3.  9829 

3-  9830 

3-  9830 

3.9831 

3.9831 

40 

iO 

3-  9832 

3-  9832 

3. 9833 

3.9833 

3-  9834 

3-  9834  3.  9834 

3-  9835 

3. 9835 

3-9836 

40 

30 

3-  9836 

3-  9837 

3-  9837 

3-9838 

3-9838 

3-  9839  3-  9839 

3-  9839 

3-  9840 

3. 9840 

40 

40 

3.  9841 

3.  9841 

3-  9842 

3-  9842 

3-  9843 

3-9843  i  3-9843 

3.9844 

3-  9844 

3-  9845 

40 

50 

3-  9845 

3.  9846 

3.  9846 

3-  9847 

3-  9847 

3-9848  1  3-9848 
3.  9852  3.  9852 

3-9848 
3.  9853 

3.  9849 

3-9849  ^ 
3-  9854 

2   41 

0 

3-  9850 

3-  9850 

3-9851 

3-9851 

3-  9852 

3.9853 

41 

10 

3-  9854 

3-  9855 

3-  9855 

3.9856 

3.9856 

3.9857  3.9857 

3-9857 

3-9858 

3-9858 

41 

20 

3-  9S59 

3-  9859 

3- 9860 

3.  9860 

3.9861 

3.9861  j  3.98(31 

3-  9862 

3.  9862 

3-  9863 

41 

30 

3-  9863 

3-  9864 

3.  9864 

3-9865 

3.9865 

3-  9865  3.  9866 

3.  9866 

3.9867 

3-9867 

41 

40 

3.  9868 

3-  9868 

3- 9869 

3-  9869 

3-  987" 

3-  9870  3-  9870 

3  9871 

3.9871 

3-  9872 

41 

50 

3.  9872 

3-  9873 

3-  9873 

3-  9874 
3.9878 

3-  9874 
3.9878' 

3-9874  '  3-9875 

3-  9875 

3.9876 

3.9876 

2   42 

0 

3-9877 

3-9877 

3-9878 

3.9079  i  3.9:379 

3.  9880 

3.  9880 

3.  9881 

42 

10 

3.9881 

3-9882 

3.  9882 

3.9882 

3-  9883 

3.9683  1  3.9884 

3.  9884 

3.9885 

3-9885 

42 

20 

3.  9S86 

3-  9886 

3.  98S6 

3-  9887 

3. 9887 

3.  98S8  ;  3.  9888 

3-  9889 

3-  9889 

3.  9890 

42 

^.0 

3.  9890 

3-  9890 

3-  9891 

3-  9891 

3. 9892 

3-9892  1  3-9893 

3  9893 

3-  9894 

3-  9894 

42 

40 

3.  9894 

3-  989s 

3-  9895 

3-  9896 

3-  9896 

3-9897  '  3-9897 

3.  9898 

3.9898 

3.  9898 

42 

50 

3-  9899 

3-  9899 
3-  9904 

3-  9900 

3-  9900 

3-  9901 

3.9901  ;  3.9902 

3.9906  !  3.9906 

3- 9902 
3- 9906 

3.  9903 
3. 9907 

3-99"3 
3- 9907 

2  43 

0 

3-  9903 

3. 9904 

3- 9905 

3-  9905 

43 

ID 

3.  9908 

3.  9908 

3.  9909 

3. 9909 

3.9910 

3.9910   3.9910 

3- 991 1 

3-99" 

3.9912 

43 

20 

3.9912 

3-9913 

3-9913 

3-9914 

3-9914 

3-9914   3-9915 

3-9915 

3.9916 

3.9916 

43 

30 

3-9917 

3-9917 

3-9918 

3-9918 

3.9918 

3.9919  !  3.9919 

3-  9920 

3-  9920 

3-9921 

43 

40 

3-9921 

3.  9922 

3.  9922 

3.  9922 

3-  9923 

3.9923  !  3-9924 

3.  9924 

3-  9925 

3-  9925 

43 

50 

3-  9926 

3-  9926 

3. 9926 

3-9927 

3-  9927 

3.9928  j  3.9928 

3-  9929 

3. 9929 

3-  9930 

2  44 

0 

3-  9930 

3- 9930 

3-9931 

3-9931 

3-  9932 

3-  9932 

3-  9933 

3-  9933 

3-  9933 

3. 9934 

44 

10 

3-  9934 

3-  9935 

3.  9935 

3- 9936 

3-  9936 

3-  9937 

3-9937 

3-9937 

3-  9938 

3-  9938 

44 

20 

3-  9939 

3-  9939 

3.  9940 

3. 9940 

3-  9941 

3-  9941 

3. 9941 

3-  9942 

3.  9942 

3-  9943 

44 

30 

3-  9943 

3-9944 

3-9944 

3-9944 

3-  9945 

3-  9945 

3.  9946 

3.  9946 

3-  9947 

3-  9947 

44 

40 

3-  9948 

3-  9948 

3.  9948 

3-  9949 

3-  9949 

3-9950  ;  3.9950 

3-9951 

3-9951 

3-  9952 

44 

50 

3-  9952 

3-  9952 

3-  9953 

3-  9953 

3. 9954 

3-9954  1  3-9955 

3-  9955 
3-  9959 

3-9955 
3.  9960 

3-  9956 
3.  9960 

2  45 

0 

3-  9956 

3-5957 

3-9957 

3-  9958 

3. 9958 

3-9959 

3-  9959 

45 

10 

3.  9961 

3-  9961 

3. 9962 

3. 9962 

3. 9962 

3.  9963 

3-  9963 

3-  99^4 

3. 9964 

3.  9965 

45 

20 

3-  99(^5 

3.  9965 

3.  9966 

3-  9966 

3-  9967 

3.9967  !  3.9968 

3.  9968 

3.  9969 

3-  9969 

45 

30 

3-  99*39 

3-  9970 

3- 9970 

3-9971 

3-9971 

3-9972  3.9972 

3-  9973 

3.  9973 

3-  9973 

45 

40 

3-  9974 

3-  9974 

3-9975 

3-  9975 

3.9976 

3-9976  1  3-9976 

3-9977 

3- 9977 

3-  9978 

45 

50 

3-  9978 

3-  9979 

3- 9979 

3- 9980 

3. 9980 

3-9980  3.9981 

3. 9981 

3. 9982 
3. 9986 

3-  9982 
3- 9987 

2  46 

0 

3-  9983 

3-  9983 

3-  9983 

3. 9984 

3.  9984 

3-  9985  3-  9985 

3-  9986 

46 

10 

3- 9987 

3-  9987 

3.9988 

3.9988 

3.  9989 

3. 9989  3-  9990 

3.  9990 

3. 9990 

3-9991 

46 

20 

3-9991 

3.  9992 

3-  9992 

3- 9993 

3. 9993 

3-  9993  3-  9994 

3-  9994 

3. 9995 

3-  9995 

45 

33 

3-  9996 

3.  9996 

3-  9997 

3-  9997 

3-9997 

3-9998  1  3-9998 

3- 9999 

3-  9999 

4.  0000 

45 

40 

4.  0000 

4.  0000 

4.  0001 

4.  0001 

4.  0002 

4.  0002  1  4.  0003 

4.  0003 

4.  0003 

4.  0004 

46 

50 

4.  0004 

4.  0005 

4.  0005 

4.  0006 

4.  0006 

4.  0007  1  4. 0007 

4.  0007 

4.  0008 

4.  0008 
4.0013 

2  47 

0 

4. 0009 

4.  0009 

4. 0010 

4.  0010 

4. 0010 

4.  001 1 

4. 001 1 

4.  0012 

4.0012 

47 

10 

4.0013 

4.0013 

4.  0014 

4.  0014 

4.  0015 

4.0015 

4.0016 

4.0016 

4.  0016 

4.0017 

47 

20 

4.0017 

4.  0018 

4.0018 

4.  0D19 

4.  0019 

4.0019 

4.  0020 

4.  0020 

4.  002 1 

4.0021 

47 

30 

4.  0022 

4.  0022 

4. 0023 

4-  0023 

4.  0023 

4.  0024  '  4.  0024 

4.  0025 

4.  0025  4.  0026 

47 

40 

4.  0026 

4.  0026 

4. 0027 

4.  0027 

4.  0028 

4.  0028  :  4.  0029 

4.  0029 

4.  0029  \   4.  0030 

47 

50 

4.  0030 

4.0031 

4.0031 

\.  0032 

4.  0032 

4.0032    4.0033 

4-  0033 

4.  0034J  4.0034 
4.  0038  4.  0038 

2  48 

0 

4. 0035 

4-  0035 

4-  0035 

4.  0036 

4.  0036 

4.0037    4-0037 

4.  0038 

48 

10 

4-  0039 

4.  0039 

4.  0040 

4.  0040 

4.  0041 

4.  0041    4.  0041 

4.  0042 

4. 0042  \   4.  0043 

48 

20 

4.  0043 

4.0044 

4.0044 

4. 0045 

4.  0045 

4.  0045  1  4.  0046 

4.  0046 

4.0047  ;  4.0047 

48 

30 

4.  0048 

4.  0048 

4.  0048 

4. 0049 

4.  0049 

4.  0050    4.  0050 

4-  005 1 

4. 005 1  1  4. 005 1 

48 

40 

4.  0052 

4.  0052 

4-  0053 

4-  0053 

4-  0054 

4.  0054    4.  0054 

4-  0055 

4.0055  4.0056 

48 

50 

4.  0056 

4.0057 

4.0057 

4.0057 

4.  0058 

4.  0058    4.  0059 

4-  0059 

4. 0060  4. 0060 

2  49 

0 

4.  0060 

4. 0061 

4.  0061 

4.0062 

4.  0062 

4.0063    4.0063 

4.  0003 

4. 0064 

4.  0064 

49 

10 

4.  0065 

4.  0065 

4.  0066 

4. 0066 

4. 0066 

4.  0067    4.  0067 

4.  0068 

4. 0068 

4.  0069 

49 

20 

4.  0069 

4.  0069 

4.  0070 

4.  0070 

4. 0071 

4.  0071  1  4.  0072 

4.  0072 

4. 0072 

4-  0073 

49 

30 

4-  0073 

4.  0074 

4.  0074 

4-  0074 

4-  0075 

4.  0075  4-  007b 

4.  0076 

4-  0077 

4. 0077 

49 

40 

4-  0077 

4.  0078 

4.  0078 

4.  0079 

4.  0079 

4.  0080  4.  0080 

4. 0080 

4.0081  4.0081  1 

49 

50 

4.  0082 

4.  0082 

4.  0083 

4.  0083 

4.  0083 

4.  0084  4.  0084 

4.  0085 

4. 0085  4. 0086  1 

TABLE  34.                   [Page  367 

V 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0' 

1^' 

r' 

3^' 

4// 

5'' 

6'^ 

^/, 

8^^ 

9'' 

0     /       // 

2   50    O 

4. 0086  ! 

4.  0086 

4. 0087 

4. 0087 

4.0088 

4. 0088 

4. 0089 

4. 0089 

4. 0089 

4. 0090 

50   10 

4.  0090 

4.  0091 

4.0091 

4. 0092 

4.  0092 

4. 0092 

4. 0093 

4.0093 

4.  0094  4- 0094 

50   20 

4.0095 

4.  0095 

4-  0095 

4. 0096 

4.  0096 

4- 0097 

4.0097 

4- 0097 

4.  0098  4. 0098 

50   30 

4. 0099 

4. 0099 

4.  OIOO 

4.0100 

4.  OIOO 

4.0101 

4.0101 

4.  0102 

4.0102  4.0103 

50   40 

4.0103 

4.0103 

4.0104 

4.0104 

4.0105 

4.0105 

4.0106 

4.  0106 

4.0106  4.0107 

50   50 

4.0107 

4.0108 

4.  0108 

4. 0109 

4.0109 

4.0109 

4.  Olio 

4.0110 

4.  OIU 

4.  on  I 
4.  01 15 

2510 

4.0111 

4.  0112 

4.0112 

4.0113 

4.0113 

4. 01 14 

4.  01 14 

4.0114 

4.0115 

51   10 

4.  0116 

4.  01 16 

4.0117 

4.0117 

4.0II7 

4.0118 

4.  0118 

4.  0119 

4.0119  4.0120 

51   20 

4.  0120 

4.0120 

4.  0I2I 

4.0x21 

4.0122 

4.0122 

4.0122 

4.0123 

4.0123  4.0124 

51   30 

4.  0124 

4.0125 

4.0125 

4-0125 

4.0126 

4.0126 

4.0127 

4.0127 

4.0128  4. 012S 

51   40 

4.  0128 

4.  0129 

4.0129 

4.0130 

4.0130 

4.  0130 

4.0131 

4.0131 

4.CI32  4.0132 

51   50 

4-0133 

4-0133 

4-0133 
4.0138 

4.0134 
4.0138 

4.0134 

4.0135 

4-0135 
4.0139 

4-0136 
4.  0140 

4.0136  4.0136 

2   52    0 

4-0137  1 

4-0137 

4.0138 

4.0139 

4.0140  4.0141 

52   10 

4.  0141 

4.0141 

4.  0142 

4. 0142 

4. 0143 

4-  0143 

4. 0144 

4.0144 

4.0144  4.0145 

52   20 

4.0145  ; 

4.0146 

4.  0146 

4. 0146 

4.0147 

4.0147 

4. 0148 

4.0148 

4.0149  4.0149 

52   30 

4.0149 

4.0150 

4.0150 

4.0151 

4.0151 

4.0152 

4.0152 

4-0153 

4.0153  4-0153 

52   40 

4.0154 

4.0154 

4-0154 

4-0155 

4-0155 

4.0156 

4.0156 

4-0157 

4.0157  4.0157 

52   50 

4.0158 

4.0158 
4.0162 

4.0159 

4-0159 

4.0159 

4.  0160 

4.  0160 
4.0164 

4.0161 

4.  0161 

4.  0162 
4.  0166 

2  53   0 

4.  0162 

4.0163 

4.0163 

4.0164 

4.  0164 

4.  0165 

4-  0165 

53  10 

4.  0166 

4.0167 

4.0167 

4.0167 

4. 0168 

4.0168 

4.  0169 

4.0169 

4.0169  4.0170 

53  20 

4.0170 

4.  01 71 

4.0171 

4.0172 

4.0172 

4.0172 

4-0173 

4-0173 

4.0174  4.0174 

53  30 

4.0175 

4-0175 

4-0175 

4.0176 

4.0176 

4.0177 

4.0177 

4.0177 

4.0178  4.0178 

53  40 

4.0179 

4-0179 

4.  0180 

4.0180 

4.0180 

4.0181 

4. 0I8I 

4.0182 

4.0182  4.0182 

53  50 

4.0183 

4-0183 

4.0184 

4.0184 

4.0185 
4.0189 

4.0185 

4.0185 

4.  0186 

4.0186  4.0187 

2  54   0 

4.0187  [ 

4.0187 

4.0188 

4.0188 

4.0189 

4. 0190 

4.  0190 

4.0190  4.0191 

54  10 

4-0191  ' 

4.0192 

4.0192 

4. 0192 

4.0193 

4-  0193 

4.0194 

4.0194 

4.0194  4-0195 

54  20 

4.0195 

4.0196 

4. 0196 

4.0197 

4.0197 

4.0197 

4.0198 

4.  0198 

4.0199  4.0199 

54  30 

4.0199 

4.  0200 

4. 0200 

4. 0201 

4.0201 

4.  0202 

4. 0202 

4.  0202 

4. 0203  4. 0203 

54  40 

4.  0204 

4.  0204 

4.  0204 

4. 0205 

4- 0205 

4.  0206 

4.  0206 

4.  0207 

4.  0207  4.  0207 

54  50 

4. 0208 

4.  0208 
4.  0212 

4. 0209 

4. 0209 

4. 0209 

4.0210 
4.0214 

4.  0210 

4.  021 1 

4.0211 

4.0211 
4.0216 

2  55   0 

4.0212 

4.0213 

4.0213 

4.0214 

4.  0214 

4.0215 

4-0215 

55  lo 

4.0216 

4.0216 

4.0217 

4.0217 

4.0218 

4.0218 

4.0219 

4.0219 

4.0219  4.0220 

55  20 

4.  0>20 

4.0221 

4.0221 

4.0221  4.0222 

4.  0222 

4.  0223 

4-  0223 

4.  0223  4.  0224 
4.  0228  4.  0228 

55  3" 

4.  0224 

4.  0225 

4-  0225 

4. 0225  4. 0226 

4.  0226 

4.0227 

4.0227 

55  40 

4.  0228 

4.  0229 

4.  0229 

4-  0230 

4-  0230 

4-  0230 

4.0231 

4.0231 

4.0232  4-0232 

55  50 

4- 0233 

4-  0233 
4-  0237 

4-  0233 
4-  0237 

4-  0234 

4.  0234 

4-  0235 
4.  0239 

4-  0235 

4- 0235 

4. 0236  4. 0236 

2  56   0 

4.0237 

4- 0238 

4.  0238 

4-  0239 

4.  0240 

4.  0240  4.  0240 

56  10 

4. 0241 

4.0241 

4.  0242 

4.  0242 

4. 0242 

4-  0243 

4.  0243 

4.0244 

4.  0244  4. 0244 

56  20 

4.  0245 

4- 0245 

4.  0246 

4.  0246  '  4.  0246 

4. 0247 

4- 0247 

4. 0248 

4.  0248  4.  0249 

56  30 

4.  0249 

4.  0249 

4.0250  4.0250  1  4.  0251 

4.0251 

4.0251 

4- 0252 

4.  0252  4.  0253 

56  40 

4-  0253 

4.  0253 

4.0254  4-0254  4.0255 

4-  0255 

4.0256 

4-  0256 

4.0256  4.0257 

56  50 

4-0257 

4. 0258 

4.  0258  4.  0258 
4.0262  '  4.0262 

4.  0259 

4-  0259 
4.  0263 

4.  0260 

4. 0260 

4.  0260  4.  0261 

2  57   0 

4.  0261 

4. 0262 

4.  0263 

4. 0264 

4. 0264 

4.  0265   4.  0265 

57  10 

4.  0265 

4.  0266 

4.  0266  4.  0267 

4.  0267 

4.  0267 

4.  0268 

4.0268 

4.  0269  4.  0269 

57  20 

4.  0269 

4.0270 

4.0270  4.0271   4.0271 

4.0271 

4.0272 

4.0272 

4.0273  4-0273 

57  30 

4-0273 

4.  0274 

4.0274  4-0275 

4-0275 

4. 0276 

4.0276 

4.0276 

4.0277  4-0277 

57  40 

4.  0278 

4.0278 

4.0278  4.0279 

4.0279 

4.  0280 

4.  0280 

4. 0280 

4.0281   4.0281 

57  50 

4.  0282 

4. 0282 

4.  0282  4.  0283 

4.0283 
4. 0287 

4.  0284 
4.  0288 

4.  0284 
4. 0288 

4. 0284 

4.  0285   4.  0285 

2  58   0 

4. 0286 

4. 0286 

4.  0287  4.  0287 

4. 0289 

4.  0289  4.  0289 

58  10 

4. 0290 

4. 0290 

4.0291   4.  0291  !  4.0291 

4.  0292 

4. 0292 

4-  0293 

4.  0293   4.  0293 

58  20 

4.  0294 

4.0294  4-0295   4-0295   4-0295 

4. 0296 

4.  0296 

4- 0297 

4.0297  4-0297 

58  30 

4. 0298 

4. 0298  4.  0299 

4.  0299  4.  0300 

4. 0300 

4.  0300 

4.0301 

4.0301   4.0302 

58  40 

4-  0302 

4.  0302  4.  0303 

4-0303 

4. 0304 

4-0304 

4-  0304 

4-  0305 

4-  0305   4-  0306 

58  50 

4.  0306 

4.0306  4-0307 

i  4-0307 

4.  0308 

4.0308 

4.0308 

4. 0309 
4-0313 

4.0309  4.0310 

2  59   0 

4.0310 

4.0310  4.0311 

4-0311 

4.0312 

'   4-0312 

4.0312 

;  4.0313  4-0314 

59  10 

4.0314 

4.0314  4-0315 

4.0315   4.0316 

4.031b 

4.0317 

1  4-0317 

4.0317  4-0318 

59  20 

4.0318 

4-0319 

4.0319 

4.0319  4.0320 

4-  0320 

4.0321 

'  4-0321 

4.0321   4-0322 

59  30 

4-  0322 

4-  0323 

4.0323   4.0323  1  4.0324 

4.0324 

4-  0325 

4-  0325 

4.  0325  4.  0326 

59  40 

4. 0326 

4.  0327 

4-0327 

4.0327  4-0328 

4-  0328 

4- 0329 

4.  0329 

,   4-0329  4-0330 

59  50 

4.  0330 

4-  0331 

4-0331 

4-0331   4-0332 

4.  0332 

4-  0333 

4- 0333 

4-0333  4-0334 

page  368]                                                  TABLE  35. 

Table  showing  the  correction  required,  on  account  of  Second  Differences  of  the  Moon's  Motion, 
the  Greenwich  Time  corresponding  to  a  Corrected  Lunar  Distance. 

in  Finding 

Apyiroximate 
interval. 

2 

Difference  of  the  proportional  logarithms  in  the  Ephemeris. 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26      28 

30 

32 

34 

36 

h.  III. 

/i.  m. 

1 

S.     1     J. 

s.       s. 

s. 

s. 

s. 

s. 

J. 

s. 

s. 

s. 

s. 

s.         s. 

J. 

s. 

s. 

0     0 

3     0 

0  1    0 

0       0 

0 

0 

0 

0        0 

0 

0 

0 

0 

0        0 

0 

0 

0 

0    10 

2  50 

0       0 

0          I 

I 

I 

I 

I   1      I 

I 

1 

2 

2 

2            2 

2 

2 

2 

0  20 

"0  30 

0  40 

0  50 

1  0 
I     10 
I    20 
I    30 

//.  111. 

2  40 

0 

I       I 

I 

2 

2 

2 

2 

2 

3 

3 

3         3         4 

4 

4 

4 

1 

9 

2  30 
2  20 
2   10 

0 
0 

I 

I 

2 

2 
2 
2 

2 
2 
3 

2 

3 

3 

2 

3 
4 

3 
3 

4 
4 
5 
5 

5 

3 
4 

5 
5 
5 
6 
6 

3 
4 
5 

4 
S 
S 

4 
5 
6 

5 
6 
6 

i 

7 
8 
8 
9 
9 

i 

7 

6 

6 

7 
8 

2     0 

I   50 
I  40 

1   30 

h.  III. 

I 
I 

2 
2 
2 
2 

2 
2 

3 
3 

3 
3 

3 
4 
4 
4 

4 
4 
4 
4 

6 
6 
6 
6 

6 
6 

7 
7 

7 

7 

7 
8 

8 
8 

8 
9 
9 
9 

9 

9 

10 

10 

9 

ID 
10 
II 

.0 
II 
II 
II 

Difference  of  the  proportional  logarithms  in  the  Ephemeris.                                             1 

38 

40 

42 

J. 

44 

46 

48 

50 

52 

54 

56 

58 

60 

62 

64 

66 

68 

70 

s. 

s. 

s. 

s. 

J. 

J. 

s. 

J. 

J. 

J. 

J. 

s. 

J. 

J. 

s. 

s. 

0      0 

3     0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0    10 
0    20 

"    30 
0   40 

0  50 

1  0 
I     10 
I    20 
I    30 

h.  in. 

2  50 
2  40 

2  20 
2  10 

2     0 

I  50 
I  40 
I  30 

//.  III. 

2 

5 

7 
8 

9_ 

lO 

II 

12 
12 

I 

7 

9 

10 

3 
5 
7 
9 
10 

3 

5 

8 

10 

II 

3 
6 

8 
10 
12 

I 

3 
6 

i 

4 
7 

4 
7 

4 

7_ 

10 

13 
15 

4 

7 

t 

4 
8 

4 
8 

4 
8 

5 
9 

8 

ID 
12 

9 
II 

13 

9 
II 

13 

9 
12 

14 

10 
12 
14 

10 
13 
15 

II 

13 
16 

II 

14 
16 

12 

14 
16 

12 

IS 
17 

12 

15 
17 

II 
12 

12 
12 

12 
12 
13 
13 

12 

13 
14 
14 

13 
14 
14 
14 

13 
14 
15 
15 

14 
15 
15 
16 

14 

;i 

,6 

17 
17 

16 
17 
17 
18 

16 

17 
18 
18 

17 

18 

19 
19 

17 
18 

19 
19 

18 

19 

20 

20 

18 

19 
20 

21 

19 
20 
21 
21 

19 
21 
21 
22 

Difference  of  the  proportional  logarithms  in  the  Ephemeris. 

72 

u 

u 

IS 
s. 

80 

82 

84      86 

88 

90 

92 

94 

96 

98 

100 

102 

104 

s. 

s. 

s. 

J. 

s. 

s. 

.y. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

J-. 

0     0 
0   10 

0    20 
0    30 
0   40 

0  50 

1  0 
I     10 
1    20 
I    30 

h.  III. 

3     0 
2  50 
2  40 
2  30 
2  20 
2  10 
2     0 

I  50 
I  40 

I  30 

li.  III. 

O          0 

5       5 
9       9 

0 

5 
9 

li 

19 
21 

22 

23 
24 

0         0 

5        5 

10         ID 

0 

5 
10 

0 

6 

ID 

0 

6 
II 

0 

6 

II 

0 

6 

II 

0 

6 

II 

0 

6 

12 

0 

6 

12 

0 

6 

12 

0 

7 
12 

0 

7 

13 

0 

7 

13 

i8 

13 

16 
19 

14 
17 
20 

14 
17 

20 

14 
18 
21 

14 
18 
21 

15 
19 

22 

15 
19 
22 

16 

19 
22 

16 
20 
23 

16 

20 

23 

17 
21 

24 

17 
21 

24 

17 
22 

25 

18 
22 
26 

18 
22 
26 

20 
21 

22 

23 

21 

22 

23 
23 

22 

23 

24 

24 

22 
24 

25 

25 

23 
24 
25 

25 

23 

26 
26 

24 

25 
26 
27 

24 
26 

27 

27 

25 

27 

28 
28 

25 
27 
28 
29 

26 
28 
29 
29 

27 
28 

29 
30 

27 
29 
30 
31 

38 
30 
31 
31 

28 

30 
31 
32 

29 

31 
32 
32 

Difference  of  the  proportional  logarithms  in  the  Ephemeris.                                                 1 

106 

s. 

108  110  112 

114     116 

118 

120 

122    124 

126 

128     130 

132 

134 

136 

138 

s. 

J.    i    s. 

S.      1       J. 

J. 

s. 

s.         s. 

J. 

s. 

s. 

s. 

J. 

s.- 

s. 

0     0 
0   10 
0  20 
0  30 
0  40 

0  50 

1  0 
I    10 
I   20 
I   30 

3    0 
2  50 
2  40 
2  30" 
2  20 
2  10 
2    0 

I  SO 
1  40 

I  30 

o 

7 

13 

-i8 

23 

2b 

29 

31 
33 

0 

7 
13 

0       0 

7  '     7 
14  ,  14 

0 

7 

14 
20 

25 
29 

0 

8 

14 

0 

8 

15 

0 
8 

IS 

0 
8 

IS 

0 
8 

15 

0 

8 

IS 

0 

8 

16 

0 

8 

16 

0 

0 

■1 

0 

9 
17 

0 

9 
17 

19  1  19  1  19 

23  :  24     24 

27  ,  27     28 

20 

25 
29 

20 

25 

29. 

21 

26 
30 

21 

26 

30 

34 

3^ 
38 

38 

21 

27 
31 
34 
37 
38 
39 

22 

27 
31 

22 

28 
32 

22 

28 
32 
36 
38 
40 
40 

23 

28. 

33 
37 
39 
41 
41 

23 
29 
33 

37 
40 

41 
42 

24 
29 
34 

38 
40 

42 

42 

24 
30 
34 
38 
41 
42 

43 

30 
32 
33 

34 

30 
32 

34 

34 

31 

33 
34 

35 

31 
34 
35 

35 

32 

34 
35 
36 

3 
3 
3 

3 

3 
5 
6 
6 

33 
35 
37 

37 

3S 
37 
39 
39 

35 
38 

39 
40 

1  tie  correction  is  to  be  added  to  the  approximate 
decreasing.,  and  subtracted  when  they  are  increasi?ig. 


proportional  logarithms  in  the  Ephemeris  are 


TABLE  36. 

Page  369 

Fpr  finding  the  value  of  N  for  Correcting  Lunar  Distances  for  the  Compression  of  the  Earth.                 1 

Table  36 

A,  giving 

1st  part  of  N. 

Table  36  B,  giving  2d  part  of  N.                      1 

Moon's  declination. 

Star's  declination.                                    | 

A  pp. 
dist. 

App. 
dist. 

1 

1 

0° 

3°i6° 

9° 

12° 

15° 

18° 

21° 

24° 

27° 

30" 

0° 

3° 

6° 

9" 

12" 

15" 

18° 

21° 

24" 

21°  30°| 

0 

II 

II 

// 

// 

// 

II 

// 

II 

II 

II 

II 

0 

// 

// 

II 

II 

II 

II 

// 

II 

II 

II 

II 

20 

— 0    3   6 

10 

13 

16 

19 

22 

25 

28 

3?, 

20 

+0 

3 

7 

10 

14 

17 

20 

24     27 

30 

33 

22 

o!3 

6 

9 

12 

14 

17 

20 

23 

25 

28 

22 

0 

3 

b 

9 

13 

lb 

19 

22     25 

27     30 

24 

0    3 

5 

8 

II 

13 

16 

18 

21 

23 

25 

24 

0 

3 

6 

9 

12 

14 

17 

20 

23 

25     28 

26 

0    2 

5 

7 

10 

12 

14 

17 

19 

21 

23 

2b 

0 

3 

5 

8 

II 

13 

lb 

18 

21 

23     26 

2S 

0    2 

4 

7 

9 

II 

13 

15 

17 

19 

21 

28 

0 

3 

5 

8 

10 

12 

IS 

17 

20 

22     24 

1O 

— 0  ;  2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

30 

+0 

2 

5 

7 

9 

12 

H 

16 

18 

21     23 

,S2 

0 

2 

4 

6 

8 

9 

II 

13 

15 

lb 

18 

32 

0 

2 

4 

7 

9 

II 

13 

15 

17 

19     21 

S4 

0 

2 

4 

S 

7 

9 

10 

12 

H 

15 

17 

34 

0 

2 

4 

b 

8 

II 

13 

15 

lb 

18     20 

^,6 

0 

2 

3 

S 

7 

8 

10 

II 

13 

14 

16 

3(> 

0 

2 

4 

b 

8 

10 

12 

14 

lb 

17  i  19 

40 

0 

2 

3 

5 

6 

8 

9 

10 

12 

13 

14 

3« 

0 

2 

4 

6 

8 

10 

II 

13 

IS 

17  1  18 

-0  J1I3 

4 

6 

7 

8 

10 

11 

12      13 

40 

+0 

2 

4 

6 

7 

9 

II 

13 

14 

16  j  18 

42 

0  [  I 

3 

4 

5 

7 

8 

9 

10 

"      13 

42 

0 

2 

4 

5 

7 

9 

10 

12 

14 

IS    17 

44 

0 

2 

4 

■; 

6 

7 

8 

10 

II      12 

44 

0 

2 

3 

5 

7 

8 

10 

12 

13 

15     16 

4fa 

0 

2 

3 

s 

6 

7 

8 

9 

10 

II 

4b 

0 

2 

3 

5 

6 

8 

10 

II 

13 

14  1  16 

48 

0 

2 

3 

4 

5 

6 
^  6 

7 

8 

9 

10 

48 

0 

2 

3 

5 

6 

8 

9 

II 

12 

14 

15 

,So 

— 0 

2 

3 

4 

5 

7 

8 

9 

10 

50 

+0 

2 

3 

5 

6 

8 

9 

II 

12 

13 

15 

,S2 

0 

2 

3 

4 

5 

5 

6 

7 

8 

9 

52 

0 

2 

3       4 

6 

9 

10 

12 

13 

14 

S4 

0 

Ii2 

3 

3 

4 

5 

6 

7 

7 

8 

.S4 

0 

I      3       4 

6 

9 

10 

II 

13 

14 

sfe 

0 

2 

2 

3 

4 

S 

$ 

6 

7 

8 

5b 

0 

3       4 

b 

8 

10 

II 

12 

14 

^a 

0 

I 

2 

3 

4 

4 

5 

6 

6 

7 

5« 

0 

3  1    4 

b 

8 

10 

II 

12 

13 

60 

— 0 

I 

2 

3 

3 

4 

5 

5 

6 

7 

60 

+0 

3       4 

5 

8 

9 

II 

12 

13 

62 

0 

I     I 

2 

3 

3 

4 

4 

5 

5 

6 

b2 

0 

3       4 

5 

8 

9 

10 

12 

13 

64 

0 

2 

2 

3 

3 

4 

4 

S 

6 

64 

0 

3       4 

S 

8 

9 

10 

II 

13 

66 

0 

* 

2 

2 

3 

3 

4 

4 

5 

5 

66 

0 

3       4 

5 

6 

8 

9 

10 

II 

12 

68 

0 

0 

2 

2 

3 

3 

4 
3 

4 
4 

5 

68 

0 

3       4 

S 

b 

8 

9 

10 

II 

12 

70 

—  0 

0 

2 

2 

3 

3 

4 

70 

+0 

3       4 

5 

6 

7 

9 

10 

II 

12 

72 

0 

0 

2 

2 

2 

3 

3 

3 

4 

72 

0 

I      2       4 

S 

b 

7 

9     10 

II     12  1 

74 

0 

0 

2 

2 

2 

3 

3 

3 

74 

0 

1,2        4  '     5   I     6 

7 

8  1  10 

II 

12 

76 

0 

0 

I 

2 

2 

2 

3 

3 

7^ 
78 

0 

12       4,5       6 

7 

8       9 

II 

12 

78 

0 

0 

0 

I 

I 

2 

2 

2 

2 

0 

12415       6 

7 

8  !     9      II 

12 

80 

— 0 

0 

0 

I 

2 

2 

2 

80 

+0 

12       4-5       6 

7 

8 

9     10 

II 

82 

0 

0 

0     0 

I 

I 

I 

I 

2 

82 

0 

12456 

7 

8 

9     10     II  1 

84 

000;  0 

0 

I 

I 

I 

I 

X 

84 

0 

12456 

7 

8 

9     10     III 

86 

0 

0 jo;   0 

0 

0 

0 

I 

I 

I 

I 

86 

0 

12       456 

7 

8       9  >  10      II  1 

88 

0 

0 

0 

0 

0 

0 

0 

0 
0 

0 

0 

0 

88 

0 

y 

2 

~2~ 

4 

5 

b 

7 
7 

8       9  1  10     II  1 

90 

— 0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

90  f+o 

4 

5 

6 

8!    9' 

10  1  II 

02 

+0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

92 

0 

2        4 

5 

b 

7 

8 

9 

10  i  II 

94 

0 

00     0 

0 

0 

0 

I 

I 

I 

I 

94 

0 

2  •     4 

5 

b 

7 

8 

9 

10     II 

96 

0 

0  0 

0 

0 

_ 

I 

I 

I 

I 

I 

96 

0 

2        4 

5 

b 

7 

8 

9 

10     II 

98 

0 

0  0 

0 

I 

I 

I 

I 

2 

98 

0 

2        4 

5 

6 

7 

8 

9 

10     II 

100 

-f  0  '00 

, 

I 

I 

2 

2 

2 

100 

+0 

12           4    '       5 

6 

7 

8  ;    9 

10     II 

102 

000 

I 

2 

2 

2 

2 

102 

0 

12-4        5 

b 

7 

8       9 

II     12 

104 

0    |0     I 

2 

•  2 

2 

3 

3 

104 

0 

I        24:5 

6 

■7 

8 

9 

II     12 

106 

0 

0 

2 

2 

2 

3 

■    3 

3 

I  Ob 

0 

I        2          4 

5 

b 

7 

8 

10 

II     12 

108 

0 

0 

— 

2 
2 

1    2 

1    2 

3 

3 

3 

4 

108 

0 

2  1     4 

5 

6 

7 

9 

10 

II     12 

no 

+0 

0 

2 

3 

3 

3 

4 

4 

no 

+0     I 

3i    4 

5 

6 

7 

9 

10 

II  i  12 

112 

0    0 

2 

2 

3 

3 

4 

4  '     5 

112 

0      I  1  3  '     4 

5 

b 

8 

9     10     II  ;  12 

114 

0    ;  I 

I  1    2 

2 

3 

3 

4  '     4 

5       5 

114 

0      I 

3  1    4 

5 

b 

8 

9     10     II     12 

116 

0       I 

I  \    2 

2 

3 

-1 

4       4 

5       6 

116 

0      I 

3 

4 

5 

7 

8 

9     10     II     13 

118 

0       I 

2 

3 

3 

4 

4 

5 

5 

6 

118 
120 

0      I 

3 

4 

5 

7 

8 

9  1  10 

12 

13 

120 

+0    ll 

2 

3 

3 

4 

■  5 

5 

6 

7 

+0  >  I 

3 

4 

S 

7 

8 

9 

II 

12 

13 

122 

0       I 

2 

3 

4 

4 

5 

6 

6 

7 

122 

0      I 

3  1    4 

b 

7 

8 

10 

II 

12 

13 

124 

012'      2 

3 

4 

i    5 

5 

6 

,     7 

8 

124 

0      I 

3 

4 

b 

7 

8 

10 

II 

12     14 

126 

0123 

3 

4 

5 

:     6 

7 

'     7 

8 

126 

0      I 

3 

4 

b 

7 

9 

10 

II 

13   ;    14 

128 

0   ili2|     3 

4 

""4 

5 

5 

5 
6 

6 

7 

,     8 

I     9 

128 

0  ,  2 

3 

4 

b 

7 

9 

10 

12 

13 ;  14 

130 

j+O    '  I  '  2  '     3 

■  7 

8 

9 

10 

130 

+0     2 

3  •    5 

6 

8 

!    9 

II 

12 

13 

_1 

The  signs  in  the  o°  column  apply  to  all  the  numbers  in  the  same  line,  and  are  to  be  used  when  the  declination  is  North. 
Wken  the  declination  is  ^oiith  change  the  sign  -|   to  —  and  —  to  +. 

24    B 


Page  370]                                               TABLE  37. 

Log.  A  and  Log.  B. 

For  Corapating  the  Equation  of  Equal  Altitudes.  For  Noon,  A  —  ;  for  Midnight,  A4-;  for  Noon  or  Midnight, 

Argument  =  Elapsed  Time. 

BJ-. 

■a 

s 

0" 

1^ 

2h 

3" 

4h 

5h 

Log.  A. 

9-  4059 
•4059 
.4059 
.4059 

.4059 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A.   Log.  B. 

Log.  A.   Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B.  1 

VI. 

0 
I 

2 

3 

4 

9 
9' 

4059 
4059 
4059 
4059 
4059 

4059 
4059 
4059 
4059 
4059 

9- 

4072 
4072 

4073 

4073 
4074 

9- 

4034 

4034 

4033 
4032 

4031 

9- 

4109  '  9. 
4110 
4111 
4112 

4113 

3959 
3957 
3955 
3953 
3952 

9- 

4172 

4173 
4174 
4175 
4177 

9 
~9 

3828 

3825 
3822 
3820 
3817 

3814 
381 1 

3809 

3806 

3803 

9 

4260 
4261 
4263 

4265 
4266 

9 

3635 
3631 
3627 
3624 
3620 

9- 

4374 
4376 
4378 
4380 

4383 

9 

3369 
3364 
3358 
3353 
3348 

3343 
3337 
3332 
3327 
3321 

5 
6 

7 
8 

9 

9-  4059 
.4060 
.4060 
.4060 
.4060 

9 

4074  9 
4074 

4075 

4075  i 
4076 

4030 
4029 
4028 
4027 
4026 

9 

4113  9 
4114 

4115 
4116 

4117 

3950 
3948 
3946 
3944 
3943 

9 

4178 

4179 
4181 
4182 
4183 

9 

4268 
4270 
4272 
4273 
4275 

9 

3616 
3612 
3608 
3604 
3600 

9 

4385 
4387 
4389 
4391 
4393 
4396 
4398 
4xj.oo 
4402 
4405 

10 
II 

12 

13 
14 

9.  4060 
.4060 
.4060 
.4060 
.4060 

9 

4059 
4059 
4058 
4058 
4058 

9 

4076  9 

4077 

4077 

4078 

4078 

4025 
4024 
4023 
4022 
4021 

9 

4118  9 
4119 
4120 
412 1 
4121 

3941  9 

3939 

3937 

3935 

3933 

4184  :  9 

4186 

4187 

4188 

4190 

3800 
3797 
3794 
3792 
3789 

9 

4277 

4279 
4280 

4282 

4284 

9 

3596 
3592 
358S 
3584 
3580 

9 

9 

3316 
331 1 

3305 
3300 

3294 

'A 

17 
iS 

•9^ 
20 
21 
22 

23 

24 

"25 
26 

27 
28 

29 

9. 4060 
.4060 
.  4060 
.4061 
.4061 

9 

4058 
4058 
4057 
4057 
4057 

9 

4079  '  9 
4079 
4080 

4080  : 
4081 

4020 
4019 
4018 
4017 
4016 

9 

4122  9 

4123 
4124 

4125 
4126 

3931  1  9 

3929 

3927 

3925 

3923 

4191   9 

4193 
4194 

4195  , 
4197  ! 

3786 

3783 
3780 

3777 
3774 

9 

4286 
4288 
4289 
4291 

4293 

9 

3576 
3572 
3568 
3564 
3559 

9 

4407 
4409 
441 1 
4414 
4416 

9 

3289 
3283 
3278 
3272 
3266 

9.4061 
.4061 
.4061 
.4061 
.4061 

9. 4062 
.4062 
.4062 
.  4062 
.4062 

9 
9 

4057 
4056 
4056 
4056 
4055 
4055 
4055 
4054 
4054 
4054 

9 

4081  9 

4082 

4083 

4083 

4084 

4015 
4014 

4013 
4012 
4010 

9 

4127  9 

4128 

4129 

4130 
4131 

3921  9 

3919 

3917 

3915 

3913 

4198  9 

4199 
4201 
4202 
4204 

3771  9 
3768 

3765 
3762 

3759 

4295 
4297 

4299 
4300 
4302 

9 

•3555 
3551 
3547 
3542 

•3538 

9 

4418 
4420 
4423 
4425 
4427 

9 

3261 

3255 
3249 
3244 
3238 

9 

4084  9 

4085 

4086 

4086 

4087 

4009 
4008 
4007 
4006 
4004 

9 

4132  9 

4133 

4134 

4135 

4136 

39" 
3909 
3907 
3905 
•3903 

9 

4205  1  9 
4207 
4208 
4209 
421 1 

■3756 
3752 
•3749 
•3746 
•3743 

9 

•4304 
.4306 
.4308 
.4310 
•4312 

9 

•  3534 
•3530 

•  3525 
•^521 
•3516 

9 

4430 
4432 
4434 
4437 
•4439 

9 

•3232 

.3226 

3220 

•  3214 
.3208 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 
40 

41 

42 

43 
44 

9. 4062 
.4063 
.4063 
.4063 

^4063 

9.  4064 
.4064 
.4064 
.  4064 
.4065 

9.  4065 
.4065 
.4065 
.4066 
.  4066 

9 

4053 

4053 

4052 

4052 
4051 

9 

4087 
4088 
4089 
4089 
4090 

9 

4003 
4002 
4001 

3999 
3998 

9 

4137  9 

4138 

4139 
4140 

4141 

.3900 

•  3898 
.3896 

•  3894 
.3892 

9 

4212 
4214 

4215 

4217 

.4218 

9 

•3740 
•3737 
•3733 
•3730 

•  3727 

9 

•43H 
•4315 
•4317 

•4319 
.4321 

9 

•3512 
•3508 
•3503 
•3499 
•3494 

9 

.4441 

4444 
4446 
4448 
4451 

9 

•3203 
•3197 
■3191 
•3185 
•3178 

9 

4051 
4050 
4050 
4049 
4949 

9 

4091 
4091 
4092 

4093 
4093 

9 

3997 
3995 
3994 
3993 
3991 

9 

4142  9 
4144 

4145 
4146 

4147 

.3889 
.3887 
.3885 
.38S2 
.3880 

9 

4220 
4221 
4223 
4224 
4226 

9 

•3723 
.3720 

•  3717 

•3713 
.3710 

0 

•4323 
•4325 
•4327 
•4329 
•4331 

9 

•3490 

•  3485 
.3480 

•3476 

•3471 

9 

4453 
4456 
4458 
4460 

4463 

9 

.3172 
.3166 
■  3160 

•  3154 
.3148 

9 

4048 
4048 
4047 
4047 
4046 

9 

4094  9 

4095  1 

4095 
409G 

409/  ' 

3990 
3988 

3987 

■3985 

3984 

9 

4148  9 
4149 

4150 
4151 
4152 

.3878 

•3875 

3873 

3871 

3868 

9 

4227  ,  9 

4229 

4231 

4232 
4234  : 

•  3707 
•3703 
.3700 
.3696 

•■3693 

9 

•4333 
•4335 
•4337 
•4339 
•4341 

0 

•3467 
.3462 

•3457 
•3453 
•  3448 

9 

4465 
4468 
4470 

4473 
4475 

9 

•  3142 

•3135 
.3129 

•3123 
.3116 

45 
46 

47 
48 

49 

9.  4066 
.4067 
.4067 
.4067 
.4068 

9 

4045 

4045 
4044 

•  4043 
4043 

9 

4097 
4098 
4099 
4100 
4100 

9 

3982 
3981 
3979 
.3978 
3976 

9 

4154  9 

4155 

4156 

4157 

4158 

.3866 

•3863 
.3861 

•3859 
•3856 

9 

4235  1  9 
4237 
4238 
4240 

4242 

.3690 
.3686 
•3683 
.3679 
•3675 

9 

•4343 
•4345 
•4347 
•4349 
•4351 

9 

•3443 
•3438 
•3433 
•3429 
•3424 

9 

4477 
4480 
4482 
4485 
4487 

9 

3110 
3103 

3097 

3091 

.3084 

50 
51 
52 
53 
54 

9. 4068 

.4068 

4069 

.4069 

.  4069 

9 

.4042 
.4041 
.4041 
.  4040 
•4039 

9 

4101 
4102 
4103 
4103 
4104 

9 

•3975 
•3973 
•3972 
3970 
•3969 

9 

4159  9 
4161 
.4162 
4163 
4164 

•  3854 
•3851 

•  3849 
.3846 

•3843 

9 

•4243  1  9 

4245 
4246 

4248 

4250 

.3672 
.3668 

•3665 
.3661 

•3657 

9 

•4353 
•4355 

•4357 

4359 
.4361 

9 

•3419 
•34H 
•3409 
•  3404 
3399 

9 

4490 
4492 
4494 
4497 
4500 

9 

3078 

3071 
3064 

3058 

3051 

51 
56 

57 

58 

59 

9.4070  9 
.4070 
.4071 
.4071 
.4071 

.4038 
.4038 

•4037 
.4036 

•4035 

9 

4105  1  9 

4106 
.4107 
.4107 
.4108 

•3967 
•3965 
3964 
.3962 
.3960 

9 

4165  9 
.4167 
4168 
4169 
4170 

.3841 
•3838 
.3836 
.3833 
•3830 

9 

4251  1  9 

4253 

4255 

4256 

425S 

3654 

•3650 

3646 

3643 
3639 

9 

•4363 
4366 

4368 

4370 

4372 

9 

3394 

•3389 

3384 

3379 

•3374 

9 

4503 
4505 
4508 
4510 
4513 

9 

3044 
3038 

3031 
3024 
3017 

60 

9. 4072  ]  9 

•4034 

9 

.4109 

9 

•3959 

9 

•4172  9 

.3828 

9 

4260  9 

•3635 

9 

•4374 

9 

•3369 

9 

4515  9 

3010 

For 

TABLE  37.                   [Page  371 

Log.  A  and  Log.  B. 

Computing  the  Equation  of  Equal  Altitudes.  For  Noon,  A  —  •  for  Midnight,  A  + ;  for  Noon  or  Midnight,  B  +. 

Argument  =  Elapsed  Time. 

•a 

6'- 

^h 

8" 

O" 

io^ 

Uh 

Log.  A. 

9-4515 
.4518 

•4521 

•4523 
.4526 

Log.  B. 

Log.  .v.  Log.  B. 

Log.  A.  Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A.   Log.  B. 

III. 
0 

I 

2 

3 

4 

9 

3010 

3"03 
2996 
2989 
2982 

9- 

9 

4685 '9 

4688 

4691 
4694 
4697 

4701  9 

4704 

4707 
4710 

4713 

2530 

2520 
2511 
2502 
2492 

2483 

2473 
2463 

2454 
2444 

9 

4884  9 

4888 

4892 

4895 
4899 

1874 
1861 
1848 

1835 
1822 

9 
9 

5"5 
5119 
5123 
5127 
5132 

9.  0943 
.0925 
.0906 
.0887 
.0867 

9- 

9 

5379 
5384 
5389 
5393 
5398 

8 

9509 

9478 

9447 
9416 

9384 

9352 
9320 

9287 

9254 
9221 

9 

5680  8 

5685 
5691 
5696 

5701 

6837 
6770 
6701 
6632 
6560 

5 
6 

7 
S 

9 

9.  4528 

•4531 
•4534 
•4536 
•  4539 

9 

2975 
2968 

2961 

2954 

2947 

9 

4902  9 

4906 

4910 

4913 

4917 

1809 
1796 
1782 
1769 
1756 

5136 
5140 

5144 
5148 
5153 

5157 
5161 
5165 
5169 
5174 

9.  0848 
.0828 
.0809 
.0789 
.0769 

5403  '   8 

5408 

5412 

5417 
5422 

Q 

5707  8 

5712 

5718 

5723 
5728 

6488 
6414 

6339 
6262 

6183 

lO 

11 

12 

'3 
14 

9- 4542 
•4544 

•4547 
•4550 
■4552 

9^4555 

•455^ 
.4561 

•4563 
.  4566 

9-  4569 
•4572 

•4574 
•4577 
.4580 

9 

2940 

2932 
2925 
2918 
291 1 

9 
9- 

4716 

4719 
4723 

4726 

4729 
4732 
4735 

4738 
4742 
4745 
4748 

4751 

4755 
4758 
4761 

9- 
9- 

2434 

2425 
2415 

2-405 
2395 
2385 
2375 
2365 
2355 
2344 

9 
9 

4921 

4924 
4928 

4932 

4935 

4939 

4943 
4946 
4950 
4954 

4958 
4961 

4965 
4969 

4973 

9 

1742 
1728 

1715 
1 701 

1687 

9 

9.  0749 
.0729 
.0708 
.0688 
.0667 

9- 

5427  '  8 
5432 
5436 
5441 
5446  ' 

9187 

9153 
9118 
9083 
9048 

9 

5734  8 

5739 

5745 

5750 

5756 

6103 
6021 
5937 
5852 
5764 

'5  ! 

i6 

17 

iS 

19 

9- 

2903 
2896 
2888 
2S81 

2873 

9 

1673 

1659 

1645 
1630 

1616 

9- 

5 1 78  9. 0646 
5182   .0625 
5186   .0604 

5191   •0583 
5195   .0561 

9- 

5451 
5456 
5461 
5466 

5470 

8 

9013 
8977 
8940 
8903 
8866 

9 

5761   8 

5767 

5772 

5778 

5783 

5674 

5583 
5488 

5392 

5293 

20 
21 
22 

23 

24 

9- 

2866 

2858 
2850 

2843 
2835 

9- 

9- 

2334 

2324 

2313 

2303 
2292 

9 

9 
'9 

1602 

1587 
1573 
1558 
1543 
1528 

1513 
1498 

1483 
1468 

9- 

5199  !  9.0540 
5204     .0518 
5208     .  0496 
5212  ^    .0474 
5217     .0452 

9 

5475 
5480 

5485 
5490 
5495 

8 

8829 
8791 

8752 
8713 
8674 

9 

5789  1  8 
5794 
5800 
5806 
581 1 

5192 
5088 
4981 
4871 
4758 

25 
26 

27 
28 
29 

9-  4583 

•4585 
.4588 
.4591 

•4594 

9 
9 

2S27 
2819 
2812 
2804 
2796 
2788 
2780 
2772 
2764 
2756 

9 
9 

4764 
4768 
4771 
4774 
477S 

9 

2282 
2271 
2261 

2250 
2239 

9 

4977 
4980 

4984 
4988 

4992 

9 

5221  i  9.0429 
5225     .  0406 
5230     .  0383 
5234     •  0360 
5238     . 0337 

9 

5500 

5505 
5510 

5515 
5520 

8 

8634 
8594 

8553 
8512 

8470 

9 

5817  1  8 

5822 

5828 

5834 

5839 

4641 
4521 

4397 
4270 

4138 

30 
31 
32 

33 

34 

9-  4597 
.  4600 
.  4602 
.4605 
.4608 

4781 

4784 
4788 

4791 
4794 

9 
9 

2228 
2217 
2206 

2195 
2184 

2173 
2162 
2151 
2140 

2128 

9 

4996  9 
5000 
5003 
5007 
501 1 

1453 
1437 
1422 
1406 
1390 

9 

5243    9-0314 
5247     . 0290 
5252     .  0266 
5256     .  0242 

5261  :  .0218 

9 

5525  ^  8 

5530 

5535 

5540 

5545 

8427 
8384 

8341 
8297 

8253 

9 

5845  :   8 

5851 
5856 
5862 
5868 

4001 
3860 

3713 
3561 
3403 

35 
36 
37 
38 
39 

9. 461 1 

.4614 
.4617 
.  4620 
.4622 
9.  4625 
.4628 
.4631 
•4634 
•4637 

9 

2747 

2739 

2731 
2723 
2714 

9 

4798 
4801 
4804 
4808 
481 1 

9 

5015 
5019 

5023 
5027 

5031 

9 

1375 
1359 

1343 
1327 

1310 

9 
9 

5265 
5269 

5274 
5278 
5283 
5287 
5292 
5296 
5301 
5305 

9.  0194 
.  0169 
.0144 
.0119 
.0094 

9 

5550 
5555 
5560 

5565 
5570 

5576 
5581 
5586 

5591 
5596 

8 

8208 
8162 
8115 
8068 
8020 

9 

5874 
5879 
5885 
5891 
5897 

8 

3239 
3067 
2888 
2701 

2505 

40 

41 

42 
43 
44 

9 

2706 
2698 
2689 
26S1 
2672 

9 

4815 
4818 

4821 

482s 
4828 

9 

2117 
2105 
2094 
2082 
2070 

9 

5035 
5038 
5042 
4046 

5050 

9 

1294 
1278 
1261 
1244 
1228 

9. 0069 
.0043 
.0017 

8.9991 
•9965 

9 
9 

8 

7972 
7923 

7873 
7823 

7772 

9 

5902 
5908 

59'4 
5920 
5926 

8 

2299 

2082 

1853 
1611 

1354 

45 
46 

47 
48 

49 

9.  4640 

•4643 
.4646 
.4649 
.4652 

9 

2664 

2655 
2646 
2638 
2629 

9 

9 
9 
9 

4832 

4835 
4839 
4842 
4846 
4849 

4853 
4856 
.4860 
4863 
.4867 
.  4870 
•4874 
.4877 
.4881 

.4884 

9 

2059 
2047 

2035 
2023 
201 1 

9 

5054  9 

5058 

5062 

5066 

5070 

1211 

1 194 
1177 

•"59 
1 142 

9 

5310  8.9938 

5315   •99" 
5319   .  9884 

5324   -9857 
5328   .  9830 

5601 
5606 
5612 

5617 
5622 

8 

7720 

7668 

.7614 

7560 

7505 

9 

5931 
5937 
5943 
5949 
5955 

8 
7 

1080 
0786 
0470 
0128 
9756 

50 
51 
52 

53 

54  1 

9^  4655 
.4658 
.  466 1 
.  4664 
.4667 

9 

2620 
2611 

2602 

•2593 
.2584 

9 

1999 
1987 

1974 
.  1962 

1950 

9 

5074  9 
5078 

.  5082 

. 5086 : 
•  5091 

1125 
.  1 107 

1089 
.  1072 
•  1054 

9 

5333  8.9802 
5337  :  -9774 
5342   . 9745 
5347   -9717 
5351   .9688 

9 

5627 
5632 
5638 

5643 
5648 

8 

7449 
•7392 

7335 
7276 

7217 

9 

5961 
5967 
5973 
5979 
5985 

7 

9348 
8897 
8391 
7817 

7154 

It 

59 
60 

9.4670  9 

•4673 
.4676 
.4679 
.4682 

•2575 

•  2566 

•2557 

•  2548 
•2539 

•  2530 

9 

9 

•  1937 

1925 

1912 

.  1900 

.  1887 

.1874 

9 
9 

•5095 
•  5099 

■5103 
5107 

.5111 
•5115 

9 

.1036 
.  1017 
.0999 
.  0981 
.  0962 

9 

5356 
5361 
5365 
5370 
5375 
•5379 

8.  9659 
.9630 
.  9600 

•9570 
.9540 

9 

5654 
5659 
5664 
5669 

5675 

8 

7156 
7094 
.7032 
6968 
6903 

9 

5991 
5997 
6003 

6009 
6015 

7 
6 

6368 

5405 
4162 

2407 
9591 

9.  4685 

9 

9 

■0943 

9 

8.9509 

9 

.5680 

8.6837 

9. 6021    /n/.      1 

Page  372]                                                TABLE  37. 

Log.  A  and  Log,  B. 

For  Computing  the  Equation  of  Equal  Altitudes.    For  Noon,  A  -  ;  for  Midnight,  A  + ;  for  Noon  or  Midnight,  B  -. 

Argument  =  Elapsed  Time. 

13 
B)  a> 

111. 
0 

I 

2 

3 
4 

12^          1 

13h 

14h 

15" 

16" 

n"           II 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

9.  6021 
. 6027 ' 

•  6033 : 

•  6039 

•  6045 

In/. 
6.  9603 

7-2431 
.4198 

■5453 

9.  6406 
.  6412 
.6419 
.6426 
•6433 

'  8.  7563 
.7641 
•7718 

•7794 
.  7S68 

9.  6841 
.6848 
.6856 
.6864 
.6872 

9 

.0971 
.  1014 

•1057 
.  1099 

.  1141 

9 

■  7333  i  9 
•  7342 

•7351 
.7360 

•7369 

.3162 

•3194 
•3225 

•325^5 
.3287 

9-  7895 
•7905 
•  7915 
■7925 
•7935 

9 
9 

.48S4 
.4911 
•4937 
•4963 
.4990 

•  5016 
.5042 
.5068 

•  5094 
.5120 

.5146' 
.5171 
•5197 
•5223 

•  5248 

9-  8539 
.8550 

.8562 

•8573 
.8585 

9-  8597 
.8608 
.8620 
.8632 
.8644 

9-  8655 
.8667 
.8679 
.8691 
.8703 

9.6383 
.6407 
.6431 

-6455 
.6478 

9.  6502 

6526 

-6550 

-6573 
.6597 

9.  6621 
.  6644 
.6668 
.  6691 

•6715 

1 

7 
8 

9 

9.6051  j 
.6057 
.  6063 
.  6069 
.6075 

7.  6428 
.  7226 
.7902 
.8488 
.9005 

9.  6440   8.  7942 
.6447     .8015 
. 6454     . 8087 
.6461 :    .8158 
.6467     .8227 

9.  6879  i   9 
. 6887 ' 

•  6895 

•  6903 
.6911 

•  1 183 
.  1224 

•  1265 
1306 

•1347 

•7378 
.7386 

•7395 

•  7404 
•7413 
.7422 

•7431 

.7440 

•  7449 
•7458 

9 
"9 

•3319 

•3350 
•3380 
■341 1 

•3442 

•3472 
•3503 
•3533 
•3563 
•3593 

9-  7945 

•7955 
.7965 

•7975 
.7986 

10 
II 
12 

13 
14 

9. 6082 
.6088 
.  6094 
.  6100 
.6106 

7.  9469 
.9889 

§.  0273 
.  0627 
•0955 

9.  6474  i  8.  8296 
. 6481  f    .  8364 
.6488,    .8432 
.  6495     .  8498 
.  6502     .  8564 

9.6509  8.8628 
.6516,    .8692 
•  6523     . 8756 
.6530     .8818 
.  6538     . 8880 

9.6919 
.  6926 

•  6934 
.6942 
.6950 

9 

•1387 
1428 
1468 
1507 
1547 

9 

9.  7996 
.  8006 
.8016 
.8027 
.8037 

9 

15 

16 

17 
18 

19 

9. 6112  < 
.6119 
■  6125 
.6131 

•  6137 

3.  1260 

•1547 
.  1816 
.  2071 
.2312 

9.  6958 
.6966 
.6974 
.6982 
.  6990 

9 

1586 
1625 
1664 
1703 
1 741 

9 

.7467 
.7476 
•7485 
•7494 
7503 

9 
9 

•3623 
•3653 
3683 
•3713 
•3742 

3772 
3801 

3831 
3860 

3889 

9.  8047 
.8058 
.8068 
.8078 
.8089 

9.  S099 
.8110 
.8120 
•  8131 
.8141 

9 

.5274 
•5300 
•5325 
•5351 
•5376 

9^8715 
.8727 

•8739 
•8751 
.8763 

9^6738 
.6762 

-6785 
.  6809 
.6832    , 

20 
21 

22 

23 
24 

9.6144  !  < 
.6150 
.6156 
.6163 
.6169 

i.  2541 

•2759 
.2967 
.3166 
•3357 

9.  6545   8.  8941 
. 6552 :    . 9002 
•  6559     . 9062 
.6566:    .9121 
.65731    -9180 

9.  6998 
.  7006 
.7014 
.  7022 
.7030 

9 

1779 
1817 

1855 

1S93 
1930 

1967 
2004 
2041 
2078 
2114 

9 
9 

7512 
7522 
7531 
7540 
7549 
7558 
7568 
7577 
7586 

7595 
7605 
7614 
7624 

7633 
7642 

9 

.5401 

•5427 

5452 

5477 

5502 

9-8775 
.8787 
.8799 
.8812 
.8824 

9.  6856 

.6879 
.6903 
.6926 
-6949 

25 
26 

27 
28 

29 

9.6175    { 
.6182 
.  6188 
.6194I 
.  6201 

i-  3540 

■3717 
.3887 
.4051 
.4210 

9.  6580  ^  8.  9238 
.  6588     . 9295 

•6595!    -9352 
.  6602     . 9408 
.  6609     .  9464 

9.  7038 
.7047 

•7055 
.7063 
.7071 

9 

• 

9 
~9 

3918 
3947 
3976 
4005 

4033 
4062 
4090 
4119 
4147 
4175 

9.8152 
.8162 

•8173 
.8184 

.8194 

9.  8205 

.8216 

.8227 

.8237 

.8248 

9 
9 

5528 

5553 
5578 
5603 
5628 

5653 
5677 
5702 

5727 
5752 

9.8836 
.S84S 
.8861 

•  8873 
.8885 

9.  8898 
.  8910 
.8923 

•8935 
.8948 

9.  6973 
.  6996 
.7019 

•  7043 
.  7066 

9.  7089 

.  7112 

-7136     i 

-7159 
.  7182 

30 
31 
32 
33 
34 

9. 6207   { 
.  6214 
.  6220 
.6226 
.6233 

M363 

•4512 

•4657I 
•4796; 
•  4932 1 

9.  6616   8.  9519   ( 
.6624     .9573 
.6631  i    .9627 
.  6638      . 9681 
•  6645      . 9734 

?•  7079 
.  7088 
.7096 
.7104 
.  7112 

9- 

2150 
2186 
2222 
2258 
2293 

9 

36 
37 
38 
39 

9.6239   i 
.  6246 
.6252 
.  6259  ! 
.6265 

i.  5064 1 
.5192 
•5318 
■5440 
•5559 

9.6653   8.9"787   ( 
. 6660 '    . 9839 
.6667     .9891 
■  6675  .    . 9942 
.  6682  1    .  9993 

).  712I 
.7129 

•7137 
.7146 
•7154 

9- 

2329 
2364 

2399 
2434 
2468 

9 

7652  ' 

7661 

7671 

7680 

7690 

9 

4204 

4232 
4260 
4288 
4316 

4343 
4371 
4399 
4426 

4454 

4481 

4509 

4536 

4563 

4590 

4617 

4644 

4671  ! 

4698 

4725 

4752 

4778, 

4805  ' 

4831  1 
4858  1 
4884  j 

Q.  8259 

'.8270 

.8281 

.8292 

•8303 

9^83i4 
.8325 
•8336 

.8347 
.8358 

9 

5777 
5801 
5826 

5850 
5875 

9.  8961     !    9.  7205 
•8973     t        -7228 

.8986  ;     .7251 

•  8999        •  7275 
.9011        .7298 

40 
41 

42 
43 
44 

9.  6272    i 
.6279 
.6285 
.  6292 
. 6298 , 

5- 5675   < 
.5788 

■5899 
.  6008 
.6114 

9.  6690   9.  0043   < 
.6697     . 0093 
.  6704     .  0142 
.6712     . 0191 
.  6719     . 0240 

^  7162 
.7171 

.7179 

.7187 
.7196 

9- 

2503 
2537 
2571 
2605 
2639 

9. 

7699     9 

7709 

7718 

772S 
7738  ,     . 

9 

5900 

5924 
5948 
5973 
5997 

9.  9024 

•9037 
.9050 

•9063 

•9075 

9-  7321 
-7344 
-7367 
-7390 
•7413 

45 
46 

47 

48 

49 

9.6305    f 
•  63 1 1 
.6318 
•6325 
•6331 

L6218  ( 
.6320 
.6419 
.6517 
•  6613 

9.6727   9.0288   ( 
•  6734     • 0336 

.  6742  ;      .  0384 
.67491      .0431 
.6757!      .0478 

^  7204 1  9. 

•  7213'    • 
.  7221 

•  7230     . 

•  7238     . 

2673 
2706 

2740 

2773 
2806 

9- 

7747  ' 
7757 
7767 
7776 

7786 

9- 
9- 

9.  8369 
.8380 
.8391 
.8402 
.8414 

9.  8425 
•  8436 

■8447  I 
.8459 
.  8470 
9.  8481  j 

•8493  t 
.8504 

.8516 

.8527 

9-  8539 

9- 

6022 
6046 
6070 
6094 
6119 

9.  9088 
.9101 
.9114 
.9127 
.9140 

9-  7436 
-7459 
-7482 

•7505 
•7529 

50 
51 

52 
53 
54 

9.6338    J 
•6345 
•6351 

.6358 

•6365 

i.  6707 

■6799 
.6890 
.6979 
•7067 

9.  6764  1  9.  0524     ( 
.6772         .0570 
.6779         .0616 
.  6787         .  0662 
.  6795   ,      .  0707 

?•  7247 
•7256 

•  7264 

•  7273 
.7281 

9- 
9- 
9- 

2839 
2872 
2905 

2937 
2970 

3002 

3034 
3066  ■ 

3098 
31.30 

9- 
9- 

7796 
7806 

7815 
7825 
7835 

9- 
9- 
9- 

6143 
6167 

6191 

6215 

6239 

6263 

6287 

63 II 

6335 
6359 

9^9154 
.9167 
.  9180 

-9193 
.  9206 

9.  9220 

•9233 
.9246 
.  9260 

-9273 

9-  7552 
•7575 
•7598 
.  7621 
.7644 

9.  7667 
.7690 

■7713 
-7736 
•7759 

11 
11 

59 

9.6372    i 
.6378 

■  6385 
.6392 

•6399 

^•7153 
•7237 
•  7321 
.7402 

•7483 

9.  6802 

.  68 10 

.6818 
.6825 
•6833 

9.0752   < 
.  0796 
.  0840 1 
.  0884 
.  0928 

5. 7290 
.7299 

■7307 
•  7316 

-7324 

7845  1  9- 
7855  ,     • 
7865  :     . 

7875       • 
7885       . 

60 

9.  6406   i 

i-  7563 

9.  6841 

9.0971    ( 

?•  7333 

3162  1 

9- 

7895  ;  9- 

6383 

9. 9287 

9-  7782 

* 

TABLE  37. 

[Page  373  | 

% 

Log.  A  and  Log.  B. 

For  Computing  the  1 

Equation  of 

Equal 

Altitudes.  For  Noon,  A  —  ; 

for  Midni 

-ht,  A+; 

for  Noon 

or  Midnight,  B  — .  | 

Argument  = 

Elapsed  Time. 

T3 

3"^ 

IS'' 

id"" 

20^ 

21" 

22'^ 

23''     1 

Log.  A. 

Log.  H. 

Log.  A.  L 

•og.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

0.  7652 

0 

9.  9287  i  9-  7782 

0.0172  19 

.9167 

0.  1249 

0.0625 

0.  2623 

0.  2279 

0.  4523 

0.4372 

0.  7689 

I 

.9300 

.7804 

.018S 

.9190 

.  1269 

.  0650 

.2649 

.2309 

.4562 

.4414 

-7765 

•7729 

2 

■93Hi 

.7827 

.0204 

.9213 

.  1290 

.  0676 

.  2676 

•2339 

.4601 

•4455 

.7842 

.7807 

3 

■9327 

.7S50 

.  0221 

•9237 

.1310 

.0701 

.  2702 

.2370 

.  4640 

•4497 

.7920 

.7886 

4 

•  9341 

•7S73 

.0237 

.  9260 

•1330 

.0727 

^  •  -7^29 

.  2401 

.4680 

.4540 

.  8000 

•  7967^ 
0.  8049 

5 

9-  9355 

9 

.7896 

0.0253  9 

.9284: 

o-  1351 

0.0753 

0.  2756 

0.2431 

0. 4720 

0. 4582 

Q.8081' 

6 

.9368 

7919 

.0270 

•9307 

•I371 

.0779 

.2783 

.  2462 

.4761 

.4625 

.8163 

•8133 

7 

•9382 

7942 

.0286 

•9331 

•1392 

.0805 

.  2810 

•  2493 

.4801 

.4668 

.8247 

.8218 

8 

•9396 

7965 

•0303 

9355 

.  I412 

.  0830 

•2838 

.2524 

.4842 

.4711 

8333 

•8305 

_9_ 

*•  941 0 

7988 

.0319 

9378 

•1433 

.0856 

•2865 

.2556 

.4884 

-4755 

8420 

•8393 
X  8483 

lO 

9. 9424 

? 

80U 

0.0336  9 

9402 

0.  1454 

0. 0S82 

0.  2893 

0.  2587 

0. 4926 

0. 4799 

0/8508' 

II 

•9437 

8034 

•0353 

9426 

•1475 

.  0909 

.  2921 

.  2619 

.4968 

.4844 

•8599 

■  8574 

12 

•9451 

8057 

.0370 

9449 

.1496 

•0935 

.2949 

.  2650 

•  5010 

.4889 

.8691 

.8667 

13 

.9465 

8080 

•  03S6 

9473 

.1517 

.  0961 

•2977 

.  2682 

-5053 

.4934 

.8786 

.8763 

14 

^9479 

8103 

•  0403 

9497 

•1538 

.0987 

•3005 

.2714 

•  5.097 

1  • 4980 

.8882 

.8860 

c.  8959 

15 

9-  9493 

9 

8126 

0. 0420  ,  9 

9520 

o^  1559 

0.  1013 

o-  3034 

0. 2746 

3.5x40 

0.  5026 

o.'898o" 

i6 

.9508 

8149 

•  0437 

9544 

.1581 

.  1040 

•3063 

.2778 

.5184 

.5072 

.  9080 

.9060 

17 

.9522 

8172 

•  0454 

9568 

.  1602 

.  1066 

.3091 

.2811 

.5229 

.5118 

.9183 

9164 

i8 

•953^ 

8195 

.0472 

9592 

•  1623 

•  1093 

.3120 

.2843 

.5274 

•5165 

.9288 

,9270 

19 

•9550 

8218 

.  0489 

9616 

.  1645 

.1119 

•3i5o_ 

.2876 

•5319 

•5213 

-9396 

•9378_ 

20 

9-  9564 

9 

8241 

0.0506  9 

9640 

0.  1667 

0.  1 146 

0-3179 

0.  2909 

0.  5365 

0.  5261 

0.  9506 

0.  9489 

21 

•9579 

8264 

•0523 

9664 

.  1689 

•I173 

.3208 

.2942 

.5411 

-5309 

.9618 

.9603 

22 

■9593 

8287 

.0541 

9687 

.1711 

.  1200 

-3238 

•2975 

■5458 

.  5358 

•9734 

.9719 

23 

.9607 

8310 

•0558 

97" 

•  1733 

.  1226 

.3268 

.3008 

•5505 

.5407 

.9853 

•9839 

24 

.  9622 

S333 

.0576 

9735 

•  1755 

•  1253 
0.  1280 

.3298 
0.  3328 

.3041 

•5553 

•5457 
o^  5507 

•9975 
I.  0100 

.9961 
1.0087 

^5 

9.9636" 

9 

8356 

0-0593  9 

9760 

0.1777 

0.  3075 

0.  5601 

26 

.9651 

8379 

.0611 

9784 

.1799 

.1308 

-3359 

.3109 

.5649 

.5557 

.  0228 

.0216 

27 

.9665 

8402 

.  0628 

9808 

.1821 

•  1335 

•3389 

•3143 

.5698 

.5608 

•0361 

•0350 

28 

.  9680  } 

S425 

.0646 

9832 

.  1844 

•  1362 

-3420 

•3177 

.5748 

.  5660 

.0497 

.0487 

29 

•  9695 

8448 

.  0664 

9S56 
9880 

.  1867 
0. 1889 

•1389 
0.  141 7 

•3451 
0. 3482 

•  3211 
0-  3245 

-5798 

•5712 

.0638 

.0628 
1.0774 

30 

9.  9709 

9- 

8471" 

0.  0682  9 

0.  5848 

0.5764 

1.0783 

31 

.9724 

8494 

. 0700  . 

9904 

.  I9I2 

•  1444 

••3514 

.3280 

•5899 

-5817 

•0934 
.  1089 

•  0925 

32 

•  9739  • 

8517 

.0718  . 

9929 

•  1935 

.1472 

•3545 

•3315 

-5951 

.5871 

.  1081 

33 

•9754 

8540 

•  0736  . 

9953 

•  1958 

•  1499 

•3577 

•3350 

.  6003 

-5925 

.  1250 

.  1242 

34 

^9769. 

8563 

_-?75_4  . 

9977^ 

.  I98I 

•1527 

.3609 

•  3385 

.6056 

_ : 5979 

.  1416 

.1409 

35" 

9.  9784 

9- 

8586 

0.  0772  0. 

0002 

0.  2004 

o-  1555 

0.  3641 

0.  3420 

0.  61 10 

0.  6034 

I.  1590 

I-  1583 

36 

.9798 

8609 

.0790  . 

0026 

.  2028 

.1582 

-3674 

•  3456 

.  6164 

.  6090 

.1770 

.1764 

37 

.9813 

8632 

.  0809 

0051 

.2051 

.  1610 

.3706 

•  3491 

.6218 

.6147 

•1958 

.1952 

38 

.9829 

8655 

. 0827  . 

0075 

•  2075 

.1638 

•3739 

•3527 

.6273 

.  6204 

.2154 

.2149 

39 

.9844 
9.  9859 

9- 

8678 

■  0845   • 

0100 

.  2098 

.  1667 

•  3772 

•  3563 

.6329 

.6261 

•2359 

-2354 

40 

8701 

0.  0864  0. 

0124 

0.  2122 

0.  1695 

0.  3805 

0. 3599 

0. 6386 

0.  6319 

1^2573 

1.2569 

41 

•9^Z4 

8724 

.0883  . 

0149 

.  2146 

•  1723 

•3839 

•3636 

-6443 

.6378 

.2799 

•2795 

42 

. 9889   . 

8748 

.  0901 

0173 

.2170 

•1751 

•3873 

■3^73 

.6501 

.6438 

•3037 

•3033 

43 

.9904 

8771 

. 0920  '  . 

0198 

.2194 

.  1780 

•3907 

•3710 

.6560 

.6498 

.3288 

•3285 

44 

.9920 

8794 

•  0939  • 

0223 

.  2218 

.  1S08 

•3941 

•3747 

.  6619 

.^6559_^ 

•3554 

-3552 

45 

9-  9935 

9- 

8817^ 

0.  0958  0. 

0248 

0.  2243 

0.  1837 

o-  3975 

0.  3784 

0. 6679 

0.6621 

I  •3837 

1.383s 

46 

•9951 

8840 

. 0976  . 

0272 

.  2267 

.1866 

.4010 

.3822 

.6740 

.6684 

.4140 

.4138 

47 

.9966 

8863 

•0995.  • 

0297 

.  2292 

.1895 

•4045 

•3859 

.6802 

.6747 

.4465 

.4463 

48 

.9982 

, 

8887 

•  1015 

0322 

.2316 

.1924 

.4080 

-3897 

.6865 

.6811 

.4815 

.4814 

49 

.  9998 
0.0013 

8910 

•  1034  • 

0347 

■  2341 

•i953__ 

-  ^4115 

-3936 

.6928 

.6876 

.5196 

_^5195_ 

50 

9- 

8933 

0.1053  0. 

0372 

0.  2366 

0.  1982 

0. 4151 

0.  3974 

0.  6993 

0.  6942 

i^56i3 

I.  5612 

51 

.0029 

8956 

.  1072 

0397 

.2391 

.  2011 

.4187 

.4013 

.7058 

.  7008 

.6074 

.6073 

52 

.0044 

8980 

.  1092 

0422 

.2416 

.  2040 

.4223 

•  4052 

.7124 

.7076 

.6588 

.6587 

53 

.0060 

9003 

.  1 1  n  . 

0447 

.2442 

.2070 

.4260 

.4091 

.7191 

.7144 

.7171 

.7171 

54 

.0076 

9026 

.1131  . 

0473 

.2467 

.2099 

.4297 

.4130 

.7259 

.7214 

■  7844 

•7843 

55 

0.  0092 

9^ 

9050 

0.  1 1 50  0. 

0498 

0.  2493 

0.  2129 

o.  4334 

0.  4170 

0.  7328 

0.  7284 

1.8638 

1.8638 

56 

.0108  . 

9073 

.1170,  . 

0523 

.  2518 

•2159 

•4371 

.  4210 

•7398 

•7355 

.  9610 

.  9610 

57 

.01241  ■ 

9096 

.  1190  . 

0548 

•2544 

.2189 

.4408 

.4250 

.7469 

.7428 

2. 0863 

2. 0863 

58 

.  0140  . 

9120 

. 1209  . 

0574 

.2570 

.  2219 

.4446 

.4291 

•7541 

-7501 

.  2627 

.  2627 

59 

.0156 

9143 

.  1229  . 
0.  1249  0. 

0599 

.2596 

.2249 

•  4485 

•433- 

.  7615 
0.  7689 

-  7576 
0.  7052 

2.  5640 

2.  5640 

60 

0.0172 

1 

9167 

0625 

0.  2623 

0. 2279 

0.  4523 

0.4372 

/.;/. 

/«/. 

II 

1  Page  374]                                                  TABLE  38. 

.JL 

'a  2 
3 

0 

10 

20 

30 
40 

50 
60 

1 

Latitude. 

I 

2 
3 

0° 

5° 

10° 

15° 

20° 

25° 

30° 

35° 

40° 

45° 

50° 

55° 

60° 

65° 

W 

75° 

0 

no 

•4 

•4 
4 
5 
7 
9 

4 

•4 

5 
6 

9 

I 

•4 

i 

8 
.2 

•5 
.6 

•7 

I.O 

•5 
•7 
•9 

1-3 

1 

.6 

.8 

I.I 

•7 
1.0 

1-5 

.8 
1.2 

2-3 

1.0 
1.6 

1 

1.3 
2.6 

1.8 

2.9 

/ 

^ 

i 

/ 

0 
no 

0 

ID 
20 

30 
40 

50 
60 

10 

20 

30 
40 

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60 

15 
20 

30 
40 

50 
60 

105 
100 

3 
•3 

3 
4 
4 
6 

3 
3 

4 

i 

9 

3 
4 

8 

I 

3 

4 
6 

7 
2 

•4 

•5 

•7 

1.0 

•4 
.6 
.8 

1-3 

•5 

•7 

I.I 

.6 

•9 

1-5 

.8 
1.2 
2.4 

•9 
1.6 

1.2 

2.7 

1.8 

3-0 

105 

10 
20 

30 
40 

50 
60 

2 
2 

2 

2 
3 
3 

2 
2 

3 
3 
4 
6 

2 

3 
3 
4 
6 

9 

3 
3 
4 
6 
8 

I 

3 
4 

5 
7 
2 

•4 

:i 

•9 

•4 
1-3 

•5 

•7 

I.I 

2.1 

.6 

•9 
1-5 

.8 
I.I 

2.4 

I.I 

1.6 

1.6 

2.7 

2.9 

100 

15 

20 

30 
40 

60 

15 
20 

30 
40 

60 
20 

30 

40 

50 
60 

70 

95 
90 

2 

I 

I 
2 
2 
3 
3 

I 
2 
2 

3 
4 
6 

2 
2 

3 
4 
6 

9 

2 

3 
4 

•3 
•3 
•5 
•7 
I.I 

•3 
•4 
.6 

•9 

•4 

•5 
.8 

1-3 

• 

1.0 
2.1 

.6 
.8 

1-5 

.8 
I.I 

2.5 

I.I 

1.6 

1-7 
2.8 

3-0 

95 

15 

20 

30 
40 

50 
60 

0 
0 
0 
0 
0 
0 

0 

I 
I 
I 
2 
2 

I 
I 
2 
2 

3 
6 

I 

I 
2 

3 
4 

5 
I 

I 

2 

3 
5 
9 

.2 
•3 

.2 

•4 

.6 

I.I 

•3 
•5 
•9 

.4 

•7 
1.3 

.6 

1.0 
2.2 

.7 
1-5 

I.I 

2.7 

1.6 

3-0 

90 

20 

30 
40 

60 
70 

20 

30 

40 

50 
60 

70 

85 

I* 
I* 
I* 
I* 

2* 

3* 

I* 

0 

0 

0 

0 

0 

0 
0 
0 
I 
I 
2 

0 

I 
I 
2 

I 

0 
I 

2 
3 

5 

I 

"i» 

0 

I 
2 

I 

I 

I 
2 
3 
5 
9 

0 

I 

2 

3 

5 
2 

.1 

.2 

•4 

•7 

.2 

•4 

.6 

I.I 

•3 

•5 
•9 

•3 

•7 

1-3 

•5 
1.0 

2-3 

.:! 

1.0 

2.7 

1.6 

3-1 

85 

20 

30 
40 

50 
60 
70 

20 

30 

40 

50 
60 

70 

80 

2* 

2* 
2* 

3^^ 
4* 
6*^ 

2* 

2* 
2* 
2* 
2* 

3* 

I* 

I** 

I* 

I* 

0 

0 

I* 

0 

0 

I 
I 
2 

.0 
.1 
•3 

•5 
•9 

.0 

.2 
•4 

■7 

,1 

I.I 

.1 

•4 
•9 

.2 
.6 

1-3 

•4 
•9 

2.4 

•5 
1-5 

.1 

^5 

3-1 

80 

20 

30 
40 

50 
60 

70 

20 

30 
40 

60 
70 

75 

I 

3* 
3* 

4* 

4* 

3* 
3" 

3* 
3^ 
4* 
6* 

2* 
2* 
2* 
2* 
2* 
3* 

2* 
2* 
I* 
I* 
I* 
0 

2* 

I* 

1* 

0 

I 

2 

I* 

I* 
0 

I 

3 
6 

.1* 

.0 

.1 

•3 

•5 

1.2 

.i» 

.1 
.2 

•5 
•9 

.1* 

.1 
•4 
•7 

.0 
.2 

■5 
I.I 

.0 

.1 
.6 

1-3 

.2 
•9 

2-5 

•3 
1-5 

.6 
3-0 

1.2 

75 

20 

30 
40 

60 
70 

20 

30 

40 

50 
60 
70 



^  1 

"c  5 

70 

i 

-2  s 

4* 

4* 
5* 
6* 

9* 

I. 

4* 

4* 

4* 

5' 
6* 

2* 

3: 
3* 

t 
3* 
4* 
6* 

3* 
3* 
2* 

K 
3* 

3* 
2" 

2* 

2* 

I* 

I* 

3: 

2* 

I* 
0 

I 
2 

.2* 

.1* 

.0 

.1 

.2 

.6 

.2* 

.1* 

.1 

•3 

•5 
1.2 

.2* 

.0 

.2 

•4 

•9 

.2* 
.0 

•3 

•7 

.2* 
.1 

•5 
I..  I 

•    .2* 
.2 
.8 

.2* 
.6 
1-3 

.2* 
.8 
2.6 

.2* 
1-5 

.2* 
31 

70 

20 

30 
40 

50 
60 
70 

0° 

5° 

10° 

15° 

20° 

25° 

30° 

35° 

40° 

45° 

50° 

55° 

60° 

65° 

70° 

75° 

i 

'•5  d 

Latitude. 

'c2 

3 

, 


TABLE  39. 

Page  376 

% 

Amplitudes. 

•a 

3 
'♦J 

2 

0 

Declination. 

V 

3 

o°.o 

0°.5 

1°.0 

1°.5 

2°.0 

2°.5 

3°.0 

3°.5 

4°.0 

4°.5 

5°.0 

5°.5 

6°.0 

0 

0 

0 

0 

0 

0 

u 

0 

0 

0 

0 

0 

0 

0 

0 

0.0 

0-5 

1.0 

1-5 

2.0 

2.5 

3-0 

3-5 

4.0 

4-5 

5-0 

5-5 

6.0 

0 

lO 

0.  0 

0-5 

1.0 

1-5 

2.0 

2.5 

3-0 

3-5 

4.1 

4.6 

5.1 

5-6 

6.1 

10 

'5 

0.  0 

0.5 

1.0 

1-5 

2. 1 

2.6 

3-1 

3.6 

4.2 

4-7 

5-2 

5-7 

6.2 

15 

20 

0.0 

0.5 

1. 1 

1.6 

2. 1 

2.7 

3-2 

3-7 

4-3 

4.8 

5-3 

5.8 

6.4 

20 

25 

0.  0 

0-5 

1. 1 

1.6 

2.2 

2.8 

3-3 

3.« 

4.4 

S-o 

5-5 

6.0 

6.6 

25 

30 

0.0 

0.  6 

1.2 

1.7 

2.3 

2.9 

3-4 

4.0 

4.6 

S-2 

5.8 

6.3 

6.9 

30 

32 

0.0 

0.6 

1.2 

1.8 

2.4 

2.9 

3-5 

4.1 

4-7 

5-3 

5-9 

6.5 

7.0 

32 

34 

0.0 

0.6 

1.2 

1.8 

2.4 

3-0 

3-6 

4.2 

4.8 

5-4 

6.0 

6.6 

7.2 

34 

^^ 

0.  0 

0.6 

1.2 

1.8 

2.5 

3-1 

3-7 

4.3 

4.9 

5-6 

6.1 

6.8 

7-4 

36 

3^ 

0.0 

0.6 

1-3 

1.9 

2.5 

3-2 

3-8 

4.4 

5-1 

S-7 

6.3 

7.0 

7.6 

38 

40 

0.0 

0.7 

1-3 

2.0 

2.6 

3-3 

3-9 

4.6 

5-2 

5-9 

6.5 

7.2 

7.8 

40 

42 

0.0 

0.7 

1-3 

2.0 

2.7 

3-4 

4.0 

4-7 

5-4 

6.1 

6.7 

7.4 

8.0 

42 

44 

0.0 

0.7 

1.4 

2. 1 

2.8 

3.5 

4.2 

4.9 

S.6 

f-3 

6.9 

7.6 

8.3 

44 

4b 

0.  0 

0.7 

1.4 

2.2 

2.9 

3-b 

4-3 

5-0 

5-8 

6.5 

7.2 

^•9 

8.6 

46 

48 

0.0 

0.7 

1-5 

2.2 

3.0 

3-7 

4.5 

5-2 

6.0 

6.7 

7-5 

8.2 

9.0 

48 

50 

0.0 

0.8 

1-5 

2.3 

3.1 

3-9 

4.7 

5-4 

6.2 

7.0 

7.8 

8.6 

9-3 

50 

51 

0.0 

0.8 

1.6 

2.4 

3-2 

4.0 

4.8 

5-6 

6.4 

7.2 

8.0 

8.8 

9-5 

51 

52 

0.  0 

0.8 

1.6 

2.4 

3-3 

4.1 

4.9 

5-7 

('.5 

7-3 

8.1 

9.0 

9-7 

52 

53 

0.  0 

0.8 

1.6 

2-5 

3.3 

4.2 

5-0 

5.8 

0.7 

7.5 

^3 

9.2 

10.  0 

53 

54 

0.0 

0.9 

1-7 

2.5 

3.4 

4-3 

5-1 

6.0 

6.8 

7-7 

8.5 

9-4 

0.2 

54 

55 

0.0 

0.9 

1-7 

2.6 

3-5 

4-4 

5-2 

6.1 

7.0 

7-9 

8.7 

9.6 

10.5 

55 

5^ 

0.0 

0.9 

1.8 

2.7 

3-6 

4-5 

5-4 

6.3 

7.2 

8.1 

9.0 

9.9 

0.8 

50 

57 

0.0 

0.9 

1.8 

2.7 

3-7 

4.6 

5-5 

6.4 

7-4 

8.3 

9.2 

10. 1 

I.  I 

57 

58 

0.0 

0.9 

1-9 

2.8 

3.« 

4-7 

5-7 

6.6 

7.6 

8.5 

9.5 

0.4 

1.4 

58 

59 

0.0 

I.  0 

1.9 

2.9 

3-9 

4-9 

5-8 

6.8 

7.8 

8.8 

9.7 

0.7 

1.7 

59 

60 

0.0 

I.O 

2.0 

3-0 

4.0 

5-0 

6.0 

7.0 

8.0 

9.0 

10. 0 

II. 0 

12.  I 

60 

61 

0.0 

1. 0 

2.  I 

3-1 

4.1 

5-2 

6.2 

7.2 

8.3 

9.3 

0.3 

1.4 

2.5 

61 

62 

0.0 

I.  I 

2.  I 

3-2 

4-3 

5-3 

6.4 

7-5 

8.5 

9.6 

0.7 

1.8 

2.9 

62 

b3 

0.0 

I.  I 

2.  2 

3-3 

4-5 

5-5 

6.6 

7-7 

8.8 

9-9 

1. 1 

2.2 

3-4 

63 

64 

0.0 

1. 1 

2.3 

3-4 

4.6 

5-7 

6.9 

8.0 

9.2 

10.3 

1.5 

2.6 

3.9 

64 

65.0 

0.0 

1.2 

2.4 

3-5 

4.8 

5.9 

7-1 

!-3 

9.5 

10.7 

11.9 

13.  I 

14.4 

65.0 

5-5 

0.0 

1.2 

2.4 

3.t> 

4.8 

6.0 

7.2 

8.5 

9-7 

0.9 

2. 1 

3-4 

4.6 

5-5 

6.0 

0.0 

1.2 

2.5 

3-7 

4.9 

6.1 

7-4 

8.6 

9.9 

1. 1 

2.4 

3.(' 

4.9 

6.0 

b.5 

0.0 

I.  2 

2.5 

3-^ 

5-0 

^•3 

7.5 

8.8 

10.  I 

1-3 

2.6 

3.9 

5-2 

6.5 

7.0 

0.0 

1-3 

2.6 

3.« 

5- 1 

6.4 

7-7 

9.0 

0-3 

1.6 

2.9 

4.2 

5-5 

7.0 

67.5 

0.0 

1-3 

2.6 

3-9 

5-2 

6.5 

7-9 

9.2 

10.  s 

II. 8 

13.2 

14.5 

15-9 

67.5 

8.0 

0.0 

1-3 

2.7 

4.0 

5-3 

6.7 

8.0 

9-4 

0.7 

2. 1 

3-5 

4.8 

6.2 

8.0 

^•5 

0.0 

1.4 

2.7 

4.1 

5-4 

6.8 

8.2 

9.6 

1.0 

2.4 

3.8 

5-2 

6.6 

8.5 

9.0 

0.  0 

1.4 

2.8 

4.2 

5-5 

7.0 

8.4 

9.8 

1.2 

2.6 

4.1 

5-5 

7.0 

9.0 

9.5 

0.0 

1.4 

2.9 

4-3 

5-7 

7.2 

8.6 

10.  0 

1-5 

2.9 

4.4 

5-9 

7.4 

9.5 

70.0 

0.0 

I- 5 

2.9 

4.4 

5.8 

7-3 

8.8 

10.3 

II. 8 

13-3 

14.8 

16.3 

17.8 

70.0 

0-5 

0.0 

1-5 

3-0 

4-5 

6.0 

7-5 

9.0 

0.  5 

2, 1 

3-<> 

5- 1 

6.7 

8.2 

0.5 

I.  0 

0.0 

1-5 

3-1 

4.b 

6.2 

7-7 

9-3 

0.8 

2.4 

3-9 

5-5 

7-1 

8.7 

I.  0 

1-5 

0.0 

1.6 

3-2 

4-7 

6.3 

7-9 

9-5 

I.  I 

2.7 

4-3 

5.9 

7.8 

9.2 

1-5 

2.0 

0.  0 

1.6 

3-2 

4.9 

b-S 

8.1 

9.8 

1-4 

3-0 

4-7 

6.4 

8.1 

9.8 

2.  0 

72.5 

0.  0 

1.7 

3-3 

5-0 

6.7 

!-3 

10. 0 

II.  7 

13-4 

15- 1 

16.9 

18.6 

20.3 

72.5 

3-0 

0.0 

I.  7 

3-4 

5-1 

6.9 

8.6 

0.3 

2.0 

3.8 

5-5 

7-4 

9-1 

0.9 

3-0 

3-5 

0.0 

I,  8 

3-5 

5-2 

7-1 

8.8 

0.6 

2.4 

4.2 

6.0 

7.9 

9-7 

1.6 

3-5 

4.0 

0.0 

1.8 

3-i> 

5-4 

7-3 

9-1 

0.9 

2.8 

4.6 

b.5 

8.4 

20.3 

2-3 

4.0 

4.5 

0.0 

1.9 

3-7 

5.8" 

7.5 

9.4 

1-3 

3-2 

5-1 

7-1 

9.0 

1.0 

3.0 

4-5 

75-0 

0.  0 

1-9 

3-8 

7-7 

9-7 

II. 7 

13-6 

15.6 

17.7 

19.7 

21.  7 

23.8 

75.0 

5-5 

0.  0 

2.0 

3-9 

6.0 

8.0 

10. 0 

2.  I 

4.1 

6.2 

8.3 

20.4 

2.5 

4.7 

5-5 

6.0 

0.  0 

2.  I 

4.0 

6.2 

8-3 

0.4 

2.5 

4.6 

6.8 

8.9 

1. 1 

3-3 

5-6 

6.0 

6.5 

0.0 

2.  I 

4.2 

6.4 

8.6 

0.8 

3-0 

5-2 

7-4 

9.6 

'•§ 

4.2 

6.6 

6.5 

7.0 

0.0 

2.2 

4.4 

6.6 

8.9 

1.2 

3-5 

5-8 

8.1 

20.4 

2.8 

5.2 

7.7 

7.0 

Page  376 

TABLE  39. 

Amplitudes. 

1) 

■a 

3 

5 

Declination. 

•a 
3 

6°.0 

6°.5 

?°.o 

7°.5 

8°.0 

8°.5 

9°.0 

9°.5 

10°.0 

10°.5 

11°.0 

11°.5 

12°.0 

o 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

6.0 

6.5 

7.0 

7-5 

8.0 

8.5 

9.0 

9-5 

10. 0 

10.5 

II. 0 

II. 5 

12.0 

0 

lO 

6.1 

6.6 

7-1 

7.6 

8.1 

8.6 

9.1 

9-7 

0. 1 

0.7 

I.  2 

1.7 

2.2 

10 

15 

6.2 

6.7 

7.2 

7.8 

^•3 

8.8 

9-3 

9.8 

0.4 

0.9 

1.4 

1-9 

2.  5 

15 

20 

6.4 

6.9 

7.4 

8.0 

^■5 

9.1 

9.6 

10.  I 

0.7 

1.2 

1-7 

2.3 

2.  8 

20 

25 

6.6 

7.1 

7-7 

«-3 

8.8 

9.4 

9.9 

0-5 

1. 1 

1.6 

2.2 

2.8 

3.3 

25 

30 

6.9 

7-5 

8.1 

8.7 

9-3 

9.8 

10.4 

II. 0 

II.  5 

12. 1 

12.7 

13-3 

13-9 

30 

32 

7.0 

7-Z 

^•3 

8.8 

9.5 

10. 0 

0.6 

1.2 

I.  8 

2.4 

1       3.0 

.3.6 

4.2 

32 

34 

7.2 

7.8 

S-5 

9.0 

9-7 

0-3 

0.8 

1-5 

2.  I 

2.7 

3-3 

3-9 

4-5 

34 

3^ 

7-4 

8.0 

8.7 

9-3 

9.9 

0.  5 

I.  I 

1.8 

2.4 

3.0 

3-6 

4.3 

4.9 

36 

3^ 

7.6 

8.2 

8.9 

9-5 

10.  2 

0.8 

1.4 

2. 1 

2.7 

3-4 

4,0 

4-7 

5-3 

38 

40 

7.8 

8.5 

9-1 

9.8 

10.5 

II.  I 

II.  7 

12.4 

13- I 

13.8 

14.4 

15- 1 

15-7 

40 

42 

8.0 

8.8 

9.4 

10.  I 

0.8 

1-5 

2.  I 

2.8 

.3-5 

4.2 

4.8 

5.6 

6.2 

42 

44 

^■3 

9.1 

9-7 

0.5 

1. 1 

1.9 

2.5 

3-3 

4.0 

4-7 

5-3 

6.1 

6.8 

44 

46 

8.6 

9.4 

10.  I 

0.8 

1-5 

^•3 

3.0 

.3-8 

4.5 

5-2 

5-9 

6.7 

7-4 

46 

48 

9.0 

9-7 

o-S 

1.2 

2.0 

2.8 

3-5 
14.  I 

4-3 
14.9 

5.0 

5-8 

6.6 

7-3 

8.1 

48 

50 

9-3 

10. 1 

10.9 

II.  7 

12.5 

13-3 

15-7 

16.5 

17.3 

18.  I 

18.9 

50 

51 

9-5 

0.4 

I.  2 

2.0 

2.8 

3-6 

4.4 

5-2 

6.  0 

6.8 

7-7 

^5 

9.3 

51 

52 

9-7 

0.6 

1.4 

2.2 

3-1 

3-9 

4-7 

5.0 

6.4 

7.2 

8.1 

8.9 

9-7 

52 

53 

10. 0 

0.8 

1-7 

2.5 

3-4 

4.2 

5-1 

5-9 

6.8 

7.6 

8.5 

9.4 

20.  2 

53 

54 

0.  2 

1. 1 

2.0 

2.  8 

3-7 

4.6 

5-4 
15.8 

b.3 
16.  7 

7.2 

8.1 

8.9 

9.8 

0.7 

54 

55 

10.5 

11.4 

12.3 

13- 1 

14.0 

14.9 

17.6 

18.5 

19.4 

20.3 

21.  2 

55 

56 

0.8 

1.7 

2.6 

3-5 

4.4 

.5-3 

6.2 

7.2 

8.1 

9.0 

9.9 

0.9 

1.8 

56 

5? 

I.  I 

2.0 

2.9 

3-9 

4.8 

5.8 

6.7 

7.7 

8.6 

9.6 

20.  5 

1-5 

2.4 

57 

5^ 

1.4 

2.3 

3-3 

4-3 

5-2 

6.2 

7.2 

8.2 

9.1 

20.  I 

I.  I 

2. 1 

3.1 

58 

59 

1.7 

2.7 

3-7 

4-7 

5.7 

6.7 

7-7 

8.7 

9.7 

0.7 

1.7 

2.8 

3-8 

59 

60 

12.  I 

13- I 

14. 1 

15-1 

16.2 

17.2 

18.2 

19.3 

20.3 

21.4 

22.4 

23.5 

24.6 

60 

6i 

2-5 

3-5 

4.6 

5.6 

6.7 

7.8 

8.8 

9-9 

I.O 

2.  I 

3-1 

4-3 

5-4 

61 

62 

2.9 

3-9 

5-1 

6.  I 

7-3 

8.4 

9.4 

20.6 

1-7 

2.9 

3-9 

5.2 

6.3 

62 

^3 

3-4 

4.4 

5.6 

6.7 

7.9 

9.0 

20.  I 

1-3 

2.5 

3-7 

4.8 

6.1 

7.2 

63 

64 

3-9 

5-0 

6.2 

7-3 
18.0 

«-5 

9-7 

0.9 
21.7 

2.1 

3-3 

4.6 

5-7 

7-1 

8.3 

64 

65.  0 

14.4 

15.5 

16.8 

19-3 

20.5 

23.0 

24.  2 

25.6 

26.8 

28.2 

29.5 

65.0 

5-5 

4.6 

5.« 

7-1 

«.3 

9.6 

0.9 

2.2 

3-5 

4.7 

6.1 

7-4 

8.7 

30.1 

5-5 

6.0 

4.9 

6.2 

7-4 

8.7 

20.  0 

1.3 

2.6 

3-9 

5.3 

6.6 

8.0 

9.3 

0.7 

6.0 

b.5 

5-2 

b.5 

7.8 

9-1 

0.4 

1.8 

3-1 

4.4 

7.2 

8.6 

^0.0 

1-4 

6.5 

7.0 

5-5 

6.8 

8.2 

9-5 

0.9 

2.2 

3-6 

5-0 

6.4 
27.0 

7.8 

9.2 

0.7 

2.  I 

7.0 

67-5 

15.9 

17.2 

18.6 

19.9 

21.3 

22.  7 

24.1 

25-5 

28.4 

29.9 

31.4 

32.9 

67-5 

8.  0 

6.2 

7.6 

9.0 

20.4 

1.8 

3-2 

4-7 

6.1 

7.6 

9.1 

30.6 

2.  2 

3.7 

8.0 

«.5 

6.6 

8.0 

9-4 

0.9 

2.3 

3-8 

5-3 

6.8 

8.3 

9.8 

1.4 

3-2 

4.6 

8.5 

9.0 

7.0 

8.4 

9.9 

1.4 

2.8 

4.4 

5.9 

7.4 

9.0 

30.6 

2.2 

.3-8 

5.5 

9.0 

9-5 

7.4 

8.9 
19.3 

20.4 

1.9 

3-4 

5-0 

b.5 

8.1 

9.7 

1.4 

3-0 

4-7 

0.4 

9.5 

70.0 

17.8 

20.9 

22.4 

24.0 

25.6 

27.2 

28.8 

30.5 

32.2 

33-9 

35-7 

37-4 

70.  0 

0.5 

8.2 

9.8 

1.4 

3.0 

4.6 

6.3 

7.9 

9.6 

1-3 

3.1 

4.9 

6.7 

8.5 

0.5 

I.  0 

8.7 

20.3 

2.0 

3.b 

5-3 

7.0 

8.7 

.30.5 

2.2 

4.0 

5-9 

7.8 

9-7 

I.  0 

1-5 

9.2 

0.9 

2.6 

4-3 

6.0 

7.8 

9.5 

1-4 

3-2 

5.0 

7.0 

8.9 

40.9 

1-5 

2.0 

9.8 

1-5 

3-2 

5-0 

6.8 

8.6 

30-4 

2.3 

4.2 

6.1 

8.1 

40.2 

2.3 

2.0 

72.5 

20.3 

22. 1 

23-9 

25.7 

27.6 

29.5 

31.4 

33-3 

35-3 

37-3 

39-4 

41-5 

43-7 

72.5 

3-0 

0.9 

2.8 

4.6 

b.5 

8.4 

30-4 

2.4 

4.4 

b-5 

8.6 

40.8 

3.0 

5-3 

3-0 

3-5 

1.6 

3-5 

5-4 

7-4 

9-3 

1.4 

3-4 

5.5 

7-7 

9-9 

2.  2 

4.6 

7.0 

3-5 

4.0 

2-3 

4.3 

6.2 

8-3 

30-3 

2.5 

4.6 

6.8 

9.1 

41.4 

.3-8 

b.3 

8.9 

4.0 

4-5 

3-0 

5-1 

7.1 

9-3 

1.4 

3-b 

5.8 

8.2 

40.5 

3-0 

5-b 

8.2 

51- I 

4.5 

75-0 

23.8 

26.0 

28.1 

30.3 

32.5 

34.8 

37.2 

39.6 

42.1 

44.8 

47.5 

50.4 

53-5 

75.0 

5-5 

4-7 

6.9 

9-1 

1.4 

3-8 

6.2 

8.7 

41.2 

3-9 

6.7 

»     9.6 

2.8 

6.2 

5-5 

6.0 

S-b 

7-9 

30.2 

2.6 

5.1 

7-7 

40.3 

3.0 

5-9 

8.9 

52.1 

5-5 

9-3 

6.0 

b.5 

6.6 

9.0 

1.4 

4.0 

6.6 

9-3 

2.  I 

5.0 

8.  I 

51-3 

4.8 

8.7 

63.  0 

6.  si 

7.0 

.7..  7 

30.2 

2.8 

5-5 

8.2 

41.  I 

4.1 

7.2 

50.5 

4.1 

8.0 

62.4 

7.6 

7.0 

TABLE  39. 

[Page  377 

%■ 

Amplitudes. 

Declination. 

•a 

12°.0 

12°.5 

13°.0 

13°.5 

14°.0 

14°.5 

15°.0 

15°.5 

16°.0 

16°.5 

n°.o 

n°.5 

18°.0 

,  ~\ 

0 

c 

0 

0 

0 

0          0 

0 

0 

0 

0 

0 

0 

0 

1 

1      0 

12.0 

12.5 ;  13.0 

13-5 

14.0 

14.5     15.0 

15-5 

16.0 

16.  5 

17.0 

17.5 

18.0 

0 

10 

2,2 

2.7 

3-2 

3-7 

4.2 

4-  7       5-  3 

5.8 

6.3 

6.8 

7.3 

7-9 

8.3 

10 

15 

2.5 

2.9 

3-5 

4.0 

4-5 

5-0       5-6 

6.1 

6.6 

7-1 

Z-7 

8.2 

8.7 

15 

20 

2.8 

3-3 

4.4 

4-9 

5.5       6.0 

6.5 

7.1 

7.6 

8.1 

8.7 

9.2 

20 

25 

3-3 

3-« 

4.4 

4-9 

5-5 

6. 1       6. 6 

7-1 

7-7 

. .  8-3 
19.2 

8.8 

9.4 

9.9 

25 

30 

13-9 

14.5 

15.0 

IS.  6 

16.  2 

16.8     17.4 

18.0 

18.6 

19.7 

20.3 

20.9 

30 

3^ 

4.2 

4.8 

5-3 

6.0 

6.6 

7.2       7.8 

8.4 

9.0 

9.6 

20.2 

0.8 

1.4 

32 

34 

4-5 

5-1 

.5-7 

6.4 

7.0 

7.6  ;    8.2 

8.8 

9-5 

20.0 

0.7 

1.3 

1.9 

34 

.(> 

4.9 

5-5 

6.1 

6.8 

7-4 

8. 0  1    8.  7 

9-3 

20.  0 

o-S 

1.2 

1.8 

2.5 

36 

3« 

5-3 

6.0 

6.6 

7.2 

7-9 

8.5 

9.2 

9.8 

0.5 

1. 1 

1.8 

2.4 

3.1 

38 

40 

15-7 

16.4 

17. 1 

17.8 

18.4 

19. 1 

19.7 

20.4 

21. 1 

21.8 

22.4 

23.1 

23.8 

40 

41 

0.0 

6.7 

7-3 

8.0 

8.7 

9. 4     20. 0 

0.8 

1.4 

2.  I 

2.8 

3-5 

4.2 

41 

42 

6.2 

6.9 

7.6 

v-3 

9.0 

9.  7  I    0.4 

I.  I 

1.8 

2.5 

3-2 

3-9 

4.6 

42 

43 

6.5 

7.2 

7-9 

8.6 

9-3 

20. 0      0. 7       1.4 

2.2 

2.9 

3-6 

4.3 

5.0 

43 

44 

6.8 

7.5 

8.2 

8.9 

9.6 

0.4      I.I       1.8 

2.6 

3-3 

4.0 

4-7 

5-4 

44 

45 

17. 1 

17.8     18.5 

19- 3 

20.0 

20.  7  !  21.5    22.2 

23.0 

23-7 

24.4 

25.2 

25-9 

45 

46 

7-4 

8.2       8.9 

9.6 

0.4 

I.I      1.9      2.6 

^■i 

4.1 

4.9 

5-7 

6.4 

46 

47 

7-7 

8.5 

9-3 

20.0 

0.8 

1-5 

2.3       3-1 

.3-8 

4.6 

5-4 

6.2 

6.9 

47 

48 

8.1 

8.9 

9-7 

0.4 

I.  2 

2.0 

2.8       3.6 

4-3 

5-1 

5-9 

6.7 

7-5 

48 

49 

8.5 

9-3 

20. 1 

0.8 

1.6 

2.4 

3-  2       4-  I 

4.9 

5-7 

6.5 

7.3 

8.1 

49 

50 

18.9 

19.7 

20.5 

21.3 

22.  I 

22. 9     23.  7     24.  6 

25.4 

26.2 

27.0 

27.9 

28.7 

50 

51 

9-3 

20.  I 

0.9 

1.8 

2.6 

3-5       4.3  '    5-1 

6.0 

6.8 

7.6 

8.5 

9-4 

51 

52 

9-7 

0.6 

1.4 

2.3 

3-1 

4.0      4.9       5.7 

6.6 

l-^ 

8.3 

9.2 

30.1 

52 

53 

20.  2 

1. 1 

1.9 

2.8 

3-7 

4.6       5.5       6.4 

Z-3 

8.2 

9.0 

30.0 

0.9 

53 

54 

0.7 

1.6 

2.5 

3-4 

4.3 

5.2;        6.  I             7.  I 

8.0 

8.9 

9.8 

0.8 

1-7 

54 

55 

21.2 

22.  2 

23.1 

24.0 

24.9 

25.9     26. 8  1  27.8 

28.7 

29.7 

30.6 

31.6 

32.  6 

55 

56 

1.8 

2.8 

3-7 

4-7 

5-(^ 

6.6       7.6       8.6 

9-5 

30- 5 

I- 5 

2.5 

3-6 

56 

57 

2.4 

3.4  1    4.4 

5-4 

6.4 

7.  4       8.  4       9.  4 

30-4 

1.4 

2.5 

3-5 

4.6 

57 

55^ 

3-1 

4-1       5-1 

6.1 

7-2 

8.2  1     9.2     30.3 

1-3 

2.4 

3-5 

4.6 

^•7 

58 

59 

3-« 

4-8  1     5-9 

6.9 

8.0 

9.1      30.2  i     1.3 

2.3 

3-5 

4.6 

5-7 

6.9 

59 

60 

24.  6 

25.6 

26.  7 

27.8 

28.9 

30.1 

31-2     32-3 

33-4 

34.6 

.35-8 

36-9 

38.2 

60 

61 

5-4 

6.5 

7.6 

8.8 

9.9 

I.  I 

2.2       3.5 

4.6 

.5-8 

7-1 

8-3 

9.6 

61 

62  . 

6.3 

7.5 

8.6 

9.8 

31.0 

2.2 

3-4       4-7 

5-9 

7-2 

8-5 

9.8 

41.2 

62 

b3 

7.2 

8.  5  1     9.  7 

31.0 

2.  2 

3-5 

4.  7       6.  I 

7.4 

8.7 

40.  I 

41-5 

2.9 

63 

64 

^•3 

9.6  I  30.9 

2.  2 

3-5 

4.8 

6.  2       7.  6 

9.0 

40.4 

1.8 

3-3 

4.8 

64 

65.0 

29-5 

30.8 

32.2 

33-5 

34-9 

.36.3 

37-  8  1  39-  2 

40.7 

42.  2 

43-8 

45-4 

47.0 

65.0 

5.5 

30.1 

1-5 

2.9 

4-3 

5-7 

7-1 

8.  6     40.  I 

1.6 

3-2 

4.8 

6.5 

8.2 

5-5 

6.0 

0.7 

2.  2 

3-b 

50 

b.5 

8.0       9. 5       1. 1 

2.7 

4-3 

5-9 

7-7 

9.4 

6.0 

b.5 

1-4 

2.9 

4.3 

5-8 

7-3 

8.  9     40.  5  1     2.  I 

.3-8 

5-4 

7-1 

8.9 

50.8 

6.5 

7.0 

2.  I 

3-^ 

5-1 

6.7 

8.2 

9.8 :  1.5 1  3.2 

4.9 

6.6 

8.4 

50-3 

2.3 

7.0 

67.5 

32.9 

34.4 

36.0 

37-6 

39-2 

40.8 

42.6     44.3 

46. 1 

47.9 

49.8 

51.8 

53-9 

67-5 

8.0 

3-7 

5-3 

6.9 

8.6 

40.  2 

1.9 

3-7  !     5-5 

7-4 

9-3 

Si-3 

3-4 

5.6 

8.0 

«.s 

4.b 

6.  2  !     7.  9 

9.6 

1-3 

3-1 

4.9       6.8 

8.8 

50.8 

2.9 

5-1 

7-5 

8.5 

9.0 

5-5 

7.2       8.9 

40.7 

2-5 

4-3 

6.2  1     8.2 

50-3 

2.4 

4.6 

7.0 

9.6 

9.0 

9.5 

6.4 

8.  2     40.  0 

1.8 

3-7 
45- 0 

5.6  [     7.6       9.7 

1-9 

4.2 

b.5 

9-1 

61.  9 

9-5 

70.0 

37-4 

39-3 

41. 1 

43- 0 

47.0     49.2     51^4 

.53.7 

56.  T 

58.7 

61.5 

64.6 

70.0 

0.5 

^•5 

40.4 

2.4 

4.4 

6.4 

8.6     50.8  !     3^2 

5-7 

8-3 

61. 1 

4-3 

7.8 

0.5 

I.O 

9-7 

1-7 

3-7 

5-8 

8.0 

50.3       2.6       5.2 

7-9 

60.  7 

3-9 

7-5 

71.7 

I.  0 

1-5 

40.9 

3-0 

5-1 

7-4 

9-7 

2.  I       4-  6       7-  4 

60.3 

3-5 

7-1 

71-4 

6.9 

1-5 

2.0 

2.3 

4.4 

6.7 

9.1 

51-5 

4.  I       6. 9 

9.9 

31 

6.8 

71. 1 

6.7 

90.0 

2.0 

72.5 

43-7 

46.0 

48.4 

50.9 

53-6 

56.4     59.4 

62.  7 

66.4 

70.9 

76.5 

90.0 

72.5 

3-0 

5-3 

7-7 

50-3 

3-0 

5-9 

8.9     62.2 

6.  I 

70.6 

b-3 

90.0 

3-0 

3-5 

7.0 

9.6 

2.3 

5-3 

8.4 

61.8 

5-S 

70-3 

6.1 

90.0 

3-5 

4.0 

8.9 

51-7 

4-7 

7.9 

61.4 

5-3 

9.8 

75-9 

90.0 

4.0 

4-5 

51.  I 

4.1 

7-3 

60.9 

4.9 

9-5 

75-5 

90.0 

4-5 

I 


Page 

378] 

TABLE  39. 

, 

Amplitudes. 

1 

5 

Declination. 

• 

•a 
3 
■a 

3    i 

18°.0 

18°.5 

19°.0 

19°.5 

20°.0 

20°.5 

21°.0 

21°.5 

22°.0 

22°.5 

23°.0 

23°.5 

24°.0 

o 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0    1 

o 

18.0 

18.5 

19.0 

19.5 

20.0 

20.5 

21.0 

21,5 

22.0 

22.  5 

23.0 

23-5 

24.  0 

0 

10 

8.3 

8.8 

9-3 

9.8 

0-3 

0.8 

1-3 

1.8 

2.3 

2.9 

3 

4 

3-9 

4.4 

10 

15 

8.7 

9.2 

9-7 

20.2 

0.7 

1-3 

1.8 

2.3 

2.8 

3-3 

3 

9 

4-4 

4.9 

15 

20 

9.2 

9-7 

20.3 

0.8 

1-4 

1-9 

2.4 

3-0 

3-5 

4.0 

4 

6 

5-' 

5-7 

20 

25 

9-9 

20.  5 

1. 1 

1.6 

2.2 

2.7 

3-3 

3-9 

4.4 

5-0 

5 

5 
'8 

6.1 

6.7 

25 

30 

20.9 

21.5 

22.  I 

22.  7 

23-3 

23.8 

24.4 

25.0 

25.6 

26.2 

26 

27.4 

28.0 

30 

32 

1.4 

2.0 

2.6 

3-2 

3-8 

4.4 

5-0 

5-b 

6.2 

6.8 

7 

4 

8.0 

8.7 

32 

34 

1-9 

2.5 

3-1 

3-8 

4.4 

S-o 

S.^' 

6.2 

6.9 

7-5 

8 

I 

8.7 

9.4 

34 

36 

2-5 

.3-1 

3-7 

4.4 

5-0 

5-7 

b.3 

6.9 

7.6 

8.2 

8 

Q 

9-5 

30.2 

36 

3^ 

3-1 

3-« 

4.4 

5-1 

5-7 

6.4 

7.0 

7.7 

?>-A 

9-1 

9 

7 

30-4 

1. 1 

38 

40 

23-9 

24.4 

25.1 

25.8 

26.5 

27.2 

27.9 

28.6 

29.3 

30.0 

30 

7 

31-3 

32.1 

40 

41 

4.2 

4.8 

5-5 

6.2 

6.9 

7-7 

8.3 

9-1 

9.8 

0-5 

I 

2 

1.8 

2.6 

41 

42 

4.6 

5-3 

6.0 

6-7 

7-4 

8.1 

8.8 

9.6 

30-3 

1.0 

I 

7 

2.4 

3-2 

42 

43 

5-0 

5-7 

6.4 

7.2 

7-9 

8.6 

9-3 

30.1 

0.8 

1.6 

2 

3 

3-0 

3-8 

43 

44 

5-4 

6.2 

6.9 

7.7 

8.4 

9-1 

9.8 

0.6 

1.4 

2.2 

2 

9 

3-6 

4-4 

44 

45 

25-9 

26.  7 

27.4 

28.2 

28.9 

29.7 

30-4 

31.2 

32.0 

32.8 

33 

5 

34-3 

35-^ 

45 

4b 

6.4 

7.2 

Z-9 

8.7 

9-5 

30-3 

1.0 

1.8 

2.6 

3-4 

4 

2 

5-0 

5-8 

46 

47 

6.9 

7-7 

«-5 

9.3 

30.1 

0.9 

1.7 

2.5 

3-3 

4.1 

4 

9 

5-7 

6.6 

47 

48 

7.5 

«-3 

9.1 

9-9 

0.7 

1.6 

2.4 

3-2 

4.0 

4-9 

5 

7 

6-5 

7-4 

48 

49 

8.1 

8.9 

9-7 

30.6 

1.4 

2.3 

3-1 

4.0 

4.8 

5-7 

6 

5 

7-4 

8-3 

49 

50 

28.7 

29.6 

30-4 

31-3 

32.1 

33- 0 

33-9 

34-8 

35.6 

36-5 

H 

4 

38-3 

39-2 

50 

51 

9.4 

30-3 

1. 1 

2.0 

2.9 

3-8 

4-7 

5.t5 

6.5 

7-4 

8 

4 

9-3 

40.  2 

51 

52 

30.1 

1.0 

1.9 

2.8 

3-7 

4-7 

5.6 

6.5 

7-5 

8.4 

9 

4 

40-3 

1-3 

52 

53 

0.9 

1.8 

2.7 

.3-7 

4.6 

5.6 

6.6 

7-5 

8.5 

9-5 

40 

5 

1.4 

2-  5 

53 

54 

1-7 

2.7 

3-6 

4.6 

5-6 

6.6 

7.6 

8.6 

9.6 

40.6 

I 

7 

2.6 

3-8 

54 

55 

32.6 

33-6 

34-6 

.3.5-6 

36.6 

.37.6 

38.7 

39-7 

40.8 

41.9 

42 

9 

44.0 

45.2 

55 

56 

3-^ 

4.6 

S-^ 

6.7 

7-7 

8.8 

9.8 

41.0 

2. 1 

3-2 

4 

S-4 

6.7 

56 

57 

4.6 

5-b 

6.7 

7.8 

8.9 

40.0 

41.  I 

^•l 

3-5 

4.6 

5 

l-°. 

8.3 

57 

5« 

5-7 

6.8 

7-9 

9.1 

40.2 

1.4 

2-5 

3-8 

S-o 

6.2 

7 

5 

8.8 

50.1 

58 

59 

0.9 

8.0 

9.2 

40.4 

1.6 

2.8 

4.1 

5-4 

6-7 

8.0 

9 

3 

50.7 

2.2 

59 

60.0 

38.2 

39-4 

40.6 

41.9 

43-2 

44-5 

45-8 

47.2 

48.6 

49-9 

51 

•  4 

52-9 

54.4 

60.  0 

0-5 

8.9 

40.  I 

1.4 

2.7 

4.0 

5-4 

6.7 

8.  I 

9.6 

51.0 

2 

5 

4-1 

5-7 

0-5 

I.  0 

9.6 

0.9 

2.  2 

3-5 

4.9 

6-3 

7-7 

9-1 

50.6 

2. 1 

3 

7 

5-3 

7.0 

I.  0 

1-5 

40.4 

1-7 

3-0 

4.4 

5-8 

7-3 

8.  7 

50.2 

1-7 

3-3 

5 

0 

6-7 

8-5 

1-5 

2.0 

I.  2 

2-5 

3-9 

5-3 

6.8 

8.3 

9.8 

1-3 

2.9 

4.6 

6 

3 

V 

60.0 

2.0 

62.5 

42.0 

43-4 

44.9 

46.3 

47.8 

49.4 

51.0 

52.6 

54-2 

56.0 

57 

.8 

59-7 

61.7 

62.5 

3-0 

2.9 

4-3 

5-9 

7-4 

8.9 

50-5 

2.2 

3-9 

5-6 

7-5 

9 

4 

61.4 

3-6 

3-0 

3-5 

3-« 

5-3 

6.9 

«-5 

50.1 

1-7 

3-5 

5-3 

7-1 

9-1 

bi 

I 

3-4 

5-7 

3-5 

4.0 

4.8 

6.4 

8.0 

9-7 

1-3 

3-0 

4.9 

t■^ 

8.7 

60.  7 

3 

.0 

5-5 

8.1 

4.0 

4-5 

5-9 

7-5 

9.2 

50-9 

2.6 

4-5 

6.4 

8.4 

60.  5 

2.8 

5 

.2 

7.8 

70.9 

4-5 

65.  0 

47.0 

48.7 

50.4 

52.2 

54- 0 

56.0 

58.0 

60.  2 

62.  5 

64.9 

67 

.6 

70.6 

74.4 

65.  0 

5-5 

8.2 

50.  0 

1.8 

.3-6 

.5-6 

7.6 

9.8 

2.2 

4-7 

7-3 

70 

•4 

4.1 

8.9 

5-5 

6.0 

9.4 

1-3 

3-2 

^■\ 

7-3 

9.4 

61.8 

4.4 

7-1 

70.2 

3 

.8 

8.6 

90.  0 

6.0 

6.5 

50.8 

2.7 

4-7 

6.8 

9.1 

61.4 

4.0 

6.8 

70.  0 

3-7 

8 

-4 

90.0 

6.5 

7.0 

2-3 

4-3 

6.4 

8.7 

61. 1 

3-7 

6-5 

9.8 

3-5 

8.3 

90 

.0 

7.0 

67.5 

53-9 

56.0 

58.3 

60.  7 

63.4 

66.2 

69-5 

73-3 

78.2 

90.0 

67-5 

8.0 

5-b 

7-9 

60.3 

.3-0 

5-9 

9.2 

73- 0 

8.1 

90.0 

8.0 

8.5 

7-5 

60.0 

2.6 

5.6 

8.9 

72.8 

7-9 

90.0 

8.5 

9.0 

9.6 

2-3 

5-3 

8.7 

72.7 

7-7 

90.0 

9.0 

9-5 

61.9 

5-0 

8.4 

72.4 

7.6 

90.0 

9-5 

70.0 

64.6 

69.  I 

72.  2 

77-4 

90.0 

70.  0 

0.5 

7.8 

71.9 

7.2 

90.0 

0-5 

I.O 

71-7 

7-1 

90.0 

I.  0 

1-5 

6.9 

90.  0 

1-5 

1    2. 0 

90.  0 

t 

2.0 

TABLE  39. 

Page 

379 

%■ 

Amplitudes. 

3 

c 

Declination. 

V 

3 

24°.0 

2r.5 

25°.0 

25°.5 

26°.0 

26°.5 

2ro  i  2r-5 

28°.0 

28°.5 

29°.0 

29°.5 

30°.0 

0 

0 

0 

0 

0 

0 

0      0 

0 

0 

0 

0 

0 

0 

0 

24.0 

24.5 

25.0 

25-5 

26.  0 

26.  5 

27.  0     27.  5 

28.0 

28.5 

29.0 

29-5 

30.0 

0 

4 

4-  I 

4.6 

51 

S.b 

6.1 

6.6 

7-1        7 

6 

8.1 

8.6 

9.1 

9.6 

0. 1 

4 

8 

4-3 

4.8 

5-3 

S.8 

6-3 

6.8 

7-3       7 

8 

8.3 

8.8 

9-3 

9.8 

0-3 

8 

12 

4.0 

51 

5-6 

6.  I 

6.6 

7-1 

7.6  ,    8 

I 

8.7 

9.2 

9-7 

20.  2 

0.7 

12 

i6 

5-0 

5-6 

6.1 

6.6 

7-1 

7.6 

8.2       8 

7 

9.2 

9.8 

30-3 

0.8 

1-3 

16 

20 

25.7 

26.  2 

26.  7 

27-3 

27.8 

28.3 

28.9  1  29 

4 

30.0 

30-5 

31- 1 

21.6 

32.1 

20 

22 

6.0 

6.6 

71 

7-7 

8.2 

8.8 

9-3       9 

9 

0.4 

1.0 

1-5 

2. 1 

2.6 

22 

^4 

0.4 

7.0 

7.6 

8.1 

8.7 

9.2 

9.8     30 

4 

0.9 

1-5 

2.0 

2.6 

3-2 

24 

26 

5.9 

7-5 

8.1 

8.6 

9.2 

9-7 

30-3       0 

9 

1-5 

2. 1 

2.6 

3-2 

,3-8 

26 

28 

7-4 

8.0 

8.6 

9.2 

9.8 

30-3 

0.9       I 

5 

2. 1 

2.7 

3-3 

3-9 

4-5 

28 

30 

28.0 

28.6 

29.2 

29.8 

30.4 

31.0 

31.6 

32 

2 

32-8 

33-4 

34- 0 

24.7 

35-3 

30 

31 

^■3 

8.9 

9-5 

30.1 

0.8 

1.4 

2.0 

2 

6 

3-2 

3.8 

4-5 

5-1 

5-7 

31 

32 

8.7 

9-3 

9-9 

0-5 

1. 1 

1-7 

2.4 

3 

0 

3-b 

4.2 

4.9 

5-5 

6.  I 

32 

33 

9.0 

9.6 

30.2 

0.9 

1-5 

2. 1 

2.8 

3 

4 

4.0 

4-7 

s-§ 

6.0 

6.6 

33 

34 

9.4 

30.0 

0.6 

31-3 

1.9 

2.6 

3-2 

3 

8 

4-5 

5- 1 

5-8 

6.4 

7-1 

34 

35 

29.8 

30-4 

31- I 

3^-7 

32.3 

33- 0 

33-6 

34 

3 

35-  0 

.35-6 

36.3 

36.9 

37-6 

35 

30 

30.2 

0.8 

1-5 

2.  I 

2.8 

3-5 

4.1 

4 

8 

5-5 

6.1 

6.8 

Z-5 

8.2 

36 

j7 

0.6 

1-3 

1.9 

2.6 

3-3 

4.0 

4.6 

5 

3 

6.0 

6.7 

7-4 

8.1 

8.8 

37 

I.  I 

1-7 

2.4 

31 

3-8 

4-5 

5-2 

5 

9 

6.6 

7-3 

8.0 

8.7 

9.4 

38 

39 

1.6 

2.  2 

2.9 

3-b 

4-3 

5-0 

5-7 

6 

5 

7.2 

7-9 

8,6 

9-3 

40.0 

39 

40 

32.  I 

32-8 

33-5 

34-2 

34-9 

35-6 

36-3 

37 

I 

37.8 

38.5 

39-3 

40.0 

40.7 

40 

41 

2.6 

3-3 

4.1 

4.8 

5-5 

6.2 

7.0 

7 

7 

8-5 

9.2 

40.0 

0.7 

1-5 

41 

42 

3-2 

3-9 

4.7 

5-4 

6.  I 

6.9 

7-7 

8 

4 

9.2 

9.9 

0.7 

1-5 

2-3 

42 

43 

3-!^ 

4-5 

5-3 

6.1 

6.8 

7.6 

8.4 

9 

2 

9.9 

40.7 

1.5 

2.3 

3-1 

43 

44 

4.4 

5.2 

6.  0 

6.8 

7-5 

8-3 

9.1 

40 

0 

40.7 

1.6 

2.4 

3-2 

4.0 

44 

45 

35- i 

35-9 

36.7 

37-5 

38.3 

39-1 

39-9 

40 

8 

41.  6 

42.5 

43.3 

44.1 

45- 0 

45 

4b 

5.8 

6.6 

7-5 

8-3 

9.1 

40.  0 

40.8 

I 

7 

2.5 

3-4 

4-3 

5-1 

6.0 

46 

47 

6.6 

7-4 

«-3 

9.1 

40.  0 

0.9 

1-7 

2 

6 

3-5 

4.4 

5-3 

6.2 

7-1 

47 

48 

7-4 

«.3 

9.2 

40.0 

0.9 

1.8 

2.7       3 

6 

4.6 

5-5 

6.4 

7-4 

8.3 

48 

49 

«-3 

9.2 

40.  I 

I.  0 

1.9 

2.8 

3-8  1    4 

7 

5-7 

b-7 

7.6 

8.6 

9.6 

49 

50 

39.2 

40.2 

41.  I 

42.0 

43- 0 

43-9 

44.9 

45 

9 

46.9 

47-9 

48.9 

50.0 

51. 1 

50 

51 

40.  2 

1.2 

2.  2 

3-2 

4.1 

5-1 

6.2 

7 

2 

8.2 

9-3 

50.4 

1.5 

2.6 

51 

52 

1-3 

2-3 

3-3 

4-4 

5-4 

6.4 

7-5 

8 

6 

9-7 

50.8 

2.0 

3-1 

4-3 

52 

53 

2-5 

3-5 

4.6 

5-7 

^•7 

7.8 

9.0     50 

I 

51-3 

2.5 

3-7 

4.9 

6.2 

53 

54 

3-« 

4.9 

6.0 

7-1 

8.2 

9-4 

50.6       I 

8 

3-0 

4.3 

5-^ 

6.9 

8.3 

54 

55- 0 

45-2 

46.3 

47-5 

48.6 

49.8 

51- I 

52.3  '  53 

6 

54.9 

56.3 

57-7 

59-1 

60.  7 

55- 0 

5-5 

5-9 

7-1 

8-3 

9-5 

50-7 

2.0 

3-3 

4 

6 

6.0 

7.4 

8.9 

60.4 

2.0 

5-5 

6.0 

6.7 

7-9 

9.  I 

50-4 

1.6 

2.9 

4-3 

5 

7 

7.1 

8.6 

60.1 

1.7 

3-4 

6.0 

6.5 

Z-5 

8.8 

50.  0 

1-3 

2.6 

3-9 

5-4 

6 

8 

8.3 

9.9 

1-5 

3-2 

5.0 

6.5 

7.0 

«-3 

9.6 

0.9 

2.  2 

3-b 

5-0 

6.5        8 

0 

9-5 

61.2 

2.9 

4-7 

6.6 

7.0 

57-5 

49.2 

50.5 

519 

53-2 

54.7 

56.2 

57-  7     59 

3 

60.9 

.62.6 

64-5 

66.4 

68.5 

57.5 

8.0 

50.1 

1-5 

2.9 

4.3 

5.8 

7-4 

8.9     60 

6 

2.4 

4.2 

6.2 

8.3 

70.7 

8.0 

8.5 

I.  I 

2-5 

4.0 

5-5 

7.0 

8.6 

60.3       2 

I 

3-9 

6.0 

8.1 

70.4 

31 

8.5 

9.0 

2.  2 

^■t 

51 

S-7 

8.3 

60.0 

1.8       3 

7 

5-7 

7.9 

70-3 

3-0 

6.2 

9.0 

9-5 

3-3 

4.8 

6.4 

8.0 

9.7 

I- 5 

3.4       5 

5 

7-7 

70.1 

2,8 

5-9 

80.1 
90.  0 

_?:5_ 
60.  0 

60.  0 

54-4 

56.0 

57-7 

59-4 

61.2 

63.2 

65.2     67 

4 

69.9 

72.6 

75.8 

80.0 

0.5 

5-7 

7-4 

9.1 

61.0 

2.9 

5.0 

7.2       9 

6 

72.4 

.5.8 

9-9 

90.0 

0.5 

I.O 

7.0 

8.8 

60.  7 

2.6 

4-7 

7.0 

9-5      72 

3 

5-5 

9.8 

90.0 

1.0 

1-5 

«-5 

60.3 

2.3 

4.4 

6.7 

9.2 

72.0       5 

4 

9-7 

90.0 

1-5 

2.0 

60.0 

2,0 

4.2 

f.5 

9.0 

71.9 

5-2       9 

6 

90.0 

2.0 

62.  5 

61.7 

63- 9 

66.2 

68.8 

71.7 

75-1 

9-5  1  90 

0 

62.  5 

3-0 

3-t> 

6.0 

8.6 

71-5 

4.9 

9.4 

90.0  I 

3-0 

3-5 

5-7 

^■3 

71-3 

4.8 

9-3 

90.0 

3-5 

4.0 

8.  I 

71.  I 

4.6 

9.2 

90.0 

4.0 

4-5 

70.9 

4.4 

9.0 

90.0 

4-5 

Page  380 

TABLE  40. 

Correctio 

n  of  the  Observed  Amplitude  as  taken  on  the  Apparent  Hor 

izon. 

6 

■V 

5 
"■*-» 

Declination. 

0°        5 

0 

10° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

O 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

o 

0.0      0 

.0 

0.  0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0,0 

0.0 

0.0 

0.0 

0 

5 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

5 

lo 

.  I 

.  I 

.  I 

.1 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

.  I 

I 

.  I 

10 

15 

.  2 

2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

2 

.2 

15 

20 

.  2 

2 

.2 

.2 

.2 

.  2 

•3 

•3 

•3 

3 

•3 

3 

■3 

20 

24 

0.3      0 

3 

0 

3 

0.3 

0.3 

0-3 

0-3 

0.3 

0.3 

0 

•3 

0-3 

0 

4 

0.4 

24 

28 

•3 

4 

4 

■4 

•4 

•  4 

•  4 

.4 

•4 

4 

.4 

4 

•4 

28 

32 

•4 

4 

4 

•4 

•4 

•  4 

•  4 

•5 

•5 

5 

•5 

5 

•5 

32 

36 

■5 

5 

5 

•5 

•5 

•5 

•5  i      -5 

.6 

6 

.6 

6 

.6 

36 

38 

•5 

5 

5 

•5 

.6 

..6 

.6 

.6 

.6 

6 

.6 

7 

•7 

38 

40 

0. 6       0 

6 

0 

6 

0.6 

0.6 

0.6 

0.6 

0.6 

C.6 

0 

7 

0.  7 

0 

7 

0.7 

40 

42 

.6 

6 

6 

.6 

.6 

.7 

•7 

•7 

•  7 

7 

.8 

8 

.8 

42 

44 

.6 

6 

7 

•7 

•7 

•7 

•7|      .7 

.8 

8 

.8 

9 

•9 

44 

45 

•7 

7 

7 

.  7 

.  7 

.8 

.8  1       .8 

.8 

9 

•9 

9 

I.  0 

46 

48 

•7 

8 

8 

.8 

.8 

.8 

.8!       .9 

•9 

I 

0 

I.O 

I 

0 

.  I 

48 

50 

0.8       0 

8 

0 

8 

0.8 

0.9 

0.9 

0.9 

0.9 

I.O 

I 

I 

1. 1 

I 

I 

1-3 

50 

52 

.8 

9 

9 

•9 

•9 

1.0 

1.0 

I.  0 

.  I 

2 

.2 

3 

•5 

52 

54 

•  9 

9 

I 

0 

1.0 

1.0 

.  I 

.  I 

.  I 

.2 

3 

•4 

5 

.8 

54 

5^ 

I.O          I. 

0 

I 

.  I 

.  I 

.2 

.2 

.2 

•3 

5 

.6 

8 

2.2 

S6 

5« 

.  I 

I 

2 

.2 

•  2 

•3 

•3 

•4 

•5 

7 

•9 

2 

3 

3-2 

58 

60 

1.2       I 

2 

I 

3 

1-3 

1-3 

1.4 

i-S 

1.6 

1-7 

2 

0 

2.4 

3 

4 

60 

62 

•3 

3 

4 

•4 

.4 

.     .6 

•7 

.8 

2. 1 

5 

3-5 

62 

64 

•4 

4 

5 

•5 

.6 

.8 

•  9 

2.2 

.6 

3 

7 

64 

66 

i      • 

5 

7 

•9 

2.0 

2-3 

.8 

3.8 

66 

68 

.6 

7 

9 

2.0 

2.  2 

2.4 

•9 

4.0 

68 

70 

1.8       I. 

9 

2. 

I 

2.  3 

2.6 

3-1 

4.3 

70 

72 

2.0       2. 

I 

5 

2.  8 

3-3 

4.6 

72 

74 

.2 

5 

3 

0 

3-5 

4.8 

74 

76 

.6       3- 

0 

8 

5.2 

76 

78 

3-1 

6 

5 

7 

7« 

80 

3.8       4. 

4 

So 

TABLE  41. 

Page  381 

»■ 

Of  Natural  Sines. 

I'rop. 

0° 

1 

° 

2 

!° 

3° 

4° 

"*  ■ 

Prop. 

parts 

29 

0 

M. 

parts 

2 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

0 

00000 

I 00000 

01745 

99985 

03490 

99939 

05234 

99863 

06976 

99756 

60 

2 

O     I 

00029 

I 00000 

01774 

99984 

03519 

99938 

05263 

99861 

07005 

99754 

59 

2 

I     2 

00058 

I 00000 

01803 

99984 

03548 

99937 

05292 

99860 

07034 

99752 

58 

2 

I   3 

00087 

I 00000 

01832 

99983 

03577 

99936 

05321 

99858 

07063 

99750 

57 

2 

2    4 

001 16 

I 00000 

01862 

99983 

03606 

99935 

05350 

99857 

07092 

99748 

56 

2 

2   5 

00145 

I 00000 

01891 

99982 

03635 

99934 

05379 

99855 

07121 

99746 

55 

2 

3   6 

_ooi75 
00204 

I 00000 

01920 

^99982 
99981 

03664 
03693 

99933 
99932 

05408 

99854 

07150 

99744 
99742 

54 

2 

3  '  7 

I 00000 

01949 

"05437 

99852 

07179 

53 

2 

4   S 

00233 

I 00000 

01978 

99980 

03723 

99931 

05466 

99851 

07208 

99740 

52 

2 

4  ,  9 

00262 

I 00000 

02007 

99980 

03752 

99930 

05495 

99849 

07237 

99738 

51 

2 

5  ,  lo 

00291 

I 00000 

02036 

99979 

03781 

99929 

05524 

99847 

07266 

99736 

50 

2 

5  " 

00320 

99999 

02065 

99979 

03810 

99927 

05553 

99846 

07295 

99734 

49 

2 

6 

12 

00349 

99999 

02094 

99978 

03839 

99926 
99925 

_o5582 
05611 

99844 

,07324 

_9973i_ 
99729 

48 
47 

2 
2 

6 

13 

00378 

99999 

02123 

99977 

03868 

99842  y  07353 

7  14 

00407 

99999 

0211^2 

99977 

03897 

99924 

05640 

99841 

07382 

99727 

46 

2 

7  15 

00436 

99999 

02181 

99976 

03926 

99923 

05669 

99839 

0741 1 

99725 

45 

2 

8   i6 

00465 

99999 

0221 1 

99976 

03955 

99922 

05698 

99838 

07440 

99723 

44 

8   17 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

9   i8 
9   19 

00524 
00553 

99999 
99998 

02269 

_  99974 

04013 

99919 
99918 

05756 
05785 

99834 
99833 

07498 
i  07527 

99719 
99716 

42 
41 

-  -  - 

02298 

99974 

04042 

10   20 

00582 

99998 

02327 

99973 

04071 

99917 

05814 

99831 

07556 

99714 

40 

10   21 

006 1 1 

99998 

02356 

99972 

04100 

99916 

05844 

99829 

07585 

99712 

39 

11    22 

00640 

99998 

02385 

99972 

04129 

99915 

05873 

99827 

07614 

99710 

38 

II    23 

00669 

99998 

02414 

99971 

04159 

99913 

05902 

99826 

07643 

99708 

37 

12   24 

00698 

99998 

02443 

99970 
99969 

04 1 88 
04217 

99912 

_  05931 

99824 

07672 

99705 

36 

—  - 

12   25 

00727 

99997 

02472 

9991 1 

05960 

99822 

"07701 

99703 

35 

13   26 

00756 

99997 

02501 

99969 

04246 

99910 

05989 

99821 

07730 

99701 

34 

13   27 

00785 

99997 

02530 

99968 

04275 

99909 

06018 

99819 

07759 

99699 

33 

14   28 

00814 

99997 

02560 

99967 

04304 

99907 

06047 

99817 

07788 

99696 

32 

14   29 

00844 

99996 

02589 

99966 

04333 

99906 

06076 

99815 

07817 

99694 

31 

15   30 
15   31 

00873 
00902 

99996 

02618 

99966 

04362 

99905 

06105 
"  06134 

99S13  _ 
99812 

07846 
"07875 

99692 
99689 

JO 

29 

99996 

02647 

99965 

^04391 

09904 

^5  32 

00931 

99996 

02676 

99964 

04420 

99902 

06163 

99810 

07904 

99687 

28 

16  33 

00960 

99995 

02705 

99963 

04449 

99901 

06192 

99808 

07933 

996S5 

27 

16  34 

00989 

99995 

02734 

99963 

04478 

99900 

06221 

99806 

07962 

99683 

26 

17  35 

01018 

99995 

02763 

99962 

04507 

99898 

06250 

99804 

07991 

99680 

25 

17  36 

01047 

99995 

02792 

99961 

04536 

99897 
99896 

06279 
06308 

99803 
99801 

08020 
08049 

99678 
99676 

24 
23 



18  37 

01076 

99994 

02821 

99960 

04565 

18  38 

01105 

99994 

02850 

99959 

04594 

99894 

06337 

99799 

0S078 

99673 

22 

19  39 

01134 

99994 

02879 

99959 

04623 

99893 

06366 

99797 

08107 

99671 

21 

19  40 

01 164 

99993 

02908 

99958 

04653 

99892 

06395 

99795 

08136   99668 

20 

20  41 

01193 

99993 

02938 

99957 

04682 

99890 

06424 

99793 

08165 

99666 

19 

20  42 

01222 

99993 

02967 

99956 

04711 

99889 

_o6453 

99792 
99790 

08194 
'08223 

99664 

18 

21 

43 

01251 

99992 

02996 

99955 

04740 

99888 

06482 

99661 

17 

21 

44 

01280 

99992 

03025 

99954 

04769 

99886 

06511   99788 

08252 

99659 

16 

22 

45 

01309 

99991 

03054 

99953 

04798 

99885 

06540  99786 

08281 

99657 

15 

22 

46   01338 

99991 

03083 

99952 

04827 

99883 

06569  99784 

08310 

99654 

14 

0 

23 

47 

01367 

99991 

03112 

99952 

04856 

99882 

06598  99782 

08339   99652 

13 

0 

23 

48 

01396 
01425 

99990 

03 141 

99951 

04885 

99881 

06627 

99780 
99778 

08368   99649 
^8397   99647 

12  , 
li  ' 

0 
0 

24 

49 

99990 

03170 

99950 

04914 

99879 

"06656 

24  50 

01454 

99989 

03199 

99949 

04943 

99878 

06685 

99776 

08426   99644 

10 

0 

25  51 

01483 

99989 

03228 

99948 

04972 

99876 

06714 

99774 

08455   99642 

9. 

0 

25  52 

01513 

99989 

03257 

99947 

05001 

99875 

06743 

99772 

08484 

99639 

8 

0 

26  53 

01542 

99988 

03286 

99946 

05030 

99873 

06773 

99770 

08513 

99637 

7 

0 

26  ,  54 

01571 

99988 
99987 

03316 

99945 

05059 

99872 

06802 

99768 

08542 

99635 

6 

0 

27  ;  55 

01600 

03345 

99944 

05088 

99870 

06831   99766 

"08571 

99632 

5 

0 

27  56 

01629 

99987 

03374 

99943 

05117 

99869 

06860  99764 

08600 

99630 

4 

0 

28  57 

01658 

99986 

03403 

99942 

05146 

99867 

06889  99762 

08629 

99627 

3 

0 

28  58 

01687 

99986 

03432 

999.^1 

05175 

99866 

06918 

99760, 

08658 

99625 

2 

0 

29  ,  59 

01716 

99985 

03461 

99940 

05205 

<)9864 

06947 

99758- 

08687   99622 

.  1 

0 

29  60 

01745 

99985 

03490 

99939 

05234 

99863 

06976 

99756 

08716   99619 

0 

0 

N.  COS.  ' 

N.  sine. 

N.  COS. 
8f 

N.  sine. 

*°        1 

X.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS.  N.  sine. 

M. 

i 

8J 

r 

0 

m 

° 

8.= 

i° 

Page  382]                   TABLE  41. 

Of  Natural  Sines. 

Prop, 
parts 

29 

M. 

5° 

6° 

r 

8° 

9° 

Prop, 
parts 

4 

N.  sine. 

N.  COS. 

N.  sine.   N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 
0 

I 
I 
2 
2 
3 

0 

I 
2 

3 
4 

I 

7 
8 

9 
10 

II 
12 

08716 

08745 
08774 
08803 
08831 
08860 
08889 
08918 
08947 
08976 
09005 
09034 
09063 

99619 
99617 
99614 
99612 
99609 
99607 
99604 

10453 
10482 
105 1 1 
10540 
10569 
10597 
10626 
10655 
10684 
10713 
10742 
10771 
10800 

99452 
99449 
99446 

99443 
99440 

99437 
99434 

12187 
12216 
12245 
12274 
12302 

1 233 1 
12360 

99255 
99251 
99248 
99244 
99240 
99237 
99233 

13917 
13946 

13975 
14004 

14033 
14001 

14090 

14119 

14148 

14177 
14205 

14234 

14203 

99027 

99023 

99019 

99015 
9901 1 

99006 

99002 

98998" 

98994 

98990 

98986 

98982 

98978 

98973 
98969 
98965 
98961 
98957 
98953 

15643 
15672 
15701 
15730 

15758 
15787 
15816 

98769 
98764 
98760 

98755 

98751 
98746 
98741 

60 

59 

58 
57 
56 
55 
54 

4 
4 

•4 
4 
4 
4 
4 

3 
4 
4 
5 

5 
6 

99602 

99599 
99596 
99594 
99591 
99588 

99431 
99428 

99424 

99421 

99418 

99415 

12389 
12418 
12447 
12476 
12504 

^  12533 
12562 
12591 
12620 
12649 
12678 
12706 

99230 
99226 
99222 
99219 

99215 
992 1 1 

15845 

15873 
15902 

1 593 1 
15959 

15988 

16017 
16046 
16074 
16103 
16132 
16160 

98737 
98732 
98728 

98723 
98718 
98714 

53 
52 
51 
50 

49 
48 

4 
3 
3 
3 

I 

6 

7 
7 
8 

8 

9 

9 
10 

ID 

II 
II 
12 

13 

14 

15 
16 

17 
18 

19' 

20 

21 
22 

23 
24 

25 
26 

27 
28 
29 

30 

31 

32 
33 
34 
35 
36 

09092 
09121 
09150 
09179 
09208 
09237 
09266 
09295 
09324 

09353 
09382 
0941 1 

99586 

99583 
99580 

99578 
99575 
99572 

10829   99412 
10858   99409 
10887   99406 
1 09 1 6  :  99402 
10945   99399 
10973   99396 

99208 
99204 
99200 
99197 

99193 
99189 

14292 
14320 
14349 
14378 
14407 

14436 

98709 
98704 
98700 

98695 
98690 
98686 

47 
46 

45 
44 

43 
42 

3 
3 
3 
3 
3 
3 

99570 
99567 
99564 
99562 

99559 
99556 

1 1002  1  99393 
1 1 03 1   99390 
1 1060   99386 
1 1089   99383 
II 1 18   99380 
1 1 147   99377 

12735  '  99186 
12764  '  99182 
12793    99178 
12822   99175 
I2S51    99171 

12880  ;   99167 

14464 

14493 
14522 

14551 
14580 

14608 

98948 

98944 
98940 

98936 

98931 
98927 

16189  '   98681 
1 62 1 8  98676 
16246  98671 
16275  98667 
16304  98662 
16333  98657 

41 
40 

39 
38 
37 
36 

3 
3 
3 
3 
2 
2 

12 
13 
13 
14 
14 
15 
15 
15 
16 
16 

17 
17 
18 
18 
19 
19 
20 
20 
21 
21 
22 
22 

23 
23 

09440 
09469 
09498 
09527 
0955t> 
09585 
09614 
09642 
09671 
09700 
09729 
09758 

99553 
99551 
99548 

99545 
99542 

99540 

1 1 176   99374 
1 1205   99370 
1:234   99367 
11263   99364 
II 29 1   99360 
1 1320   99357 

12908     99163 
12937     99160 
12966     99156 
12995     99152 
13024     99148 
13053     99144 

14637 
14666 

14695 
14723 

14752 
14781 

98923 
98919 
98914 
98910 
98906 
98902 

I 636 I  98652 
16390  1  98648 
1 64 1 9  1  98643 
16447  '   98638 
16476  98633 
16505  1  98629 

35 
34 
33 
32 
31 
30 

2 
2 
2 
2 
2 
2 

99537 
99534 
99531 
99528 
99526 

99523^ 
99520 

99517 
99514 

995" 
99508 
99506 

1 1349  i  99354 
1 1378  ,    99351 
11407  1  99347 

1 1436   99344 
1 1465   99341 

1 1494   99337 

I3081     9914 1 
I3IIO     99137 

I3I39     99133 
I3I68     99129 

I3I97  i   99125 
13226     99122 

14810 
14838 
14867 
14896 
14925 
14954 

98897 
98893 
98889 
98884 
98880 
98876 

16533  98624 
16562  98619 
I 659 I  98614 
16620  98609 
16648  i  98604 
16677  98600 

29   2 
28   2 

27  1  2 
26   2 
25  !  2 
24   2 

37 
38 
39 
40 
4( 
42 

09787 
09816 
09S45 
09874 
09903 
09932 

1 1 523  1  99334 
1 1552  '  99331 
1 1 580   99327 
1 1609  ,  99324 
1 1638   99320 
I 1667   99317 

13254     991  18 
13283     991  14 
I33I2     99IIO 
I334I     99106 
13370     99102 
13399  :    99098 

14982 
15011 
•5040 
15069 

15097 
15126 

98871 
98867 
98863 
98858 
98854 
98849 

16706 

16734 
16763 
16792 
16820 
16849 

98595 
98590 

98585 
98580 

98575 
98570 

23 
22 
21 
20 

19 
18 

17 
16 

15 

14 

13 
12 

2 

43 
44 

45 
46 

47 
48 

09961   99503 
09990   99500 
10019   99497 
10048   99494 
10077   99491 
10 106   99488 

1 1696   99314 
1 1 725   99310 
1 1 754   99307 
1 1 783   99303 
11812  I  99300 
1 1 840  !  99297 

13427  1    99094 
13456     99091 
13485      99087 
135  14     99083 
13543     99079 
13572  1    99075 

15155 
15184 

15212 

15241 

15270 

15299 

98845 
98841 
98836 
98832 
98827 
98823 

16878  98565 
16906  98561 

16935  '  98556 
16964  98551 
16992  98546 
1 702 1   98541 

24 
24 
25 
25 
26 
26 

49 

50 
51 
52 
53 
54 

10135   99485 
10 1 64   99482 
10192   99479 
10221  \    99476 
10250  '  99473 
10279  ,  99470 

1 1 869  1  99293 
1 1 898  i  99290 
1 1927   99286 
11956   99283 
II 985   99279 
12014   99276 

13600 
13629 
13658 
13687 
I3716 

13744 

99071 
99067 
99063 
99059 
99055 
99051 

15327 
15356 
15385 
15414 
15442 
15471 

98818 
98814 
98809 
98805 
98800 
98796 

17050  98536 
17078  98531 
1 7107  98526 
17136  98521 
1 7164  98516 
17193  ,  98511 

II 

10 

9 
8 

7 
6 

I 
0 
0 

27  1  55 
27  '   56 

28 :  57 

28  58 

29  59 
29  60 

10308   99467 

10337  ,  99464 
10366   99461 

10395   99458 
10424   99455 
10453   99452 

12043  '    99272 
1 20  7 1   99269 
I 2 100   99265 
12129   99262 
12158   99258 
12187   99255 

13773 
13802 

13860 
13889 

13917 

99047 
99043 
99039 
99035 
99031 
99027 

15500 
15529 

15557 
15586 

15615 
15643 

98791 

98787 

98782 

98778 

98773 
98769 

17222  98506 
17250  98501 
17279  98496 
17308  98491 
1 7336  98486 
17365  98481 

5  !  0 
4   0 
3   0 
2   0 
I   0 
0   0 
i 

N.  cos.   N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

'- 

84° 

8 

^° 

82° 

81° 

80° 

TABLE 

41. 

Page 

383 

1 

% 
h 

Of  Natural  Sines. 

I'rop. 

10° 

11° 

12° 

13° 

14° 

Prop. 

jiarts 

parts 

6 

6 

28 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine.  N.cos. 

N.  sine. 

N.  cos. 

j 
o  1  o 

17365 

98481 

1 908 1 

98163 

20791 

97815 

22495   97437 

24192 

97030 

60 

0     I 

17393 

98476 

19109 

98157 

20820 

97809 

22523   97430 

24220  \   97023 

59 

6 

I     2 

17422 

98471 

19138 

98152 

20848 

97803 

22552  ,   97424 

24249   97015 

58 

6 

I   3 

1 745 1 

98466 

19167 

98146 

20877 

97797 

22580  ■   97417 

24277   97008 

57 

6 

2    4 

17479 

98461 

19195 

98140 

20905 

97791 

22608   9741 1 

24305   97001 

56 

6 

2     5 

17508 

98+55 

19224 

98135 

20933 

97784 

22637  '  97404 

24333   96994 

55 

6 

3  ^ 

17537 

98450 

19252 

98129 

20962 

97778 

22665   97398 

24362   96987 

54 
53 

5 
5 

3  '  7 

17565 

98445 

1 928 1 

98124 

20990 

97772 

22693  '  97391 

24390  !  96980 

4:  S 

17594 

98440 

19309 

98118 

21019 

97766 

22722  •   97384 

24418   96973 

52 

5 

4  '  9 

17623 

98435 

19338 

98112 

21047 

97700 

22750   97378 

24446   96966 

51 

5 

5   lo 

1 765 1 

98430 

19366 

98107 

21076 

97754 

22778  97371 

24474   96959 

50 

5 

5  " 

17680 

98425 

19395 

98101 

21104 

97748 

22807  97365 

24503   96952 

49 

5 

6    12 

17708 

98420 

19423 

98096 
98090 

JL1IJ2^ 

97742 

_22835  ,  97358 

24531    96945 

48 

5 
5 

6  13 

17737 

98414 

19452 

2I161 

97735 

22863  '  97351 

24559   96937 

47 

7   H 

17766 

98409 

1 948 1 

98084 

21189 

97729 

22892  97345 

24587  '  96930 

46 

5 

7  15 

17794 

98404 

19509 

98079 

2I218 

97723 

22920  97338 

24615   96923 

45 

5 

7  16 

17823 

98399 

19538 

98073 

21246 

97717 

22948  97331 

24644   96916 

44 

4 

8   17 

17852 

98394 

19566 

98007 

21275 

97711 

22977  97325 

24672   96909 

43 

4 

8  18 

17880 

98389 

19595 

98061 

21303 

97705 
97698 

23005  97318 

24700   96902 

42 

4 

9^  19 

17909 

98383" 

19623 

98056 

2I33I 

23033  973" 

"24  728" '"968947 

41 

4 

9  20 

17937 

98378 

19652 

98050 

21360 

97692 

23062  97304 

24756   96887 

40 

4 

10  21 

17966 

98373 

19680 

98044 

21388 

97686 

23090  97298 

24784  !  96880 

39 

4 

10  22 

1 7995 

98368 

19709 

98039 

21417 

97680 

23118  97291 

24813  ;  96873 

38 

4 

II   23 

18023 

98362 

19737 

98033 

21445 

97673 

23146  97284 

24841    96806 

37 

4 

11   24 

18052 

98357 

19766 

98027 
98021 

21474 
21502 

97607 

23175  ,  97278 

24869    96858 

36 
35 

4 

12  1  25 

1[8o8F 

98352 

19794 

97661 

23203  j  97271 

24897  :  96857" 

4 

12  ,  26 

18109 

98347 

19823 

98016 

21530 

97655 

23231   97264 

24925  ;  96844 

34 

3 

13  1  27 

181 38 

98341 

1 985 1 

98010 

21559 

97648 

23260  ■  97257 

24954  96837 

33 

3 

13   28 

18166 

98336 

19880 

98004 

21587 

97642 

23288  97251 

24982   96829 

32 

3 

14  ;  29 

18195 

98331 

19908 

97998 

21616 

97636 

23316  97244 

25010 1 96822 

31 

3 

14  1  30 

18224 

98325 

J  993  7 

97992 

21644 

97630 

_  23345  97237 

25038  !  96815 

30 

3 

14  1  31 

18252 

98320 

19965 

97987 

21672 

97623 

23373  97230 

25066  :  96807 

29 

3 

15   32 

18281 

98315 

19994 

97981 

217OI 

97617 

23401   97223 

25094  96800 

28 

3 

15  33 

18309 

98310 

20022 

97975 

21729 

97611 

23429  97217 

25122  96793 

27 

-> 
J 

16  1  34 

18338 

98304 

20051 

97969 

21758 

97604 

23458  97210 

25 15 1  1  96786 

26 

3 

16  35 

18367 

98299 

20079 

97963 

21786 

97598 

23486  97203 

25179  96778 

25 

3 

17  ;  36 

18395 

98294 

20108 

97958 

21814 
^21843" 

97592 

23514  97196 

25207  1  96771 

24 

2 

17  1  37 

18424 

98288 

20136 

97952 

97585 

23542  '  97189 

25235  1  96764 

23 

2 

18  1  38 

18452 

98283 

20165 

97946 

21871 

97579 

23571  971S2 

25263  1  96756 

22 

2 

18  :    39 

1 848 1 

9S277 

20193 

97940 

21899 

97573 

23599  ,  97176 

25291  ;  96749 

21 

2 

19  1  40 

18509 

98272 

20222 

97934 

21928 

97566 

23627  97169 

25320    96742 

20 

2 

19   41 

18538 

98267 

20250 

97928 

21956 

97560 

23656  97162 

25348    96734 

19 

7. 

20 

42  1 

18567 

98261 

20279 

97922 

21985 

97553 

23684  1  97155 

25376^  |_96727_ 

18 

2 

20   43 

18595 

98256 

20307' 

97916 

22013 

97547 

23712  •'   97148 

25404  1  96719 

17 

2 

21  j  44 

18624 

98250 

20336 

97910 

22041 

97541 

23740  97141 

25432  96712 

16 

2 

21  1  45 

18652 

98245 

20364 

97905 

22070 

97534 

23769  97134  i 

25460  96705 

15 

2 

21  !  46 

1 868 1 

98240 

20393 

97899 

22098 

97528 

23797  97127 

25488  ,  96697 

14 

22  :  47 

18710 

98234 

20421 

97893 

22126 

97521 

23825  97120 

25516  96690 

13 

22  !  48 

18738 

98229 

20450 

97887 

22155 

97515 
97508 

23853  '•   971 13 

25545 

96682 

12 

23  49 

18767 

'  98223 

20478 

97881 

22183 

23882  97106 

25573 

96675 

u 

23    50 

18795 

98218 

20507 

97875 

22212 

97502 

23910  :  97100 

25601 

96667 

10 

24  :  51 

18824 

98212 

20535 

97869 

22240 

97496 

23938  .    97093 

25629  96660 

9 

24  !  52 

18852 

98207 

20563 

97863 

22268 

97489 

23966  1  97086 

25657  96653 

8 

25  i  53 

1 888 1 

98201 

20592 

97857 

22297 

97483 

23995    97079 

25685  ;  96645 

7 

25  i  54 

18910 

98196 
98190 

20620 

97851 

22325 

97476 

24023    97072 

25713   96638 

6 

26  55 

18938 

20649 

97845 

2235'3 

97470 

24051    07065 

25741  '  96630 

5 

26  56 

18967 

98 1 85 

20677 

97839 

22382 

97463 

24079    97058 

25769   96623 

4 

0 

27  57 

18995 

98179 

20706 

97S33 

22410 

97457 

24108    97051 

25798  1  96615 

■3 

0 

27  5^ 

19024 

98174 

20734 

97827 

22438 

97450 

24136    97044 

25826   90608 

2 

0 

28  59 

19052 

98168 

20763 

97821 

22467 

97444 

24164    97037 

25854   96600 

1 

0 

28 

bo 

1 908 1 

98163 

20791 

97815 

22495 

97437 

24192    97030 

25882  ,  96593 

0 
M. 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.cos.  N.sine. 

N.  cos.  N.  sine. 



: 

9° 

7 

S° 

1 

r 

76° 

75° 

Page  384 

TABLE  41. 

- 

Of  Natural  Sines. 

Prop.' 
parts 

15° 

16° 

ir 

18° 

19° 

Prop, 
parts 

9 

9 

27 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.cos. 

o   o 

25882 

96593 

27564 

96126 

29237 

95630 

30902 

95106 

32557 

94552 

60 

O  ,   I 

25910 

96585 

27592 

96118 

29265 

95622 

30929 

95097 

32584 

94542 

59 

9 

I  i   2 

25938 

96578 

27620 

961 10 

29293 

95613 

30957 

95088 

32612 

94533 

58 

9 

I   3 

25966 

96570 

27648 

96102 

29321 

95605 

30985 

95079 

32639 

94523 

57 

9 

2    4 

25994 

96562 

27676 

96094 

29348 

95596 

31012 

95070 

32667 

94514 

56 

8 

2   5 

26022 

96555 

27704 

96086 

29376 

95588 

31040 

95061 

32694 

94504 

55 

8 

3 

6 

^7" 

26050 

96547 

22731 

96078 

29404 

95579 

31068 

95052 

32722 
32749 

94495 
94485 

54 

53 

8 

3 

26079 

96540 

27759 

96070 

29432 

95571 

31095   95043 

8 

4   « 

26107 

96532 

27787 

96062 

29460 

95562 

3II23 

95033 

32777 

94476 

52 

8 

4   9 

26135 

96524 

27815 

96054 

29487 

95554 

3I151 

95024 

32804 

94466 

51 

8 

5   10 

26163 

96517 

27843 

96046 

29515 

95545 

31 1  78 

95015 

32832 

94457 

50 

8 

5  II 

26191 

96509 

27871 

96037 

29543 

95536 

31206 

95006 

32859 

94447 

49 

7 

5  12 

26219 

96502 

27899 

96029 

29571 

95528 

31233 

94997 

32887 
32914 

94438 

48 

7 

6   13 

26247 

96494 

27927 

96021 

29599 

95519 

31261 

94988 

94428 

47 

7 

6  14 

26275 

96486 

27955 

96013 

29626 

955 1 1 

31289 

94979 

32942 

94418 

46 

7 

7   15 

26303 

96479 

27983 

96005 

29654 

95502 

31316 

94970 

32909 

94409 

45 

7 

7  16 

26331 

96471 

2801 1 

95997 

296S2 

95493 

31344 

94961 

32997 

94399 

44 

7 

8  17 

26359 

96463 

28039 

95989 

29710 

95485 

31372   94952 

33024 

94390 

43 

6 

8  18 

26387 

96456 
96448 

28067 
28095 

95981 

29737 

95476 

31399 

94943 

33051 

94380 

42 

6 

9  19 

26415 

95972 

29765 

95467 

31427 

94933 

33079 

94370 

41 

6 

9  20 

26443 

96440 

28123 

95964 

29793 

95459 

31454 

94924 

33106 

94361 

40 

6 

9  21 

26471 

96433 

28150 

95956 

29821 

95450 

31482 

94915 

33134 

94351 

39 

6 

10  22 

26500 

96425 

28178 

95948 

29849 

95441 

31510 

94906 

33161 

94342 

38 

6 

10  23 

26528 

96417 

28206 

95940 

29876 

95433 

31537 

94897 

33189 

94332 

37 

6 

II  24 

26556 

96410 

28234 

95931 

29904 

95424 

31565 

94888 

33216 

94322 

36 

35 

5 

5 

II   25 

26584 

96402 

28262 

95923 

29932 

95415 

31593 

94S78 

33244 

94313 

12  26 

26612 

96394 

28290 

95915 

29960 

95407 

31620 

94869 

33271 

94303 

34 

5 

12  27 

26640 

96386 

28318 

95907 

29987 

95398 

31648 

94860 

33298 

94293 

33 

5 

13  28 

26668 

95379 

28346 

95898 

30015 

95389 

31675 

94851 

33326 

94284 

32 

5 

13  29 

26696 

.  96371 

28374 

95890 

30043 

95380 

31703 

94842 

33353 

94274 

31 

5 

14  30 

26724 

9^5363 

28402 

95882 

30071 

95372 

31730 

94832 

33381 

94264 

30 

5 

14  31 

26752 

96355 

28429 

95874 

30098 

95363 

31758   94823 

33408 

94254 

29 

4 

14  32 

26780 

9^347 

28457 

95865 

30126 

95354 

31786   94814 

33436 

94245 

28 

4 

15  33 

2680S 

96340 

28485 

95857 

30154 

95345 

31813   94805 

33463 

94235 

27 

4 

15  34 

26S36 

96332 

28513 

95849 

30182 

95337 

31841   94795 

33490 

94225 

26 

4 

16  35 

26864 

96324 

28541 

95841 

30209 

95328 

31868 

94786 

33518 

94215 

25 

4 

16 

3b 

37 

26S92 

96316 

28569 

95832 
95824 

30237 
30265 

95319 
95310 

3i896_ 
31923 

94777 
94768 

33545 

94206 
94196 

24 
23 

4 

1/ 

20920 

96308 

28597 

33S73 

3 

17  3S 

26948 

96301 

28625 

95816 

30292 

95301 

31951 

94758 

33600 

94186 

22 

3 

18  39 

26976 

96293 

28652 

95807 

30320 

95293 

31979 

94749 

33627 

94176 

21 

3 

18  40 

27004 

96285 

28680 

95799 

30348 

95284 

32006 

94740 

33655 

94167 

20 

3 

18  41 

27032 

96277 

28708 

95791 

30376 

95275 

32034 

94730 

33682 

94157 

19 

3 

19 

42 

27060 

96269 

28736 

95782 

30403 

95266 

32061 

94721 

33710 

94147 
94137 

18 
17 

3 
3 

19 

43 

2708S 

96261 

28764 

95774 

30431 

95257 

32089 

94712 

33737 

20   44 

27116 

96253 

28792 

95766 

30459 

95248 

32116 

94702 

33764 

94127 

lb 

2 

20   45 

27144 

96246 

28820 

95757 

30486 

95240 

32144 

94693 

33792 

941 18 

15 

2 

21    46 

27172 

96238 

28847 

95749 

30514 

95231 

32171 

94684 

33819 

94108 

14 

2 

21   47 

27200 

96230 

28875 

95740 

30542 

95222 

32199 

94674 

33846 

94098 

13 

2 

22  48 

22  49 

27228 

27250 

96222 

28903 

95732 

30570 

95213 

95204 

32227 
32254 

94665 
94656 

33874 
33901 

94088 

12 

2 

96214 

28931 

95724 

30597 

94078 

II 

2 

23   50 

27284 

96206 

28959 

95715 

30625 

95195 

32282 

94646 

33929 

94068 

10 

2 

23   51 

27312 

96198 

28987 

95707 

30653 

95186 

32309 

94637 

33956 

94058 

q 

23   52 

27340 

96190 

29015 

95698 

30680 

95177 

32337 

94627 

33983 

94049 

8 

24  53 

27368 

96182 

29042 

95690 

30708 

95168 

32364 

94618 

3401 1 

94039 

7 

24  54 

25  55 

27396 
27424 

96174 

29070 

95681 
95673 

30736 

95159 

32392 

94609 
94599 

34038 
34065 

94029 

b 

Y 

96166 

29098 

30763 

95150 

32419 

94019 

5 

25  5b 

27452 

96158 

29126 

95664 

30791 

95142 

32447 

94590 

34093 

94009 

4 

26  57 

27480 

96150 

29154 

95656 

.30819 

95133 

32474 

94580 

34120 

93999 

3 

0 

26  58 

27508 

96142 

29182 

95647 

30846 

95124 

32502 

94371 

34147 

93989 

2 

0 

27  59 

27536 

96134 

29209 

95639 

30874 

95115 

32529 

94561 

34175 

93979 

I 

0 

27  60 

27564 
N.  COS. 

96126 

29237 

95630 

30902 

95106 

32557 

94552 

34202 

93969 

0 

0 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.cos. 

N.sine. 

M. 

1i 

\° 

r. 

t° 

T. 

J° 

n° 

70°    1 

TABLE  41. 

Page 

385 

> 

Of  Natural  Sines. 

Prop, 
parts 

11 

II 

Frop. 
parts 

'21 

o 

20° 

21 

[° 

22 

!° 

23° 

24° 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N  sine. 

N.  COS. 

N.sine. 

N.  COS. 

0 

34202 

93969 

35837 

93358 

37461 

92718 

39073 

92050 

40674 

91355 

60 

0 

r 

34229 

93959 

35864 

93348 

374S8 

92707 

39100 

92039 

40700 

91343 

59 

I  I 

I 

-> 

34257 

93949 

35891 

93337 

37515 

92697 

39127 

92028 

40727 

91331 

58 

11 

I 

-> 

0 

34284 

93939 

3591S 

93327 

37542 

92686 

39153 

92016 

40753 

91319 

57 

10 

2 

4 

3431 1 

93929 

35945 

93316 

37569 

92675 

39180 

92005 

40780 

91307 

56 

10 

2 

5 

34339 

93919 

35973 

93306 

37595 

92664 

39207 

91994 

40806 

91295 

55 

10 

3 

6 
"  7 

_  34366 
34393 

93909^ 

36000 

93295 

37622 

_^2653_ 

39234 

91982 

40833 
40860 

91283 
91272 

54 
53 

10 
10 

93899 

36027 

93285 

37649 

92642 

39260 

91971 

4 

^ 

34421 

93S89 

36054 

93274 

37676 

92631 

39287 

91959 

40886 

91260 

52 

10 

4 

9 

3444S 

93879 

36081 

93264 

37703 

92620 

39314 

91948 

40913 

91248 

■;! 

9 

5 

10 

34475 

93869 

36108 

93253 

37730 

92609 

39341 

91936 

40939 

91236 

50 

9 

5 

XI 

34503 

93859 

36135 

93243 

37757 

92598 

39367 

91925 

40966 

91224 

49 

9 

5 
6 

12 

34530 

93849 

36162 

93232 
93222 

37784 

92587 

39394 

91914. 

40992 
41019 

91212 
91200 

48 

9 

13 

34557 

93S39 

36190 

37811 

92576 

39421 

91902 

47 

9 

6 

14 

34584 

93829 

36217 

932 1 1 

37838 

92565 

39448 

91891 

41045 

91188 

46 

8 

7 

15 

34612 

93819 

36244 

93201 

37865 

92554 

39474 

91879 

41072 

91176 

45 

8 

7 

16 

34639 

93809 

36271 

93190 

37892 

92543 

39501 

91868 

41098 

91164 

44 

8 

S 

17 

34666 

93799 

36298 

93180 

37919 

92532 

39528  91856 

41125 

91152 

43 

8 

8 
9 

18 
19 

34694 
34721 

93789 
93779 

36325 
36352 

93169 
93159 

37946 

92521 

39555 

91845 

41151 

91140 

42 

8 

37973 

92510 

39581 

91833 

41178 

91128 

41 

8 

9 

20 

34748 

93769 

36379 

93148 

37999 

92499 

39608 

91822 

41204 

91116 

40 

7 

9   21 

34775 

93759 

36406 

93137 

38026 

92488 

39635 

91810 

41231 

91 104 

39 

7 

lO   22 

34803 

93748 

36434 

93127 

38053 

92477 

39661 

91799 

41257 

91092 

38 

7 

lo  23 

34830 

93738 

36461 

931 16 

38080 

92466 

39688 

91787 

41284 

91080 

37 

7 

II 

24 

34857 

93728 

36488 

93106 

38107 

92455 

39715 

91775 

41310 

91068 

36 

7 

II 

25 

348S4 

93718 

36515 

93095 

38134 

92444 

39741 

91764 

41.^,37 

91056 

35 

6 

12   26 

34912 

93708 

36542 

93084 

^I'tl 

92432 

39768 

91752 

41363 

91044 

34 

6 

12 

27 

34939 

93698 

36569 

93074 

38188 

92421 

39795 

91  741 

41390 

91032 

33 

6 

13 

28 

34966 

93688 

36596 

93063 

38215 

92410 

39822 

91729 

41416 

91020 

32 

6 

13 

29 

34993 

93677 

36623 

93052 

38241 

92399 

39848 

9171S 

41443 

91008 

31 

6 

14 

30 

35021 

93667 

36650 

93042 

38268 

92388 

39875 

91706 

41469 

90996 

30 
29 

6 

14 

31 

35048 

93657 

■  36677' 

93031 

3829T 

92377 

39902 

91694 

41496   90984 

5 

14   32 

35075 

93647 

36704 

93020 

38322 

92366 

39928 

91683 

41522 

90972 

28 

5 

15  33 

35102 

93637 

36731 

93010 

38349 

92355 

39955 

91671 

41549 

90960 

27 

5 

15 

34 

35130 

93626 

36758 

92999 

38376 

92343 

39982 

91660 

41575 

90948 

26 

5 

16 

35 

35157 

93616 

36785 

92988 

38403 

92332 

40008 

91648 

41602 

90936 

25 

5 

16 

3^ 

35184 

93606 
93596 

36812 
36839 

92978 
92967 

38430 
38456 

92321 
92310 

40035 
40062 

91636 
91625 

41628 

90924 

24 

4 

17 

37 

35211 

"41655 

90911 

23 

4 

17  3« 

35239 

93585 

36867 

92956 

38483 

92299 

40088 

91613 

41681 

90899 

22 

4 

i-'S  39 

35266 

93575 

36894 

92945 

38510 

92287 

40115 

9160I 

41707 

90887 

21 

4 

iS 

40 

35293 

93565 

36921 

92935 

38537 

92276 

40141 

91590 

41734   90875 

20 

4 

iS 

41 

35320 

93555 

36948 

92924 

38564 

92265 

40168 

91578 

41700   90863 

19 

3 

19 

42 

35347 

93544 

36975 

92913 
92902 

38591 

92254 

40195 

91566 

41787 

90851 
90839 

18 
17 

3 

19  43  1 

35375 

93534 

37002 

-   38617 

92243 

40221 

91555" 

41813 

3 

20 

44 

35402 

93524 

37029 

92892 

38644 

92231 

40248 

91543 

41840   90826 

16 

3 

20 

45 

35429 

93514 

37056 

92881 

38671 

92220 

40275 

91531 

41866   90814 

15 

3 

21 

46 

35456 

93503 

37083 

92870 

38698 

92209 

40301 

91519 

41892   90802 

14 

3 

21 

47 

35484 

93493 

37110 

92859 

38725 

92198 

40328 

91508 

41919   90790 

13 

2 

22 

48 

355" 

93483  5 

37137 

92849 

3S752 

92186 

40355 

91496^ 

41945   90778 

12 

2 
2 

22 

49 

35538 

93472 

37164 

92838 

38778 

92175 

40381 

91484 

41972 

90766 

II 

23 

50 

35565 

93462 

37191 

92827 

38805 

92164 

40408 

91472 

41998 

90753 

10 

2 

23 

51 

35592 

93452 

37218 

92816 

38832 

92152 

40434  9 1 40 1 

42024 

90741 

9 

2 

0  -» 
-J 

52 

35619 

93441 

37245 

92805 

3^^59 

92141 

40461   91449 

42051 

90729 

8 

24 

53 

35047 

9343' 

37272 

92794 

38886 

92130 

40488  91437  42077 

90717 

7 

24 

54 

35674 

93420 
93410 

37299 
37326 

92784 
92773 

389 I 2_ 

^_92iJ9_ 

40514  ,  91425  42104 

90704 

6 



25 

55 

35701 

38939 

92107 

40541 

91414 

42130   90692 

^5" 

25 

5*' 

35728 

93400 

37353 

92762 

38966 

92096 

40567 

91402 

42 1 56   90680 

4 

26 

57 

35755 

93389 

37380 

92751 

38993 

9208=; 

40594 

91390 

42183 

90668 

3 

26 

58 

35782 

93379 

37407 

92740 

39020 

92073 

4002 1 

91378 

42209 

90655 

2 

0 

27 

59 

35810 

93368 

37434 

92729 

39046 

92062 

40647 

91366 

42235 

90643 

1 

0 

27 

60 

35837 

93358 
N.  sine. 

37461 
N.  COS. 

92718 

39073  1 

92050 

40674 

91355 

42262   90631  1 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

N.sine.  1  N.cos.  j 

N.  sine. 

M. 

_ 

Oil 

° 

«)h 

0» 

0 

06°     1    65° 

25    B 


Page  386 

TABLE 

:  41. 

^^""" 

Of  Natural  Sines. 

Prop. 

Prop. 

25° 

26° 

27° 

28° 

29° 

parts 

26 

parts 

14 

14 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

60 

0 

0 

42262 

90631 

43837 

89879 

45399 

89101 

46947  i  88295 

4S481 

87462 

O     I 

42288 

90618 

43863 

89867 

45425 

89087 

46973  ,  88281 

48506 

87448 

59 

14 

I     2 

42315 

90606 

43889 

89854 

45451 

89074 

46999   88267 

48532 

87434 

58 

14 

I   3 

42341 

90594 

43916 

89841 

45477 

89061 

47024  '   88254 

48557 

87420 

57 

13 

2    4 

42367 

90582 

43942 

89828 

45503 

8904S 

47050   88240 

48583 

87406 

56 

13 

2   5 

42394 

90569 

43968 

89816 

45529 

89035 

47076   ;   88226 

48608 

87391 

55 

13 

3   6 

42420 

_90557 

_43994_ 

89803 

45554 

89021 

47IOI 
47127 

88213 
88199 

48634 
48659 

87377 
87363 

54 
53 

13 
12 

3  '  7 

^42446" 

90545 

44020 

89790 

45580 

"89008" 

3   8 

42473 

90532 

44046 

89777 

45606 

8S995 

47153 

88185 

48684 

87349 

52 

12 

4   9 

42499 

90520 

44072 

89764 

45632 

88981 

47178     88172 

48710 

87335 

51 

12 

4   10 

42525 

90507 

44098 

89752 

45658 

8S968 

47204  '   88158 

48735 

87321 

50 

12 

5  ,  II 

42552 

90495 

44124 

89739 

45684 

88955 

47229     88144 

48761 

87306 

49 

II 

5  '  12 

42578 

90483 

44151 

89726 

45710 

88942 
88928' 

47255     88130 

47281  1  881 1 7 

48786 

87292 

48 

" 

6  13 

42604 

90470 

44177 

89713 

45736 

48811 

87278 

47 

II 

6  14 

42631 

90458 

44203 

89700 

45762 

88915 

47306  '  88103 

48837 

87264 

46 

II 

7   15 

42657 

90446 

44229 

89687 

45787 

8S902 

47332  ,  88089 

48862 

87250 

45 

II 

7  .  16 

42683 

90433 

44255 

89674 

45813 

88S88 

4735S 

88075 

48888 

87235 

44 

10 

7  17 

42709 

90421 

44281 

89662 

45839 

88875 

47383  1  88062 

48913 

87221 

43 

10 

8  18 

42736 

90408 

44307 

89649 
89636 

458<35 

88862 

^47409 

88048 

48938 

87207 

42 

10 

8  19 

42762 

90396 

44333 

45891 

88848 

47434 

88034 

48964 

87193 

41 

10 

9  20 

42788 

90383 

44359 

89623 

45917 

88835 

47460  !  88020 

48989 

87178 

40 

9 

9  21 

42815 

90371 

44385 

89610 

45942 

88822 

47486  88006 

49014 

87164 

39 

9 

10  22 

42841 

90358 

444" 

89597 

45968 

88808 

475 1 1  87993 

49040   87150 

38 

9 

10  23 

42867 

90346 

44437 

89584 

45994 

88795 

47537  1  87979 

49065 

87136 

37 

9 

10  1  24 

11  !  25 

42894 
42920 

90334 
90321 

44464 
44490 

89571 
89558 

46020 
46046 

88782 
"88768" 

47562 
47588 

87965 
87951 

49090 

87121 

36 

8 

49116   87107 

35 

8 

II   26 

42946 

90309 

44516 

89545 

46072 

88755 

47614  i  87937 

49141  1  87093 

34 

8 

12  !  27 

42972 

90296 

44542 

89532 

46097 

88741 

47639  87923 

49166  i  87079 

33 

8 

12  !  28 

42999 

90284 

44568 

89519 

46123 

88728 

47665  ;  87909 

49192 

87064 

32 

7 

13  -9 

43025 

90271 

44594 

89506 

46149 

88715 

47690  i  87896 

49217 

87050 

31 

7 

13  30 

43051 

_  9_02i9_ 

44620 

89493 
89480 

46175 
46201 

88701 
88688" 

47716  87882 

49242  i_87036_ 

30 

7 

13  31 

43077 

90246 

44646 

47741  1  87868 

49268  87021 

29 

7 

H  32 

43104 

90233 

44672 

89467 

46226 

88674 

47767  >   87854 

49293  87007 

28 

7 

14  33 

43130 

90221 

44698 

89454 

46252 

88661 

47793  87840 

49318  86991 

27 

6 

15  34 

43156 

90208 

44724 

89441 

46278 

88647 

47818  87826 

49344  ■  86978 

26 

6 

15  35 

43182 

90196 

44750 

89428 

46304 

88634 

47844  '  87812 

49369  i  86964 

25 

6 

16  36 

43209 
43235 

90183 
90171 

44776 
44802 

__894i5 
89402 

46330 
46355 

88620 
88607 

47869  j  87798 
"47895"'  8778^ 

_49394_ 
49419 

86949 

24 

6 

16  37 

86935 

23 

5 

16  1  38 

43261 

90158 

44828 

89389 

46381 

88593 

47920  87770 

49445   86921 

22 

5 

17  39 

45287 

90146 

44854 

89376 

46407 

88580 

47946  1  S7756 

49470  86906 

21 

5 

17  40 

43313 

90133 

44880 

89363 

46433 

88566 

47971  j  87743 

49495  '  86892 

20 

5 

18  41 

43340 

90120 

44906 

89350 

46458 

88553 

47997  87729 

49521  \   86878 

19 

4 

18 

42 
43 

43366 

90108 

_  44932 

89337 
89324 

46484 
46510 

88539 
88526 

48022 
^480^8" 

871i5_ 

49546  j  86863 

18 

4 

19 

''  43392" 

90095 

44958 

87701 

49571  j  86849 

17 

4 

19  44 

43418 

90082 

44984 

893 1 1 

46536 

88512 

48073  87687 

49596  86834 

16 

4 

20  45 

43445 

90070 

45010 

89298 

46561 

88499 

48099  87673 

49622   86820 

15 

4 

20  46 

43471 

90057 

45036 

89285 

46587 

88485 

48124  87659 

49647  86805 

14 

3 

20  47 

43497 

90045 

45062 

89272 

46613 

88472 

48150  87645 

49672  86791 

13 

3 

21  48 
21  49 

_  43523_ 
43549 

90032 

45088 

89259 

_46639_ 

88458 
"  88445 

_48i75 
48201 

87631 

49697  j  86777 

12 

3 

90019 

45114 

89245 

46664 

87617 

49723  !  86762 

II 

3 

22  i  50 

43575 

90007 

45140 

89232 

46690 

88431 

48226  87603 

49748  1  86748 

10 

2 

22  51 

43602 

89994 

45166 

89219 

46716 

88417 

48252  87589 

49773  1  86733 

9 

2 

23  52 

43628 

89981 

45192 

89206 

46742 

88404 

48277  87575 

49798  86719 

8 

2 

23  1  53 

43654 

89968 

45218 

89193 

46767 

88390 

48303  87561 

49824  86704 

7 

t 

23 

54 

55 

43680 
43706 

89956 
89943 

45243 
45269 

89180 
89167 

_  46793 
46819 

88377 
88363 

48328 
48354 

87546 

49849  ,  86690 

6 

24 

87532 

49874  j  86675 

5 

I 

24  56 

43733 

89930 

45295 

89153 

46844 

88349 

48379  87518 

49899  86661 

4 

I 

25  57 

43759 

89918 

45321 

89140 

46870 

88336 

48405  '  87504 

49924  86646 

3 

I 

25  58 

43785 

89905 

45347 

89127 

46896 

88322 

48430  87490 

49950  86632 

2 

0 

26  59 

4381 1 

89892 

45373 

89114 

46921 

88308 

48456  ,  87476 

49975  86617 

I 

0 

26  '  60 

43837 

1  89879 

45399 

89101 

46947 

88295 

48481  i  87462 

50000  86603 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos.  i  N.  sine. 

N.cos.  N.sine. 

M. 

1 

64° 

63° 

6 

2° 

61° 

««° 

TABLE  41. 

Page 

387 

%. 

Of  Natural  Sines. 

Prop. 

I'rop. 

30° 

31° 

32° 

33° 

34° 

parts 

•25 

o 

parts 

16 

M. 

N.sine. 

N.  COS. 
86603 

N.  sine. 
51504 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

0 

50000 

85717 

52992 

84805 

_ 
54464 

83867 

55919 

82904 

60 

16 

0 

I 

50025 

86588 

51529 

85702 

53017 

84789 

54488 

83851 

55943 

82887 

59 

16 

I 

2 

50050 

86573 

51554 

85687 

53041 

84774 

54513 

83835 

55968 

82871 

58 

15 

I 

50076 

86559 

51579 

85672 

53066 

84759 

54537 

83819 

55992 

82855 

57 

15 

7 

4 

50101 

86544 

51604 

85657 

53091 

84743 

54561 

83804 

56016 

82839 

56 

15 

O 

5 

50126 

86530 

51628 

85642 

53115 

84728 

54586 

83788 

56040 

82822 

55 

15 

3 

6 

50151 

86515 

51653 

85627 

53140 

84712 

54610 
54635 

83772 
83756^ 

56064 
"56088^ 

82806 
82790 

54 
53 

14 
14 

3 

7" 

50176 

86501 

51678 

85612 

53164 

84697 

3 

8 

50201 

86486 

51703 

85597 

53189 

84681 

54659 

83740 

56112 

82773 

52 

14 

4 

9 

50227 

86471 

51728 

85582 

53214 

84666 

54683 

83724 

56136 

82757 

51 

14 

4 

10 

50252 

86457 

51753 

85567 

53238 

84650 

54708 

83708 

56160 

82741 

50 

13 

5 

II 

50277 

86442 

51778 

85551 

53263 

84635 

54732 

83692 

56184 

82724 

49 

13 

5 

5 

12 

50302 

86427 

51803 

85536 

53288 
53312 

84619 
84604 

54756 

54781 

83676 
83660 

56208 
" 56232 

82708 

48 

13 

i3~ 

50327 

"  86413 

51828 

85521 

82692 

47 

13 

6 

14 

50352 

86398 

51852 

85506 

S3237 

84^,88 

54805 

83645 

56256 

82675 

46 

12 

6 

15 

50377 

86384 

51877 

85491 

53361 

84573 

S4829 

83629 

56280 

82659 

45 

12 

7 

lb 

50403 

86369 

51902 

85476 

53386 

84557 

54854 

83613 

56305 

82643 

44 

12 

/ 

17 

50428 

86354 

51927 

85461 

5341 1 

84542 

54878 

83597 

56329 

82626 

43 

II 

8 

18 

50453 

86340 

51952 

85446 

53435 

84526 

54902 

83581 

56353 

56377 

82610 

42 

II 

8 

19 

50478 

86325 

51977 

85431 

53460 

845 1 1 

54927 

83565 

82593 

41 

Ti^ 

8 

20 

50503 

86310 

52002 

85416 

53484 

84495 

54951 

83549 

56401 

82577 

40 

II 

9 

21 

50528 

86295 

52026 

85401 

53509 

84480 

54975 

83533 

56425 

82561 

39 

10 

9 

22 

50553 

86281 

52051 

853S5 

53534 

84464 

54999 

83517 

50449 

82544 

38 

10 

10 

23 

50578 

86266 

52076 

85370 

53558 

84448 

55024 

83501 

56473 

S2528 

37 

10 

_  lO   24  1 

50603 

86251 

52101 

85355 
85340 

53583 

84433 

55048 
55072 

83485 
83469 

56497 
56521 

825 1 1 
"82495" 

36 
35 

10 
~9  ~ 

lO 

25 

50628 

"86237 

52126 

53607 

84417 

II 

26 

50654 

86222 

52151 

85325 

5.632 

84402 

55097 

83453 

56545 

82478 

34 

9 

II 

27 

50679 

86207 

52175 

85310 

53656 

84386 

55121 

83437 

56569 

82462 

33 

9 

12 

28 

50704 

86192 

52200 

85294 

53681 

84370 

55145 

83421 

56593 

82446 

32 

9 

12 

29 

50729 

86178 

52225 

85279 

53705 

84355 

55169 

83405 

56617 

82429 

31 

8 

13 

30 

50754 

86163 

52250 

85264 

53730 

84339 

55194 
55218 

83389 
83373 

56641 
56665 

82413 
82396" 

30 
29 

8 
8 

13 

31 

50779 

" 86148 

52275 

85249 

53754 

84324 

13 

32 

50804 

86133 

52299 

85234 

53779 

84308 

55242 

83356 

56689 

82380 

28 

7 

H 

>  -> 

50829 

861 19 

52324 

85218 

53804 

84292 

55266 

83340 

56713 

82363 

27 

7 

H 

34 

50854 

86104 

52349 

85203 

53828 

84277 

55291 

83324 

56736 

82347 

26 

7 

15 

35 

50879 

86089 

52374 

85188 

53853 

84261 

55315 

83308 

56760 

82330 

25 

7 

15 
15 

36 

50904 

86074 

52399 

85173 

53877 

84245 

55339 
55363 

83292 

56784  82314 

24 

6 

37 

50929 

86059 

52423 

85157 

53902 

84230 

83276 

56808  82297 

23 

6 

16 

38 

50954 

86045 

52448 

85142 

53926 

84214 

55388 

83260 

56832 

82281 

22 

6 

16 

39 

50979 

86030 

52473 

85127 

53951 

84198 

55412 

83244 

56856 

82264 

21 

6 

17 

40 

51004 

86015 

52498 

85112 

53975 

84182 

55436 

83228 

56880 

82248 

20 

5 

17 

41 

51029 

86000 

52522 

85096 

54000 

84167 

55460 

83212 

56904 

82231 

19 

5 

18 
18 

42 

51054 

85985 

52547 

85081 

54024 

841 5 1 
84135 

55484 
55509 

83195 
83179 

56928 
56952 

82214 
82198 

18 

5 

43 

51079 

85970 

52572 

85066^ 

54049 

17 

5 

18 

44 

51 104 

85956 

52597 

85051 

54073 

84120 

55533 

83163 

56976 

82181 

16 

4 

19  45 

51129 

85941 

52621 

85035 

54097 

84104 

55557 

83147 

57000 

82  1 65 

15 

4 

19  46 

51154 

85926 

52646 

85020 

54122 

84088 

55581 

83131 

57024  82148 

14 

4 

20 

47 

51179 

8591 1 

52671 

85005 

54146 

84072 

55605 

83115 

57047  82132 

13 

3 

20 
20 

48 
49 

51204 
51229 

85896 

52696 

84989 

54171 

_  84057 

55630 

83098 

57071   82115 

12 

3 

85881 

52720 

84974 

54195 

84041 

55654 

83082 

57095 

82098 

II 

3 

21 

50 

51254 

85866 

52745 

84959 

54220 

84025 

55678 

83066 

57119 

82082 

10 

3 

21 

51 

51279 

85851 

52770 

84943 

54244 

84009 

55702 

83050 

57143 

82065 

9 

2 

2'* 

52 

51304 

85836 

52794 

84928 

54260 

83994 

55726  83034 

57167  82048 

8 

2 

22 

53 

51329 

85821 

52819 

84913 

54293 

83978 

55750 

83017 

57191 

82032 

7 

2 

23 
23 

54 

55 

51354 
51379 

85806 

52844 

84897 

54317 

83962 

55775 

83001 

57215 

82015 

6 

2 

85792" 

■  52869 

84882 

54342 

83946 

55799  82985 

57238" 

81999" 

5 

I 

23 

56 

51404 

85777 

52893 

84866 

54366 

83930 

55823 

82969 

57262  S1982 

4 

I 

24 

57 

51429 

85762 

52918 

84851 

54391 

83915 

55847 

82953 

57286  8 I 965 

■> 

■3 

I 

24 

5^ 

51454 

85747 

52943 

84836 

54415 

83899 

55871  82936 

57310 

81949 

2 

I 

25 

59 

51479 

85732 

52967 

84820 

54440 

83883 

55895  82920 

57334 

81932 

I 

0 

25 

60 

51504 

85717 

52992 

84805 

54464 

83867 

55919  82904 
N.  COS.  ,  N.  sine. 

57358 

N.  COS. 

5 

81915 

0 

0 

N.  COS. 

N.sine. 

N.  COS. 

X.  sine. 

N.  COS. 

N.  sine. 

X.  sine. 

5° 

-M. 

5 

9° 

5 

s° 

5 

V 

56° 

Page  388 

TABLE  41. 

Of  Natural  Sines. 

, 

Prop. 

35° 

36° 

3^° 

38° 

39° 

Prop. 

parts 

23 

parts 

18 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.sine. 

N.  COS. 

o 

0 

57358 

81915 

5^779 

80902 

60182 

79864 

61566 

78801 

62932 

77715 

60 

18 

O     I 

57381 

81899 

58802 

80885 

60205 

i   79846 

61589  1  78783 

62955 

77696 

59 

18 

I     2 

57405 

81882 

58826 

80867 

60228 

79829 

61612  '    78765 

62977 

77678 

58 

17 

I   3 

57429 

81865 

58849 

80850 

60251 

7981 1 

61635 

78747 

63000 

77660 

57 

17 

2    4 

57453 

81848 

5^^73 

80833 

60274 

79793 

61658 

78729 

63022 

77641 

56 

17 

2     5 

57477 

^'^32 

58896 

80816 

60298 

79776 

61681 

78711 

63045 

77623 

55 

17 

2  1   6 

57501 

81815 

58920 

80799 

60321 

79758 

61704 

78694 
78676 

63068 

77605 

54 
53 

16 
16 

3   7 

57524 

^81798^ 

58943 

80782 

60344 

79741 

61726 

'63090" 

77586 

3  '  8 

57548 

81782 

58967 

80765 

60367 

79723 

61749  1  78658 

63113 

77568 

52 

16 

3  :  9 

57572 

81765 

58990 

80748 

60390 

79706 

61772 

78640 

63135 

77550 

51 

15 

4  I  10 

57596 

81748 

59014 

80730 

60414 

79688 

6179s 

78622 

63158 

77531 

50 

15 

4 

II 

57619 

8173I 

59037 

80713 

60437 

79671 

61818 

78604 

63180 

77513 

49 

15 

5 
5 

12 

57643 

81714 
81698" 

59061 

80696 

60460 

79653 
79635 

61841 

78586 

63203 
63225 

77494 
77476 

48 
47 

14 

13 

57667 

59084 

80679 

60483 

61864  1  78568" 

14 

5 

14 

57691 

816S1 

59108 

806^2 

60506 

79618 

61887 

78550 

63248 

77458 

46 

14 

6  15 

57715 

-81664 

59131 

80644 

60529 

79600 

61909 

78532 

63271 

77439 

45 

14 

6  i6 

57738 

81647 

59154 

80627 

60553 

79583 

61932 

78514 

63293 

77421 

44 

13 

7  17 

57762 

81631 

59178 

80610 

60576 

79565 

61955  '  78496 

63316 

77402 

43 

13 

7  i8 

57786 
57810 

81614 

81597" 

59201 

80593 

60599 

79547 

61978 

7S478 

63338 
63361 

77384 

42 

.\3 

7  19 

59225 

80576 

60622 

79530 

62001 

78460 

77366 

41 

12 

8  :  20 

57833 

81580 

59248 

80558 

60645 

79512 

62024 

78442 

63383 

77347 

40 

12 

8  21 

57857 

81563 

59272 

80541 

60668 

79494 

62046 

78424 

63406 

77329 

39 

12 

8 

22 

57881 

81546 

59295 

80524 

60691 

79477 

62069 

78405 

63428 

77310 

38 

11 

9 

23 

57904 

81530 

59318 

80507 

60714 

79459 

62092 

78387 

63451 

77292 

37 

11 

9 
10 

24 

25" 

57928 

_JjL5y_^ 

59342 

80489 

60738 

79441 

62115 

78369 
78351"^ 

63473 
63496 

77273 

36 

u 

57952 

81496 

59365 

"80472* 

60761 

79424 

"6213-8" 

77255 

35 

11 

10 

26 

57976 

81479 

59389 

80455 

60784 

79406 

62160 

78333 

63518 

77236 

34 

10 

10  i  27 

57999 

81462 

59412 

80438 

60807 

79388 

62183 

78315 

63540 

77218 

33 

10 

II   28 

58023 

81445 

59436 

80420 

60830 

79371 

62206 

78297 

63563 

77199 

32 

10 

II   29 

58047 

81428 

59459 

80403 

60853 

79353 

62229 

78279 

63585 

77181 

31 

9 

12 
12 

30 
31 

58070 

81412 

59482 

80386 
80368 

60876 
60899 

79335 
79318 

62251 
"62274- 

78261 
78243 

63608 

77162 

30 

_9 
9 

"58094" 

81395 

59506 

63630 

77144 

29 

12  32 

58118 

81378 

59529 

80351 

60922 

79300 

62297   78225 

63653 

77125 

28 

8 

13  33 

58141 

81361 

59552 

80334 

60945 

79282 

62320   78206 

63675 

77107 

27 

8 

13  34 

58165 

81344 

59576 

80316 

60968 

79264 

62342  !  78188 

63698 

77088 

26 

8 

13  ,  35 

58189 

81327 

59599 

80299 

60991 

79247 

62:565  78170 

63720 

77070 

25 

8 

14  36 

58212 

81310 

59622 

80282 

6101.5 

79229 

62388 

78152 
78134 

63742 
63765 

_7705i 

24 

7 

14 

37 

58236 

81293 

59646 

80264 

"61038 

792 1 1 

62411 

77033 

23 

7 

15 

38 

58260 

81276 

59669 

80247 

61061 

79193 

62433  1  781 16 

63787 

77014 

22 

7 

15 

39 

58283 

81259 

59693 

80230 

61084 

79176 

62456 

78098 

63810 

76996 

21 

6 

15  1  40 

58307 

81242 

59716 

80212 

61107 

79158 

62479 

78079 

63832 

76977 

20 

6 

16  41 

58330 

81225 

59739 

80195 

61130 

79140 

62502 

78061 

63854 

76959 

19 

6 

16  1  42 
16  1  43 

58354 

81208 

59763 

80178 

__6ii53 

79122 
79105 

62524  !  78043 
'62547   78025" 

63877 

76940 

18 

5 

58378 

81191 

59786 

80160 

61 1 76 

63899 

76921 

17 

5 

17  44 

58401 

81 1 74 

5980-) 

80143 

61 199 

79087 

62570   78007 

63922 

76903 

16 

5 

17  45 

58425 

81157 

59832 

80125 

61222 

79069 

62592    77988 

63944 

76884 

15 

5 

18  I  46 

58449 

81 140 

59856 

8010S 

61245 

79051 

62615   77979 

63966 

76866 

14 

4 

18  1  47 

58472 

81123 

59879 

8009 1 

61268 

79033 

62638  77952 

63989 

70847 

13 

4 

18  48 

58496 

81100 

59902 

80073  _ 
80056 

61291 

79016 

_6266o_  _77934_ 

6401 1 

76828 

12 

4 

19  49 

58519 

81089 

59926 

"  613147 

78998 

62683  77916 

64033 

76S10 

11 

3 

19  50 

58543 

81072 

59949 

"80038 

61337 

78980 

62706 

77897 

64056 

76791 

10 

3 

20  51 

58567 

81055 

59972 

80021 

61360 

78962 

62728 

77879 

64078 

76772 

9 

3 

20  52 

58590 

81038 

59995 

80003 

61383 

78944 

62751 

77861 

64100 

76754 

8 

2 

20  53 

58614 

81021 

60019 

79986 

61406 

78926 

62774 

77843 

64123 

76735 

7 

2 

21 

54 

58637 

81004 

60042 

79968 

61429 

78908 

62796 

77824 
77806 

64145 
64167 

76717 
76698 

6 

2 

21 

55 

58661 

80987 

60065 

79951 

"61451 

"78891' 

"628  ly 

5  1 

2 

21 

56 

58684 

80970 

60089 

79934 

61474 

78873 

62842 

77788 

64190 

76679 

4 

I 

22  57 

58708 

80953 

601 12 

79916 

61497 

78S55 

62864   77769 

64212 

76661 

3 

I 

22  58 

58731 

80936 

60135 

79899 

61520 

78837 

62887   77751 

64234   76642  1 

2 

1 

23 

59 

58755 

80919 

60158 

79881 

61543 

78819 

62909  ;  77733 

64256 

76623 

1 

0 

23 

60 

58779 

80902 

60182 

79864 

61566 

78801 

62932  i  77715 

64279 

76604 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS.  N.  sine. 

M.t 

5 

r 

51 

J° 

5 

2° 

51° 

50 

° 

TABLE  41.                    [Page 

389 

%. 

Of  Natural  Sines. 

Prop. 

40° 

41 

[° 

42° 

43° 

44° 

Prop. 

parts 

22 

M. 

parts 

19 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

0 

0 

64279 

76604 

65606 

75471 

66913 

74314 

68200 

7313s 

69466  1  71934 

60 

19 

0 

I 

64301 

76586 

65628 

75452 

66935 

74295 

68221 

73116 

69487   71914 

59 

19 

I 

2 

64323 

76567 

65650 

75433 

66956 

74276 

68242 

73096 

69508   71894 

58 

18 

I 

0 

64346 

76548 

65072 

75414 

66978 

74256 

68264 

73076 

69529   71873 

57 

18 

I 

4 

64368 

76530 

65694 

75395 

66999 

74237 

682S5 

73056 

69549   71853 

56 

18 

2 

5 

64390 

765 1 1 

65716 

75375 

67021 

74217 

6S306 

73036 

69570   71833 

55 

17 

2 

6 

64412 

76492 

65738 

75356 

67043 

74198 

68327 

73016 

69591   71813 

54 

17 

7 

64435 

76473 

65759 

75337 

67064 

74178 

68349   72996 

69612   71792 

53 

17 

8 

^•445  7 

76455 

65781 

75318 

67086 

74159 

68370  ,  72976 

69633   71772 

52 

16 

9 

64479 

76436 

65803 

75299 

67107 

74139 

68391  ,  72957 

69654   71752 

51 

16 

4 

10 

64501 

76417 

65825 

75280 

67129 

74120 

6S412  ;  72937 

69675   71732 

50 

16 

4 

II 

64524 

76398 

65847 

75261 

67151 

74100 

68434  ,  72917 

69696  1  71711 

49 

16 

4 
5 

12 

64546 

76380 

65869 

75241 

67172 

740S0 

68455   72897 
68476   72877 

69717 
69737 

71691 

48 

15 

13 

64568 

76361 

65891 

75222 

67194 

74061 

71671 

47 

15 

S 

14 

64590 

76342 

65913 

75203 

67215 

74041 

68497   72857 

69758   71650 

•46 

IS 

6 

15 

64612 

76323 

65935 

75184 

67237 

74022 

68518   72S37 

69779   71630 

45 

14 

6 

16 

64635 

76304 

65956 

75165 

67258 

74002 

68539  •   72817 

69800  '  71610 

44 

14 

6 

17 

64657 

762S6 

6597S 

75146 

67280 

73983 

68561   72797 

69821  i  71590 

43 

14 

7 

18 

64679 

76267 

66000 

75126 

67301 

73963 

68582  1  72777 

69842   71569 

42 

13 

7 

19 

64701 

76248 

66022 

75107 

67323 

73944 

68603   72757 

69862  1  71549 

41 

13 

7 

20 

64723 

76229 

66044 

75088 

67344 

73924 

68624  1  82737 

69883  ,  71529 

40 

13 

8 

21 

64746 

76210 

66066 

75069 

67366 

73904 

68645   72717 

69904   71508 

39 

12 

8 

22 

64768 

76192 

66088 

75050 

67387 

73885 

68666   72697 

69925   71488 

38 

12 

8 

23 

64790 

761-73 

66109 

75030 

67409 

73865 

68688  '  72677 

69946   71468 

37 

12 

9 

24 

64812 

7615  ^ 

66131 

7501 1 

67430 

73846 

68709  72657 

69966   71447 

36 

II 

9 

25 

64834 

76135 

66153 

74992 

67452 

73826 

68730  72637 

69987  '  71427 

35 

II 

10 

26 

64856 

761 16 

6bi75 

74973 

67473 

73806 

68751   72617 

70008  ,  71407 

34 

11 

10 

27 

64878 

76097 

66197 

74953 

67495 

73787 

68772   72597 

70029   71386 

33 

10 

10 

2S 

64901 

76078 

66218 

74934 

67516 

73767 

68793  72577 

70049   71366 

32 

10 

II 

29 

64923 

76059 

66240 

74915 

67538 

73747 

68814  72557 

70070   71345 

31 

10 

II 

30 

64945 

76041 

66262 

74896 

67559 

73728 

68835   72537 

70091  1  71325 

30 

29 

10 

II 

31 

64967 

76022 

66284 

74876 

67580 

73708 

68857  ^  72517 

701  12    71305 

9 

12 

32 

64989 

76003 

66306 

74857 

67602 

73688 

68878  :   72497 

70132   71284 

28 

9 

12 

1  -> 

6501 1 

75984 

66327 

74838 

67623 

73669 

68899     72477 

70153    71264 

27 

9 

12 

34 

65033 

75965 

66349 

74818 

67645 

73649 

68920  1   72457 

70174   71243 

26 

8 

IS 

3S 

6505s 

75946 

66371 

74799 

67666 

73629 

68941   ,   72437 

70195   71223 

25 

8 

13 

3^) 

65077 

75927 

66393 

74780 

67688 

73610 

68962  1   72417 

70215    71203 

24 

8 

14  37 

65  I  GO 

75908 

66414 

74760 

67709 

73590 

68983   1   72397 

70236 

71182 

23 

7 

14 

3« 

65122 

75889 

66436 

74741 

67730 

73570 

69004 

72377 

70257 

71162 

22 

7 

14 

39 

65144 

75870 

66458 

74722 

67752 

73551 

69025 

72357 

70277 

71 141 

21 

7 

15 

40 

65166 

75851 

66480 

74703 

67773 

73531 

69046 

72337 

70298 

71121 

20 

6 

15 

41 

65188 

75832 

66501 

74683 

67795 

735" 

69067  1   72317 

70319 

71100 

19 

6 

15 

42 

65210 

75813 

66523 

74664 
74644 

67816 

73491 

69088     72297 

70339 

71080 

18 

6 

16  43 

65232 

75794 

66545 

67837 

73472 

69109     72277 

70360 

71059 

17 

S 

16  44 

65254 

75775 

66566 

74625 

67859 

73452 

69130  !  72257 

70381 

71039 

16 

5 

17  45 

65276 

75756 

66588 

74606 

67880 

73432 

69151   72236 

70401 

71019 

15 

s 

17 

46 

65298 

75738 

66610 

74586 

67901 

73413 

69172  ,  72216 

70422 

70998 

14 

4 

17 

47 

65320 

75719 

66632 

74567 

67923 

73393 

69193   72196 

70443 

70978 

13 

4 

18 

48 

65342 

75700 

66653 
66675 

74548 

67944 

73373 

69214   72176 

70463 

70957 

12 

4 

18 

49 

65364 

75680 

74528 

67965 

73353 

69235   72156 

70484 

70937 

II 

3 

18 

50 

65386 

75661 

66697 

74509 

67987 

73333 

69256  1  72136 

70505 

70916 

10 

3 

19 

51 

65408 

75642 

66718 

74489 

•  68008 

73314 

69277  1  721 16 

70525 

70896 

9 

3 

19 

52 

65430 

75623 

66740 

74470 

68029 

73294 

69298   72095 

70546 

70875 

8 

3 

19 

53 

65452 

75604 

66762 

74451 

68051 

73274 

69319   72075 

70567 

70855 

7 

2 

20  54 
20  55 

65474 
65496 

75585 
75566 

66783 

74431 

68072 

73254 

69340   72055 

70587 

70834 

6 

2 

66805 

74412 

68093 

73234 

69361   72035 

70608 

70813 

5 

2 

21   i;6 

65518 

75547 

66827 

74392 

681 15 

73215 

69382  1  72015 

70628 

70793 

4 

I 

21 

57 

65540 

75528 

66848 

74373 

6813b 

73195 

69403  1  7 '995 

70649 

70772 

0 

1 

21 

5« 

65562 

75509 

66870 

74353 

68157 

73175 

69424  71974 

70670 

70752 

2 

1 

22 

59 

65584 

75490 

66891 

74334 

68179 

73155 

69445  \   71954 

70690 

70731 

I 

0 

22 

bo 

65606 

75471 

66913 

74314 

68200 

7313s 

69466 

71934 

7071 1 

70711 

0 

0 

N.  COS. 

X.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

N.  sine. 

M. 

48 

)° 

48 

° 

4^ 

0 

46° 

45° 

Page  390 

TABLE  42. 

Logarithms  of  Numbers 

No.  I loo. 

Log.  0.00000 2.00000. 

No. 

Log. 

No.       Log. 

No. 

Log. 

No.      Log. 

No.      Log. 

I 

0. 00000 

21       I 

32222 

41 

I.  61278 

61      I. 

78533 

81      I. 

90849 

2 

0.30103 

22        I 

34242 

42 

1.62325 

62      I. 

79239 

82      I. 

91381 

3 

0.47712 

23        I 

36173 

43 

1-63347 

63      I. 

79934 

83      I 

91908 

4 

0. 60206 

24        I 

38021 

44 

1.64345 

64      I 

80618 

84      I 

92428 

5 

0. 69897 

25        I 

39794 

45 

I- 65321 

65      I 

81291 

85      I 

92942 

6 

0.  7781S 

26        I 

41497 

46 

1.66276 

66     I 

81954 

86     I 

93450 

7 

0.  84510 

27        I 

43136 

47 

I.  67210 

67     1 

82607 

87     I 

93952 

8 

0. 90309 

28        I 

44716 

48 

I.  68124 

68     I 

83251 

88     I 

94448 

9 

0. 95424 

29        I 

46240 

49 

1.09020 

69     I 

83885 

89     I 

94939 

lO 

I. 00000 

30        I 

47712 

50 

1.69897 

70     I 

84510 

90     I 

95424 

II 

1. 04139 

31        I 

49136 

51 

I.  70757 

71     -I 

85126 

91     I 

95904 

12 

I.  07918 

32        I 

50515 

52 

I.  71600 

72     I 

85733 

92     I 

96379 

13 

I.  "394 

33     I 

51851 

53 

I.  72428 

73     I 

86332 

93     I 

96848 

14 

I. 14613 

34     I 

53148 

54 

I-  73239 

74     I 

86923 

94     I 

97313 

15 

I. 17609 

35     I 

54407 

55 

I.  74036 

75     I 

87506 

95     I 

97772 

16 

I. 20412 

36     I 

55630 

56 

I.  74819 

76     I 

88081 

96     I 

98227 

17 

1-23045 

37     I 

56820 

57 

I-  75587 

77     I 

88649 

97     I 

98677 

18 

1-25527 

38 

57978 

S8 

I-  76343 

78     I 

89209 

98     I 

99123 

19 

1.27S75 

39     I 

59106 

59 

1.77085 

79     I 

-  89763 

99     I 

99564 

20 

I.  30103 

40     I 

60206 

60 

1-77815 

80     I 

90309 

100     2 

. 00000 

TABLE  42. 
Logarithms  of  Numbers. 


[Page  391 


No.  100- 


-1600. 


Log.  00000 20412. 


No. 


1 


100 

lOI 

102 
103 
104 

105 

106 

107 

loS 

io9_ 

110 

III 

[12 

"4. 

'15 

116 

[17 
18 
[I9_ 
120 
121 
122 
[23 
124 


00000 
00432 
00860 
01284 
01703 
02119 
02531 
0293S 
03342 
°3743_ 

04139 

04532 

04922 

05308 

05690^ 

06070 

06446 

06819 

07188 

^o75_55_ 
07918 
08279 
08636 
08991 
09342 


125 
126 

[28 
129^ 

■30 
131 
f32 
'33 
'34^ 

'35 
36 

37 
3« 
39 
40 
41 
42 

43 
44_ 

45 
46 

47 
48 

49^ 
50 
51 
52 

53 
54 

55 

56 
57 
58 
59 

No. 


09691 
10037 
10380 
10721 
1 1059 


1 1394 
1 1 727 

12057 

12385 
12710 

13033^ 
13354 
13672 
13988 

1 430 1 
14613 
14922 
15229 
15534 
15836 
16137 

16435 
16732 

17026 

J7j_i9__ 

17609 

17898 

18184 

18469 

18752 

19033 
19312 
19590 
19866 
20140 

0 


00043 

00475 
00903 

01326 

01745 
02160 
02572 
02979 

03383 
03782 

04179 

04571 
04961 

05346 

05729^ 

06108 

06483 

06856 

07225 

07591 

07954 
08314 
08672 
09026 

_  09317^ 
09726 

0072 
0415 
0755 
1093 

1428 
1760 
2090 
2418 

2743^ 

3066 

3386 

3704 
4019 

4333_ 
4644 

4953 
5259 
5564 
5866_ 

6167 
6465 
6761 
7056 
7348 

7638" 

7926 

8213 

8498 

8780 

9061 

9340 
9618 

9893 
20167 

1 


00087 
00518 

00945 
01368 

01787 


02202 
02612 
03019 

03423 
03822 


00130 
00561 
00988 
01410 
01828 


04218 

04610 

04999 

05385 
05767 


02243 
02653 
03060 

03463 
03862 


00173 
00604 
01030 
01452 
01870 


00217 
00647 
01072 
01494 
01912 


06145 
06521 
06893 
07262 
07628 

07990 
08350 
08707 
09061 
09412 


04258 
04650 
05038 

05423 
05805 

^6183" 
06558 
06930 
07298 
07664 
08027 
08386 

08743 
09096 
09447 


09760 
10106 
10449 
10789 
11126 


11461 

1 1 793 
12123 

12450 
12775 


09795 
10140 

10483 

10823 

1 1160 


02284 
02694 
03100 

03503 
03902 


04297 
04689 
05077 
05461 
05843 


02325 

02735 
03141 

03543 

°394L 

04336 

04727 

05115 

05500 

05881 


06221 
06595  ' 

06967  ! 

07335  i 
07700  i 

08063 
08422 
08778 
09132 
09482 


06258 
06633 
07004  1 
07372 
07737 


13098 
13418 

13735 
14051 

14364 

14675 
14983 
15290 

15594 
15897 


16197 
16495 
1679I 
17085 

i737i: 
17667 

17955 
1 824 1 
18526 
18808 


19089 
19368 

19645 
19921 
20194 


1 1494 
11826 
12156 
12483 
i28o8_ 

1 3 130" 

13450 

13767 
14082 

14391 

14706 

15014 

15320 

15625 

i5927_ 

16227 
16524 
16820 
17114 

J  7406^1 
17696  1 
17984 
18270 

18554 
18837 


09830 

0175 
0517 
0857 
1 193 


19117 

19396 

19673 
19948 

20222 


1528 
i860 
2189 
2516 
2840 


08099 

08458 

08814 

09167 

09517 

09864 

10209 

10551 
10890 

11227 


3162 

3481 

3799 
4114 
4426 

4737 

5045 

5351 

5655 

5957 


11561 
11893 
12222 

12548 
12872 

13194 
13513 
13830 
14145 
14457 


6256 

6554 
6850 

7143 
7435  ' 


14768 
15076 

15381 
15685 

15987 


7725 
8013 
8298 
8583 
8865_| 


9145 

9424 
9700 

9976 
20249 


16286 
16584 
16879 

'7173 
17464, 

17754 
18041 
18327 
1861 1 
18893 

191 73 

1 945 1 
19728 
20003 
20276 


00260 

00689 

01115 

01536 

°1?S3_ 

02366 

02776 

03181 

03583 
03981 

04376 
04766 

05154 
05538 

_°59_i_8_ 
06296 
06670 
07041 
07408 
07^73^ 

08135 

08493 
08849 
09202 

09552^ 

09899 

10243 

10585 

10924 

1 1261 

~"594~^ 
11926 
12254 
12581 
i^2905_ 
13226 

13545 
13862 

14176 

14489 

14799 
15106 

15412 

15715 
16017 


00303 

00732 
01157 
01578 

01995 
02407 
02816 
03222 
03623 
04021 


16316 
16613 
16909 
17202 

17493 


17782 
18070 

18355 
18639 
1 892 1 


19201 

19479 
19756 
20030 
20303 

6 


8 


9 


00346 
00775 
01 199 
01620 
02036 
02449 
02857 
03262 
03663 
04060 


04415 
04805 

05192 

05576 

05956^ 

06333 
06707 

07078 

07445 
07809 

08171 

08529 

08884 

09237 

_^9587_ 

09934 

0278 
0619 

0958 
i294_ 

1628 

1959 

2287 

2613 
2937 


04454 
04844 

05231 
05614 

05994 
06371 
06744 
07115 
07482 
07846 
08207 
08565 
08920 
09272 
09621 


00389 
00817 
01242 
01662 
02078 
02490 
02898 
03302 

03703 
04100 

^4493 
04883 
05269 
05652 
06032 


06408 
06781 
07151 
07518 
_o7882 

08243 
08600 

08955 
09307 

09656 


09968 
0312 

0653 
0992 

1327 
r66i 
1992 
2320 
2646 
2969 


3258 

3577 

3893 
4208 

4520^ 
4829 

5137 
5442 
5746 
604  7_ 

6346 
6643 
6938 

7231 
7522 
7811 
8099 

8384 
8667 
8949 
9229 

9507 

9783 

20058 

20330 


3290 
3609 

3925 
4239 

±ssi 

4860 
5168 

5473 
5776 

6077 


6376 

6673 
6967 
7260 

751i_ 

7840 

8127 

8412 

8696 

8977 


9257 

9535 
9811 

20085 

20358 

8 


0003 
0346 
0687 
1025 
1361 


1694 
2024 
2352 
2678 
3001 


3322 

3640 

3956 
4270 

4582 
4891 
5198 
5503 
5806 
6107 


6406 

6702 

6997 
7289 
7580 

7869 

8156 
8441 

8724 
9005 


9285 

9562 

9838 

20112 

20385 

9 


43^ 

4 

9 

13 

17 

22 

26 
30 
34 

41 


4 

8 

12 

16 

21 

25 
29 

33 
37 


42 

4 


17 
21 

25 
29 

34 
38 

40 


39 

1 

4 

2 

8 

3 

12 

4 

16 

S 

20 

6 

23 

7 

27 

8 

31 

9 

35 

12 

16 

20 

24 
28 
32 

36_ 
38 


At 

4 

7 

II 

15 
19 
22 
26 
30 
33 


35 


4 

7 

II 

14 
18 
21 

25 
28 

32 

33 

3' 

7 

10 

13 

17 
20 

23 
26 

30 


4 

8 
11 

15 
19 
23 

27 
30 
i_4_ 

Jl_ 

4 

7 

II 

14 

18 
22 

25 
29 

32 


34 

3 

7 
10 

14 
17 
20 

24 
27 

31 

32 


3 
6 

10 

13 
16 

19 
22 
26 
29 


Page  392 

TABLE  42. 
Logarithms  of  Numbers. 

No.  1600 — 

—2200. 

Log.  20412 34242.   1 

No. 

0 

1 

2 

3 

4 

5 

6 

Y 

8 

9 

160 
161 
162 

163 
164 

165 
166 
167 
168 
169 

20412 
20683 
20952 
21219 
21484 
21748 
2201 1 
22272 
22531 
22789 

20439 
20710 
20978 
21245 
21511 

20466 

20737 
21005 
21272 

21537 

20548 
20817 
21085 
21352 
21617 

20575 
20844 

20602 
20871 

20629 

20898 
21165 
21431 
21696 
21958 
22220 
22479 

22737 
22994 

20656 
20925 
21192 
21458 
21722 

21985 
2224b 

22505 
22763 
23019 

20763  ,  20790 

31 

30 

21032 
21299 
21564 

21059 

21325 
21590 

21112  21139 
21378  j  21405 
21643  21669 

I 

2 

3 
4 
5 
6 

7 
8 

9 

3 
6 

9 
12 
16 

19 
22 

25 
28 

3 

6 

9 
12 

\l 

21 

24 
27 

21775 
22037 
22298 

22557 
22814 

21801 
22063 
22324 
22583 
22840 

21827 
22089 
22350 
22608 
22866 

21854 
22115 
22376 
22634 
22891 

21880 
22141 
22401 
22660 
22917 

21906 
22167 
22427 
22686 

22943 

21932 
22194 

22453 
22712 
22968 

170 
171 
172 

173 
174 

23045 
233C0 

23553 
23805 
24055 

23070 
•  23325 

23578 
23830 
24080 

23096 
23350 
23603 

23855 
24105 

23121 

23376 
23629 
23880 
24130 

23147 
23401 

23654 
23905 
24155 

23172 

23426 

23679 
23930 
24180 

23198 

23452 

23223 
23477 

23249  1  23274 
23502  23528 
23754  23779 
24005  24030 
24254  1  24279 

I 

2 

3 
4 

5 
6 

7 
8 

29 

3 

6 

9 
12 

15 

17 
20 

23 

28 

23704  :  23729 
23955  ,  23980 
24204  ^  24229 

3 

6 

8 

II 

14 

17 

20 
22 

25 

175 
176 
177 
178 
179 

24304 
24551 
24797 
25042 
25285 

24329 
24576 
24822 
25066 
25310 

24353 
24601 

24846 

25091 

25334 

24378 
24625 
24871 
25115 
25358 

24403 
24650 
24895 
25139 
25382 

24428 
24674 
24920 
25164 
25406 

24452 
24699 
24944 
25188 

25431 
25672 

25912 
26150 
26387 
26623 

24477 
24724 
24969 

25212 

25455 

25696 

25935 
26174 

26411 

26647 

26881 
27114 
27346 

27577 
27807 

28035 
28262 

284.88 

24502 
24748 
24993 
25237 
_25479_ 
25720 

25959 
26198 

26435 
26670 

26905 
27138 

27370 
27600 
27830 

24527 

24773 
25018 

25261 

25503  , 

25744 

25983 

26221 

26458 

26694 

26928 

27161 

27393 
27623 

27852 

180 
181 

182 

183 
184 

25527 
25768 
26007 
26245 
26482 

25551 
25792 
26031 
26269 
26505 

25575 
25816 
26055 
26293 
26529 

25600 

25624 

25648 
25888 
26126 
26364 
26600 

9  26 

25840  '  25864 

I 
2 

3 
4 

5 
6 

7 
8 

9 

2; 

26 

26316 
26553 

26340 
26576 

3 

II 

14 
16 

19 

22 

24 

3 

5 

8 

10 

13 
16 
18 
21 

23 

i«5 
186 

187 

188 

189 

26717 
26951 

27184 
27416 
27646 

26741 
26975 
27207 

27439 
27669 

26764 
26998 
27231 
27462 
27692 

26788 
27021 
27254 
27485 
27715 

2681 1 

27045 
27277 
27508 
27738 

26834 
27068 
27300 

27531 
27761 

27989 
28217 
28443 
28668 
28892 

26858 
27091 

27323 
27554 
^7784 
28012 
28240 
28466 

190 
191 
192 

193 

194 

27875 
2810^ 

28330 
28556 
28780 

27898 
28126 

28578 
28803 

2792] 
28149 

28375 
28601 

28825 

27944 
28171 
28398 
28623 
28847 

27967 
28194 
28421 
28646 
28870 

28058 
28285 
28511 

28735 
28959 

28081 
28307 

28533 
28758 
28981 

29203 

29425 

29645 
29863 

30081 
30298 

nnr"  T  a 

25  i  24 

2S691    28713 
28914   28937 

I 
2 

3 
4 

i 

7 
8 

9 

3  1  2 
5  !  5 

195 
196 
197 
198 
199 

29003 
29226 

29447 
29667 
29885 

29026 
29248 

29469 
29688 
29907 

29048 
29270 
29491 
29710 
29929 

29070 
29292 

29513 
29732 
29951 

29092 
29314 
29535 
29754 
29973 

29115 
29336 

29557 
29776 

_29994 
302 1 1 
30428 

30643 
30856 
31069 

29137 
29358 

29579 
29798 
30016 

30233 
30449 
30664 
30878 
31091 

31302 
31513 
31723 
31931 
32139 

29159 
29380 
29601 
29820 
30038 

30255" 

30471 

30685 

30899 

31112 

29181 

29403 
29623 
29842 
30060 
30276 

8 
10 

13 

\l 

20 
23 

7 
10 

12 
14 
17 
19 
22 

200 

201 
202 
203 
204 

30103 
30320 

30535 
30750 
30963 

30125 
30341 
30557 
30771 
30984 

30146 
30363 
30578 
30792 
31006 

30168 

30384 
30600 
30814 
31027 

31239 
31450 
31660 
31869 
32077 

30190 
30406 
30621 

3083s 
31048 

3'-'4y-   o^j^t 

30707  30728 

23 

22 

30920 
31133 

30942 
31154 

I 
2 

3 
4 

5 
6 

7 
8 

9 

2 

5 
7 

9 
12 

14 
16 
18 
21 

2 
4 
7 
9 
u 

13 

15 

18 
20 

205 
206 
207 
208 
209 

31175 
31387 

31597 
31806 

32015 

3II97 

31408 

3I6I8 
31827 

32035 

31218 
31429 
31639 
31848 
32056 

31260 

31471 
31681 
31890 
32098 

31281 
31492 
31702 
31911 
32118 

31323 
31534 
31744 
31952 
32160 

32366 

^2572 

31345 
31555 
31765 

31973 
32I8I 

32387 
32593 
32797 
33001 
33203 

33405 
33606 
33806 
34005 
34203 

31366 
31576 
31785 
3 '994 
32201 

210 
211 
212 

213 
214 

216 
217 
218 
219 

32222 
32428 

32634 
32838 
33041 
33244 
33445 
33646 
33846 
34044 

32243 
32449 
32654 

32858 

33062 

33264 
33465 
33666 
33866 
34064 

32263 
32469 
32675 
32879 
33082 

33284 
33486 
33686 

33885 
34084 

32284 
32490 

32695 
32899 

33102 

33304 
33506 
33706 
33905 
34104 

32305 
32510 

32715 
32919 

33122 

32325 
32531 
32736 
32940 

33143 

33345 
33546 
33746 
33945 
34143 

32346 
32552 

32408 
32613 
32818 
33021 
33224 

33425 
33626 
33826 

34025 
34223 

32756  ,  32777 

21 

20 

32960 
33163 
33365 

33766 
33965 
34163 

JZ90U 
33183 

'33385 
33586 
33786 
33985 
34183 

1 
2 
3 
4 

1 

7 
8 

9 

2 

2 

A 

33325 
33526 
33726 

33925 
34124 

4      T 

6   6 

8   8 

11   10 

13   12 

15   14 

,1.  1   -/" 

No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

17 
19 

10    1 

TABLE  42. 
Logarithms  of  Numbers. 


[Page  393 


No.  22c 


-2800. 


Log.  34242 44716. 


No. 


0 


1 


220 
22 1 

TOO 


220 

227 

228 

229 

2 

2 


30  r 
31 


234^ 
235 ' 


238 

239_ 
240 
241 

242 

243 
^4 

245" 
24(1 

247 

24S 

249 


250 
251 

2  ^2 

253 
254^ 

'255 
256 

257 
25S 

259_ 

260 

261 

262 

263 

2(>4 

"265^ 

266 

207 

2()8 

209 
270 
271 

272 

273 
274 

275 

276 

277 
278 

279 

No. 


34242 
34439 
34635 
34830 
3J025 

352 1 8 
3541 1 
35603 

35793 
J5984 

36173 
36361 
36549 
36736 
36922 

T7ior 
37291 

37475 
37658 
37840 
3S021 
38202 
38382 
38561 

38917 
39094 
39270 

39445 
39620 

39794 
39967 
40140 
40312 
40483 
40654 
40824 

40993 
41162 
41330^ 

41497 
4 1 664 
41830 

41996 
42160 

42325" 
42488 
42651 
42813 

429 75 _ 

43136 

43297 

43457 
43616 

43775 

43933 
44091 

44248 

44404 
44560 

0 


34262 

34459 
34655 
34S50 

J5044 
35238 
35430 
35622 

35813 

3^3_ 

^6192 

36380 

36568 

36754 
36940 
37125 
37310 

37493 
37676 

37858 

38039 

38220 

38399 
38578 
38757 
38934 
39111 
39287 
39463 
39637 


39811 
39985 
40157 
40329 
_405oo 

40671 
40841 
41010 

41179 
41347 
41514 
416S1 
41847 
42012 
42177 


34282 
34479 
34674 
34869 

35064 

35257 
35449 
35641 
35832 
36021 

362 1 1 

36399 
36586 

36773 
J^959_ 

37144 
37328 
37511 
37694 
37876 

38057 
38238 

38417 

38596 

,38775 

38952 

39129 

39305 
39480 

39655^ 

39829 

40002 

4017s 
40346 

40518 


34301 
34498 
34694 

34889  ! 

_35o83 

35276 
35468 
35660 

35851 
36040  j 

36229  j 
36418  j 
36605  ! 

36791  } 
36977 

37162 
37346 
37530 
37712  I 

J7i?4L 

38075  1 
38256 

38435 
38614 
38792 


42341 
42504 
42667 
42830 
42991 
43152 
43313 
43473 
43632 
43791 

43949 
44107 
44264 
44420 
44576 


40688 
40858 
41027 
41 196 

41363 

41531 
41697 
41863 
42029 
_4ri?3_ 

42357 
42521 
42684 
42846 
4300^ 

43169 
43329 
43489 
43648 
43807 

'43965 
44122 
44279 
44436 
44592 


38970 
39146 
39322 

39498 
3967^ 

39846 
40019 
40192 
40364 
_40535 
40705 
40875 
41044 
41212 
41380^ 

41547 
41714 
41880 
42045 
42210 


42374 

42537 

42700 

42862 

J.3024 

43185 
43345 
43505 
43664 

J:3823_ 
43981 
44138 
44295 
44451 
44607 


34321 

34518 

34713 
34908 

35102 

35295 
35488 

35679 
35870 
36059 


6 


34341 
34537 
34733 
34928 
_35i22 

35315 
35507 
35698 
35889 
36078 


36248 

36436 
36624 
36810 
36996 


37181 

37365 
37548 
37731 
37912 

38093 
38274 

38453 
38632 
38810 


37199 
37383 
37566 

37749 
37931 
38112 

38292 

38471 
38650 
38828 


38987 
39164 
39340 

39515 
39690 


39863 
40037 
40209 
40381 
_405i2_ 
40722 
40892 
41061 
41229 
41397 
41564 

41731 
41896 
42062 
42226 
42390 

42553 
42716 

42878 

43040 


39005 
39182 
39358 
39533 
39707 
39881 
40054 
40226 
40398 
40569 

40739 
40909 
41078 
41246 
41414 
41581 
41747 

41913 
42078 

42243 


43201 
43361 
43521 
43680 

43838 
43996 
44154 
443" 

44467 
44623 


42406 
42570 

42732 
42894 
43056 

43217 
43377 
43537 
43696 
.43854 
44012 
44170 
44326 

44483 
44638 


36267  , 

36455 
36642  I 

36829 
37014 


34361 

34557 
34753 
34947 
35141 J. 

35334  1 
35526  , 
35717 
35908 
36097 

36286 

36474 
36661  I 

36847 

J7^33_i 

37218 

37401 

37585 
37767 

37949  ^ 

38130  ; 

38310 

38489 
38668 

38846 


39023 
39199 
39375 

39550  ; 
39724 

39898  : 
40071 
40243 
40415 

40586_ 

40756 :' 

40926 
41095 
41263 
41430 

41597 
41764 

41929 
42095 
42^59^  _ 

42423 
42586 

42749 
4291 1 

43072 


34380 
34577 
34772 
34967 
35160 
35353 
35545 
35736 

35927 
361 16 

36305 

36493 
36680 
36866 

37051 

37236 

37420 

37603 

37785 

37967_ 

38148 

38328 

38507 

38686 

J8863 

39041 
39217 
39393 
39568 
39742 


8 


34400 
34596 
34792 
34986 
35180 
35372 
35564 
35755 
35946 

^36135 
36324 
36511 
36698 
36884 
37070 


37254 

37438 
37621 

37803 
J  7985 
38166" 

38346 
38525 
38703 
38881 


39915 
40088 
40261 

40432 
40603 


40773 

40943 
41111 

41280 
41447 


43233  I 

43393 

43553 

43712 

43870 

44028 

44185 

44342 

44498 

44654 

6 


41614 
41780 
41946 
42 1 II 
32275 

42439 

42602 

42765 

42927 

43088^ 

43249 

43409 

43569 

43727 

43886 

44044 
44201 
44358 
44514 
44669 


39058 

39235 
39410 

39585 
J9759 

39933 
40106 
40278 

40449 
40620 

40790 
40960 
41 128 
41296 
J.1464 

41631 

41797 

41963 
42127 

42292 


9 


34420 
34616 
34811 
35005 
35199 


42455 
42619 
42781 

42943 
^3104 

43265" 
43425 
43584 
43743  I 
43902  I 

44059 
44217 

44373  I 

44529 

44685 

8 


35392 
35583 
35774 
35965 
36154 
36342 
36530 
36717 
36903 
37088 

37273 
37457 
37639 
37822 

38003 
38184 
38364 
38543 
38721 
38899 

39076 

39252 
39428 
39602 

39777 


39950 
40123 
40295 
40466 
40637 

40807 
40976 
41145 
41313 
41481 

"41647 
41814 

41979 
42144 
42308 


42472 
42635 

42797 
42959 

43281 

43441 
43600 

43759 
_43^17. 

44075 
44232 
44389 

44545 
44700 


I 
2 

3 
4 

5 
6 

7 
8 


20 

2 

4 

6 

8 

10 
12 

14 
16 
18 


19 


4 
6 


10 
II 
13 
15 
17 


18 


2 
4 
5 
7 
9 
II 

13 

14 
16 


17 


2 

3 

5 

7 

9 

10 

12 

14 

15 


16 


2 
3 

5 
6 

8 

10 

II 

13 

14 


2 

3 

5 


I 
2 
3 

4 

5 

6 

7 

8  ^ 

9  '  14 


9 
II 

12 


Page  394 

TABLE  42. 
Logarithms  of  Numbers. 

Nc 

).  2800 — 

-3400. 

Log.  44716 

53148. 

No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

280 
281 

282 

283 
284 

44716 

44871 
45025 
45179 
45332 

44731 
44886 
45040 
45194 
45347 

44747 
44902 
45056 
45209 
45362 

44762 

44917 
45071 
45225 
45378 

44778 
44932 
45086 

45240 
45393 

44793 
44948 
45102 

45255 
45408 

45561 
45712 
45864 
46015 
46165 

44809 
44963 
45117 
45271 
45423 

44824 
44979 

45133 
45286 

45439 

44840 
44994 
45148 
45301 
45454 

44855 
45010 

45163 
45317 
45469 
45621 

45773 
45924 

46075 
46225 

16 

1 
2 

3 
4 

1 

7 
8 

9 

2 

5 

6 

8 

10 

11 

13 

14 

285 
286 

287 
288 
289 

45484 
45637 
45788 

45939 
46090 

45500 
45652 
45803 
45954 
46105 

45515 
45667 
45818 
45969 
46120 

45530 
45682 

45834 
45984 
46135 

45545 
45697 
45849 
46000 
46150 

45576 
45728 

45879 
46030 

46180 

45591 
45743 
45894 
46045 
46195 

45606 
45758 

45909 
46060 
46210 

290 
291 
292 

293 

294 

46240 

46389 
46538 
46687 

46835 

46255 
46404 

46553 
46702 
46850 

46270 
46419 
46568 
46716 
46864 

46285 
46434 
46583 
46731 
46879 

46300 
46449 
46598 
46746 
46894 

46315 
46464 

46613 

46761 

46909 

46330 

46479 
46627 
46776 
46923 

46345 
46494 
46642 
46790 
46938 

46359 
46509 

46657 
46805 

46953 

46374 
46523 
46672 
46820 

46967 
47114 
47261 
47407 
47553 
47698 

1 

15 

295 
296 

297 

298 

299 

46982 
47129 
47276 
47422 
47567 

46997 
47144 
47290 

47436 

47582 

47012 
47159 
47305 
47451 
47596 

47026 

47173 
47319 
47465 
47611 

47041 
47188 

47334 
47480 

47625 
47770 
47914 
48058 
48202 

48344 

47056 
47202 

47349 
47494 
47640 

47070 
47217 

47363 
47509 
47654 

47085 
47232 
47378 
47524 
47669 

47100 
47246 
47392 
47538 
47683 

1 
2 

3 

4 

5 
6 

7 
8 

9 

2 

3 
5 
6 

8 

9 
11 
12 
14 

300 
301 
302 

303 
304 

47712 

47857 
48001 

48144 
48287 

47727 
47871 
48015 

48159 
48302 

47741  < 

47885 

48029 

48173 
48316 

47756 
47900 
48044 
48187 
48330 

47784 
47929 
48073 
48216 

48359 

47799 
47943 
48087 
48230 

48373 

47813 
47958 
48101 
48244 
48387 

47828 
47972 
48116 
48259 
48401 

47842 
47986 
48130 
48273 
48416 

48558 
48700 
4S841 
48982 
49122 

1 

305 
306 

307 
308 

309 

48430 
48572 
48714 

48855 
48996 

48444 
48586 
48728 
48869 
49010 

48458 
48601 
48742 
48883 
49024 

48473 
48615 

48756 
48897 
49038 

48487 
48629 

48770 
48911 
49052 

48501 
48643 

48785 
48926 
49066 

48515 
48657 
48799 
48940 
49080 

48530 
48671 
48813 

48954 
49094 

48544 
48686 
48827 
48968 
49108 

14 

I 
2 

3 
4 

i 

7 
8 

9 

1 

3 
4 
6 

7 

8 

10 

11 

13 

310 

3" 
312- 

313 
314 

49136 
49276 

49415 
49554 
49693 

49150 
49290 
49429 
49568 
49707 

49164 
49304 

49443 
49582 

49721 

49178 

49318 

49457 
49596 

49734 

49192 
49332 
49471 
49610 
49748 

49206 

49346 

49485 
49624 
49762 

49220 
49360 

49499 
49638 
49776 

49234 
49374 
49513 
49651 
49790 

49248 

49388 

49527 
49665 

49803 

49262 
49402 

49541 
49679 
49817 

316 

318 
319 

49831 
49969 
50106 
50243 
50379 

49845 
49982 

50120 

50256 

50393 

50529 
50664 

50799 
50934 
51068 

49859 
49996 

50133 
50270 
50406 

49872 
50010 

50147 
50284 
50420 

49886 
50024 
50161 
50297 
50433 
50569 
50705 
50840 

50974 
51108 

49900 

50037 
50174 

503 1 1 
50447 

49914 

50051 
50188 

50325 
50461 

49927 
50065 
50202 
50338 
50474 

49941 
50079 
50215 

50352 
50488 

49955 
50092 
50229 

50365 
50501 

50637 
50772 
50907 
51041 

51175 
51308 
51441 
51574 
51706 

51838 

1 

13 

320 
321 
322 

323 

324 

50515 
50651 
50786 
50920 

51055 

50542 
50678 

50813 
50947 
51081 

50556 
50691 
50826 
50961 
51095 

50583 
50718 

50853 
50987 
51121 

50596 
50732 
50866 
51001 

51135 

50610 

50745 
50880 
51014 
51148 

50623 
50759 
50893 
5102S 
51162 

I 
2 

3 
4 

5 
6 

7 
8 

9 

I 

3 
4 
5 

7 
8 

9 
10 
12 

325 
326 

327 
328 

329 

5ii&i 
51322 
51455 
51587 
51720 

51202 

51335 

51468 

51601 

51733 
51865 
51996 
52127 

52257 
52388 

51215 
51348 
S1481 
51614 
51746 
51878 
52009 
52140 
52270 
52401 

51228 
51362 

51495 

51627 

51759 

51242 

51375 
51508 
51640 

51772 

51255 
51388 

51521 

51654 
51786 

51268 
51402 

51534 
51667 

51799 

51930 
52061 
52192 

52323 
52453 

51282 

51415 
51548 
516S0 
51812 

51295 
51428 

51561 

51693 
51825 

330 
331 
332 
333 
334 

51851 
51983 
52114 

52244 
52375 
1  5'2504 
52634 
52763 
52892 
53020 

51891 
52022 

52153 
52284 

52414 

51904 

52035 
52166 
52297 
52427 

51917 

52048 

52179 
52310 
52440 

51943 
52075 
52205 

52336 
52466 

51957 
52088 

52218 

^  52349 
52479 

51970 
52101 

52231 
52362 
52492 

1 

I 
2 

3 
4 
5 
6 

7 
8 

9 

12 

1 
2 
4 

5 
6 

1 

10 
11 

335 
336 
337 
338 
339 

52517 
52647 
52776 
52905 
53033 

52530 
52660 

52789 
52917 
53046 

52543 
52673 
52802 

52930 
53058 

52556 
52686 
52815 

52943 
53071 

52569 
52699 
52827 

52956 
53084 

52582 

52711 
52840 
52969 
53097 

52595 
52724 

52853 
52982 
53"o 

52608 

52737 
52866 

52994 
53122 

52621 
52750 
52879 
53007 
53135 

1  No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

V 

TABLE  42. 
Logarithms  of  Numbers. 

Page 

395 

No. 

5.  3400 

—4000. 

Log.  53148 

60206. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

340 
341 
34^ 
j4j 
344 

345 
34b 
347 
348 
349 

53148 

53275 
53403 
53529 
53656 
53782 
53908 

54033 
54158 
54283 

53161 

53288 

53415 
53542 
53668 

53173 

53301 
53428 

53555 
536^1 

53186 
53314 
53441 
53567 
53694 

53199 
53326 

53453 
53580 
53706 

53832 

53958 
54083 
54208 
54332 

53212 

53339 
53466 

53593 
53719 

53845 
53970 

54095 
54220 

54345 

53224 
53352 
53479 
53605 
53732 

53857" 

53983 

54108 

54233 
54357 

53237 
53364 
53491 
53618 
53744 
53870 

53995 
54120 

54245 
54370 

54494 
54617 
54741 
54864 
54986 

53250 

53377 

53504 

53631 

53757 

53882- 

54008 

54133 
54258 
54382 
54506 
54630 
54753 
54876 
54998 

53263 

53390 
53517 
53643 
53769 

53895 
54020 

54145 
54270 
54394 
54518 
54642 

54765 
54888 

5501 1 

I 
2 

3 

4 

5 
6 

7 
8 

9 

13 



1 

3 

4 
5 
7 
8 

9 
10 
12 

53794 
53920 

54045 
54170 

54295 
54419 
54543 
54667 
54790 
54913 

53807 

53933 
54058 
54183 
54307 

53820 

53945 
54070 

54195 
54320 

350 
351 

352 

-»  r  -^ 

354 

54407 
54531 
54*554 

54777 
54900 

54432 
54555 
54679 
54802 

54925 

54444 
54568 

54691 
54814 

54937 

54456 
54580 
54704 
54827 
54949 

54469 
54593 
54716 

54839 
54962 

54481 
54605 
54728 
54851 
54974 

355 
356 
357 
358 
359 

55023 
55145 
55267 
55388 
55509 

55035 

55157 
55279 
55400 
55522 

55047 
55169 

55291 
55413 
55534 

55060 

55182 
55303 
55425 
55546 

55072 
55194 
55315 
55437 
55558 

55084 
55206 

55328 
55449 
55570 

55096 
55218 
55340 
55461 

55582 

55108 
55230 
55352 
55473 
55594 

55121 
55242 
55364 

55606 

55133 

55255 
55376 

55497 
55618 

I 

2 

3 

4 

5 
6 

7 
8 

9 

12 

I 

2 

4 

5 
6 

7 

8 

10 

II 

360 
361 
362 

364 

55630 
55751 
55871 
55991 
56110 

55642 
55763 
55883 
56003 
56122 

55654 

55775 

55895 
56015 

56134 

55666 
557S7 
55907 
56027 

56146 

55678 
55799 
55919 
56038 

56158 

55691 
55811 

55931 
c;6o5o 

56170 

55703 
55823 

55943 
56062 
56182 

55715 
55835 
55955 
56074 
56194 

55727 
55847 
55967 
56086 
56205 

55739 
55859 
55979 
56098 

56217 

366 

367 

368 

369 

56229 
56348 
56467 
56585 
56703 

56241 
56360 
56478 
56597 
56714 

56253 
56372 

56490 
56608 
56726 

56265 

56384 
56502 
56620 
56738 

56277 
56396 

56514 
56632 

56750 

56289 

56407 
56526 

56644 
56761 

56301 
56419 
56538 
56656 

56773 

56312 
56431 
56549 
56667 

56785 

56324 

56443 
56561 

56679 

56797 

56336 

56455 

56573 
56691 

56808 
56926 

57043 
57159 
57276 

57392 

370 
371 

372 
373 
374 

56820 

56937 
57054 
57171 
57287 

56832 

56949 
57066 

57183 
57299 

56844 
56961 

57078 
57194 
57310 

56855 
56972 
57089 
57206 
57322 

56867 

56984 
57101 

57217 
57334 

56879 
56996 

57113 
57229 
57345 

56891 
57008 
57124 
57241 
57357 

56902 

57019 
57136 
57252 
57368 

56914 

57031 
57148 
57264 
57380 

11 

I 
2 

3 

4 

5 
6 

7 
8 

9 

I 
2 

3 
4 
6 

7 
8 

9 
10 

375 
376 
377 
378 
379 

57403 
57519 
57634 
57749 
57864 

57415 

57530 
57646 

57761 

57875 

57426 

57542 
57657 
57772 
57887 

57438 
57553 
57669 
57784 
57S98 

57449 

57565 
57680 

57795 
57910 

57461 
57576 
57692 

57807 
57921 

57473 
57588 

57703 
57818 

57933 

58047 
58161 

58274 
58388 

58501 

57484 
57600 

57715 
57830 
57944 

57496 
57611 
57726 
57841 
57955 

57507 
57623 
57738 
57852 
57967 
58081 

58195 
58309 
58422 

58535 

380 

381 
3S2 

384 

57978 
58092 
58206 
58320 
58433 

57990 
58104 

58218 

58331 
58444 

58001 

58115 
58229 

58343 
58456 

58013 

58127 
58240 
58354 
58467 

58024 

58138 
58252 

58365 
58478 

58035 
58149 
■;8263 

58377 
58490 

58058 

58172 
58286 

58399 
58512 

58070 
58184 

58297 
58410 

58524 

385 
386 

387 
388 

389 

58546 
58659 

58771 
588S3 

58995 

58557 
58670 
58782 

58894 
59006 

58569 
58681 

58794 
58906 

59017 

58580 
58692 
58805 

58917 
59028 

58591 
58704 
58816 
58928 
59040 

58602 

58715 
58827 

58939 
59051 

58614 

58726 
5S838 

58950 
59062 

58625 

58737 
58850 

58961 
59073 

58636 

58749 
58861 

5S973 
59084 

58647 
58760 

58872 
58984 
59095 
59207 
59318 
59428 
59539 
59649 

10 

390 
391 
39-^ 
393 
394 

59106 

59218 
59329 
59439 
59550 

59118 

59229 
59340 
59450 
59561 

59129 

59240 

59351 
59461 

59572 

59140 

59251 
59362 
59472 
59583 

59151 

59262 

59373 
59483 
59594 

59162 
59273 
59384 
59494 
59605 

59173 
59284 

59395 
59506 
59616 

59184 

59295 
59406 

59517 
59627 

59195 
59306 

59417 
59528 
59638 

I 
2 

3 

4 

5 
6 

7 
8 

9 

I 

2 

3 
4 

5 
6 

7 
8 

9 

395 
396 
397 
398 
399 

59660 
59770 
59879 
59988 
60097 

59671 

59780 

59890 

59999 
60108 

59682 

59791 
59901 
60010 
601 19 

59693 
59802 

59912 
60021 
60130 

59704 
59813 
59923 
60032 
60141 

59715 
59824 
59934 
60043 
60152 

59726 

59835 
59945 
60054 

60163 

59737 
59^6 
59956 
60065 
60173 

59748 

59857 
59966 
60076 
60184 

59759 
59868 

59977 
60086 
60195 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

Page  396 

TABLE  42. 
Logarithms  of  Numbers. 

N( 

)   4.000 

— 4.600 

Log.  60206 66276. 

No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

1 

400 
401 
402 

403 
404 

60206 
60314 
60423 

60531 
60638 

60217 
60325 

60433 
60541 

6ob49 

60228 
60336 
60444 
60552 
60660 

60239 
60347 

60455 
60563 

60670 

60249 
60358 
60466 

60574 
60681 

60260 
60369 
60477 
60584 
60692 

60271 
60379 
60487 

60595 
60703 

60282 
60390 
60498 
60606 
60713 

60293 
60401 
60509 
60617 
60724 

60304 

60412 
60520 
60627 

60735 

11 

I 

2 

3 
4 

5 
6 

7 
8 

9 

I 
2 

3 
4 
6 

7 
8 

9 
10 

405 
406 

407 
408 
409 

60746 
60853 

61066 
61 1 72 

60756 
60863 
60970 
61077 
61 183 

60767 
60874 
60981 
61087 
61 194 

60778 
60885 
60991 
61098 
61204 

60788 
60895 
61002 
61 109 
61215 

60799 
60906 
61013 
61119 
61225 

60810 
60917 
61023 
61130 
61236 

60821 
60927 
61034 
61140 
61247 

60831 
60938 
61045 
61151 
61257 

60842 

60949 
61055 

61162 

61268 

410 
411 
412 

413 
414 

61278 
61384 
61490 

61595 
61700 

61289 

61395 
61500 
61606 
61711 

61300 
61405 
61511 
61616 
61721 

61310 
61416 
61521 
61627 
61731 

61321 

61426 

61532 
61637 
61742 

61331 

61437 
61542 
61648 
61752 

61342 
61448 

61553 
61658 
61763 

61352 
61458 

61563 
61669 

61773 

61363 
61469 

61574 
61679 
61784 

61374 
61479 
61584 
61690 

61794 

415 

416 

417 
418 
419 
420 
421 
422 
423 
424 

425 
426 

427 
428 

429 

61805 
61909 
62014 
62118 
62221 

61815 
61920 
62024 
62128 
62232 

61826 
61930 
62034 
62138 
62242 

61836 
61941 
62045 
62149 
62252 

61847 
61951 
62055 
62159 
62263 

61857 
61962 
62066 
62170 
.  62273 

61868 
61972 
62076 
62180 
62284 

61878 
61982 
62086 
62190 
62294 

61888 

61993 
62097 
62201 
62304 

61899 
62003 
62107 
62211 

62315 
62418 
62521 

62624 
62726 
62829 

62325 
62428 

62531 
62634 

62737 

62839 

62941 

63043 
63144 
63246 

62335 
62439 
62542 
62644 
62747 
62849 
62951 

63053 
63155 
63256 

62346 
62449 
62552 
62655 
62757 
62859 
62961 
63063 
63165 
63266 

62356 

62459 
62562 

62665 

62767 

62870 

62972 

63073 

63175 
63276 

62366 
62469 
62572 
62675 
62778 
62880 
62982 
630S3 

63185 
63286 

62377 
62480 

62583 
62685 
62788 

62890 
62992 
63094 

63195 
63296 

62387 
62490 

62593 
62696 

62798 

62397 
62500 
62603 
62706 
62808 

62408 
62511 
62613 
62716 
62818 

10 

62900 
63002 
63104 
63205 
63306 

62910 
63012 
631 14 
63215 
63317 

62921 
63022 
63124 
63225 
63327 

62931 

63033 

63134 

63236 

63337 

63438^ 

63538 

63639 
63739 
63839 

I 
2 

3 

4 

5 
6 

7 
8 

9 

I 

2 

3 

4 

5 
6 

7 
8 

9 

430 
431 
432 
433 
434 

63347 
63448 

63548 
63649 

63749 

63357 
63458 
63558 
63659 
63759 

63367 
63468 

63568 

63669 

63769 

63377 
63478 
63579 
63679 
63779 

63387 
63488 

63589 
63689 

63789 

63397 
63498 

63599 
63699 

63799 

63407 
63508 
63609 
63709 
63809 

63417 
63518 

63619 
63719 
63819 

63428 
63528 
63629 
63729 
63829 

435 
436 
437 
438 
439 

63849 

63949 
64048 
64147 
64246 

63859 
63959 
64058 

64157 
64256 

63869 
63969 
64068 
64167 
64266 

63879 
63979 
64078 
64177 
64276 

63889 
63988 
64088 
64187 
64286 

63899 
63998 
64098 
64197 
64296 

63909 
64008 
64108 
64207 
64306 

63919 
64018 
64118 
64217 
64316 

63929 
64028 
64128 

64227 
64326 

63939 

64038 

64137 
64237 
64335 

440 
441 

442 

443 
444 

64345 
64444 
64542 
64640 
64738 

64355 
64454 

64552 
64650 

64748 

64365 
64464 
64562 
64660 

64758 

64375 
64473 
64572 
64670 
64768 

64483 
64582 
64680 
64777 

64395 
64493 
64591 
64689 

64787 

64404 

64503 
64601 

64699 
64797 
^  64895 
64992 
65089 
65186 
65283 

64414 

64513 
64611 

64709 
64807 

64904 
65002 

65099 
65196 
65292 

64424 

64523 
64621 
64719 
64816 

64434 
64532 

64631 

64729 
64826 

445 
446 
447 

44« 
449 

64836 

64933 
65031 
65128 
65225 

64846 

64943 
65040 

65137 
65234 

64856 

64953 
65050 

65147 
65244 

64865 
64963 
65060 
65157 
65254 

64875 
64972 
65070 
65167 
65263 

64885 
64982 
65079 
65176 

65273 

64914  I  64924 
65011  !  65021 
65108  i  65118 
65205  ■  65215 
65302   65312 

9 

450 
451 
452 
453 
454 

455 
456 
457 
458 
459 

65321 
65418 

65514 
65610 
65706 

65331 
65427 
65523 
65619 

65715 

65341 
65437 

65629 
65725 

65350 
65447 
65543 
65639 
65734 

65360 
65456 
65552 
65648 

65744 

65466 
65562 
65658 

65753 

65379 
65475 
65571 
65667 

65763 

65389 
65485 
65581 
65677 
65772 
65868 

65963 
66058 

66247 

6C1qS     f\CAr,R 

65495 
65591 
65686 

65782 

65877 
65973 
66068 

66162 
66257 

65504 

65600 
65696 

65792 
65887 
659S2 

66077 
66172 
66266 

I 

2 

3 
4 

5 
6 

7 
8 

9 

I 

2 

3 
4 

5 

5 
6 

65801 
65896 
65992 
66087 
66181 

6581 1 
65906 
66001 
66096 
66191 

65820 
65916 
6601 1 
66106 
66200 

65830 

65925 
66020 

66115 
66210 

65839 

65935 
66030 

66124 

66219 

65849 
65944 
66039 
66134 
66229 

65858 

65954 
66049 

66143 
66238 

No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

TABLE  42 

Page  397 

> 

Logarithms  of  Numbers. 

N 

D.  4600 

—5200. 

Log.  66276 7160a.    1 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

460 

66276 

66285 

66295 

66304 

66314 

66323 

66332 

66342 

66351 

66361 

10 

461 

66370 

66380 

66389 

66398 

66408 

66417 

66427 

66436 

66445 

66455 



462 

66464 

66474 

66483 

66492 

66502 

665 1 1 

66521 

66530 

66539 

66549 

1 

I 

463 

66558 

66567 

66577 

66586 

66596 

66605 

66614 

66624 

66633 

66642 

2 

2 

464 

66652 

66661 

66671 

66680 

66689 

66699 

66708 
66801 

66717 
66811 

66727 
"^66820 

66736 
66829 

3 
4 

4 

465' 

"  66745 

66755 

66764 

66773 

66783 

66792 

466 

66S39 

66848 

66857 

66867 

66876 

66885 

66894 

66904 

66913 

66922 

5 

5 

467 

66932 

66941 

66950 

66960 

66969 

66978 

66987 

66997 

67006 

67015 

6 

6 

468 

67025 

67034 

67043 

67052 

67062 

67071 

67080 

67089 

67099 

67108 

7 

7 

469 

67II7 

67127 
67219 
67311 

67136 

67228' 

67321 

67145 
67237 
67330 

_67i54^ 
67247 
67339 

67164 

67173, 

67182 

67191 

67201 

8 
9 

8 
9 

470 

67210 

67302 

67256 
67348 

67265 
67357 

67274 
67367 

67284 
67376 

"67293" 
67385 

471 

472 

67394 

67403 

67413 

67422 

67431 

67440 

67449 

67459 

67468 

67477 

473 

67486 

67495 

67504 

67514 

67523 

67532 

67541 

67550 

67560 

67569 

474 

__  67^78 

675S7 
67679 

67596 
67688 

67605 

67614 

67624 
67715 

67633 
67724 

67642 
67733 

67651 
67742 

67660 
"67752" 

475 

67669 

67697 

67706 

476 

67761 

67770 

67779 

67788 

67797 

67806 

67815 

67825 

67834 

67843 

477 

67852 

67861 

67870 

67879 

67888 

67897 

67906 

67916 

67925 

67934 

47S 

67943 

67952 

67961 

67970 

67979 

67988 

67997 

68006 

68015 

68024 

479 
480 

6S034 

68043 
68133 

68052 
^68142" 

68061 

68070 

68079 

68088 

68097 
68187 

68106 
68196 

68115 

6SI24 

68151 

~68r6o" 

68169 

68178 

68205 

48 1 

6S2I5 

68224 

68233 

68242 

68251 

68260 

68269 

68278 

68287 

68296 

482 

6S305 

6S314 

68323 

68332 

68341 

68350 

68359 

68368 

68377 

683S6 

483 

68395 

68404 

68413 

/^  0  — 

68422 

68431 

,-  0  ^ 

68440 

/-  0  _ 

6S449 

/-  0  ^  _  0 

68458 

68467 

/-  0  _  _  ZT 

68476 

4S4 

68485 

68494 

68502 

6851 1 

08520 

68529 

68538 

68547 

68556 

68565 

n. 

485^ 
486 

"  68574 

68664 

6S583 
68673 

68592 
6868 1 

6860  r 
68690 

^"68610 
68699 

68619 

68708 

68628 
68717 

68637 
68726 

68646 

68735 

68655 
68744 

« 

48  7 

68753 

68  762 

68771 

68780 

68789 

68797 

68806 

68815 

68824 

68833 

1 

1 

48S 

68842 

68851 

68860 

68869 

68878 

68886 

68895 

68904 

68913 

68922 

2 

2 

489 

68931 

68940 

68949 

68958 

68966 

_.^8975 

68984 

68993 

69002 

69011 

3 

3 

490 

69020 

69028 

^69037^ 

69046 

69055 

69064 

69073 

69082 

69690 

69099 

4 
5 

4 

5 

I 

491 

69108 

69117 

69126 

69135 

69144 

69152 

69161 

69170 

69179 

69188 

492 

69197 

69205 

69214 

69223 

69232 

69241 

69249 

69258 

69267 

69276 

7 
8 

493 

69285 

69294 

69302 

693 1 1 

69320 

69329 

69338 

69346 

69355 

69364 

I 

494 

_  69373 

69461 

69548 

69381 
69469 

69557 

69390 

69399 

69408 

69417 

69425 

69434 

69443 

69531 

69618 

69452 

69539 
69627 

9 

495 
496 

69478 
69566 

69487 
69574 

69496 
69583 

69504 
69592 

69513 
69601 

69522 
69609 

497 

69636 

69644 

69653 

69662 

69671 

69679 

69688 

69697 

69705 

69714 

49S 

69723 

69732 

69740 

69749 

69758 

69767 

69775 

69784 

69793 

69801 

„499_ 
500 

69810 

'  69897 

69819 
69906 

69827 
69914 

69836 

69845 

69854 

69862 
69949 

69871 
69958 

69880 
69966 

69888 
"69975" 

69923 

69932 

69940 

501 

69984 

69992 

70001 

70010 

70018 

70027 

70036 

70044 

70053 

70062 

502 

70070 

70079 

70088 

70096 

70105 

70114 

70122 

70131 

70140 

70148 

503 

70157 

70105 

70174 

70183 

70191 

70200 

70209 

70217 

70226 

70234 

504 

70243 

70252 

70260 

70269 

70278 

70286 

70295 

70303 

70312 

70321 

505 

70329 

70338 

70346 

"70355" 

70364 

70372 

70381 

703^9 

70398 

70406 

506 

70415 

70424 

70432 

70441 

70449 

70458 

70467 

70475 

70484 

70492 

507 

70501 

70509 

70518 

70526 

70535 

70544 

70552 

70501 

70569 

70578 

50S 

705  8 'J 

70595 

70603 

70612 

70621 

70629 

70638 

70646 

70655 
70740 

70825 

70663 

509 
510 

70672 
70757 

70680 
70766 

70689 
"  70774^ 

70697 
70783 

70706 

_7°7i4 

70723 

70731 

70749 
70834 

H 

70791 

70800 

70808 

70817 

1 

5" 

70842 

70851 

70859 

70868 

70876 

70885 

70893 

70902 

70910 

70919 

1  !  1 

512 

70927 

70935 

70944 

70952 

70961 

70969 

70978 

70986 

70995 

71003 

2   2 

513 

71012 

71020 

71029 

71037 

71046 

71054 

71063 

71071 

71079 

710S8 

3   2 

514 

71096 

71 105 

7U13 

71122 
71206 

71 130 

71139 

71147 

71155 

71164 

71172 

71257 

4  '  3 

5  4 

515 

711S1 

71189 

71198 

71214 

71223 

71231 

71240 

71248 

516 

71265 

71273 

71282 

71290 

71299 

71307 

71315 

71324 

71332 

71341 

6   5 

517 

71349 

71357 

71366 

71374 

71383 

71391 

71399 

71408 

71416 

71425 

7   6 

5i« 

71433 

71441 

71450 

71458 

71466 

71475 

71483 

71492 

71500 

71508 

8   6 

519 

71517 

71525 

71533 

71542 

71550 

71559 

71567 
6 

71575 

7 

71584 

8 

71592 

9   7 

No. 

0 

1 

2 

3 

4 



5 

9 

i 


Page 

398] 

TABLE  42. 

Logarithms  of  Numbers. 

No.  5200 — 

—5800, 

Log.  7 

1600 76341 

• 

No. 

0 

1 

2 

3 

4 

5 

6 

% 

8 

9 

520 

521 

522 

523 
524 

71600 
71684 
71767 
71850 

71933 

71609 
71692 

71775 
71858 

__7i94i_ 
72024 
72107 
72189 
72272 

•_72354  _ 
72436 
72518 

72=;99 
72681 
72762 

71617 
71700 

71784 
71867 
71950 

71625 
71709 
71792 

71875 
71958 

71634 
71717 
71800 

71883 
71966 

71642 

71725 
71809 
71892 
71975 

71650 
71734 
71817 
71900 

71983 

71659 
71742 
71825 
71908 
71991 

71667 

71750 
71834 
71917 
71999 

71675 
71759 

71842 

71925 
72008 

9 

1 
2 

■y 

4 

5 
6 

7 
8 

9 

I 
2 

3 
4 

5 
5 

b 

7 
8 

5^1 
526 

527 
528 

529 
530 
531 
532 
533 
534 

535 
536 
537 
538 
_539__ 
540 
541 
542 
543 
544 

""545"" 
546 
547 
54S 
549 
550 
55' 
552 
553 
554 

555 

556 

557 

558 

559  _ 

560 

561 
562 

563 
504 

72016 
72099 
72181 

72263 
72346 
72428 
72509 
72591 
72673 
72754 

72835 
72916 

72997 
73078 
73159 

73239 

73320 
73400 
73480 
73560 

•/2032 
72115 
72198 
72280 
72362 

72041 
72123 
72206 
72288 
72370 

72049 
72132 
72214 
72296 
72378 
72460 

72542 
72624 
72705 
72787 

72057 
72140 

72222 
72304 
72387 

72066 
72148 
72230  i 
72313 

72395 

72074 
72156 

72239 
72321 
72403 

72082 
72165 
72247 
72329 
72411 

72090 
72173 
72255 
72337 
72419 

72444 
72526 
72607 
72689 
72770 

72452 

72534 
72616 
72697 
72779 

72469 
72550 
72632 

72713 
7279s 

72477 

72558 
72640 
72722 
72803 
72884 

72965 
73046 
73127 
73207 

72485 
72567 
72648 

72730 
7281 1 

72493 

72575 
72656 

72738 
72819 

72501 

72583 
72665 

72746 
72827 

72nS43 
72925 
73006 
73086 
73167 

73247 
73328 
73408 
73488 
73568 

72852 

72933  > 

73014  ' 

73094 

73175 

73255 

7333^ 

73416 

73496 

73576  : 

72860 

72941 
73022 
73102 
73183 

72868 

72949 
73030 
731 " 
73191 

72876 

72957 
73038 
73119 
73199 
73280 
73360 
73440 
73520 
73600 

72892 

72973 
73054 
73135 
73215 

72900 
72981 
73062 

73143 
73223 

72908 
72989 
73070 
73151 
73231 

73263 
73344 
73424 
73504 
73584 

73272 
73352 
73432 
73512 
73592 

73288 
73368 
73448 
73528 
73608 

73296 
73376 
73456 
73536 
73616 

73304 

73384 
73464 
73544 
73624 

73312 
73392 
73472 
73552 
73632 



8 

73640 

73719 
73799 
73878 
73957 
74036 

741 15 
74194 

74273 
74351 
74429 
74507 
74586 
74663 
74741 
74819 
74896 
74974 

75051 
75.28 

73648 

73727 
73807 
73886 

73965 

73656  1 

73735 

73815 

73894 

73973 

73664 

73743 
73823 
73902 
73981 

73672 

73751 
73830 
73910 
73989 

73679 
73759 
73838 
73918 
73997 

73687 
73767 
73846 
73926 
74005 

73695 
73775 
73854 
73933 
74013 

73703 
73783 
73862 

73941 
74020 

73711 

73791 
73870 

73949 
74028 

I 
2 

3 
4 

5 
6 

7 
8 

9 

I 

2 

2 

j> 

4 

5 
6 

6 
7 

74044 
74123 
74202 
74280 
74359 

74052 

74131 

74210 
74288 
74367 

74060 

74139 

74218 

74296 
74374 

74068 

74147 
74225 

74304 
74382 

74076 
74155 
74233 
74312 
74390 

74084 
74162 
74241 
74320 
74398 

■  74092 
74170 
74249 
74327 
74406 

74099 
74178 
74257 
74335 
74414 

74107 
74186 
74265 

74343 
74421 

74437 

74515 
74593 
74671 
74749 
74827 
74904 
74981 
75059 
75136 

75213 
75289 
753'j6 
75442 
75519 

75595 
75671 
75747 
75823 
75899 

74445 

74523 
74601 

74679 

74757 

74834 
74912 

74989 
75066 

75143 

74453 

74531 
74609 

74687 

74764 

74842 
74920 

74997 
75074 
75151 

74461 
74539 
74617 
74695 
74772 
74850 

74927 
75005 
75082 

75159 

74468 
74547 
74624 
74702 
74780 
74858 

74935 
75012 
75089 
75166 

74476 
74554 
74632 
74710 
74788 

74865 

74943 
75020 

75097 
75174 

74484 
74562 
74640 
74718 
74796 

74492 

74570 
74648 
74726 
74803 

74500 
74578 
74656 

74733 
74811 

74889 
74966 

75043 
75120 

75197 
75274 
75351 
75427 
75504 
75580 

74873 
74950 
75028 

75105 
75182 

74881 
74958 
75035 
75113 
75189 

565 
566 

567 
568 

569 

570 

571 
572 
573 
574 

576 

577 
578 
579 

75205 
75282 

75358 
75435 
75511 
"  75587 
75664 
75740 
75815 
75891 

75967 
76042 
761 18 

76193 
76268 

75220 
75297 
75374 
75450 
75526 

75228 

75305 

75381 
75458 
75534 

75236 
75312 
75389 
75465 
75542 

75243 
75320 
75397 
75473 
75549 
75626 
75702 
75778 
75853 
75929 

75251 

75328 

75404 
75481 

75557 

75633 
75709 
75785 
75861 

75937 

75259 
75335 
75412 
75488 
75565 
75641 
75717 

75793 
75868 

75944 

75266 

75343 
75420 

75496 
75572 

t 

75603 
75679 
75755 
75831 
75906 

75610 
75686 
75762 
75838 
75914 

75618 
75694 
75770 
75846 
75921 

75648 

75724 
75800 

75876 

75952 

75656 

75732 
75808 

75884 
75959 

I 

2 

3 

4 

5 
6 

7 
8 

9 

1 
1 

2 

3 

4 

4 

5 
6 

6 

75974 
76050 
76125 
76200 
76275 

75982 

76057 

76133 
76208 

76283 

75989 
76065 
76140 

76215 
76290 

75997 
76072 
76148 
76223 
76298 

76005 
76080 

76155 
76230 

76305 

76012 
76087 
76163 
76238 
76313 

76020 
76095 
76170 

76245 
76320 

76027 
76103 
76178 
76253 
76328 

76035 
76110 

76185 
76260 

76335 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

I'ABLE  42. 

Page  399 

»» 

Logarithms 

,  of  Numbers. 

No 
Xo. 

.  5800 

-6400. 

Log.  76343 

S0618. 

1 
0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

5  So 

76343 

76350 

76358 

76365 

76373 

76380 

76388 

76395 

76403 

76410 

1 

8 

5^1 

76418 

76425 

7^433 

76440 

76448 

76455 

76462 

76470 

76477 

76485 

5S2 

70492 

76500 

76507 

76515 

76522 

76530 

76537 

76545 

76552 

76559 

1 

I 

5^3 

76567 

76574 

76582 

76589  1 

76597 

76604 

76612 

76619 

76626 

76634 

2 

2 

5S4 

76641 

76649  , 

76656 

76664 

76671 

76678 

76686 

76693 

76701 

76708 

3 
4 

0 
3 

sss 

76716 

76723  ' 

76730 

76738 

76745  ■ 

76753 

76760  1 

76768 

76775 

76782 

5S6 

76790 

76797 

76805 

76812 

76819 

76827  ! 

76834 

76842 

76849 

76856 

5 

4 

587 

768(34 

76871 

76879 

76886 

76893 

76901 

76908 

76916 

76923 

76930 

6 

5 

:;S8 

76938 

76945 

76953 

76960 

76967 

76975 

76982 

76989 

76997 

77004 

y 

6 

5S9 

77012 

77019 

77093 
77166 

77026  1 

77034 

77041 

77048 

77056 

77129 
77203 

77063 

77070 

77078 

8 
9 

6 

7 

590 
591 

77085 
77159 

77100  1 
77173  I 

77107 
77181 

77115 

77188 

77122  i 
77195 

77137 
77210 

77144 

77217 

77151 

77225 

592 

77232 

77240 

77247 

77254 

77262 

77269 

77276 

77283 

77291 

77298 

593 

77305 

77313 

77320 

77327 

77335 

77342 

77349 

77357 

77364 

77371 

594 
595 

77379 

77386 

77393 
77466 

77401 

77408 

77415 
77488  1 

77422 

77430 

77437 

77444 

77452 

77459 

77474 

77481 

77495 

77503 

77510 

77517 

596 

77525 

77532 

77539 

77546 

77554 

77561 

77568 

77576 

77583 

77590 

597 

77597 

77605 

77612 

77619 

77627 

77634 

77641 

77648 

77656 

77663 

598 

77670  ' 

77677 

77685 

77692 

77699 

77706 

77714 

77721 

77728 

77735 

599 

77743  1 

77750 

77757  1 
77830 

77764 
77837 

77772 
77844 

77779 
77851 

77786 
77859 

77793 
77866 

77801 

77808 

600 

77815 

77822  ! 

77873 

77880 

601 

77887 

77895 

77902 

77909 

77916 

77924 

77931 

77938 

77945 

77952 

602 

77960 

77967 

77974 

77981 

77988 

77996 

78003 

78010 

78017 

78025 

603 
604 

78032 
78104 

78039 
781 1 1 

78046 
78118 

78053 
78125 

78061 
78132 

78068 
78140 

78075 
78147  . 

78082 
78154 

78089 
78161 

78097 
78168 

1 

605 

78176 

78183 

78190 

78197 

78204 

782 1 1 

78219 

78226 

78233 

78240 

606 

78247 

7S254 

78262 

78269 

78276 

78283 

78290 

78297 

78305 

7^-^'^ 

607 

78319 

78326 

78333 

78340 

78347 

78355 

78362 

78369 

78376 

78383 

60S 

78390 

78398 

7S405 

78412 

78419 

78426 

78433 

78440 

78447 

78455 

609 

78462 

7S469 

78476 
78547 

78483 
78554 

78490 
78561 

78497 
78^569  ■ 

7S504 
78576 

78512 

78519 

78526 
7^597 

3 

4 

5 
6 

3 

4 
4 

610 

78533 

78540  1 

78583 

78590 

611 

78604 

7861 1 

78618 

78625 

78633 

78640 

78647 

78654 

78661 

78668 

612 

7S675 

78682, 

78689 

78696 

78704 

78711 

78718 

78725 

78732 

78739 

7 
8 

613 

7S746 

78753 

78760 

78767 

78774 

78781 

78789 

78796 

78803 

78810 

614 

78817 

78824 
78895 

78831 
78902 

78838 
78909 

78845 

78852 
7892^ 

_.78859 
789^0 

78866 
78937 

78873 
78944 

78880 
1  78951 

9 

6 

615 

78888 

78916 

6ib 

78958 

7S965 

78972 

78979 

78986 

78993 

79000 

79007 

79014 

'  7902 I 

617 

79029 

79036 

79043 

79050 

79057 

79064 

79071 

79078 

79085 

:       79092 

618 

79099 

79106 

79113 

79120 

79127 

79134 

79141 

79148 

79155 

79162 

619 
620 

79169 

79176 

79183 

79190 

79197 
79267 

79204 
79274 

792 1 1 
79281 

79218 

79225 

79232 

79239 

79246 

79253 

79260 

79288 

79295 

79302 

621 

79309 

79316 

79323 

79330 

79337 

79344 

79351 

79358 

79365 

79372 

622 

79379 

79386 

79393 

79400 

79407 

79414 

79421 

79428 

79435 

{   79442 

623 

79449 

79456 

79463 

79470 

79477 

79484 

79491 

79498 

79505 

79511 

624 

79518 

79525 
79595 

_  79532 
79602 

79539 
79609 

__  79546 
79616 

79553 
79623 

79560 
79630 

79567 

79574 

79581 

625 

79588 

79637 

79644 

79650 

626 

79657 

79664 

79671 

79678 

79685 

79692 

79699 

79706 

79713 

79720 

627 

79727 

79734 

79741 

79748 

79754 

79761 

79768 

79775 

79782 

79789 

628 

79796 
79865 

79803 
79872 

79941 

79810 

79879 
79948 

79817 
79886 

79955 

79824 

79893 
79962 

79831 
79900 

79837 
79906 

79844 

79913 
79982 

79851 
79920 

79S58 

629 

1   79927 

6 

630 

79934 

79969 

79975 

79989 

I   79996 

(^31 

80003 

80010 

80017 

80024 

80030 

80037 

80044 

80051 

80058 

80065 

1 

I 

632 

80072 

80079 

80085 

80092 

80099 

80106 

80113 

80120 

80127 

80134 

2 

1 

fa>3 

80140 

80147 

80154 

80161 

80168 

80175 

801 82 

80188 

80195 

'   80202 

3   2 

634 

80209 

80216 

80223 

80229 

80236 

80243 

80250 

80257 

80264 

80271 

4   2 

635 

80277 

80284 

80291 

80298 

80305 

80312 

80318 

80325 

80332 

80339 

5   3 

636 

80346 

80353 

80359 

80366 

80373 

80380 

80387 

80393 

80400 

80407 

6   4 

b37 

S0414 

80421 

80428 

80434 

80441 

80448 

80455 

80462 

80468 

80475 

7   4 

638 

80482 

80489 

80496 

80502 

80509 

80516 

80523 

80530 

80536 

,       80543 

8   5 

639 

80550 

80557 

80564 

80570 

80577 

80584 
5 

80591 

80598 
7 

80604 

80611 

9,  5 

No. 

0 

1 

2 

3 

4 

6 

8 

0 

Page 

Nc 

400] 

TABLE  42. 
Logarithms  of  Numbers. 

).  6400 — 

—7000. 

Log.  8 

0618   1 

^'+j*"-'' 

No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

640 
641 

642 

643 
644 

645 
646 

647 
648 
649 

650 
651 
652 
653 
654 

655" 
656 

657 
658 

659 
660 
661 
662 
663 
664 
665 
666 
667 
668 
669 

80618 
80686 

80754 
80821 
80889 

80956 

81023 

81090 

8II58 

81224 

"81291 

81358 

81425 

SI49I 

81558 

81624 
81690 

81757 
81823 
81889 
81954 
82020 
82086 
82I5I 
82217 
"  82282 

82347 

82413 
82478 
82543 

80625 
80693 

80760 

80828 
80895 
80963 

81030 
81097 
8II64 
81231 
81298 

81365 
81431 
81498 
81564 
8I63I 
81697 

81763 

81829 
81895 

80632 
80699 
80767 
80835 
80902 

80638 
80706 

80774 
80841 
80909 

80645 

^°7i3 
80781 

80848 

80916 

80652 
80720 

80787 
80855 
80922 

80659 
80726 
80794 
80862 
80929 

80665 

80801 
80S68 
80936 

80672 
80740 
80808 
80875 

80943 

80679 
80747 
80814 
80882 
80949 

1 

. 
2 

3 

4 

5 
6 

7 
8 

9 

I 
1 
2 
3 
4 
4 
5 
6 
6 

80969 
81037 
81104 
81171 
8123b 

81305 
81371 
81438 
81505 
81571 

80976 
81043 
81111 

81178 
81245 

80983 
81050 
81117 
81184 
81251 

80990 
81057 
81 124 
81191 
81258 
81327 
81391 
81458 
81525 
81591 

80996 
81064 
81131 
81198 
81265 

81331 

81398 
81465 

81531 
81598 

81664 
81730 
81796 
81862 
81928 

81003 
81070 

811.37 

81204 

81271 

81338 

81405 

SI47I 

8.538 

81604 

81671" 

81737 
81803 
81869 

81935 

81010 
81077 
81144 
8.211 

81278 

81345 
81411 

81478 

8.544 
8i6ii 

8.017 
81084 
81151 
81218 
81285 

8135 1 
81418 
81485 

81551 
81617 

81311 
81378 

81445 
81511 

81578 

81318 

81385 
81451 
81518 
81584 

• 

81637 
81704 
81770 
81836 
81902 

81644 
81710 
81776 
81842 
81908 

81651 

81717 
81783 
81849 
81915 

81657 
81723 
81790 
81856 
8192X 

81677 

81809 
81875 
81941 
82007 
82073 
82138 
82204 
82269 

81684 
8.750 
81816 
81882 
81948 
82014 
82079 
82145 
82210 
82276 

81961 

82027 
82092 

82158 
82223 
82289" 
82354 

82419 

82484 
82549 

81968 
82033 
82099 
82164 
82230 

82295 
82360 
82426 
82491 
82556 

81974 
82040 
82105 
82171 
82236 

81981 
82046 
82112 
82178 
82243 

81987 
82053 
82119 
82184 
82249 

81994 
82060 
82125 
82191 

82256 
82321 

82387 
82452 
825.7 
82582 

82000 

82066 
82132 
82197 
82263 
t  "82328" 

82393 

82458 
82523 

82588 

82653 
82718 

82782 
82847 

82911 

82302 

82367 

82432 
82497 
82562 

82308 

82373 
82439 
82504 
82569 

82315 

82380 

82445 
82510 
82575 

82334 
82400 
82465 
82530 

82595 
82659 
82724 
82789 
82853 
82918 

82341 
82406 
82471 
82536 
82601 

""82666" 
82730 

82795 
82860 

82924 

670 
671 
672 
673 
674 

82607 
82672 

82737 

82802 
82866 

82614 
82679 

82743 
82808 

82872 

82620 
82685 
82750 
82814 
82879 

82627 
82692 
82756 
82821 
82885 

82633 
82698 
82763 
82827 
82892 

82640 
82705 
82769 
82834 
82898 

82646 
82711 

82776 
82840 
82905 

675 
676 

677 
678 

679 

82930 

82995 
83059 
83123 

83187 

82937 

83001 

83065 
83129 

83193 

82943 
83008 
83072 

83136 
83200 

83264 
83327 
83391 

83455 
83518 

82950 
83014 
83078 
83142 
83206 
"  83270 
83334 
83398 
83461 

83525 

82956 
83020 
83085 
83149 
83213 

82963 

83027 

83091 

83155 
83219 

82969 

83033 
83097 
83161 

83225 

82975 

83040 

83104 
83168 

83232 

82982 
83046 
831 10 

83174 
83238 

. 82988 
83052 

83117 
83.81 

83245 

680 
681 
682 
683 
684 

83251 
83315 

83378 

83442 
83506 

83257 
83321 
83385 

83448 
83512 

83276 
83340 
83404 
83467 
83531 

83283 

83347 
83410 

83474 
83537 

83289 

83353 
83417 

83480 

83544 

83296 

83359 
83423 
83487 
83550 

83302 
83366 
83429 
83493 
83556 
83620 
83683 
83746 
83809 
83872 

83308 
83372 
83436 
83499 
83563 
83626 
83689 

83753 
838.6 

83879 

685 
686 
687 
688 
689 

83569 

83632 
83696 

83759 
83822 

83575 
83639 
83702 

83765 

83828 
83891 
83954 

84017 

84080 

84142 

84205 

84267 

84330 
84392 

84454 

83582 

83645 
83708 

S3771 
83835 

83588 

83651 
83715 
83778 
83841 

83594 
83658 
83721 

83784 
83847 

83601 
83664 

83727 
83790 

83853 

83607 
83670 
83734 
83797 
83860 

83613 
83677 
83740 
83803 
83866 

6 

690 
691 
692 

693 
694 

695 
696 

697 

698 

699 

83885 
83948 

840 1 1 

84073 
84136 

84198 

84261 

84323 
84386 

84448 

83897 
83960 
84023 
84086 
84148 
842 1 1 

84273 
■84336 

1  84398 
84460 

83904 
83967 
84029 
84092 
84155 

83910 

83973 
84036 
84098 
84161 

83916 

83979 
84042 
84105 
84167 
84230 
84292 

84354 
84417 
84479 

83923 

83985 

84048 

'    84111 

'  84173 
84236 
84298 
84361 
84423 
84485 

83929 
83992 
84055 

841 1 7 
84180 
84242 
84305 
84367 
84429 
84491 

83935 
83998 

84061 

84123 

84186 

84248 

843 1 1 

84373 
84435 
84497 

83942 
84004 
84067 
84130 
84192 
""84Y55" 
84317 
84379 
84442 
84504 

I 

2 

3 

4 

5 
6 

7 
8 

9 

I 

I 
2 
2 

3 
4 
4 

5 
5 

84217 
84280 

84342 
84404 
84466 

84223 
84286 
84348 
84410 

84473 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

> 

TABLE  42. 
Logarithms  of  Numbers. 

Page  401 

No 

.  7000 — 

-7600. 

Log.  84510 88081.    1 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

S 

9 

1 

700 
701 
702 

703 
704 

84510 

84572 
84634 
84696 

84757 

84516 

84578 
84640 
84702 
84763 
84S25 
84SS7 
84948 
85009 
85071 

85132 
85193 
85254 
85315 
85376 

85437 
85497 
85558 
85618 

85679 

84522 

84584 
84646 
84708 
84770 
84831 
84893 
84954 
85016 
85077 
85138 
85199 
85260 
85321 
85382 

85443 
85503 
85564 
85625 
85685 

84528 

84590 
84652 
84714 
84776 

84837 
84899 
84960 
85022 
85083 

84535  ' 
84597 
84658 
84720 
84782 
^4^44 
84905 
84967 
85028 
85089 

84541 
84603 

84665 
84726 
84788 
84850 
8491 1 

84973 
85034 
85095 
85156. 
85217 
85278 

85339 
85400 

85461 

85522 
85582 

85643 
85703 

85763 
85824 
85884 

85944 
86004 

86064 
86124 
86183 
86243 
86303 
86362 
86421 
86481 
86540 
86599 
86658 
86717 
86776 
86835 
86894 

84547 
84609 
84671 

84733 
84794 
84856 

84917 
84979 

85040  : 

85 1 01 

85163 

85224 
85285 

85345 
85406 

85467 
85528 
85588 
85649 
85709 

85769 
85830 
85890 

85950 
86010 

86070 

86130 

86189 

86249 

86308 

86368^ 

86427 

86487 

86546 

86605 

86664 

86723 

86782 

86841 

86900 

86958" 

87017 

87075 
87134 
87192 

84553 
84615 

84677 
84739 
84800 

84862" 

84924 
84985 
85046 
85107 

85169 

85230 
85291 

85352 
85412 

84559  ' 

84621 

84683 

84745 
84807 

84868 
84930 
84991 
85052 
85114  1 

84566 
84628 
84689 

84751 
84813 

' "84874 
84936 
84997 
85058 
85120 

1 

7 

I 

2  ' 

3  ' 

4 

5 
6 

7 
8 

9 

1 
I 
2 

3 
4 
4 

5 
6 
6 

705 
706 

707 
708 
709 
710 

711 
712 

713 
714 

84819 
848S0 
84942 

85003 
85065 

85126  i 

85187 
85248 

85309 
85370 

85144 
85205 
85266 

85327 
85388 

85449 
85509 
85570 
85631 
85691 

85150 
85211 
85272 

85333 
85394 

85455 
85516 
85576 
85637 
85697 

85175  i 

8523^ 

85297 

^5358 

85418 

85181 

85242 

85303 
85364 
85425 

715 
716 

717 

718 

720 

721 
722 

723 
724 

725 
726 

727 
728 
729 

85431 
85491 

85552 
85612 

85673 

85733 
85794 
85854 
85914 
85974 
80034 
80094 
86153 
8j2I3 
86273 

85473 

85534 
85594 
85655 
85715 

85479 
85540 
85600 
85661 
85721 

85485 
85546 
85606 
85667 
85727 

85739 
85800 
85860 
85920 
85980 
86040 
86100 
86159 
86219 
86279 

85745 
8580L) 

85866 

85926 

85986 

85751 
85812 

85872 

85932 
85992 

85757 
85818 
85878 
85938 
85998 

85775 
85836 
85896 

85956 
86016 

86076 
86136 
86195 
86255 
86314 

86374" 

86433 

86493 
86552 

8661 1 

85781 

85842 

85902 

85962 

86022 

86082' 

86141 

86201 

86261 

86320 

86380 

86439 

86499 

86558 

86617 

85788 
85848 
85908 
85968 
86028 

86088 

86147 

86207 

86267 

86326 

86386 

86445 
86504 

86564 

86623 

86682 

86741 

86800 

86859 

86917 

86976 

87035 

87093 

87151 
87210 

6 

86046 
86106 
86165 
86225 
86285 

86052 

861 12 

86171 

86231 

86291 

86350. 

86410 

86469 

86528 

86587 

86646 

86705 

86764 

86823 

86882 

86058 
86118 
86177 
86237 
86297 

86356 
86415 

86475 
86534 
86593 
86652 
8671 1 
86770 
86829 
86888 

I 

2 

3 
4 

I 

7 
8 

9 

I 
I 
2 
2 

3 

4 
4 
5 
5 

730 

731 
732 

734 

86332 
86392 
86451 
86510 
86570 

86338 
86398 

86457 
S6516 
86576 

!  86344 
86404 
86463 
86522 
86581 

86641 
86700 

86759 
S6817 

86S70 

80935 
86994 
87052 
87111 
S7169 

736 
737 
738 

740 

741 

742 

743 
744 

S6629 
86688 
86747 
8f)8o6 
86864 
86923 
86982 
87040 
87009 
87157 

86635 
86694 

86753 
86812 

868  70 
86929 
86988 
87046 
87105 
87163 
87221 
87280 
87338 
87396 
87454 
87512 

87570 
87628 
87685 
87743 

86670 
86729 
86788 
86847 
86906 
86964 
87023 
87081 
87140 
87198 

86676 

86735 
86794 
86853 
8691 1 
86970 
87029 
87087 
87146 
87204 

86941 
86999 
87058 
87116 

87175 

86947 
87005 
87064 
87122 
87181 

86953 
8701 1 

87070 

87128 

87186 

745 
746 

747 

748 

749 

87216 

87274 
87332 
87390 
87448 

87227 
87286 

87344 
S7402 
87460 

87233 
87291 

87349 
87408 

87466 

87239 
87297 

87355 

87413 
87471 

87529 
87587 
87645 
87703 
87760 

87818 
87875 

87933 
87990 

88047 

87245 
87303 
87361 
87419 

87477 

87251 
87309 
87367 
87425 
87483 

87256 
87315 
87373 
87431 
87489 

87262 
87320 
87379 
87437 
87495 

87268 
87326 

87384 
87442 
1  87500 
"87558"" 
87616 
87674 
87731 
87789 

5 

750 

751 
752 
753 
754 

87^06 

87564 
87622 

87679 

87737 

87518 

87576 

87633 
87691 

87749 

87523 
87581 

87639 
87697 
87754 
87812 
87869 
87927 

87984 
88041 

87535 
87593 
87651 
87708 
87766 

87541 
87599 
87656 

87714 

87772 

87547 
87604 
87662 
87720 
87777 

87552 
87610 
87668 
87726 
87783 

I 

2 

3' 
4 
5 
6 

7 
8 

9 

I 

1 
2 
2 

3 
3 
4 
4 

5 

755 
756 
757 
758 
759 

87795 
8  785  2 
87910 
87967 
88024 

87800 
87858 

87915 
87973 
88030 

8780b 
87864 
87921 

87978 
88036 

87823 
87881 
87938 
87996 
88053 

87829 

878S7 

87944 
88001 
88058 

87835 
87892 

87950 
88007 
88064 

87841 
87898 

87955 
88013 
88070 

S7846 
87904 
87961 
88018 
88076 

No. 

0 

1 

2 

3 

1 

4 

!   5 

6 

1 

8 

9 

1 

26  p 


Pag 

e402] 

TABLE  42. 
Logarithms  of  Numbers. 

No.  7600 — 

—8200. 

Log.  88081 9 1 38 1.    1 

No. 

0 

1 

2 

3 

4 

5 

6 

% 

8 

9 

1 

760 
761 
762 

763 
764 

766 
767 
768 
769 

88081 
88138 
88195 
88252 
88309 

88087 
88144 
88201 
88258 

88315 

88093 
88150 
88207 
88264 
88321 

88098 
88156 
88213 
88270 
88326 

88104 
88161 
88218 
88275 
88332 

881 10 
88167 
88224 
88281 
88338 

881 16 

88173 
88230 

88287 
88343 

88121 

88178 

88235 
88292 

88349 

88127 

88184 
88241 
88298 
88355 

88133 
88190 

88247 
88304 
88360 

6 

I 

2 

4 

5 
6 

I 

9 

I 

1 

2 
2 

3 
4 
4 
5 
5 

88366 
88423 
88480 
88536 

88593 

88372 
88429 

88485 
88542 
88598 

^^377 
88434 
88491 

88547 
88604 

88383 
88440 
88497 

88553 
88610 

1  88389 
88446 
88502 

88559 
88615 

88395 

88451 
88508 
88564 
88621 

88400 

88457 
885,3 

88570 

88627 

88406 
88463 
88519 
88576 
88632 

88412 
88468 
88525 
88581 
88038 

88417 

88474 
88530 
88587 
88643 

770 
771 

772 

773 
774 

88649 
88705 
88762 
88818 
88874 

88655 
8871 1 
88767 
88824 
88880 

88936" 
88992 

89048 
89104 

89159 

88660 
88717 

88773 
88829 

88885 

88941 

88997 

89053 
89109 

89165 

88666 
88722 
88779 
88835 
88891 

88947^ 
89003 
89059 
891 1 5 
89170 

88672 
88728 
88784 
88840 
88897 

88953 
89009 
89064 
89120 
89176 

88677 

88734 
88790 
88846 
88902 
88958 
89014 
89070 
89126 
89182 

88683 
88739 

88795 
88852 
88908 
88964 
89020 
89076 
89131 
89187 

88689 

88745 
88801 

88857 
88913 
{'8969 
89025 
89081 
89137 
89193 
89248 
89304 
89360 

89415 
89470 

89526 
89581 
89636 
89691 
89746 

88694 
!  88750 
88807 
88863 
88919 

88700 
88756 
88812 
88868 
88925 
88981 

89037 
89092 
89148 
89204 
89260 

89315 
89371 
89426 
89481 

89537' 
89592 

89647 

89702 

89757 

775 
776 

777 
778 

779 

88q^,o 

8898  J 

89J42 
89098 

89154 

88975 
89031 

89087 

89143 
89198 

89254 
89310 

89365 
89421 
89476 

8953 « 
89586 
89642 
89697 
89752 

780 
781 

782 
783 
784 

89209 

89265 
89321 

89376 

89432 

89215 
89271 
89326 
89382 
89437 

89221 
89276 
89332 
89387 
89443 

89226 
89282 
89337 
89393 
89448 

89232 
89287 

89343 
89398 
89454 

89237 
89293 
89348 
89404 

89459 

89243 
89298 

89354 
89409 
89465 

785 
786 

787 
788 

789 
790 
791 
792 

793 
794 

89487 
89542 

89597 
S9653 

89708 

89763 

89818 

89873 

89927 
89982 

89492 

89548 

89603 

89658 

89713 
89  768 
89823 
89878 

89988 

89498 

89553 
89609 

89664 
89719 

89774 
89829 
89883 
89938 

89993 

89504 
89559 
89614 
89669 
89724 

89779 
89834 
89889 
89944 
89998 

89509 
89564 
89620 

89675 
89730 

89785 
89840 
89894 

89949 
90004 

89515 
89570 
89625 
89680 

89735 
89790 
89845 
S9900 

89955 
90009 

89520 

89575 
89631 

89686 

89741 

89796 
89851 

89905 
89960 
90015 

89801 
89856 
8991 1 
89966 
90020 

89807 
89862 
89916 
89971 
90026 

89812 
89867 
89922 

89977 
.  90031 

795 
796 

797 
798 
799 

90037 

90091 
90146 
90200 

90255 

90042 

90097 
90I5I 

90206 
90260 

90048 
90102 

90157 
902 1 1 

90266 

90053 
90108 
90162 
90217 
90271 

90059 
90113 

90168 

90222 

90276 

9*0064 
901 19 

90173 
90227 
90282 

90069 
90124 
90179 
90233 
90287 

90075 
90129 
90184 
90238 
90293 

90080 

90135 
90189 

90244 
90298 

90086 
90140 
90195 
90249 
90304 

800 
801 
802 
803 
804 

90309 

90363 
90417 

90472 

90526 

90314 
90369 
90423 
90477 
90531 

90585 
90639 
90693 

90747 

90800 

90320 

90374 
90428 
90482 
90536 

90325 
90380 

90434 
90488 
90542 

90331 
90385 
90439 
90493 
90547 

90336 
90390 

90445 
90499 

90553 

90342 
90396 
90450 
90504 
90558 
90612 
90666 
90720 

90773 
90827 

90347 
90401 

90455 
90509 

_?0563 

90617 

90671 

90725 

90779 

90832 

90352 
90407 
90461 

90515 
90569 

90623 
90677 

90730 
90784 
90838  j 

90358 
90412 
90466 
90520 
90574 
90628 
90682 
90736 

90789 
90843 

805 
806 

So  7 

808 

809 

8io 

811 

812 

813 
814 

90580 
90634 

90687 

90741 
90795 

90590 
90644 
90698 
90752 
90806 
90859" 

90913 
90966 
91020 

91073 

90596 
90650 
90703 
90757 
9081 1 

90601 

90655 
90709 

90763 
90816 

90607 
90660 
90714 
90768 
90822 

3 

90849 
90902 

90956 

91009 
91062 

90854 
90907 

90961 
9IOI4 
91068 

90865 
90918 
90972 
91025 
91078 

90870 
90924 
90977 
91030 
91084 

90875 
90929 
90982 
91036 
91089 

90881 

90934 
90988 
91041 
91094 

90886 
90940 

90993 
91046 
91 100 

90891 

90945 
90998 
91052 
91 105 

90897 
90950 
91004 

91057 
91110 

91164 
91217 
91270 

91323 
91376 

I 
3 

! 

6 

7 
8 

9 

I 
1 

2 
2 

3 
3 
4 
4 
5 

815 
816 

817 
818 
819 

9III6 
91 169 
91222 

91275 
91328 

9II2I 
91 1 74 
91228 
91281 
91334 

91126 
91 180 

91233 
91286 

91339 

91132 
91185 
91238 
91291 

91344 

91137 
91 190 

91243 
91297 

91350 

91 142 
91196 
91249 
91302 

91355 

91 148 
91201 
91254 
91307 
91360 

91153 
91206 

91259 

9IgI2 

91365 

91158 
91212 
91265  ; 
91318 
91371 

No. 

0 

1 

2   , 

3 

4 

5 

6 

7 

8 

1 

» 

TABLE  42. 
Logarithms  of  Numbers. 

Page  403 

N 
No. 

0.  8200 — 
0 

-8800. 

" 

Log.  91381 94448.    1 

1 

2 

3 

4 

5 

6 

1 

8 

9 

1 

820 

821 
822 

824 

9I38I 

91434 

91487 

91540 
91593 

91387 
91440 
91492 

91545 
91598 

91392 

91445 
91498 

91551 
91603 

91397 
91450 

91503 

91556 

,  91609 

91403 

91455 
91508 

91561 

91614 

91408 
9 146 1 

91514 
91566 
91619 

91413 
91466 

91519 
91572 
91624 

91418 
91471 
91524 
91577 
91630 

91424 
91477 

91529 
91582 

91635 

91429 
91482 

91535 
91587 
91640 

6 

I 
2 

3 

4 

5 
6 

7 
8 

9 

I 
I 
2 
2 

■-> 

4 
4 
5 
5 

825 
S26 
827 
828 
829 

9 '645 
91698 

91751 

91803 

91855 

91651 

91703 
91756 
91808 
91861 

91656 

91709 
91 761 
91814 
91866 

9 1 661 
91714 
91766 
91819 
91871 

91666 
91719 
91772 
91824 
91876 

91672 
91724 
91777 
91829 
91882 

91677 

91730 
91782 

91834 
91887 

91682 

91735 
91787 

91840 

91892 

91687 
91740 

91793 
91845 
91897 

91693 

91745 
91798 
91850 
91903 

If. 

pi 

834 

91908 
91960 
92012 
92065 
92117 

91913 
91965 

92018 

92070 

92122  , 

91918 
91971 
92023 

92075 
92127 

91924 
91976 
92028 
92080 
92132 

91929 
91981 
92033 
92085 
92137 

91934 
91986 
92038 
92091 

92143 

91939 
91991 
92044 

92096 
92148 

91944 
91997 
92049 
92101 
92153 

91950 
92002 

92054 
92106 
92158 

9195s 
92007 

92059 
92111 
92163 

835 
836 

837 
838 

839 

92169 
92221 

92273 
92324 
92376 

92174 
92226 
92278 
92330  . 
92381  i 

92179 
92231 
92283 

92335 
92387 

92184 
92236 
92288 

92340 
92392 

92189 
92241 
92293 

92345 
92397 

92195 
92247 
92298 
92350 
92402 

92200 

92252 

92304 

92355 
92407 

92205- 
92257 
92309 
92361 
92412 

92210 
92262 

92314 
92366 
92418 

92215 
92267 
92319 
92371 
92423 

S40 
841 
842 

843 
844 

92428 
92480 

92531 
92583 
92634 

92433  1 
92485 
92536 
92588 

92639 

92438 
92490 

92542 

92593 
92645 

92443 
92495 
92547 
92598 
92650 

92449 
92500 

92552 
92603 

92655 

92454 
92505 
92557 
92609 

92660 

92459 
92511 
92562 
92614 
92665 

92464 
92516 

92567 
92619 
92670 

92469 
92521 
92572 
92624 

92675 

92474 
92526 

92578 
92629 
92681 

5 

845 
846 

847 
848 

849 
850 

85  r 
852 
S53 
854 

"855 
856 

857 
858 

859 
860 
861 
862 
863 
864 

'  865 
866 
867 
868 
869 
870^ 
87 1 
872 

873 
874 

92686 

92737 
92788 

92840 
92891 
92942 

92993  ' 
93044 
93095 
93146 

93197 
93247 
93298 

93349 
93399 
93450 
93500 

93551 
93601 

93651 

92691 
92742 
92793 

92845 
92896 

92696 
92747 
92799 
92850 
92901 

92701 
92752 
92804 

92855 
92906 

92706 

92758 
92809 

92860 

929 1 1 

9271 1 

92763 
92814 
92865 
92916 

92716 
92768 
92819 
92870 
92921 

92722 

92773 
92824 

92875 
92927 

92727 
92778 
92829 
92881 
92932 

92983 
93034 
93085 
93136 
93186 

93237 
93288 

93339 
93389 
93440 

92732 
92783 
92834 
92886 
92937 
92988 

93039 
93090 

93141 
93192 

93242 
93293 
93344 
93394 
93445 

1 

2 
3 

I 

1 
2 

92947  ' 
92998 

93049 
93100 

93151 
93202 
93252 

93303 
93354 
93404 

93455 
93505 
93556 
93606 

93656 

92052 
93003 
93054 
93105 
93156 

92957 
93008 

93059 
93110 

93161 

92962 

93013 
93064 

93115  , 
93166 

92967 
93018 

93069 
93120 

93171 

92973 
93024 

93075 
93125 
93176 

92978 

93029 
93080 

93131 
93181 

4  ^ 

5  3 

6  3 

7  :    4 

8  :  4 

9  5 

93207 

93258 
93308 
93359 
93409 

93212 
93263 
93313 
93364 
93414 

93217 
93268 

93318 
93369 
93420 

93222 

93273 
93323 
93374 
93425 

93227 
93278 
93328 
93379 
93430 

93232 
93283 
93334 
93384 
93435 

93460 
93510 

93561 
9361 1 
93661 

93465 
93515 
93566 
93616 
93666 

93470 
93520 

93571 
93621 
93671 

93475 
93526 
93576 
93626 

93676 

93480 

93531 
93581 

93631 
93682 

93485 
93536 
93586 
93636 
93687 

93490 
93541 
93591 
93641 
93692 

93495 
93546 
93596 
93646 
93697 

93702 

93752 
93802 

93852 
93902 

93707 
93757 
93807 
93857 
93907 

93712 
93762 
93812 
93862 
93912 

93717 
93767 
93817 
93867 
93917 

93722 
93772 
93822 
93872 
93922 

93727 

93777 
93827 
93877 
93927 

93732 
93782 
938^2 
93882 
93932 

93737 
93787 
93837 
93887 
93937 

93742 
93792 

93842 
93892 

93942 

93747 
93797 
93847 
93897 
93947 

4 

93952 
94002 

94052 
94101 

94151 

93957 
94007 

94057 
94106 
94156 

93962 
94012 
94062 
941 1 1 
94161 

93967 
94017 

94067 
941 16 
94166 

93972  ! 
94022 

94072 
94I2I  j 

94I7I  j 

93977 
94027 
94077 
94126 
94176 

93982 

94032  ■ 
94082 

94131 
94181 

93987 
94037 
94086 

94136 
94186 

93992 
94042 
94091 
94141 
94191 

93997 
94047 
94096 
94146 
94196 

I 
2  - 

4 

5 
6 

7 
8 

9| 

0 

I 
I 
2 
2 
2 
3 
3 
4 

875 
876 

877 
878 

870 

94201 

94250 
94300 
94349 
94399 

94206 

94255 
94305 
94354 
94404 

942 1 1 

94260 

94310 

94359 
94409 

94216 

94265 

94315 
94364 
94414 

94221  j 

94270 

94320 

94369 

94419 

94220 

94275 
94325 
94374 
94424 

94231 

94280 

94330 

94379 
94429 

94236 

94285 
94335 
94384 
94433 

94240 
94290 
94340 
94389 
94438 

94245 
94295 
94345 
94394 
94443 

Xo. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

1 

Pag( 

3  404 

TABLE  42. 
Logarithms  of  Numbers. 

N 

0  8800 — 

— QACiO. 

Log.  94448 97313. 

No. 

0 

1 

2 

3 

4 

5 

6 

> 

8 

9 

1 

880 
881 

882 
883 
884 

94448 
94498 
94547 
94596 
94645 

94453 
94503 
94552 
94C01 

94650 
94699 
94748 

94797 
94846 

94895 

94458 

94507 
94557 
94606 

94655 

94463 
94512 
94562 
9461 1 
94660 

94468 

94517 
94567 
94616 

94665 

94473 

94522 

94571 
94621 
94670 

94478 

94527 
94576 
94626 

94675 

94483 
94532 
94581 
94630 
94680 

94488 

94537 
94586 

94635 
94685 

94734 
94783 
94832 
94880 

94929 

94493 
94542 

94591 
94640 

94689 

I 
2 

3 
4 

I 

7 
8 

9 

5 

I 
I 
2 
2 

3 
3 
4 
4 

5 

885 
886 
887 
888 
889 

94694 
94743 
94792 
94841 
94890 

94704 

94753 
94802 

94851 
94900 

94709 

94758 
94807 
94856 

94905 

94714 
94763 
94812 
94861 
94910 

94719 
94768 

94817 
94866 

94915 

94724 
94773 
94822 
94871 
94919 

94729 

94778 
94827 

94876 
94924 

94738 
94787 
94836 
94885 
94934 

94983 
95032 
95080 

95129 
95177 
95226 

95274 
95323 
95371 
95419 

890 
891 
892 

893 
894 

94939 
94988 

95036 
95085 
95134 

94944 
94993 
95041 
95090 

95139 
95187 
95236 
95284 
95332 
95381 

94949 
94998 
95046 
95095 
95143 

94954 
95002 

95051 
95100 

95148 

94959 
95007 
95056 
95105 
95153 

94963 
95012 

95061 

95109 
95158 

94968 

95017 
95066 

95 1 14 
95163 

94973 
95022 

95071 
95"9 
95168 

94978 
95027 

95075 
95124 
95173 

89s 
896 
897 
898 
899 

95182 

95231 
95279 
95328 
95376 

95192 

95240 
95289 
95337 
95386 

95197 
95245 
95294 
95342 
95390 

95202 

95250 
95299 
95347 
95395 

95207 

95255 
95303 
95352 
95400 

95211 
95260 
.95308 
95357 
95405 

95216 
95265 
95313 
95361 
95410 

95221 

95270 
95318 
95366 

95415 

900 
901 
902 

903 
904 

95424 
95472 
95521 
95569 
95617 

95429 

95477 
95525 
95574 
95622 

95434 
95482 

95530 
95578 
95626 

95439 
95487 
95535 
95583 
95631 

95444 
95492 
95540 
95588 
95636 

95448 

95497 
95545 
95593 
95641 

95453 
95501 
95550 
95598 
95646 

95458 
95506 

95554 
95602 

95650 

95463 
955" 
95559 
95607 

95655 

95468 
95516 

95564 
95612 
95660 

95708" 

95756 

95804 

95852 

95899 

95947 

95995 
96042 

96090 
96137 

905 
906 
907 
908 
909 

95665 

95713 
95761 
95809 
95856 

95670 
95718 
95766 

95813 
95861 

95674 
95722 

95770 
95818 
95866 

95679 
95727 
95775 
95823 
95871 

95684 

95732 
95780 
95828 

95875 
95923 
95971 
96019 
96066 
961 14 

95689 
95737 
95785 
95832 
95880 

95928 
95976 
96023 
96071 
961 18 

95694 
95742 
95789 
95837 
95885 

95933 
95980 
96028 
96076 
96123 

95698 
95746 
95794 
95842 
95890 

95938 
95985 
96033 
96080 
96128 

95703 
95751 
95799 
95847 
95895 
95942 
95990 
96038 
96085 

96133 

910 
911 
912 

913 
914 

95904 
95952 
95999 
96047 
96095 

95909 
95957 
96004 
96052 
96099 
96147 
96194 
96242 
96289 
96336 
96384 

96431 
90478 

96525 
96572 

95914 
95961 
96009 
96057 
96104 

959  In' 
9596^ 
96014 
96061 
96109 

915 
916 
917 
918 
919 
920 
921 
922 

923 
924 

96142 
96190 
96237 
96284 
_  96332 

96379 
96426 

96473 
96520 
96567 

96152 
96199 
96246 
96294 
96341 
96388 

96435 
96483 
96530 
96577 

96156 
96204 
96251 
96298 
96346 

96393 
96440 

96487 

96534 
96581 

96161 
96209 
96256 

96303 
96350 

96166 
96213 
96261 
96308 

96355 

96171 
96218 
96265 

96313 
96360 

96175 
96223 

96270 

96317 
96365 

96180 
96227 
96275 
96322 
96369 

96185 
96232 
96280 
96327 
96374 

96398 
96445 
96492 

96539 
96586 

96402 
96450 
96497 

96544 
96591 

96407 
96454 
96501 
96548 
96595 

96412 
96459 
96506 

96553 
96600 

96417 
96464 
965 1 1 

96558 
96605 

96421 
96468 

96515 
96562 

96609 

925 
926 
927 
928 
929 

96614 
96661 
967CJ 

96755 
96802 

96619 
96666 
96713 

96759 
96806 

96624 
96670 
96717 
96764 
9681 1 

96628 
96675 
96722 
96769 
96^16 

96633 
9^680 
9O727 

96774 
96820 

96638 
96685 
96731 

96778 
96825 

96642 
96689 
96736 

96783 
96830 

96876 
96923 
96970 
97016 
97063 
97109 

97155 
97202 

97248 

97294 

96647 
96694 
96741 
96788 
96834 

96652 
96699 

96745 
96792 

96839 

96656 
96703 
96750 
96797 
96844 

I 
2 

3 
4 

5 
6 

7 
8 

9 

4 

0 

T 
I 

2 
2 
2 

-t 

3 
4 

930 
931 
932 
933 
934 

9684S 
96895 
96942 
96988 
97035 

96853 
96900 
96946 
96993 
97039 

96858 
96904 
96951 
96997 
97044 

96862 
96909 
96956 
97002 
97049 

9G867 
96914 
95960 
97007 
97053 

96872 
96918 
96965 
9701 1 
97058 

96881 
96928 
96974 
97021 
97067 
97114 
97160 
97206 

97253 
97299 

968S0 
96932 
90979 
97025 
97072 

96890 

96937 
96984 
97030 
97077 

935 
936 
937 
938 
939 

97081 
97128 

97174 
97220 
97267 

97086 
97132 

97179 
97225 

97271 

97090 
97137 
97183 
97230 
97276 

97095 
97142 

97188 

97234 
97280 

97100 
97146 
97192 

97239 
97285 

97104 
97151 
97197 

97243 
97290 

97118 

97165 
97211 

97257 
97304 

97123 
97169 
97216 
97262 
97308 

No. 

0 

1 

2 

3 

i 

5 

6 

X 

8 

9 

I 


I 


^% 

TABLE  42. 
Logarithms  of  Numbers. 

Page  405 

Nc 

.  9400 

-I 0000. 

Log.  97313 9999^ 

. 

No. 

0 

1 

2 

3 

4 

5 

6 

% 

8 

9 

940 
941 
942 
943 
944 

97313 
97359 
97405 
97451 
97497 

97317 
97364 
97410 

97456 
97502 

97322 
97368 
97414 
97460 
97506 

97327 
97373 
97419 
97465 
975" 

97331 
97377 
97424 
97470 
97516 

97336 
97382 
97428 

97474 
97520 

97566 
97612 

97658 
97704 

97749 

97340 
97387 
97433 
97479 
97525 

97345 
97391 
97437 
97483 
97529 

97350 
97396 
97442 
97488 

97534  1 

97354 
97400 

97447 
97493 
97539 

97585 
97630 
97676 
97722 
97768 

1 

2 

4 

5 
6 

9 

5 

1 
1 
2 
2 
3 
0 
4 
4 
5 

945 
946 

947 
948 

949 

97543 

97589 

97635 
97681 

97727 

97548 

97594 
97640 

97685 
97731 

97552 
97598 

97644 
97690 

97736 

97557 
97603 
97649 

97695 
97740 

97562 
97607 

97653 
97699 
97745 

97571 
97617 

97663 

97708 

97754 

97575 
97621 
97667 

97713 
97759 

97580  1 

97626  ; 

97672 

97717 

97763 
97809 

97855 

97900  ; 

97946 

97991 

950 
951 
952 
953 
954 

97772 
97818 
97864 
97909 

97955 

97777 
97823 
97868 
97914 
97959 

97782 
97827 

97873 
97918 
97964 

97786 
97832 

97877 
97923 
97968 

97791 
97836 
97882 
97928 
97973 

97795 
97841 
97886 

97932 
97978 
98023 
98068 
98114 

98159 
98204 

97800 

97845 
97891 

97937 
97982 

98028 

98073 
98118 
98164 
98209 

97804 
97850 
97896 

97941 
97987 

98032 
98078 
98123 
98168 
98214 

97813 
97859 
97905 
97950 
97996 

955 
956 

957 
95^ 
959 

98000 
9S046 
98091 

98137 
98182 

98005 
98050 
98096 
98141  i 
98186 

98009 

98055 
98100 
98146 
98191 

98014 
98059 
98105 
98150 

98195 
98241 
98286 

98331 
98376 
98421 

98019 
98064 
98109 

98155 
98200 

98037 
98082 
98127 

98173 
98218 

98041 
98087 
98132 
98177 
98223 

960 
961 
962 

963 
964 

965 

966 

967 
96S 
969 
070 

071 
972 

973 
974 

975 
970 

977 
978 

979 

98227 
98272 
98318 

98363 
98408 

98453 
98498 

98543 
98588 

98632 

98232 

98277 

98322 

98367 
98412 

98236 
9S281 

98327 
98372 
98417 

98245 
98290 
98336 
98381 
98426 

98250 

98295 
98340 

98385 
98430 

98254 
98299 

98345 
98390 

98435 
98480 

98525 
98570 

98614 

98659 

98704 

98749 

98793 
98838 

98883 

98259 
98304 
98349 
98394 
98439 
98484 
98529 

98574 
98619 
98664 

"98709 
98753 
98798 

98843 
98887 

98263 
98308 
98354 
98399 
98444 
98489 
98534 
98579 
98623 
98668 

98713 
98758 
98802 
98847 
98892 

98268 

98313 
98358 

98403 
98448 

98493 
98538 
98583 
98628 

98673 
98717 
98762 
98807 
98851 
98896 

98457 
98502 

98547 
98592 
98637 

98462 
98507 

98552 

9S597 
98641 

98466 
985 1 1 

98556 
98601 
98646 

98471 
98516 

98561 
98605 
98650 

98475 
98520 

98565 
98610 

98655 
98700 

98744 
98789 
98834 
98878 

98923 
98967 
99012 
99056 
99100 

"  99145 
99189 

99233 
99277 

99322 

99366 

99410 

99454 
99498 
99542 

98677 
98722 
98767 
9881 1 
98856 

98682 
98726 
98771 
98816 
98860 

98686 

98731 
98776 

98820 

98865 

98691 

98735 
98780 

98825 
98869 

98695 
98740 
98784 
98829 
98874 

98900 

98945 
98989 

99034 
C9078 

98905 
98949 
98994 
99038 
99083 

98909 

98954 
98998 

99043 
99087 

98914 
98958 
99003 

99047 
99092 

98918 
98963 
99007 

99052 
99096 

98927 
98972 
99016 
99061 
99105 
99149 
99193 
99238 
99282 

99326 

99370 
99414 
99458 
99502 
99546 

98932 
98976 
99021 
99065 
99109 

98936 
98981 
99025 
99069 
99114 

98941 
98985 
99029 

99074 
99118 

99162 
99207 
99251 

99295 
99339 

9S0 
981 
982 

983 
984 

99123 
99167 
9921 1 

99255 
99300 

99127 
99171 
99216 
99260 
99304 

99131 
99176 

99220 

99264 
99308 

99136 
99180 
99224 
99269 
99313 

99140 
99185 

i  99229 
99273 

1  99317 

99154 
99198 
99242 
99286 
99330 

99158 
99202 
99247 
99291 

99335 

985 
986 

987 
988 

989 

99344 
99388 

99432 
99476 
99520 

99348 
99392 
99436 
99480 

99524 

99352 
99396 
99441 

99484 
99528 

99357 
99401 

99445 
99489 

99533 

99361 
99405 
99449 
99493 
'  99537 

99374 
99419 

99463 
'  99506 

99550 

99379 
99423 
99467 

995" 
99555 

99383 
99427 
99471 
99515 
99559 

4 

990 
991 
992 

993 
994 

99564 
99607 

99651 
99695 

99739 

99568 
99612 
99656 

99699 
99743 

99572 
99616 
99660 
99704 
99747 

99577 
99621 
99664 
99708 
99752 

99581 

i  99625 

99669 

99712 
99756 

99585 
99629 
99673 
99717 
99760 

99590 
99634 
99677 
99721 
99765 
99808 

99852 
99896 

99939 
99983 

99594 
99638 
99682 
99726 
99769 

99813 
99856 
99900 

99944 
99987 

99599 
99642 
99686 
99730 

99774 

99817 
99861 

99904 
99948 
99991 

99003 

99647 
99691 

99734 
^99778 

99822 
99865 

99909 
99952 
99996 

1 
2 

3 

4 

5 
6 

7 
8 

9 

0 
\     I 
1 
2 
2 
2 
3 
3 
4 

995 
996 

997 
998 
999 

99782 
99826 
99870 

99913 
99957 

99787 
99830 
99874 
99917 
99961 

i  99791 

1  99835 
99878 
99922 

99965 

99795 
99839 
99883 
99926 
99970 

99800 

99843 
99887 
99930 

99974 

99804 
99848 
99891 

99935 
99978 

No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

1 

Page  406]                                                TABLE  43.                                                                 fl 

Logarithmic  Sines,  Tangents,  and  Secants  to  every  Point  and  Quarter  Point  of  the  Compass.                  1 

Points. 

Sine. 

Cosine. 

Tangent. 

Cotangent. 

Secant. 

Cosecant. 

o 

Inf.  neg. 
8.  69080 

8.  99130 

9.  16652 

10. ooooo 
9-  99948 
9- 99790 
9- 99527 

Inf.  neg. 

8.  69132 
8. 99340 

9.  17125 

Infinite. 
11.30868 
11.00660 
10.  82875 

10.  ooooo 
10.00052 
10.00210 
lo.  00473 

Infinite. 
11.30920 
11.00870 
10. 83348 

8 

VA 

I 

1% 

9.  29024 

9.38557 
9.  46282 

9-52749 

9-99157 
9.  98679 
9. 98088 
9- 97384 

9.  29866 

9-  39879 
9.48194 

9- 55365 

10.  70134 
10.60121 
10. 51806 
10. 44635 

10.  00843 
10.01321 
10.01912 
10.02616 

10.  70976 
10.  61443 
10.53718 
10.47251 

7 

6X 
(^% 
6X 

2 

'^ 

2K 
2^ 

3 

rx 

3K 

9.  58284 
9-  63099 

9-  67339 
9.71105 

9. 96562 
9.95616 
9- 94543 
9-93335 

9.  61722 
9-  67483 
9-  72796 
9.  77770 

10.38278 
10.32517 
10. 27204 
10.  22230 

10. 03438 
10. 04384 

10.05457 
10.06665 

10.41716 
10.  36901 
10.32661 
10.  28895 

6 

5X 
5>^ 
5X 

9-  74474 
9-  77503 
9. 80236 

9.82708 

9.91985 

9-  90483 
9.  88819 
9- 86979 

9.  82489 
9.  87020 
9.91417 
9-95729 

10.17511 
10. 12980 
10.08583 
10.04271 

10.08015 
10.09517 
10.  11181 
10.  13021 

10. 25526 
10.  22497 
10.  19764 
10.  17292 

5 

4 

9.  84949 

9.  84949 

10.00000 

10.  ooooo 

10.  15051 

10. 15051 

4 

Cosine. 

Sine. 

Cotangent. 

Tangent. 

Cosecant. 

Secant. 

Points. 

- 

LOGAKITHMIC  FUNCTIONS. 

Page  407 

» 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

0° 

119° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff.  i'. 

1 

Cosecant. 

Tangent. 

Diff.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

12  0  0 

000 

Inf.  neg. ; 

Infinite. 

Inf.  neg. 

Infinite. 

1 0.  00000 

10.  00000 

60 

I 

II  59  52  t 

0  8 

6.  46373 

30103 

13-53627 

6.46373 

30103 

13- 53627 

00000 

00000 

59 

"» 

59  44 

0  16 

76476 

17609 

23524 

76476 

17609 

23524 

00000 

00000 

58 

^ 
J 

59  36 

0  24 

94085  j 

12494  ' 

05915 

94085 

12494 

05915 

00000 

00000 

57 

4 

5928 

0  32 

7.06579^ 
7.  16270 

9691 
7918 

12.93421 
12.83730' 

7.06579 
7.  16270 

9691 
7918 

12.93421 

00000 

00000 

56 

S 

II  59  20 

0  0  40 

12.83730 

10. 00000 

10. 00000 

5S 

6 

59  12 

0  48 

24188 

6694 

75812 

24188 

6694 

75812 

00000 

00000 

S4 

7 

59  4 

0  56 

30882 

5800 

69118 

30882 

5800 

691 18 

00000 

00000 

SS 

S 

5856 

I  4 

36682 

S115  1 

63318 

36682 

5115 

63318 

00000  , 

00000 

52 

9 

58  48 

I  12 

41797 

4576  1 
4139 

58203 
12.53627 

41797 
7-46373 

4576 

58203 

00000 

00000 

51 

10 

II  58  40 

0  I  20 

7-46373 

4139 

12.53627 

10.00000 

10.00000 

50 

11 

5832 

I  28 

50512 

3779 

49488 

50512 

3779 

49488 

00000 

00000 

49 

12 

58  24 

I  36 

54291 

3476 

45709 

54291 

3476 

45709 

00000 

00000 

48 

IS 

58  16 

I  44 

57767 

3218 

42233 

57767 

3219 

42233 

00000 

00000 

47 

H 

IS 

58  8 
II  58  0 

I  52 

60985 

2997 

39015 

60986 

2996 

39014 

00000 

00000 

46 

020 

7.  63982 

2802 

12. 36018 

7.  63982 

2803 

12. 36018 

10.  00000 

10.00000 

45 

i6 

57  52 

2  8 

66784 

2633 

33216 

66785 

2633 

33215 

00000 

00000 

44 

17 

57  44 

2  16 

69417 

2483 

30583 

69418 

2482 

30582 

0000 1 

9- 99999 

43 

i8 

57  36 

2  24 

71900 

2348 

28100 

71900 

2348 

28100 

OOOOI 

99999 

42 

J9 

20 

57  28 
II  57  20 

2  32 

74248 

2227 
2119 

25752 

74248  ' 

2228 

25752 
12.23524 

0000 1 

99999 

41 

0  2  40 

7-  76475 

12.23525 

7.  76476 

2119 

10.00001 

9- 99999 

40 

21 

57  12 

2  48 

78594 

2021 

21406 

78595 

2020 

21405 

OOOOI 

99999 

,S9 

22 

57  4 

2  56 

80615 

1930 

19385 

80615 

1931 

19385 

00001 

99999 

38 

2S 

5b  56 

3  4 

82545 

1848 

17455 

82546 

1848 

17454 

OOOOI 

99999 

37 

24 

2S 

5648 
I'  56  40 

3  12 
0  3  20 

84393 
'7.86166 

1773 

15607 

84394 

1773 

15606 

OOOOI 

99999 

36 

1704 

12. 13834 

7.  86167 

1704 

12. 13833 

'10.00001 

9-  99999 

35 

26 

56  32 

328 

87870 

1639 

I2I3O 

87871 

1639 

12129 

OOOOI 

99999 

34 

27 

56  24 

3  36 

89509 

1579 

10491 

89510 

1579 

10490 

OOOOI 

99999 

33 

2S 

56  16 

3  44 

91088 

1524 

08912 

91089 

1524 

0891 1 

OOOOI 

99999 

32 

29 

.so 

56  8 

3  52 

92612 

1472 

1424 

07388 
12.05916 

_  9261 3_ 
7. 94086 

1473 

07387 

00002 

99998 

31 

II  56  0 

040 

7,  94084 

1424 

12.  05914 

10. 00002 

9- 99998 

30 

^i 

55  52 

4  8 

95508 

1379 

04492 

95510 

1379 

04490 

00002 

99998 

29 

?>- 

55  44 

4  16 

96887 

1336 

031  13 

96889 

1336 

031 1 1 

00002 

99998 

28 

55  36 

4  24 

98223 

1297 

01777 

98225 

1297 

01775 

00002 

99998 

27 

34 

ss 

5528 
II  55  =0 

4  32 

99520 

1259 

00480 

.  99522 

1259 

00478 

00002 

99998 

26 

0  4  40 

8. 00779 

1223 

II. 99221 

8.00781 

1223 

II. 99219 

10.  00002 

9- 99998 

25 

S6 

55  12 

4  48 

02002 

1 190 

97998 

02004 

1 190 

97996 

00002 

99998 

24 

S7 

55  4 

456 

03192 

1158 

96808 

03194 

1159 

96806 

00003 

99997 

23 

SH 

54  56 

5  4 

04350 

1128 

95650 

04353 

1 128 

95647 

00003 

99997 

22 

39 

40 

54  48 
II  54  40 

5  12 

05478 

1 100 

94522 

05481 

HOC 

94519 

00003 

99997 

21 

0  5  20 

8.06578 

1072 

11.93422 

8.06581 

1072 

1 1. 93419 

10. 00003 

9- 99997 

20 

41 

54  32 

5"f 

07650 

1046 

92350 

07653 

1047 

92347 

00003 

99997 

19 

42 

54  24 

5  36 

08696 

1022 

91304 

08700 

1022 

91300 

00003 

99997 

18 

4. 

54  16 

5  44 

09718 

999 

90282 

09722- 

998 

90278 

00003 

99997 

17 

44 

4=; 

54  8 
II  54  0 

5  52 

10717 

976 

89283 

10720 

976 
955 

89280 
1 1 . 88304 

00004 

99996 

16 

060 

8.  1 1 693 

954 

11.88307 

8. 11696 

10. 00004 

9.  99996 

15 

46 

53  52 

6  8 

12647 

934 

87353 

1 265 1 

934 

87349 

00004 

99996 

14 

47 

53  44 

6  16 

13581 

914 

86419 

13585 

915 

86415 

00004 

99996 

13 

48 

53  36 

6  24 

14495 

896 

85505 

14500 

895 

85500 

00004 

99996 

12 

49 

so 

53  28 
II  53  20 

632 

15391 

877 
860' 

84609 
11.83732' 

15395 
8.  16273 

878 

84605 

00004 

99996 

II 

0  6  40 

8. 16268 

860 

11.83727 

10.00005 

99995 

10 

SI 

53  12 

6  48 

■   17128 

843 

82872 

17133 

843 

82867 

00005 

99995 

9 

S2 

53  4 

!    6  56 

1 7971 

827 

82029 

17976 

828 

82024 

00005 

99995 

8 

ss 

52  56 

7  4 

18798 

812 

81202 

18804 

812 

81 196 

00005 

99995 

7 

54 

52  48 

7  12 

19610 

797 

80390 

19616 

797 

80384 

00005 

99995 

6 

SS 

II  52  40 

0  7  20 

8. 20407 

782 

11-79593 

8. 20413 

782 

11.79587 

10. 00006 

9. 99994 

5 

S6 

52  32 

728 

21189 

769 

7881 1 

21195 

769 

78805 

00006 

99994 

4 

S7 

52  24 

736 

21958 

755 

78042 

21964 

756 

78036 

00006 

99994 

3 

S8 

52  16 

7  44 

22713 

'      743 

77287 

22720 

742 

77280 

00006 

99994 

2 

59 

52  8 

7  52 

23456 

1   730 

76544 

23462 

730 

76538 

00006 

99994 

I 

60 

52  0 

8  0 

24186 

717 

75814 

24192 

718 

75808 

00007 

99993 

0 

M. 

Hour  V.  M. 

Hour  A.  M. 

Cosine. 

Diff.  i'. 

Secant. 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant. 

Sine. 

M. 

90° 

89°  1 

\ 


Page  408 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

1° 

1^8° 

M. 

Hour  A.  M. 

Hour  p.  u. 

Sine. 

Diff.  i'. 

Cosecant. 

Tangent. 

Diff.  i'. 

Cotangent. 

Secant. 

Cosine. 

M. 

o 

II  52  0 

080 

8.  24186 

II.  75814 

8.  24192 

718 

11.75808 

10. 00007 

9-  99993 

60 

I 

51  52 

8  8 

24903 

706  :   75097 

24910 

706 

75090 

00007 

99993 

59 

2 

51  44 

8  lO 

25609 

695  1   74391 

25616 

696 

74384 

00007 

99993 

58 

0 

51  36 

8  24 

26304 

684 

73696 

26312 

684 

736S8 

00007 

99993 

57 

4 

51  28 

832 

26988 
8. 27661 

673 
663 

73012 

26996 

673 

73004 

00008 

99992 

56 

5 

11  51  20 

0  8  40 

I1T72339" 

"8.27669" 

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51  12 

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71676 

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54 

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51  4 

8  56 

28977 

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71023 

28986 

643 

71014 

00008 

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50  56 

9  4 

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634 

70379 

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634 

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0  9  20 

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624 

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11.69112 

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0  10  0 

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8.  33875 

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11.63322 

8.  36689 

540 

11.  6331 1 

10.  00012 

9.  99988 

40 

21 

49  12 

10  48 

37217 

533 

62783 

37229 

533 

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22 

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526 

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527 

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38 

23 

48  56 

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520 

61724 

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520 

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24 

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II  12 

3S796 

514 

61204 

38809 
8.  39323 

514 
509 

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9- 99987 

36 

35 

25 

II  48  40 

0  II  20 

8.39310 

508 

1 1 .  60690 

11.60677 

10.00013 

26 

48  32 

II  28 

30818 

502    60182 

39832 

502 

60168 

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0,9986 

34 

27 

48  24 

II  36 

40320 

496    59680 

40334 

496 

59666 

00014 

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28 

48  16 

II  44 

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491    59184 

40830 

491 

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32 

29 

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II  52 

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41307 
8.41792 

485 

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41321 

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10.00015 

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9- 99985 

31 
30 

30 

II  48  0 

480 

II. 58208 

8.41807 

480 

II. 58193 

31 

47  52 

12  8 

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474 

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42287 

475 

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29 

32 

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470 

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28 

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464 

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27 

34 

35 

47  28 
II  47  20 

12  32 
0  12  40 

43680 
8.44139 

459 

455 

56320 
II.  55861 

43696 
8.44156 

460 

56304 

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99984 

26 

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11.55844 

10.  00017 

9.  999S3 

25 

36 

47  12 

12  48 

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450 

55406 

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99983 

24 

37 

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445 

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45061 

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45507 

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8.  46366 

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433 

11-53634 

8. 46385 

432 

11-53615 

10.  00018 

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20 

41 

46  32 

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416 

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11-51515 

8.  48505 

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11-51495 

10.  00020 

9-  99980 

15 

46 

45  52 

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408 

51104 

48917 

408 

51083 

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14 

47 

45  44 

14  16 

49304 

404 

50696 

49325 

404 

50675 

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99979 

13 

48 

45  36 

14  24 

49708 

400 

50292 

49729 

401 

50271 

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99979 

12 

49 
50 

45  28 

14  32_ 

0  14  40 

50108 

396 

49892 

50130 

397 

49870 

00022 
10.00022 

99978 
9-  99978 

11 

10 

II  45  20 

8.  50504 

393 

11.49496 

8. 50527 

393 

11-49473 

51 

45  12 

14  48 

50897 

390 

49103 

50920 

390 

49080 

00023 

99977 

9 

52 

45  4 

14  56 

51287 

386 

48713 

51310 

386 

48690 

00023 

99977 

8 

53 

44  56 

15  4 

51673 

382 

48327 

51696 

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48304 

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54 
55 

44  4'S 

15  12 

52055 

379 
376 

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11.47566 

52079 

380 

47921 

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10.  00024 

99976 

6 

II  44  40 

0  15  20 

8. 52434 

8.  52459 

376 

11-47541 

9-  99976 

5 

56 

44  32 

15  28 

52810 

373 

47190 

52835 

373 

471^5 

00025 

99975 

4 

57 

44  24 

15  36 

53 1  S3 

369 

46817 

53208 

370 

46792 

00025 

99975 

3 

58 

4V  16 

15  44 

53552 

367 

46448 

53578 

367 

46422 

00026 

99974 

2 

59 

44  8 

15  52 

53919 

363 

46081 

53945 

363 

46055 

00026 

99974 

I 

6o 
M. 

44  0 

16  0 

54282 

360 

45718 

54308 

361 

45692 

00026 

99974 

0 
M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.  i'. 

Secant. 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant. 

Sine. 

91^ 

8S°| 

TABLE  44. 

Page  409 

». 

Log.  Sines,  Tangents,  and  Secants. 

2^ 

nr 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff.  1'. 

Cosecant. 

Tangent. 

Diff.  i'. 

Cotangent. 

Secant. 

Cosine. 

M. 

o 

II  44  0 

0  16  0 

8.  54282 

360 

II. 45718 

8. 54308 

361 

11.45692 

10.00026 

9.  99974 

60 

I 

43  52 

16  8 

54642 

357 

45358 

54669 

358 

45331 

00027 

99973 

59 

-» 

43  44 

16  16 

54999 

355 

45001 

55027 

355 

44973 

00027 

99973 

58 

3 

43  36 

16  24 

55354 

351 

44646 

55382 

352 

44618 

00028 

99972 

57 

4 

5 

43  28 

16  32 

557o5_ 
8.  56054 

349 

44295 

55734 
8. 56083 

349 
346 

44266 
II.  43917 

00028 

99972 

56 

II  43  20 

0  16  40 

346 

11.43946 

10.00029 

9.99971 

55  1 

() 

43  12 

16  48 

56400 

343 

43600 

56429 

344 

43571 

00029 

99971 

54 

7 

43  4 

16  56 

56743 

341 

43257 

56773 

341 

43227 

00030 

99970 

53 

a 

42  56 

17  4 

57084 

337 

42916 

57114 

338 

42886 

00030 

99970 

52 

9 

42  48 

17  12 
0  17  20 

57421 
8.57757' 

336 

332 

42579 

57452 

336 

42548 
II.  42212 

00031 
10.  00031 

99969 
9. 99969 

51 

50 

10 

II  42  40 

11.42243 

8.57788 

333 

II 

42  32 

17  28 

58089 

330 

41911 

58121 

330 

41879 

00032 

99968 

49 

12 

42  24 

17  36 

58419 

328 

41581 

58451 

328 

41549 

00032 

99968 

48 

13 

42  16 

17  44 

58747 

325 

41253 

58779 

326 

41221 

00033 

99967 

47 

14 

42  8 

17  52 
0  18  0 

59072 
8.  59395 

3n 
320 

40928 

5910S 

323 

40895 
11.40572 

00033 
10.00033 

99967 
9. 99967 

46 
45 

15 

II  42  0 

1 1 .  40605 

8. 59428 

321 

lb 

41  52 

18  8 

59715 

318 

40285 

59749 

319 

40251 

00034 

99966 

44 

17 

41  44 

18  16 

60033 

316 

39967 

60068 

316 

39932 

00034 

99966 

43 

iS 

41  36 

18  24 

60349 

313 

39651 

60384 

314 

39616 

00035 

99965 

42 

19 

41  28 

18  32 

6ob62 
8.  60973" 

3" 
309 

^39338_ 

II. 39027 

60698 

3" 

39302 
1 1. 38991 

00036 
10. 00036 

99964 

41 

20 

II  41  20 

0  18  40 

8. 61009 

310 

9. 99964 

40 

21 

41  12 

18  48 

61282 

307 

38718 

61319 

307 

38681 

00037 

99963 

39 

22 

41  4 

18  56 

61589 

305 

3841 1 

61626 

305 

38374 

00037 

99963 

38 

23 

40  56 

19  4 

61894 

302 

38106 

61931 

303 

38069 

00038 

99962 

7^7 

24 

40  48 

19  12 
0  19  20 

62196 

301 

37804 

62234 

301 

37766 

00038 
10.00039 

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9.99961 

36 
35 

25 

II  40  40 

8. 62497 

298 

11-37503 

8.62535 

299 

11.37465 

25 

40  32 

19  28 

62795 

296 

37205 

62834 

297 

37166 

00039 

99961 

34 

27 

40  24 

19  36 

63091 

294 

36909 

63 13 1 

295 

36869 

00040 

99960 

33 

28 

40  16 

19  44 

63385 

293 

36615 

63426 

292 

36574 

00040 

99960 

32 

29 

40  8 

19  52 
0  20  0 

63678 

290 

36322 
11.36032 

63718 

291 

36282 

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31 

30 

II  40  0 

8.  63968 

288 

8. 64009 

289 

II. 35991 

10.00041 

9- 99959 

30 

31 

39  52 

20  8 

64256 

287 

35744 

64298 

287 

35702 

00042 

99958 

29 

32 

39  44 

20  16 

64543 

284 

35457 

64585 

285 

35415 

00042 

99958 

28 

39  36 

20  24 

64827 

283 

35173 

64870 

284 

35130 

00043 

99957 

27 

34 
35 

39  28 
II  39  20 

20  32 

65110 

281 

34890 

65154 

281 

34846 
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10.  00044 

99956 

26  1 

0  20  40 

8. 65391 

279 

1 1 .  34609 

8.  65435 

280 

9. 99956 

25 

3b 

39  12 

20  48 

65670 

277 

34330 

65715 

278 

34285 

00045 

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24 

37 

39  4 

20  56 

65947 

27b 

34053 

65993 

276 

34007 

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99955 

23  1 

3^ 

38  56 

21  4 

66223 

274 

33777 

66269 

274 

33731 

00046 

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22 

39 
40 

3848 
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21  12 
0  21  20 

66497 

272 

33503 

66543 

273 

33457 

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10.  00047 

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9- 99953 

21 
20 

8.  66769 

270 

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8. 66816 

271 

II. 33184 

41 

38  32 

21  28 

67039 

269 

32961 

67087 

269 

32913 

00048 

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19 

42 

38  24 

21  36 

67308 

267 

32692 

67356 

268 

32644 

00048 

99952 

18 

43 

38  16 

21  44 

67575 

266 

32425 

67624 

266 

32376 

00049 

99951 

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44 

38  8  , 

21  52 

67841 

263 
263 

32159 

67890 

264 

321 10 
II.  31846 

00049 
10.00050 

99951 

lb 

45 

11  38  0  ' 

0  22  0 

8. 68104  ! 

II.  31896 

8.68154 

263 

9. 99950 

15 

4b 

37  52 

22  8 

68367 

260 

31633 

68417 

261 

31583 

00051 

99949 

14 

47 

37  44 

22  16 

68627 

259 

31373 

68678 

260 

31322 

00051 

99949 

13 

48 

37  36 

22  24 

68886 

258 

31114 

68938 

258 

31062 

00052 

99948 

12 

49 

37  28 

22  32 
0  22  40 

69144 
8. 69400 

256 

30856 

69196 

257 
255 

30804 

00052 

99948 

II 

50 

II  37  20  1 

254 

1 1 . 30600 

8. 69453 

11.30547 

10. 00053 

9- 99947 

10 

51 

37  12 

22  48 

69654 

253 

30346 

69708 

254 

30292 

00054 

99946 

3 

52 

37  4 

22  56 

69907 

252 

30093 

69962 

252 

30038 

00054 

99946 

M 

53 

3656 

23  4 

70159 

250 

29841 

70214 

251 

29786 

00055 

99945 

7 

54 

36  48  1 

23  12 

70409 
8.  70658 

249 
247 

29591 

70465 

249 
248 

29535 

00056 

99944 

b 

55 

1 1 36  40 ! 

0  23  20 

11.29342 

8.  70714 

11.29286 

10.00056 

9.  99944 

5 

S^ 

36  32 : 

23  28 

70905 

246 

29095 

70962 

246 

29038 

00057 

99943 

4 

5? 

36  24 

23  36 

71151 

244 

28849 

71208 

245 

28792 

00058 

99942 

-y 

5^ 

36 16 

23  44 

71395 

243 

28605 

71453 

244 

28547 

00058 

99942 

2 

59 

36  8 

23  52 

71638 

242 

28362 

71697 

243 

28303 

00059 

99941 

I 

60 

36  0 

24  0 

71880 

240 

28120 

71940 

241 

28060 

00060 

99940 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diflf.  i'. 

Secant. 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant. 

Sine. 

92° 

87°  1 

I 


Page  410 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

3" 

176° 

M. 

Hour  A.M. 

Hour  P.M. 

Sine. 

Diff.  i'. 

Cosecant. 

Tangent. 

Diff.  i'. 

Cotangent. 

Secant. 

Cosine. 

M. 

o 

II  36  0 

0  24  0 

8.  71880 

240 

II. 28120 

8.  71940 

241 

11,28060 

10.  00060 

9.  99940 

60 

I 

35  52 

24  8 

72120 

239 

27880 

72181 

239 

27819 

00060 

99940 

59 

2 

35  44 

24  16 

72359 

i   238 

27641 

72420 

239 

27580 

00061 

99939 

58 

3 

35  36 

24  24 

72597 

237 

27403 

72659 

237 

27341 

00062 

99938 

57 

4 

35  28 

24  32 

72834 

235 

27166 

72896 

236 

27104 

00062 

99938 
9-99937 

56 

55 

5 

II  35  20 

0  24  40 

8.  73069 

234 

u. 26931 

8.  73132 

234 

11.26868 

10.  00063 

6 

35  J2 

24  48 

73303 

232 

26697 

73366 

234 

26634 

00064 

99936 

54 

7 

35  4 

24  56 

73535 

232 

26465 

73600 

232 

26400 

00064 

99936 

53 

8 

34  56 

25  4 

73767 

230 

26233 

73832 

231 

26168 

00065 

99935 

52 

9 

34  48 

25  12 

73997 

229 

26003 

74063 

229 

25937 
11.25  708 

00066 

99934 

51 

lO 

II  34  40 

0  25  20 

8.  74226 

228 

11.25774 

8.  74292 

229 

ID.  00066 

9^  99934 

50 

II 

34  32 

25  28 

74454 

226 

25546 

74521 

227 

25479 

00067 

99933 

49 

12 

34  24 

25  36 

74680 

226 

25320 

74748 

226 

25252 

00068 

99932 

48 

13 

34  16 

25  44 

74906 

224 

25094 

74974 

225 

25026 

00068 

99932 

47 

H 

34  8 

25  52 

75130 

223 

24870 

75199 

224 

24801 

00069 

99931 

46 

15 

II  34  0 

0  26  0 

8-  75353 

222 

II.  24647 

8.  75423 

222 

11.24577 

10. 00070 

9.  99930 

45 

lb 

33  52 

26  8 

75575 

220 

24425 

75645 

222 

24355 

00071 

99929 

44 

I? 

33  44 

26  16 

75795 

220 

24205 

75867 

220 

24133 

00071 

99929 

43 

i8 

33   36 

26  44 

76015 

219 

23985 

76087 

219 

23913 

00072 

99928 

42 

19 

33   28 

26  32 

76234 

217 

23766 

76306 

219 

23694 

00073 

99927 

41 

20 

II  33  20 

0  26  40 

8.  76451 

2X6 

"•23549 

8.  76525 

217 

"•23475 

10.00074 

9.  99926 

40 

21 

33  12 

26  48 

76667 

216 

23333 

76742 

216 

23258 

00074 

99926 

39   i 

22 

33    4 

26  56 

76883 

214 

231 1 7 

76958 

215 

23042 

00075 

99925 

38 

23 

32  56 

27  4 

77097 

213 

22903 

77173 

214 

22827 

00076 

99924 

37 

24 

32  48 

27  12 

77310 

212 

22690 

77387 

213 

22613 

00077 

99923 
9. 99923 

36 
35 

25 

I'  32  40 

0  27  20 

8.  77522 

211 

11.22478 

8.  77600 

211 

11.22400 

10.  00077 

26 

32  32 

27  28 

77733 

210 

22267 

7781 1 

211 

22189 

00078 

99922 

34 

27 

32  24 

27  36 

77943 

209 

22057 

78022 

210 

21978 

00079 

99921 

33 

28 

32  16 

27  44 

78152 

208 

21848 

78232 

209 

21768 

00080 

99920 

32 

29 
30 

32  8 

27  52 

78360 

208 
206 

21640 

78441 

208 

21559 

00080 

99920 

31   1 

I'  32  0 

0  28  0 

8.  78568 

II.  21432 

8.  78649 

206 

11.21351 

10.00081 

9.99919 

30 

31 

3  52 

28  8 

78774 

205 

21226 

78855 

206 

21145 

00082 

99918 

29      ! 

32 

31  44 

28  16 

78979 

204 

21021 

79061 

205 

20939 

00083 

99917 

28 

?i3 

31  36 

28  24 

79183 

203 

20817 

79266 

204 

20734 

00083 

99917 

27 

34 

35 

31  28 

II  31  20 

28  32 

79386 

202 

20614 

79470 
8.  79673 

203 
202 

20530 
II.  20327 

00084 

99916 
9-99915 

26 
25 

0  28  40 

8.  79588 

201 

II.  20412 

10.  00085 

36 

31  12 

28  48 

79789 

201 

202 1 1 

79875 

201 

20125 

00086 

99914 

24 

37 

31  4 

28  56 

79990 

199 

20010 

80076 

201 

19924 

00087 

99913 

23 

3^ 

30  56 

29  4 

80189 

199 

19811 

80277 

199 

19723 

00087 

99913 

22    , 

39 
40 

30  48 

29  12 

0  29  20 

80388 

197 
197 

196 1 2 
11-19415 

80476 

198 

19524 

00088 

99912 

21 

II  30  40 

8.  80585 

8.  80674 

198 

II. 19326 

10.  00089 

9. 9991 1 

20 

41 

30  32 

29  28 

80782 

196 

19218 

80872 

196 

19128 

ooogo 

99910 

19 

42 

30  24 

29  36 

80978 

195 

19022 

81068 

196 

18932 

00091 

99909 

18 

43 

30  16 

29  44 

f"73 

194 

18827 

81264 

195 

18736 

00091 

99909 

17 

44 

45 

30  8 

29  52 

81367 

193 

18633 
II. 18440 

81459 

194 

18541 

00092 

99908 

16 

II  30  0 

0  30  0 

8.81560 

192 

8.81653 

193 

II.  18347 

10.  00093 

9. 99907 

15 

4b 

29  52 

30  8 

81752 

192 

18248 

81846 

192 

18154 

00094 

99906 

14 

'^l 

29  44 

30  16 

81944 

190 

18056 

82038 

192 

17962 

00095 

99905 

13 

4cS 

29  36 

30  24 

82134 

190 

17866 

82230 

190 

17770 

00096 

99904 

12    1 

49 

29  28 

30  32 

82324 

189 

17676 

82420 

190 

17580 

00096 

99904 

II     } 

50 

II  29  20 

0  30  40 

8.82513 

188 

II. 17487 

8.82610 

189 

II. 17390 

10.  00097 

9-  99903 

10 

51 

29  12 

30  48 

82701 

187 

17299 

82799 

188 

1 7201 

00098 

99902 

9 

52 

29  4 

30  56 

82888 

187 

17112 

82987 

188 

1 7013 

00099 

99901   8  1 

53 

28  Sb 

31  4 

83075 

186 

16925 

83175 

186 

16825 

00 1 00 

99900 

7 

54 
55 

28  48 

31  12 

83261 

185 

16739 

83361 

186 

16639 

OOIOI 

99899 

6 

II  28  40 

0  31  20 

8. 83446 

184 

II.  16554 

8. 83547 

185 

II.  16453 

10.  00102 

9. 99898 

5 

5^ 

28  32 

31  28 

83630 

183 

16370 

83732 

184 

16268 

00102 

99898 

4 

H 

28  24 

31  36 

83813 

183 

16187 

83916 

184 

16084 

00103 

99897 

3 

s^ 

28  16 

31  44 

83996 

181 

16004 

84100 

182 

15900 

00104 

99896 

2 

59 

28  8 

31  52 

84177 

181 

15823 

84282 

182 

15718 

00105 

99895 

I 

bo 

28  0 

32  0 

84358 

181 

15642 

84464 

182 

15536 

00106 

99894 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.  i'. 

Secant. 

Cotangent. 

Diff.  1'. 

Tangent. 

Cosecant. 

Sine. 

M. 

93° 

86°  1 

TABLE  44. 

Page  411 

^ 

Log.  Sines,  Tangents,  and  Secants, 

4^ 

175° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff.  i'. 

Cosecant. 

Tangent. 

Diff.  i'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

II  28  0 

0  32  0 

8.84358 

181 

II. 15642 

8. 84464 

182 

"- 15536 

10.  00106 

9. 99894 

60 

I 

27  52 

32  8 

84539 

179 

1 546 1 

84646 

180     15354 

00107 

99893 

59 

2 

27  44 

32  lb 

84718 

179 

15282 

84826 

180     15174 

00108 

99892 

58 

"» 
J 

27  36 

32  24 

84897 

178 

15103 

8500b 

179  1   14994 

00109 

99891 

57 

4 

5 

27  28 

32  32 

85075 
X85252 

177 

14925 

85185 

178 

148 1 5 

00109 

99891 

56 

II  27  20 

0  32  40 

177 

II.  14748 

8.  85363 

177 

II. 14637 

10. 001 10 

9.  99890 

S5 

6 

27  12 

3248 

85429 

17b 

14571 

85540 

177  1   14460 

001 1 1 

99889 

54 

7 

27  4 

32  56 

85605 

175 

14395 

85717 

176  1   14283 

001 12 

99888 

S3 

S 

26  56 

33  4 

85780 

175 

14220 

85893 

176     I4107 

001 13 

99887 

S2 

9 

2b  48 

33  12 

85955 

173 

14045 

86069 

174     13931 

001 14 

99886 

51 

10 

II  26  40 

0  ^i   20 

8.8bi28 

173 

II. 13872 

8. 86243 

174  11-13757 

10. 001 15 

9.  99885 

SO 

II 

2b  32 

3328 

86301 

173 

13699 

86417 

174  i   13583 

001 16 

99884 

49 

12 

26  24  i   33  3b 

86474 

171 

13526 

86591 

172  1   13409 

001 1 7 

99883 

48 

I.S 

26  16    33  44 

86645 

171 

13355 

86763 

172     13237 

001 18 

99882 

47 

H 

2b   8 

33  52 

868  lb 

171 

13184 

86935 

171  !   13065 

001 19 

99881 

46 

IS 

II  2b  0 

34  0 

8. 8b987 

169 

II. 13013 

8. 87106 

171 

II. 12894 

10.  00120 

9. 99880 

45 

i6 

25  52 

34  8 

87156 

169 

12844 

87277 

170 

12723 

00121 

99879 

44 

I? 

25  44 

34  16 

87325 

169 

12675 

87447 

169 

12553 

00121 

99879 

43 

iS 

25  36 

34  24 

87494 

ib7 

12506 

87b  lb 

169 

12384 

00122 

99878 

42 

19 

25  28 

34  32 

87661 

168 

12339 

87785 

168 

12215 

00123 

99877 

41 

40 

20 

II  25  20 

0  34  40 

8.  87829 

166 

II.  12171 

8.87953 

167 

II.  12047 

10.00124 

9.  9987b 

21 

25  12  1   34  48 

8799s 

166 

12005 

88120 

167 

1 1880 

00125 

99875 

39 

22 

25  4    34  56 

88161 

165 

1 1839 

88287 

166 

I1713 

0012b 

99874 

38 

2.S 

24  56    35  4 

88326 

164 

"674 

88453 

165 

"547 

00127 

99873 

>7 

24 

24  48  1   35  12 

88490 

164 

I1510 

88b  1 8 

165 

1 1382 

00128 

99872 
9.  99871 

36 

3S 

25 

II  24  40  0  35  20 

8. 88654 

163 

II.  1134b 

8.  88783 

165 

II.  11217 

10.  00129 

2b 

24  32  ;     35  28 

88817 

163 

1 1 183 

88948 

163 

1 1052 

00130 

99870 

U 

27 

24  24    35  36 

88980 

162 

1 1020 

891 1 1 

16,3 

10889 

00131 

998b9 

3^1 

28 

24  lb    35  44 

89142 

162 

10858 

89274 

163 

10726 

00132 

99868 

32 

29 

24  8 

35  52 

89304 

160 

iob9b 

89437 

161 

10563 

00133 

99867 

31 

30 

30 

II  24  0 

0  36  0 

8.  89464 

161 

II.  10536 

8. 89598 

162 

II. 10402 

10.00134 

9. 99866 

31 

23  5^^    36  8 

89625 

159 

10375 

897bo 

160 

10240 

00135 

99865 

2Q 

32 

23  44 

36  16 

89784 

159 

10216 

89920 

160 

10080 

0013b 

99864 

28 

33 

23  36 

36  24 

89943 

159 

10057 

90080 

160 

09920 

00137 

99863 

27 

34 
35 

23  28 

36  32 

90102 

158 

09898 

90240 

159 

09760 

00138 

998b2 

26 

25 

II  23  20 

0  3b  40 

8. 90260 

157 

11.09740 

8. 90399 

1.58 

II.  09601 

10.00139 

9.  998b  I 

3b 

23  12 

36  48 

90417 

157 

09583 

90557 

I.S8 

09443 

00140 

998bo 

24 

37 

23  4 

3656 

90574 

156 

09426 

90715 

157 

09285 

00141 

99859 

23 

3« 

22  5b 

37  4 

90730 

155 

09270 

90872 

157 

09128 

00142 

99858 

22 

39 

22  48 

37  12 

90885 

155  , 

09115 

91029 

156 

08971 

00143 

99857 
9- 99856 

21 
20 

40 

II  22  40 

0  37  20 

8. 91040 

1.55  ! 

1 1 . 08960 

8.  91 185 

155 

II. 08815 

10.  00144 

41 

22  32 

3728 

91195 

154 

08805 

91340 

155 

08660 

00145 

99855 

19 

42 

22  24 

37  36 

91349 

153 

08651 

91495 

155 

08505 

0014b 

99854 

18 

43 

22  lb 

37  44 

91502 

153 

08498 

9ib5o 

153 

08350 

00147 

99853 

17 

44 

22   8 

37  52 

91655 

152 

08345 

91803 

154 

08197 

00148 

99852 

16 
15 

45 

II  22   0 

°  38  0 

8.91807 

152  ! 

II.  08193 

8.91957 

153 

11.08043 

10. 00149 

9.99851 

4b 

21  52 

38  8 

91959 

151 

08041 

92110 

152 

07890 

00150 

99850 

14 

47 

21  44 

38  16 

92110 

151 

07890 

92262 

152 

07738 

00152 

99848 

13 

4S 

21  36 

3824 

92261 

150 

07739 

92414 

151 

07586 

00153 

99847 

12 

49 

21  28 

3832 

924 II 

150 

07589 

92565 

151 

07435 

00154 

99846 

II 

10 

50 

II  21  20 

0  38  40 

8.92561 

149 

11.07439 

8.92716  i 

150 

11.07284 

10.00155 

9- 99845 

51 

21  12 

3848 

92710  ; 

149 

07290 

92866 

150 

07134 

00156 

99844 

9 

52 

21   4 

38  56 

92859 

148 

07141 

93016  ' 

149 

06984 

00157 

99843 

8 

53 

20  56 

39  4 

93007 

147 

06993 

93165 

148 

06835 

00158 

99842 

7 

54 

20  48 

39  12 

93154 

147 

06846 

93313 

149 

06687 

00159 

99841 

b 

55 

J I  20  40 

0  39  20 

8-93301  1 

147 

1 1 . 06699 

8.  93462 

147 

11.06538 

10.00160 

9. 99840 

5 

S^ 

20  32 

39  28 

93448  ' 

146 

06552 

93609 

147 

06391 

00161 

99839 

4 

^l 

20  24 

39  36 

93594 

146  I 

ob4ob 

93756 

147 

06244 

00162 

99838   3  1 

5^ 

20  lb 

39  44 

93740 

145 

06260 

93903 

146 

06097 

00163 

998^7  •  2  1 

59 

20  8 

39  52 

93885 

145 

06x15 

94049 

146 

05951 

00164 

99836 

I 

bo 

M. 

20  0 

40  0 

94030 

144 

05970 

94195 

145 

05805 

00166 

99834 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.  i'. 

Secant. 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant. 

Sine. 

M. 

94° 

85°  1 

II 


Page  412 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

5° 

A 

A 

B 

B 

C          C   114° 

M. 
o 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

IX  20  00 

0  40  0 

8.  94030 

0 

11.05970 

8. 94195 

0 

11.05805 

10. 00166 

0 

9.  99834 

60 

I 

1952 

40  8 

94174 

2 

05826 

94340 

2 

05660 

00167 

0 

99833 

59 

2 

1944 

40  16 

94317 

4 

05683 

94485 

4 

.  05515 

00168 

0 

99832 

S8 

3 

1936 

40  24 

94461 

7 

05539 

94630 

7 

05370 

00169 

0 

99831 

57 

4 

5 

1928 
II  19  20 

40  32 

94603 

9 

05397 

94773 

9 

05227 

00170 

0 

99830 

56 

55 

0  40  40 

8.  94746 

II 

11.05254 

8.94917 

II 

11.05083 

10.  001 71 

0 

9. 99829 

6 

19  12 

40  48 

94887 

13 

05113 

95060 

13 

04940 

00172 

0 

99828 

54 

7 

19  4 

40  56 

95029 

15 

04971 

95202 

15 

04798 

00173 

0 

99827 

5^ 

8 

1856 

41  4 

95170 

18 

04830 

95344 

18 

04656 

00175 

0 

99825 

52 

_  9_ 

10 

1848 
II  18  40 

41  12 
0  41  20 

95310 
8.  95450 

20 

04690 

95486 

20 

04514 

00176 

0 

99824 

51 

22 

11.04550 

8.95627 

22 

"•04373 

10.00177 

0 

9. 99823 

50 

II 

1832 

41  28 

9555^9 

24 

0441 1 

95767 

24 

04233 

00178 

0 

99822 

49 

12 

1824 

41  36 

95728 

26 

04272 

95908 

27 

04092 

00179 

0 

99821 

48 

13 

18  16 

41  44 

95867 

29 

04133 

96047 

29 

03953 

00180 

0 

99820 

47 

14 

18  8 

41  52 

96005 

31 

03995 

96187 
8.  96325" 

31 

03813 

00181 

0 

99819 

46 

15 

II  18  0 

0  42  0 

8. 96143 

33 

11.03857 

33 

11.03675 

10.  00183 

0 

9.99817 

45 

16 

1752 

42  8 

96280 

35 

03720 

96464 

35 

03536 

00184 

0 

99816 

44 

17 

174^1 

42  16 

96417 

37 

03583 

96602 

38 

03398 

00185 

0 

99815 

43 

18 

1736 

42  24 

96553 

39 

03447 

96739 

40 

03261 

00186 

0 

99814 

42 

19 

1728 

42  32 

96689 
8.  96825 

42 
44 

033 1 1 

96877 

42 

03123 

00187 

0 

99813 

41 

20 

II  1 7  20 

0  42  40 

"•03175 

8.97013 

44 

11.02987 

10. 00188 

0 

9.99812 

40 

21 

17  12 

42  48 

96960 

4b 

03040 

97150 

46 

02850 

00190 

0 

99810 

39 

22 

17  4 

42  56 

97095 

48 

02905 

97285 

49 

02715 

00I9I 

0 

99809 

38 

23 

16  56 

43  4 

97229 

50 

02771 

97421 

51 

02579 

00192 

0 

99808 

M 

24 

1648 

43  12 

0  43  20 

97363 
8. 97496 

S3 

55 

02637 

97556 

53 

02444 

00193 

0 

99807 

36 

25 

II  16  40 

11.02504 

8.  97691 

55 

11.02309 

10.  00194 

9.  99806 

35 

26 

1632 

43  28 

97629 

57 

02371 

97825 

58 

02175 

00196 

99804 

34 

27 

16  24 

43  36 

97762 

S9 

02238 

97959 

bo 

02041 

00197 

99803 

33 

2S 

16  16 

43  44 

97894 

61 

02106 

98092 

62 

01908 

00198 

99802 

^^2 

29 

16  8 

43  52 

98026 

64 
66 

01974 

98225 
8.98358 

64 

01775 

00199 

99801 

31 

30 

II  16  0 

0  44  0 

8.98157 

II.  01843 

66 

II.  01642 

10. 00200 

9. 99800 

30 

31 

15  52 

44  8 

98288 

68 

01712 

98490 

69 

01510 

00202 

99798 

29 

32 

1544 

44  16 

98419 

70 

01581 

98622 

71 

0137S 

00203 

99797 

28 

33 

1536 

44  24 

98549 

72 

OI451 

9^753 

73 

01247 

00204 

99796 

27 

34 

15  28 

44  32 

98679 

75 

01321 

98884 
8.99015 

75 

01116 

00205 

99795 

26 
25' 

35 

II  15  20 

0  44  40 

8.  98808 

n 

II.OII92 

77 

1 1 .  00985 

10.00207 

9-  99793 

3(5 

15  12 

44  48 

98937 

79 

01063 

99145 

80 

00855 

00208 

99792 

24 

37 

15  4 

44  56 

99066 

81 

00934 

99275 

82 

00725 

00209 

99791 

■2.\ 

3^ 

1456 

45  4 

99194 

83 

00806 

99405 

84 

00595 

00210 

99790 

22 

39 
40 

1448 
II  14  40 

45  12 

99322 

86 
88 

00678 
11.00550 

99534 
8.  99662 

86 
89 

00466 

00212 

99788 

21 

0  45  20 

8.  99450 

11.00338 

10.00213 

9.  99787 

20 

41 

1432 

45  28 

99577 

90 

00423 

99791 

91 

00209 

00214 

99786 

19 

42 

1424 

45  36 

99704 

92 

00296 

99919 

93 

00081 

00215 

99785 

18 

43 

14  16 

45  44 

99830 

94 

00170 

9. 00046 

95 

10. 99954 

00217     I 

99783 

17 

44 

14  8 

45  52 

99956 

96 

00044 

00174 

97 

99826 

00218 

99782 

16 

45 

II  14  0 

0  46  0 

9. 00082 

99 

10.  99918 

9. 00301 

100 

10.  99699 

10.00219 

9.  99781 

15 

4b 

1352 

46  8 

00207 

lOI 

99793 

00427 

102 

99573 

00220 

99780 

14 

47 

1344 

46  16 

00332 

103 

99668 

•  00553 

104 

99447 

00222 

99778 

13 

48 

1336 

46  24 

00456 

105 

99544 

00679 

106 

99321 

00223 

99777 

12 

49 

13  28 

46  32 
0  46  40 

00581 
9. 00704 

107 
no 

99419 
10.  99296 

00805 
9. 00930 

108 

99195 

00224 

99776 

II 

50 

II  13  20 

III 

10.99070 

10.  00225 

9-99775 

10 

51 

13  12  1 

46  48 

00828 

112 

99172 

01055 

"3 

98945 

00227 

99773   9 

52 

13  4 

46  5b 

00951 

114 

99049 

01 179 

"5 

98821 

00228 

99772   8 

53 

12  56 

47  4 

01074 

116 

98926 

01303 

117 

98697 

00229 

99771   7 

54 

55 

12  48 
II  1 2  40 

47  12 

01 196 

118 

98804 

01427 

120 

98573 

00231     I 

99769   6 

0  47  20 

9.01318 

121 

10.  98682 

9-01550 

122 

10.98450 

10.  00232 

99768 

5 

5<3 

12  32 

47  28 

01440 

123 

98560 

01673 

124 

98327 

00233 

99767 

4 

57 

12  24 

47  36 

01561 

125 

98439 

01796 

126 

98204 

00235 

99765 

3 

5« 

12  lb 

47  44 

01682 

127 

98318 

01918 

128 

98082 

00236 

99764 

2 

59 

12  8 

47  52 

01803 

129 

98197 

02040 

131 

.  97960 

00237 

99763 

I 

60 

12  0 

48  0 

01923 

132 

98077 

02162 
Cotangent. 

133 

97838 

00239 

99761 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

95° 

A 

A 

B 

B 

C         C    84°  1 

Seconds  of  time 

1» 

2« 

3» 

4, 

5' 

6» 

7- 

Prop,  parts  of  cols.  •<  B 

16 

17 
0 

33 
33 

° 

49 
0 

66 

66 

I 

82  $9 

83  1CX> 
I     I 

"1 
116 

% 

TABLE  44. 

Page  413 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

6° 

A          A 

B          B 

C         C   173° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

II  12  0 

0  48  0 

9.  01923 

0 

10. 98077 

9.02162 

0 

10. 97838 

10.00239 

0 

9.99761 

60 

I 

II  52 

48  8 

02043 

2 

97957 

02283 

2 

97717 

00240 

0 

99760 

59 

2 

II  44 

48  16 

02163 

4 

97837 

02404 

4 

97596 

00241 

0 

99759 

S8 

^ 
0 

II  36 

48  24 

02283 

b 

97717 

02525  i  6 

97475 

00243 

0 

99757 

57 

4 

II  28 

4832 

02402 

_7_ 
Q 

97598 

02645 

8 

97355 

00244 

0 

99756 

56 

S 

II  II  20 

0  48  40 

9.  02520 

10.  97480 

9.  02766 

9 

10. 97234 

10. 00245 

0 

9-99755 

55 

6 

II  12 

48  48 

02639 

II  !   97361 

02885 

II 

97115 

00247 

0 

99753 

54 

7 

II   4 

4856 

02757 

13  i   97243 

03005 

13 

96995 

00248 

0 

99752 

5S 

8 

10  56 

49  4 

02874 

15  I   97126 

03124   15 

96876 

00249 

0 

99751 

52 

9 

10  48 

49  12 

02992 

17 
19 

97008 
10.96891 

03242 
9.03361 

17 

96758 

00254 

0 

99749 

51 

50 

10 

II  10  40 

0  49  20 

9.03109 

19 

10. 96639 

10. 00252 

0 

9. 99748 

11 

10  32 

49  28 

03226 

20 

96774 

03479   21  '           96521 

00253 

0 

99747 

49 

12 

10  24 

49  3t> 

03342 

22 

96658 

03597   23      96403 

00255 

0 

99745 

48 

13 

10  16 

49  44 

03458 

24 

96542 

03714  i  24  1     96286 

00256 

0 

99744 

47 

14 
15 

10  8 

49  52 

03574 

26 

96426 
10.96310 

03832   26 
9. 03948   28 

96168 

00258 

0 

99742 

46 

II  10  0 

0  50  0 

9. 03690 

28 

10. 96052 

10.  00259 

0 

9.99741 

45 

16 

952 

50  8 

03805 

30 

96195 

04065  !  30 

95935 

00260 

0 

99740 

44 

17 

9  44 

50  16 

03920 

31 

96080 

04181 

32 

95819 

00262 

0 

99738 

43 

iS 

936 

50  24 

04034 

33 

95966 

04297 

34 

95703 

00263 

0 

99737 

42 

19 

928 

50  32 

04149 

35 

95851 

04413 

36 

95587 

00264 

0 

99736 

41 

20 

II  9  20 

0  50  40 

9. 04262 

37 

10.95738 

9. 04528 

38 

10.  95472 

10. 00266 

0 

9-  99734 

40 

21 

9  12 

50  48 

04376 

39 

95624 

04643 

39 

95357 

00267 

99733 

39 

22 

9  4 

50  56 

04490 

41 

95510 

04758  !  41 

95242 

00269 

99731 

^8 

23 

856 

51  4 

04603 

43 

95397 

04873   43     95127 

00270 

99730 

37 

24 

25 

848 
II  8  40 

51  12 
0  51  20 

04715 

44 

95285 

04987  !  45  !    95013 

00272 

99728 

36 

9.  04828 

46 

10.95172 

9. 05101  1  47 

10. 94899 

10.00273 

9.99727 

35 

26 

832 

SI  28 

04940 

48 

95060 

05214  j  49 

94786 

00274 

99726 

34 

27 

824 

51  36 

05052 

50 

94948 

05328  i  51  !      94672 

00276 

99724 

1 1 

28 

8  16 

51  44 

05164 

52 

94836 

05441  1  53 

94559 

00277 

99723 

32 

29 

8  8 

51  52 

05275 

54 

94725 

05553 

54 
56" 

94447 

00279 

99721 

31 

30 

II  8  0 

0  52  0 

9. 05386 

56 

10. 94614 

9. 05666 

10. 94334 

10. 00280 

9. 99720 

30 

31 

752 

52  8 

05497  57 

94503 

05778  ;  58  '      94222 

00282 

99718 

29 

32 

7  44 

52  16 

05607  !  59 

94393 

05890    60  1      941 10 

00283 

99717 

28 

736 

52  24 

05717  61 

94283 

06002  i  62  1      93998 

00284 

99716 

27 

34 

728 

52  32 

05827  63 

94173 

061 13 

64 
"66" 

93887 

00286 

99714 

26 

35 

II  7  20 

0  52  40 

9-05937  1  65 

10. 94063 

9. 06224 

10.93776 

10.  00287 

9-99713 

25 

36 

7  12 

52  48 

06046  67 

93954 

06335  68  [    93665 

00289 

997" 

24 

37 

7  4 

52  56 

06155  i  69  i   93845 

06445  69  j    93555 

00290 

99710 

23 

3!^ 

656 

53  4 

06264  70    93736 

06556  71  '    93444 

00292 

99708 

22 

39 
40 

648 

53  12 

063 72_ 
9.  06481 

72  ;    9362b 

06666  73 

93334 

00293 

99707 

21 

II  6  40 

0  53  20 

74  1  10.93519 

9-  06775  75 

10.  93225 

10.00295 

9-  99705 

20 

41 

632 

53  28 

06589  76     9341 1 

06885  77 

93115 

00296 

99704 

19 

42 

6  24 

53  36 

06696  78     93304 

06994  :  79 

93006 

00298 

99702 

18 

43 

6  16 

53  44 

06804  80     93196 

07103  8i 

92897 

00299 

99701 

17 

44 

6  8 

53  52 

0691  I    81  ;     93089 

072 1 1   83  :    92789 

00301 

99699 

lb 

45 

II  6  0 

0  54  0 

9.07018  1  83    10.92982 

9. 07320  84   10. 92680 

10. 00302 

9- 99698 

15 

4b 

5  52 

54  8 

07124   85       92876 

07428  86     92572 

00304 

I    99696 

14 

47 

544 

54  16 

07231    87  '      92769 

07536  88     92404 

00305 

I  !    99695 

13 

48 

536 

54  24 

07337    89       92663 

07643  90  ,    92357 

00307 

I  i    99693 

12 

49 

528 

54  32 

07442    91       92558 

07751  92 

92249 

00308 

I     99692 

II 

50 

II  5  20 

0  54  40 

9-07548  1  93  10.92452 

9.07858  94 

10.92142 

10.00310 

9. 99690 

10 

51 

5  12 

54  48 

07653  94    92347 

07964  '  96 

92036 

003 1 1 

99689 

9 

52 

5  4 

54  56 

07758  96  ,    92242 

08071   :  98  ;       91929 

00313 

99687 

S 

53 

4  5(5 

55  4 

07863  98     92137 

08177  99  '        91823 

00314 

99686 

7 

54 
55 

448 

II  4  40 

55  12 

07968  !ioo    92032 

08283  loi  :   91717 

00316 

996S4 

6 

0  55  20 

9. 08072 

102  10.91928 

9.08389  103  10. 91611 

10.00317 

9. 99683 

5 

5b 

432 

55  28 

08176 

104    91824 

08495  105  !   91505 

00319 

99681 

4 

57 

4  24 

55  36 

08280  106    91720 

08600  107  1   91400 

00320 

I  !   99680 

3 

S^ 

4  16 

55  44 

08383  107    91617 

08705  109    91295 

00322 

I  !  99678 

2 

59 

4  8 

55  52 

08486  109    915 14 

08810  III     91 190 

00323   I    99677 

I 

60 

4  0 

56  0 

08589  |iii 

91411 
Secant. 
A 

08914  113    91086 

00325   I    99675 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Cotangent.  Diff. 

Tangent. 
B 

Cosecant.  Diff.   Sine. 

1 

M. 

96° 

A 

B 

C          C    83°| 

Seconds  of  time. . . 

1« 

2» 

3» 

4» 

5» 

«» 

1' 

Prop,  parts  of  cols. 

\t 

14 

14 
0 

28 

28 

0 

42 
42 

I 

56 

56 
I 

69 
70 

I 

83 

84 

I 

97 
98 

I 

Page  414 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

r 

A 

A 

B 

B 

C         C   172° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difif. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

II  4  0 

0  56  0 

9. 08589 

0 

IO.9141I 

9.  08914 

0 

10.  91086 

10.  00325 

0 

9.  99675 

60 

I 

352 

56  8 

08692 

2 

91308 

09019 

2 

90981 

00326 

0 

99674 

59 

2 

3  44 

56  16 

08795 

3 

91205 

09123 

3 

90877 

00328 

0 

99672 

58 

S 

336 

56  24 

08897 

5 

91 103 

09227 

5 

90773 

00330 

0 

99670 

57 

4 

328 

56  32 

08999 

6 

91001 

09330 

7 

90670 

00331 

0 

99669 

56 

S 

II  3  20 

0  56  40 

9.  09101 

8 

10. 90899 

9.  09434 

8 

10. 90566 

10.  00333 

0 

9. 99667 

55 

6 

3  12 

56  48 

09202 

10 

90798 

09537 

10 

90463 

00334 

0 

99666 

54 

7 

3  4 

56  56 

09304 

II 

90696 

09640 

11 

90360 

00336 

0 

99664 

53 

8 

2  56 

57  4 

09405 

13 

90595 

09742 

13 

9025S 

00337 

0 

99663 

52 

9 

2  48 

57  12 

09506 

14 

90494 

09845 

15 
16 

90155 

00339 

0 

99661 

51 

lO 

II  2  40 

0  57  20 

9. 09606 

16 

10. 90394 

9. 09947 

10.90053 

10.  00341 

0 

9- 99659 

50 

II 

232 

57  28 

09707 

18 

90293 

10049 

18 

89951 

00342 

0 

99658 

49 

12 

2  24 

57  36 

09807 

19 

90193 

10150 

20 

89850 

00344 

0 

99656 

48 

M 

2  16 

57  44 

09907 

21 

90093 

10252 

21 

89748 

00345 

0 

99655 

47 

14 
IS 

2  8 
II  20 

57  52 

10006   22 

89994 

10353 

23 
24 

89647 
10. 89546 

^00347^ 

10.  00349 

Q 
0 

99653 

46 

0  58  0 

9.  IOIO6 

24 

10. 89894 

9.  10454 

9.99651 

45 

i6 

I  52 

58  8 

10205 

26 

89795 

10555 

26 

89445 

00350 

0 

99650 

44 

17 

I  44 

58  16 

10304 

27 

89696 

10656 

28 

89344 

00352 

0 

99648 

43 

i8 

136 

58  24 

10402   29 

89598 

10756 

29 

89244 

00353 

99647 

42 

19 

I  28 

58  32 

IO50I   30 

89499 

10856 

31 

89144 

00355 

99645 

41 

20 

II  I  20 

0  58  40 

9. 10599 

.32 

10. 89401 

9.  10956 

33 

10. 89044 

10.00357 

9-  99643 

40 

21 

I  12 

58  48 

10697 

34 

89303 

11056 

34 

88944 

00358 

99642 

39 

22 

I  4 

5856 

10795 

35 

89205 

II155 

36 

88845 

00360 

99640 

38 

2^, 

0  56 

59  4 

10893 

37 

89107 

1 1254 

37 

88746 

00362 

99638 

37 

24 

2S 

048 

59  12 

10990 

38 

89010 

"353 

39 

88647 

00363 

99637 

36 

II  0  40 

0  59  20 

9.  II087 

40 

10.  88913 

9.11452 

41 

10. 88548 

10.  00365 

9. 99635 

35 

26 

0  32 

59  28 

1 1 184 

42 

88816 

11551 

42 

88449 

00367 

99633 

34 

27 

0  24 

59  36 

1 1 281  i  43 

88719 

11649 

44 

88351 

00368 

99632 

33 

28 

0  16 

59  44 

II377 

45 

88623 

1 1 747 

46 

^f"53 

00370 

99630 

32 

29 

30 

0  8 

59  52 

1 1474 

46 

88526 

11845 

47 

88155 

00371    I 

99629 

31 

II  0  0 

I  0  0 

9.  1 1570 

48 

10. 88430 

9- "943 

49 

10.88057 

10.00373    I 

9.99627 

30 

r 

10  59  52 

0  8 

1 1 666 

50 

88334 

12040  51 

87960 

00375    I 

99625 

29 

59  44 

0  16 

1 1 761 

51 

88239 

12138 

52 

87862 

00376 

99624 

28 

■J   T 

593b 

0  24 

"857 

53 

88143 

12235 

54 

87765 

00378 

99622 

27 

34 

3=; 

5928 

0  32 

1 1952 

54 

88048 

12332 

55 

87668 

00380 

99620 

26 

10  59  20 

I  0  40 

9.  12047 

56 

10. 87953 

9. 12428 

57 

10.  87572 

1 0.  00382 

9.99618 

25 

36 

59  12 

0  48 

12142  '  58 

87858 

12525  !  59 

87475 

00383 

99617 

24 

37 

59  4 

0  56 

12236  59 

87764 

12621    60 

87379 

00385 

99615 

23 

3« 

5856 

I  4 

12331  ,   61 

87669 

12717 

62 

87283 

00387 

99613 

22 

39 

40 

5848 

X  12 

12425  62 

87575 

12813 

64 

87187 

00388 

99612 

21 

10  58  40 

I  I  20 

9.  12519  64 

10.87481 

9. 12909    65 

10. 87091 

10.00390 

9.99610 

20 

41 

5832 

I  28 

12612  66 

87388 

13004 

67 

86996 

00392 

99608 

19 

42 

5824 

•  36 

12706  67 

87294 

13099 

68 

86901 

00393 

99607 

18 

43 

58  16 

I  44 

12799  ,  69 

87201 

13194 

70 

86806 

00395 

99605 

17 

44 

4S 

58  8 
10  58  0 

I  52 

12892  1  70 

87108 

13289 

72 

86711 

00397 

99603 

16 

I  2  0 

9.  12985   72 

10.87015 

9-  13384 

73 

10.86616 

10.  00399 

9. 99601 

15 

4b 

5752 

2  8 

13078  74 

86922 

13478 

75 

86522 

00400 

99600 

14 

47 

57  44 

2  16 

13171   75 

86829 

13573  77 

86427 

00402 

99598 

13 

48 

5736 

2  24 

13263  ,  77 

86737 

13667  78 

86333 

00404 

99596 

12 

49 
50 

5728 
10  57  20 

2  32 

13355  !  78 

86645 

13761 

80 

86239 

00405 

99595 

II 

I  2  40 

9.  13447  80 

10. 86553 

9-  13854 

81 

10.86146 

10.  00407 

9-  99593 

10 

51 

57  12 

2  48 

13539  82 

86461 

13948  83 

86052 

00409 

99591 

9 

52 

57  4 

2  56 

13630  83 

86370 

14041 

85 

o5959 

0041 1 

99589 

8 

53 

5^'5fa 

3  4 

13722  85 

86278 

14134 

86 

85866 

00412 

99588 

7 

54 

5648 

3  12 

13813  87 

86187 

14227 

88 

85773 

00414 

2 

99586 

6 

55 

10  56  40 

I  3  20 

9.  13904  88 

10. 86096 

9. 14320 

90 

10. 85680 

10.  00416 

2 

9. 99584 

5 

St- 

5632 

3  28 

13994  90 

86006 

14412 

91 

85588 

00418 

2  1    99582 

4 

57 

5624 

3  36 

14085  91 

85915 

14504 

93 

85496 

00419 

2    99581   3  1 

5^ 

56  16 

3  44 

14175  93 

85825 

14597 

95 

85403 

00421 

2  ,   99579   2  1 

59 

56  8 

3  52 

14266  95 

85734 

14688 

96 

85312 

00423 

2  ,   99577  1 

I 

00 

56  0 

4  0 

14356  96 

85644 

14780 

98 

85220 

00425 

2 

99575 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine.  |  Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

97° 

A 

A 

B 

B 

C         C    82°  1 

Seconds  of  time. 


Prop,  parts  of  cols.  <  B 
C 


4 


I' 


12 

12 


24 

24 


3» 


36 

37 


48 

49 


60 
61 


72 

73 
I 


84 

86 


% 

TABLE  44. 

Page  415 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

8° 

A 

A      B 

B 

c                 c     iii° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diflf. 

Cosine. 

M. 

o 

10  56  0 

I  4  0 

9. 14356 

0 

10.  85644 

9. 14780 

0 

10.  85220 

10.  00425 

0 

9-99575 

60 

I 

5552 

4  8 

14445 

I 

85555 

14872 

I 

85128 

00426 

0 

99574 

59 

2 

55  44 

4  16 

14535 

.3 

85465 

14963 

3 

85037 

00428 

0 

99572 

58 

"» 
J 

5536 

4  24 

14624 

4 

85376 

15054 

4 

84946 

00430 

0 

99570 

57 

4 

5528 

4  32 

I4714 

6 

85286 

15145 

6 

84855 

00432 

0 

99568 

56 

S 

10  55  20 

I  4  40 

9.  14803 

7 

10.85197 

9.  15236   7 

10. 84764 

10.  00434 

0 

9-  99566 

55 

6 

55  12 

4  48 

1 489 1 

8 

85109 

15327   9 

84673 

00435 

0 

99565 

54 

7 

55  4 

4  56 

14980 

10 

85020 

15417   10 

84583 

00437 

0 

99563 

53 

S 

5456 

5  4 

15069 

II 

84931 

15508  12 

84492 

00439 

0 

99561 

52 

9 

5448 

5  12 

15157 

13 

84843 

15598  13 

84402 

00441 

0 

99559 

51 

10 

10  54  40 

I  5  20 

9- 15245 

14 

ID.  84755 

9. 15688  14 

10.84312 

10.00443 

0 

9-99557 

50 

II 

5432 

5  28 

15333 

16 

84667 

15777  16 

84223 

00444 

0 

9955b 

49 

12 

5424 

536 

1 542 1 

17 

84579 

15867  17 

84133 

00446 

0 

99554 

48 

U 

54  16 

5  44 

15508 

18 

84492 

15956  19 

84044 

00448 

0 

99552 

47 

14 

54  8 

5  52 

15596 

20 

84404 

16046  1  20 

83954 

00450 

0 

99550 

46 

IS 

10  54  0 

160' 

9. 15683 

21 

10.84317 

9.  16135  22 

10. 83865 

10.  00452 

0 

9-  99548 

45 

i6 

5352 

6  8 

15770 

23 

84230 

16224  23 

^3776 

00454 

99546 

44 

17 

53  44 

6  16 

15857 

24 

84143 

16312  25 

83688 

00455 

99545 

43 

i8 

5336 

6  24 

15944 

25 

84056 

16401  26 

83599 

00457 

99543 

42 

19 

5328 

6  32 

16030 

27 

83970 

16489  27 

835 II 

00459 
10.00461 

99541 

41 

20 

10  53  20 

I  6  40 

9.  161 16 

28 

10.  83884 

9.  16577  29 

10. 83423 

9- 99539 

40 

21 

53  12 

6  48 

16203 

30 

83797 

16665  1  30 

83335 

00463 

99537 

39 

22 

53  4 

6  56 

16289 

31 

837" 

16753  1  32 

83247 

00465 

99535 

38 

2^ 

5256 

7  4 

16374 

32 

83626 

I 684 I  33 

83159 

00467 

99533 

37 

24 

25 

5248 

7  12 

16460 

34 

83540 

16928  35 

83072 

00468 

99532 

36 

10  52  40 

I  7  20 

9. 16545 

35 

10. 83455 

9.  1 7016  36 

10. 82984 

10.  00470 

9- 99530 

35 

26 

5232 

728 

16631 

37 

83369 

17103  37 

82897 

00472 

99528 

34 

27 

5224 

736 

16716 

38 

83284 

1 7190  39 

82810 

00474 

99526 

28 

52  16 

7  44 

1 680 1 

39 

83199 

17277  40 

82723 

00476 

99524 

32 

29 

52  8 

7  52 

16886 

41 

831 14 

17363  42 

82637 

00478 

99522 

31 

so 

10  52  0 

I  8  0 

9.  16970 

42 

10.  83030 

9.17450  43 

10, 82550 

10.  00480 

9.  99520 

30 

.V 

51  52 

8  8 

17055 

44 

82945 

17536  45 

82464 

00482 

99518 

29 

,^2 

51  44 

8  16 

17139 

45 

82S61 

17622  46 

82378 

00483 

99517 

28 

51  36 

824 

17223 

47 

82777 

17708  48 

82292 

00485 

99515 

27 

34 

5128 

832 

17307 

48 

82693 

17794  49 

82206 

00487 

99513 

26 
25 

35 

10  51  20 

I  8  40 

9-17391 

49 

10. 82609 

9.  1 7880  1  50 

10.82120 

10.  00489 

9- 995 1 1 

3b 

51  12 

8  48 

17474 

51 

82526 

17965  '   52 

-2035 

00491 

99509 

24 

37 

51  4 

8  56 

17558 

52 

82442 

1805 1  53 

81949 

00493 

I  i   99507 

23 

3« 

5056 

9  4 

1 7641 

54 

82359 

18136  55 

81864 

00495 

I  !     99505 

22 

39 

5048 

9  12 

17724 

55 

82276 

18221 

56 
.58" 

81779 

10.81694 

00497 

99503 

21 

40 

10  50  40 

I  9  20 

9.17807 

56 

10.82195 

9. 18306 

10.  00499 

9.  99501 

20 

41 

5032 

9  28 

17890 

58 

821 10 

18391  59 

81609 

00501 

-99499 

19 

42 

5024 

9  36 

17973 

59 

82027 

18475  61 

81525 

00503 

99497 

iS 

43 

50  16 

9  44 

18055 

61 

81945 

18560  62 

SI440 

00505 

99495 

17 

44 

50  8 

9  52 

18137 

62 

81863 

18644  ,  63 

81356 

00506 
10.  00508 

99494 

16 
15^ 

4S 

10  50  0 

I  10  0 

9. 18220 

63 

10.  817S0 

9. 18728  65 

10.81272 

9- 99492 

46 

4952 

10  8 

18302 

65 

81698 

18812  66 

8II88 

00510 

I       99490 

14 

47 

49  44 

1     10  16 

18383 

66 

81617 

18896  68 

81 104 

00512 

I       99488 

13 

48 

4936 

10  24 

18465 

68 

81535 

18979  69 

8I02I 

00514 

2      99486 

12 

49 

4928 

10  32 

18547 

69 

81453 

19063 

71 
72 

80937 
10. 80854 

00516 

2      994S4 

II 

50 

10  49  20 

I  ID  40 

9. 18628 

71 

10.81372 

9. 19146 

10.00518 

2    9. 99482 

10 

51 

49  12 

10  48 

18709 

72 

8129I 

19229  74 

80771 

00520 

2      994S0 

9 

52 

49  4 

10  56 

18790 

73 

812IO 

19312  75 

80688 

00522 

2  i     99478 

8 

53 

4856 

II   4 

18871 

75 

81 129 

19395  76 

80605 

00524 

2      99476 

7 

54 

4848 

II  12 

18952 

76 

81048 

19478  78 

80522 

00526 
10.  00528 

2      99474 

6 

55 

10  48  40 

I  II  20 

9. 19033 

78 

10.  80967 

9. 19561   79 

10. 80439 

2  i  9-99472 

5 

5b 

4832 

II  28 

19113 

79 

80887 

19643  81 

80357 

00530 

2      99470 

4 

57 

4824 

II  36 

19193 

80 

80807 

19725  82 

80275 

00532 

2      9946S 

3 

5« 

48  16 

II  44 

19273 

82 

80727 

19807  84 

80193 

00534 

2      99466 

2 

59 

48  8 

II  52 

19353 

83 

80647 

19889  85 

801 1 1 

00536 

2      99464 

I 

60 

48  0 

12   0 

19433 

85 

80567 

19971 

87 
Diflf. 

80029 
Tangent. 

00538 
Cosecant. 

2 

99462 

0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Diflf. 

Secant. 

Cotangent. 

Diflf. 

Sine. 

M. 

98° 

A 

A        B 

B 

C          C    81°  1 

Seconds  of  time. . . 

l» 

2' 

3» 

4. 

5' 

«» 

7» 

Prop,  parts  of  cols. 

It 

It 

II 

0 

21 

22 
0 

32 
32 

I 

42 

43 

I 

S3 
54 

I 

65 
I 

76 
2 

I 


Page  416 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

9° 

M. 

A 

A 

B 

B 

c               c   no° 

Hour  A.M. 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff 

Cosine. 

M. 

o 

10  48  0 

I  12  0 

9.  19433 

0 

10.  80567 

9.  19971 

0 

10.  80029 

10.  00538 

0 

9. 99462 

60 

I 

4752 

12   8 

19513 

I 

80487 

20053 

1 

79947 

00540 

0 

99460 

59 

2 

47  44 

12  16 

19592  1  3 

80408 

20134 

3 

79865 

00542 

0 

99458 

S8 

3 

4736 

12  24 

19672  1  4 

80328 

20216  1  4 

79784 

00544 

0 

99456 

57 

4 

5 

4728 

12  32 

19751 

1  5 

80249 
10.  80170 

20297  1  5 

79703 

00546 

0 

99454 

56 

10  47  20 

I  12  40 

9. 19830 

6 

9.20378   6 

10.  79622 

10.  00548 

0 

9.  99452 

55 

6 

47  12 

12  48 

19909 

8 

80091 

20459  1  8 

79541 

00550 

0 

99450 

54 

7 

47  4 

12  56 

19988 

9 

80012 

20540   9 

79460 

00552 

i  0 

99448 

53 

8 

4656 

13  4 

20067 

10 

79933 

20621   10 

79379 

00554 

0 

99446 

52 

_9 

10 

4648 

13  12 

20145 

II 

79855 
10.  79777 

20701 

12 
13 

79299 

10.  79218 

00556 

0 

99444 

51 

10  46  40 

I  13  20 

9. 20223 

13 

9. 20782 

10.  00558 

0 

9.  99442 

50 

II 

4632 

13  28 

20302 

14 

79698 

20862   14 

79138 

00560 

0 

99440 

49 

12 

46  24 

13  36 

20380   15 

79620 

20942   16 

79058 

00562  '  0 

99438 

48 

13 

46  16 

13  44 

20458   16 

79542 

21022  ^  17 

78978 

00564  ,  0 

99436 

47 

14 

46  8 

13  52 

20535   18 

79465 

21 102  1  18 

78898 

00566 

0 

99434 

46 

15 

10  46  0 

;  I  14  0 

9.20613 

19 

10.  79387 

9. 21182 

19 

10.  78818 

10.  00568 

9-  99432 

45 

i6 

45  52 

14  8 

20691 

20 

79309 

21261 

21 

78739 

00571 

99429 

44 

17 

45  44 

14  16 

20768 

21 

79232 

21341 

22 

78659 

00573 

99427 

43 

iS 

4536 

14  24 

20845 

23 

79155 

21420 

23 

78580 

00575 

99425 

42 

19 

4528 

14  32 

20922 

24 

79078 

21499 

25 

78501 

00577 

99423 

41 

20 

10  45  20 

I  14  40 

9. 20999   25 

10.  79001 

9.21578  26 

10. 78422 

10.00579 

9.99421 

40 

21 

45  12 

14  48 

21076   26 

78924 

21657  1  27 

78343 

00581 

99419 

39 

22 

45  4 

14  56 

21153   28 

78847 

21736  ■   28 

78264 

00583 

99417 

38 

23 

4456 

15  4 

21229 

29 

78771 

21814  30 

78186 

00585 

99415 

37 

24 

25 

4448 
10  44  40 

15  12 

21306 

30 

78694 

21893  31 

78107 

00587 

99413 

36 

1  15  20 

9.21382 

31 

10.  78618 

9.21971  :  32 

10. 78029 

10.  00589 

9.  9941 1 

35 

26 

4432 

15  28 

21458 

33 

78542 

22049  ;  34 

77951 

00591 

99409 

34 

27 

44  24 

15  36 

21534 

34 

78466 

22127  35 

77873 

00593 

99407 

33 

28 

44  16 

15  44 

2l6lO 

35 

78390 

22205  36 

77795 

00596 

99404 

S2 

29 

44  8 

15  52 

21685 

37 

78315 

22283  38 

77717 

00598 

99402 

31 

30 

ID  44  0 

1  16  0 

9.  2I76I 

38 

10. 78239 

9.22361  39 

10.  77639 

10. 00600 

9.  99400 

30 

31 

43  52 

16  8 

21836 

39 

78164 

22438  40 

77562 

00602 

99398 

29 

32 

43  44 

16  16 

2I9I2 

40 

78088 

22516  41 

77484 

00604 

99396  28  1 

4336 

16  24 

21987  42 

78013 

22593  43 

77407 

00606 

99394  27  1 

34 

4328 

16  32 

22062  i  43 

77938 

22670  44 

77330 

00608 

I 

99392 

26 

35 

10  43  20 

I  16  40 

9.22137  44 

10.  77863 

9. 22747  45 

10.  77253 

10.00610 

9.  99390 

25 

3b 

43  12 

16  48 

2221 1  45 

77789 

22824  47 

77176 

00612 

-I 

99388 

24 

^l 

43  4 

16  56 

22286  47 

77714 

22901   48 

77099 

00615   i   '       99385 

2S 

3^ 

42  56 

17  4 

22361  48 

77639 

22977  49 

77023 

00617  '  I 

99383 

22 

1  39 
1  40 

4248 

17  12 

22435  49 

77565 

23054  50 

76946 

00619 

I 

99381 

21 

10  42  40 

I  17  20 

9. 22509  50 

10.  77491 

9.23130   52 

10.  76870 

10.00621 

I 

9-99379 

20 

B  41 

4232 

17  28 

22583  52 

77417 

23206  53 

76794 

00623 

1 

99377 

19 

42 

42  24 

'7  30 

22657  53 

77343 

23283  54 

76717 

00625 

1 

99375 

18 

43 

42  16 

17  44 

22731   54 

77269 

23359  ,  56 

76641 

00628 

2 

99372 

17 

44 

42  8 

17  52 

22805  1  55 

77195 

23435  1  57 

76565 

00630 

2 

99370 

16 

45 

10  42  0 

I  18  0 

9.22878  57 

10.77122 

9.23510  I   58 

10.  76490 

10.00632 

2 

9. 99368 

15 

4b 

41  52 

18  8 

22952  58 

77048 

23586  60 

76414 

00634 

2 

99366 

14 

47 

41  44 

18  16 

23025  59 

76975 

23661  61  j 

76339 

00636 

2 

99364 

13 

4^ 

4J  36 

18  24 

23098  60 

76902 

23737  62 

76263 

00638 

2" 

99362 

12 

49 
50 

41  28 

18  32 

231 71  62 

76829 

23812  63 

76188 

00641 

2 

99359 
9-99357 

II 
10 

10  41  20 

I  18  40 

9. 23244 

63 

10.  76756 

9.23887  65 

10.  761 13 

10.  00643 

2 

5i 

41  12 

18  48 

23317  1 

64  i 

76683 

23962  66  j 

76038 

00645 

2 

99355 

9 

52 

41  4 

18  56 

23390 

65 

76610 

24037  ,  67 

75963 

00647 

2 

99353 

8 

53 

40  56 

19  4 

23462 

67 

76538 

241 1 2  69 

75888 

00649 

2 

99351 

7 

54 
55 

40  48 
10  40  40 

19  12 

23535 

68 

76465 

24186  1  70 

75814 

00652 

2 

99348 

6 

I  19  20 

9.23607  , 

69' 

10.  76393 

9.24261   71 

10.75739 

10.00654 

2 

9- 99346 

5 

5" 

40  32 

19  28 

23679 

71 

76321 

24335   73 

75665 

00656 

2 

99344 

4 

57 

40  24  ' 

19  36 

23752 

72 

76248 

24410  74 

75590 

00658 

2 

99342 

-> 

5^ 

40  16 

19  44 

23823 

73 

76177 

24484  75 

75516 

00660 

2 

99340 

2 

59 

40  8 

19  52 

23895   74 

76105 

24558   76  ; 

■  75442 

00663 

2 

99337 

I 

60 

40  0 
Hour  1'.  M. 

20  0 

23967   76 

76033 

24632   78 

75368 

00665 

2 

99335 

0 

Hour  A.M. 

Cosine.   Diff. 

Secant. 

Cotangent.  1  Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

99° 

A 

A 

B 

B 

C          C    80°  1 

Seconds  of  time. 

i> 

2- 

3> 

4- 

6" 

«• 

7- 

Prop,  parts  of  cols. 

!i 

9 

JO 

0 

19 
19 

88 

«9 

I 

38 

39 

I 

47 

49 

1 

57 

58 

2 

66 
68 

2 

TABLE  44. 

Page  417 

S'. 

% 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

10° 

A 

A 

B 

B 

C 

C   169° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diflf. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 

10  40  0 

I  20  0 

9. 23967 

0 

10.  76033 

9.  24632 

0 

10.  75368 

10.  00665 

0 

9-  99335 

60 

I 

3952 

20  8 

24039 

I 

75961 

24706 

I 

75294 

00667 

0 

99333 

59 

-> 

39  44 

20  16 

24110 

2 

75890 

24779 

2 

75221 

00669 

0 

99331 

ScS 

3 

3936 

20  24 

24181 

3 

75819 

24853 

4 

75147 

00672 

0 

99328 

57 

4 

3928 

20  32 

24253 

5 

75747 

24926 

5 

75074 

00674 

0 

99326 

56 

5 

10  39  20 

I  20  40 

9.  24324 

6 

10.  75676 

9.  25000 

6 

10. 75000 

10. 00676 

0 

9- 99324 

55 

0 

39  12 

20  48 

24395 

75605 

25073 

7 

74927 

00678 

0 

99322 

S4 

7 

39  4 

20  56 

24466 

8 

75534 

25146 

8 

74854 

00681 

0 

99319 

S3 

8 

3856 

21  4 

24536 

9 

75464 

25219 

9 

74781 

00683 

0 

99317 

S2 

Q 

3848 

21  12 

2460/ 

10 

75393 

25292 

II 

74708 

00685 
10.  00687 

0 

99315 

51 

10 

10  38  40 

I  21  20 

9. 24677 

II 

10.  75323 

9-  25365 

12 

10.  74635 

0 

9-99313 

50 

II 

3832 

21  28 

24748 

13 

75252 

25437 

13 

74563 

00690 

0 

99310 

49 

12 

3824 

21  36 

24818 

H 

75182 

25510 

14 

74490 

00692 

0 

99308 

48 

13 

3816 

21  44 

248S8   15 

75112 

25582 

15 

744IS 

00694 

99306 

47 

14 

38  8 

21  52 

24958 

16 

75042 

25'555 

16 

74345 

00696 

99304 

46 

15 

10  38  0 

I  22  0 

9.  25028 

17 

10.  74972 

9.25727 

18 

10.  74273 

10.  00699 

9.99301 

45 

16 

3752 

22  8 

25098 

18 

74902 

25799 

19 

74201 

00701 

I 

99299 

44 

17 

37  44 

22  16 

25168 

19 

74832 

25871 

20 

74129 

00703 

99297 

43 

18 

3736 

22  24 

25237  ,  20 

74763 

25943 

21 

74057 

00706 

99294 

42 

19 

3728 

22  32 

25307 

22 

74693 

26015 

22 

73985 

00708 

99292 

41 

20 

10  37  20 

I  22  40 

9.25376 

23 

10.  74624 

9. 26086 

24 

10.  73914 

10.00710 

9. 99290 

40 

21 

37  12 

22  48 

25445 

24 

74555 

26158 

25 

73842 

00712 

99288 

39 

22 

37  4 

22  56 

25514 

25 

74486 

26229 

26 

73771 

00715 

99285 

38 

23 

3656 

23  4 

25583 

26 

74417 

26301 

27 

73699 

00717 

99283 

37 

24 

3648 

23  12 

25652 

27 

74348 

26372 

28 

73628 

00719 

99281 

36 

25 

10  36  40 

I  23  20 

9.25721   28 

10.  74279 

9.  26443 

29 

10.73557 

10.  00722 

9- 99278 

35 

2t) 

3632 

23  28 

25790 

30 

74210 

26514 

31 

73486 

00724 

99276 

34 

27 

3624 

23  36 

25858 

31 

74142 

26585 

32 

73415 

00726 

99274 

33 

28 

3616 

23  44 

25927 

32 

74073 

26055 

33 

73345 

00729 

99271 

32 

29 

36  8 

23  52 

25995 

33 

74005 

26726 

34 

73274 

00731 

99269 

31 

30 

10  36  0 

I  24  0 

9. 26063 

34 

10.  73937 

9.  26797 

35 

10.  73203 

10.  00733 

9.  99267 

30 

31 

35  52 

24  8 

26131  1  35 

73869 

26867 

36 

73133 

00736 

99264 

29 

32 

35  44 

24  16 

26199   36 

73801 

26937 

38 

73063 

00738 

99262 

28 

3536 

24  24 

26267 

38 

73733 

27008 

39 

72992 

00740 

99260 

27 

34 

3528 

24  32 

26335 

39 

73665 

27078 

40 

72922 

00743 

99257 

26 

35 

10  35  20 

I  24  40 

9.  26403 

40 

10.  73597 

9.27148 

41 

10. 72852 

10.  00745 

9. 99255 

25 

3b 

35  12 

24  48 

26470 

41 

73530 

27218 

42 

727S2 

00748 

99252 

24 

J/ 

35  4 

24  56 

26538  I  42 

73462 

27288 

44 

72712 

00750 

99250 

23 

3« 

3456 

25  4 

26605  1  43 

73395 

27357 

45 

72643 

00752 

99248 

22 

39 

3448 

25  12 

26672 

44 
45 

_  73328^ 
10.  73261 

27427  46 

72573 

00755 

2 

99245 

21 

40 

10  34  40 

I  25  20 

9.  26739 

9.  27496 

47 

10.  72504 

10.00757 

2 

9-  99243 

20 

41 

3432 

25  28 

26806  47 

73194 

27566 

48 

72434 

00759 

2 

99241 

19 

42 

3424 

25  36 

26873  1  48 

73127 

27635 

49 

72365 

00762 

2 

99238 

18 

43 

34  16 

25  44 

26940  :  49 

73060 

27704 

51 

72296 

00764 

2 

99236 

17 

44 

34  8 

25  52 

27007 

50 
51 

72993 

27773 

52 

72227 

00767 

2 

99233 

15 

45 

1034  0 

I  26  0 

9.  27073 

10. 72927 

9.27842 

53 

10,  72158 

10.  00769 

2 

9.99231 

15 

4b 

3352 

26  8 

27140  52 

72860 

27911 

54 

72089 

00771 

2 

99229 

14 

47 

33  44 

26  16 

27206  !  53 

72794 

27980 

55 

72020 

00774 

2 

99226 

13 

48 

33  3^ 

26  24 

27273  55 

72727 

28049  56 

71951 

00776 

2 

99224 

12 

49 

3328 

26  32 

27339 

56 

57 

72661 

28117 

58 

718S3 

00779 

2 

99221 

II 

50 

ID  33  20 

I  26  40 

9.  27405 

10.  72595 

9.  28186 

59 

10,  71814 

10.00781 

2 

9.99219 

10 

51 

33  12 

26  48 

27471  58 

72529 

28254 

■  71746 

007S3 

2 

99217 

9 

52 

Jj  4 

26   56 

27537  59 

72463 

28323 

61 

71677 

00786 

2 

99214 

8 

53 

3256 

27  4 

27602  60 

72398 

28391 

62 

71609 

00788 

2 

99212 

7 

54 

3248 

27  12 

27668  ;  61 

-   72332 

28459 

63 

71541 

00791 

2 

99209 

6 

55 

10  32  40 

I  27  20 

9-27734  63 

10.  72266 

9.28527 

65 

10.  71473 

10.  00793 

2 

9. 99207 

5 

S^ 

3232 

27  28 

27799  64 

72201 

28595 

66 

71405 

00796 

2 

99204 

4 

57 

3224 

27  36 

27864  65 

72136 

28662 

67 

71338 

00798 

2 

99202 

3 

5^^ 

32  16 

27  44 

27930  ,  66 

72070 

28730 

68 

71270 

00800 

2 

99200 

2 

59 

32  8 

27  52 

27995  i  67 

72005 

28798 

69 

71202 

00803 

2 

99197 

I 

bo 
M. 

32  0 

28  0 

28060 
Cosine. 

68 

71940 

28865 

71 

71135 

00805 

2 

99195 

0 

Hour  p.  M. 

Hour  A.M. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

100 

0 

A 

A 

B 

B 

C 

C    ?9°| 

27    B 


Seconds  of  time 

V 

2" 

3» 

4, 

5» 

6» 

7, 

(A 
Prop,  parts  of  cols.  <  B 

9 
9 

0 

17 
i8 

I 

26 
26 

I 

34 
35 

I 

43 
44 

I 

51 

53 

2 

60 

62 

2 

Page  418 

TABLE  44. 

■ 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

M. 

0 

A 

A 

B 

B 

c 

C   168^  1 

Hour  A.M. 

Hour  V.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant 

Diff. 

Cosine. 

M, 

10  32  0 

I  28  0  1 

9.  28060 

0 

10.  71940 

9.  28865 

0 

10.  71 135 

10.  00805 

0 

9-99195 

60 

I 

31  52  !   28  8 

28125 

I 

71875 

28933 

I 

71067 

00808 

0 

99192 

S9 

2 

31  44  1   28  16 

28190 

2 

71810 

29000 

2 

71000 

00810 

0 

99 1 90 

S8 

S 

31  36    28  24 

28254 

3 

71746 

29067 

70933 

00813 

0 

99187 

57 

4 

31  28  i   28  32 

28319 

4 

71681 

29134 

4 

70866 

00815 

0 

99185 

56 

10  31  20   I  28  40 

9. 28384 

5 

10.  71616 

9.  29201 

5 

10.  70799 

10.00818 

0 

9.99182 

55 
54 
S3 

6 

31  12  ,   28  48 

28448 

6 

71552 

29268 

6 

70732 

00820 

0 

99180 

7 

31  4  1   28  56 

28512 

7 

71488 

29335 

8 

70665 

00823 

0 

99177 

8 

30  56    29  4 

28577 

8 

71423 

29402 

9 

70598 

00825 

0 

99175 

S2 

9, 

10 

30  48  !    29  12 

28641 

9 

71359 

29468 

10 

70532 

00828 

0 

99172 

51 

10  30  40   I  29  20 

9. 28705 

10 

10.  71295 

9- 29535 

II 

10.  70465 

10.  00830 

0 

9.99170 

50 

II 

3032 

29  28 

28769 

II 

71231 

29601 

12 

70399 

00833 

0 

99167 

49 

12 

3024 

29  36 

28833 

12 

71167 

29668 

13 

70332 

00835 

99165 

48 

n 

30  16     29  44 

28896 

13 

71104 

29734 

14 

70266 

00838 

99162 

47 

14 

30  8    29  52 

28960 

14 

71040 

29800 

15 

70200 

00840 

99160 

46 

IS 

10  30  0 

I  30  0 

9. 29024 

16 

10.  70976 

9. 29866 

It) 

10.  70134 

10. 00S43 

9-99157 

45 

i6 

2952  ' 

30  8 

29087 

17 

70913 

29932 

17 

70068 

00845 

99155 

44 

17 

2944 

30  16 

29150 

18 

70850 

29998 

18 

70002 

00848 

99152 

43 

18 

2936 

30  24 

29214 

19 

70786 

30064 

19 

69936 

00850 

99150 

42 

19 

29  28 

30  32 

29277 

20 

70723 

30130 

20 

69870 

00853 

99147 

41 

20 

10  29  20   I  30  40 

9.  29340 

21 

10.  70660 

9.30195 

22 

10.  69805 

10. 00855 

9-99145 

40 

21 

29  12    30  48 

29403 

22 

70597 

30261 

23 

69739 

00858 

99142 

39 

22 

29  4    30  56 

29466 

23 

70534 

30326 

24 

69674 

00860 

99140 

38 

2^ 

28  56    31  4 

29529 

24 

70471 

30391 

25 

69609 

00863 

99137 

37 

24 

28  48  1   31  12 

29591 

25 

70409 

30457 

26 

69543 

00865 

99135 

36 

35 

2S 

10  28  40  I  31  20 

9. 29654 

26 

10.  70346 

9. 30522 

27 

10.  69478 

10. 00868 

9.99132 

26 

2832    31  28 

29716 

27 

70284 

30587 

28 

69413 

0087c 

99130 

34 

27 

2824    31  36 

29779 

28 

70221 

30652 

29 

69348 

00873 

99127 

33 

28 

28  16    31  44 

29841 

29 

70159 

30717 

30 

69283 

00876 

99124 

32 

29 

28  8    31  52 

29903 

30 

70097 

30782 

31 

69218 

00878 

99122 

31 

30 

10  28  0  i  I  32  0 

9. 29966 

31 

10.  70034 

9. 30846 

32 

10.69154 

10, 00881 

9.99119 

30 

^I 

2752    32  8 

30028 

32 

69972 

3091 1 

33 

69089 

00883 

991 1 7 

29 

.l2 

2744    32  16 

30090 

33 

69910 

30975 

35 

69025 

00886 

991 14 

28 

^S 

27  36  j   32  24 

30151 

34 

69849 

31040 

36 

68960 

00888 

99112 

27 

34 
SS 

27  28    32  32 

30213 

35 

69787 

31 104 

37 

68896 

00891 

99109 

26 

10  27  20  !  I  32  40 

9-  30275 

36 

10.  69725 

9.  31 168 

38 

10.  68832 

10. 00894 

2 

9.  99106 

25 

36 

27  12  !   32  48 

30336 

37 

69664 

31233 

39 

68767 

00896 

2 

99104 

24 

37 

27  4     32  56 

30398 

38 

69602 

31297 

40 

68703 

00899 

2 

99101 

23 

3« 

26  56    33     4 

30459 

39 

69541 

31361 

41 

68639 

00901 

2 

99099 

22 

39 

2648    33  12 

30521 

40 

69479 

31425 

42 

68575 

00904 

2 

99096 

21 

40 

10  26  40   I  33  20 

9.  30582 

41 

10.69418 

9.31489 

43 

10.  6851 1 

10. 00907 

2 

9. 99093 

20 

41 

26  32  '   33  28 

30643 

42 

69357 

31552 

44 

68448 

00909 

2 

99091 

19 

42 

26  24    33  36 

30704 

43 

69296 

31616 

45 

68384 

00912 

2 

99088 

18 

43 

26  16    33  44 

30765 

45 

69235 

31679 

46 

68321 

00914 

2 

99086 

17 

44 

26  8    33  52 

30826 

46 

69174 

31743 

47 

68257 

00917 
10. 00920 

2 

99083 

16 

45 

10  26  0  j  I  34  0 

9.30887 

47 

10. 691 13 

9. 31806 

49 

10.68194 

2 

9. 99080 

15 

46 

25  52  i   34  8 

30947 

48 

69053 

31870 

50 

68130 

00922 

2 

99078 

14 

47 

25  44    34  16 

31008 

49 

68992 

31933 

51 

68067 

00925 

2 

99075 

13 

48 

25  36    34  24 

31068 

50 

68932 

31996 

52 

68004 

00928 

2 

99072 

12 

49 

25  28    34  32 

31 129 

51     68871 

32059 

53 

67941 

00930 

2 

99070 

II 

50 

ID  25  20   I  34  40 

9.31189 

52 

10. 6881 I 

9.32122 

54 

10.  67878 

10. 00933 

2 

9. 99067 

10 

51 

25  12     34  48 

31250 

53 

68750 

32185 

55 

67815 

00936 

2 

99064 

9 

52 

25  4    34  56 

31310 

54  ,   68690 

32248 

56 

67752 

00938 

2 

99062 

8 

53 

24  56    35  4 

31370 

55    68630 

323" 

57 

67689 

00941 

2 

99059 

7 

54 

2448    35  12 

31430 

56    68570 

32373 

58 

67627 

00944 

2 

99056 

6 

5" 

55 

10  24  40 

I  35  20 

9.31490 

57 

10.68510 

9-  32436 

S9 

10.  67564 

10.  00946 

2 

9-  99054 

5^ 

2432 

35  28 

31549 

58 

68451 

32498 

60 

67502 

00949 

2 

99051 

4 

57 

2424 

35  36 

31609 

59 

68391 

32561 

61 

67439 

00952 

2 

99048 

3 

5« 

24  16 

35  44 

31669 

60 

68331 

32623 

63 

67377 

00954 

2 

99046 

2 

59 

24  8 

35  52 

31728 

61 

68272 

32685 

64 

67315 

00957 

3 

99043 

I 

60 

24  0 

36  0 

31788 

62 

68212 

32747 

65 

67253 

00960 

3 

99040 

0 

M. 

Hour  p.  M. 

'•  Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

101 

0 

A 

A 

B 

B 

C 

C   78°  1 

Seconds  of  time. 


Prop,  parts  of  cols. -<  B 
C 


16 
16 

I 


23 
24 


.11 
32 


39 
40 


47 

49 

2 


54 
57 


TABLE  44. 

[Page  419 

S'. 

% 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

12° 

A 

A 

B 

B 

C 

c    ler 

M. 

Hour  A.M. 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difif. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 

10  24  0 

I  36  0 

9.31788 

0 

10.68212 

9-  32747 

0 

10.  67253 

10.00960 

0 

9.  99040 

60 

I 

2352 

36  8 

31847 

I 

68153 

32810 

I 

67190 

00962 

0 

99038 

59 

7 

23  44 

36  16 

31907 

2 

68093 

32872 

2 

67128 

00965 

0 

99035 

58 

,> 

2336 

36  24 

31966 

3 

68034 

32933 

3 

67067 

00968 

0 

99032 

57 

4 

2328 

36  32 

32025 

4 

67975 
10.67916 

32995 

4 

-  67005 

00970 

0 

99030 

56 

S 

10  23  20 

I  36  40 

9.  32084 

5 

9-33057 

5 

10.  66943 

10.00973 

0 

9-  99027 

55 

() 

23  12 

36  48 

32143 

6 

67857 

33119 

6 

66881 

00976 

0 

99024 

54 

7 

23  4 

3656 

32202 

7 

67798 

33180 

7 

66820 

00978 

0 

99022 

53 

S 

22  56 

37  4 

32261 

8 

67739 

33242 

8 

66758 

00981 

0 

99019 

52 

9 

22  48 

37  12 

32319 

9 
10 

67681 
10.  67622 

33303 
9- 33365 

__9 

10 

66697 

00984 
10. 00987 

0 
0 

99016 

51 

10 

10  22  40 

I  37  20 

9-32378 

10.  66635 

9- 99013 

50 

II 

2232 

37  28 

32437 

10 

67563 

33426 

II 

66574 

00989 

990 II 

49 

12 

22  24 

37  36 

32495 

II 

67505 

33487 

12 

66513 

00992 

99008 

48 

1,1 

22  16 

37  44 

32553 

12 

67447 

33548 

13 

66452 

00995 

99005 

47 

14 

22  8 

37  52 

32612 

13 

14 

67388 

33609 

14 

66391 

00998 

99002 

46 

10  22  0 

I  38  0 

9.  32670 

10.  67330 

9- 33670 

15 

10.  66330 

10.  OIOOO 

9. 99000 

45 

10 

21  52 

38  8 

32728 

i.S 

67272 

33731 

lb 

66269 

01003 

98997 

44 

17 

21  44 

38  16 

32786 

16 

67214 

33792 

17 

6620S 

01006 

98994 

43 

i8 

21  36 

38  24 

32844 

17 

67156 

33853 

18 

66147 

01009 

98991 

42 

19 

21  28 

3832 

32902 

18 

67098 

33913 

19 

66087 

OIOII 

98989 

41 

20 

10  21  20 

I  38  40 

9. 32960 

19 

10, 67040 

9- 33974 

20 

10.  66026 

10.  OIOI4 

9. 98986 

40 

21 

21  12 

38  48 

33018 

20 

66982 

34034 

21 

65966 

OIOI7 

98983 

39 

22 

21  4 

3856 

33075 

21 

66925 

34095 

22 

65905 

01020 

989S0 

38 

2,> 

20  56 

39  4 

33133 

22 

66867 

34155 

23 

65845 

01022 

98978 

37 

24 

20  48 

39  12 

33190 

23 

66810 

34215 

24 

65785 
10.65724 

01025 

98975 

36 

2S 

10  20  40 

I  39  20 

9- 33248 

24 

10. 66752 

9.34276 

25 

10.01028 

9-  98972 

35 

26 

20  32 

39  28 

33305 

25 

66695 

34336 

2b 

65664 

OI03I 

98969 

34 

27 

20  24 

39  36 

333(>2 

26 

66638 

34396 

27 

65604 

01033 

98967 

33 

2S 

20  16 

39  44 

33420 

27 

66580 

34456 

28 

65544 

01036 

98964 

32 

29 

20  8 

39  52 

33477 

28 

66523 

34516 

29 

65484 

01039 

98961 

31 

30 

10  20  0 

I  40  0 

9- 33534 

29 

10.  66466 

9-34576 

30 

10.  65424 

10. 01042 

9- 98958 

30 

;.i 

1952 

40  8 

33591 

29 

66409 

34635 

31 

65365 

01045 

98955 

29 

32 

1944 

40  16 

33647 

30 

66353 

34695 

32 

65305 

01047 

98953 

28 

.i> 

1936 

40  24 

33704 

31 

66296 

34755 

33 

65245 

01050 

2 

98950 

27 

34 

1928 

40  32 

33761 

32 

66239 

34814 

34 

65186 

01053 

10.01056 

2 

98947 

26 

35 

10  19  20 

I  40  40 

9.33818 

33 

10. 66182 

9-  34874 

35 

10.65126 

2 

9-  98944 

25 

3^ 

19  12 

40  48 

33874 

34 

66126 

34933 

36 

65067 

01059 

2 

98941 

24 

37 

19  4 

40  56 

33931 

35 

66069 

34992 

37 

65008 

01062 

2 

98938 

23 

3« 

1856 

41  4 

33987 

36 

66013 

35051 

38 

64949 

01064 

2 

98936 

22 

39 

1848 

41  12 

34043 

37 

65957 

35111 

39 

648S9 

01067 

2 

98933 

21 

40 

10  18  40 

I  41  20 

^9^34100 

38 

10.  65900 

9-35170 

40 

10.  64830 

10.01070 

2 

9- 98930 

20 

41 

1832 

41  28 

34156 

39 

65844 

35229 

41 

64771 

01073 

2 

98927 

19 

42 

1824 

41  36 

34212 

40 

65788 

35288 

42 

64712 

01076 

2 

98924 

18 

43 

18  16 

41  44 

34268 

41 

65732 

35347 

43 

64653 

01079 

2 

98921 

17 

44 
45 

18  8 

41  52 

34324 

42 

65676 

35405 

44 

64595 

0108 1 

2 

98919 

16 

10  18  0 

I  42  0 

9- 34380 

43 

10.  65620 

9-  35464 

45 

10. 64536 

10.01084 

2 

9. 98916 

15 

4b 

1752 

42  8 

34436 

44 

65564 

35523 

46 

64477 

01087 

2 

98913 

14 

47 

1744 

42  16 

34491 

45 

65509 

35581 

47 

64419 

01090 

2 

98910 

13 

4S 

1736 

42  24 

34547 

46 

65453 

35640 

48 

64360 

01093 

2 

98907 

12 

49 

1728 

42  32 

34602 

47     65398 

35698 

49 

64302 

01096 
10.01099 

2 

98904 

II 

50 

10  17  20 

I  42  40 

9- 34658 

48   10. 65342 

9-35757 

50 

10. 64243 

2 

9.  98901' 

10 

51 

17  12 

42  48 

34713 

48  ,    65287 

35815 

51 

64185 

01 102 

2 

98898 

9 

52 

17  4 

42  56 

34769 

49     65231 

35873 

52 

64127 

01 104 

2 

98896 

8 

53 

'^56 

43  4 

34824 

50     65176 

35931 

53 

64069 

OII07 

2 

98893 

7 

54 

1648 

43  12 

34879 

51 

65 12 1 

35989 

54 

640II 

OHIO 

3 

98890 

6 

S  55 

10  16  40 

I  43  20 

9- 34934 

52 

10.  65066 

9. 36047 

55 

10. 63953 

10. 01 113 

3 

9. 98887 

5 

5b 

1632 

43  28 

.34989 

53 

6501 1 

36105 

56 

63895 

0III6 

3 

98884 

4 

57 

16  24 

43  36 

35044 

54 

64956 

36163 

57 

(^3837 

0UI9 

3 

98881 

1 

J 

5^ 

16  16 

43  44 

35099 

55  1   64901 

36221 

58 

63779 

OII22 

3 

98878 

2 

59 

16  8 

43  52 

35154 

56  1   64846 

36279 

59 

63721 

OII25 

3 

98875 

I 

bo 
M. 

16  0 

44  0 

35209 

57 

64791 
Secant . 

36336 
Cotangent. 

60 
Diff. 

63664 

Tangent. 

OII28 

3 
Diff. 

98872 
Sine. 

0 
M. 

Hour  i>.  M. 

Hour  A.  M. 

Cosine. 

Diflf. 

Cosecant. 

102 

3 

A 

A 

B 

B 

c 

c      n°| 

Seconds  of  time . 


Prop,  parts  of  cols.-j  B  ' 


!• 


14 

15 


21 
22 


29 

I 


36 

37 

2 


43 

45 

2 


50 

52 

2 


Page  420 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

13° 

A 

A 

B 

B 

c 

C   166° 

M. 

Hour  A.M. 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diflf. 

Cotangent. 

Secant. 

Diflf. 

Cosine. 

M. 

o 

10  16  0 

I  44  0 

9-  35209 

0 

10.  64791 

9- 36336 

0 

10.  63664 

10.  01128 

0 

9.  98872 

60 

I 

15  52 

44  8 

35263 

I 

64737 

36394 

I 

63606 

01131 

0 

98869 

59 

2 

1544 

44  16 

35318 

2 

64682 

36452 

2 

63548 

01133 

0 

98867 

58 

3 

1536 

44  24 

35373 

3 

64627 

36509 

3 

63491 

CI  136 

0 

98864 

57 

4 

1528 

44  32 

35427 

4 

64573 

36566 

4 

63434 
10.  63376 

01 139 

0 

98861 

56 

55 

5 

10  15  20 

I  44  40 

9- 35481 

4 

10.64519 

9.  36624 

5 

10.  01 142 

0 

9.  98858 

6 

15  12 

44  48 

35536 

5 

64464 

36681 

6 

63319 

01 145 

0 

98855 

54 

7 

15  4 

44  56 

35590 

b 

64410 

36738 

6 

63262 

01 148 

0 

98852 

5^, 

8 

1456 

45  4 

35644 

7 

64356 

36795 

7 

63205 

01151 

0 

98849 

52 

9 

1448 

45  12 

35698 

8 

64302 

36852 

8 

63148 

01154 

0 

98846 

51 

lO 

10  14  40 

I  45  20 

9-35752 

9 

10. 64248 

9. 36909 

9 

10.63091 

IO.OI157 

9-  98843 

50 

II 

1432 

45  28 

35806 

10 

64194 

36966 

10 

63034 

01 160 

98840 

49 

12 

1424 

45  36 

35860 

II 

64140 

37023 

II 

62977 

01 163 

98837 

48 

13 

14  16 

45  44 

35914 

II 

64086 

37080 

12 

62920 

01166 

98834 

47 

15 

14  8 

45  52 

35968 

12 

64032 

37137 

13 

62863 

01 169 

98831 

46 

10  14  0 

I  46  0 

9. 36022 

13 

10.  63978 

9-37193 

14 

10.  62807 

10.  01 1 72 

9.  98828 

45 

I6 

1352 

46  8 

36075 

14 

63925 

37250 

15 

62750 

01175 

98825 

44 

17 

1344 

46  16 

36129 

15 

63871 

37306 

lb 

62694 

01 1 78 

98822 

43 

i8 

1336 

46  24 

36182 

lb 

63818 

37363 

17 

62637 

01181 

98819 

42 

19 

1328 

46  32 

36236 

17 

63764 

37419 

18 

62581 

01 184 

98816 

41 

20 

10  13  20 

I  46  40 

9.  36289 

18 

10. 6371 1 

9-37476 

19 

10.  62524 

10. 01 187 

9.98813 

40 

21 

13  12 

46  48 

36342 

18 

63658 

37532 

19 

62468 

01 190 

98810 

39 

22 

13  4 

46  56 

36395 

19 

63605 

37588 

20 

62412 

01 193 

98807 

38 

23 

12  56 

47  4 

36449 

20 

63551 

37644 

21 

62356 

01196 

98804 

37 

24 

25 

12  48 

47  12 

36502 

21 

63498 

37700 

22 

62300 

01199 

98801 

36 

10  12  40 

I  47  20 

9-  36555 

22 

10. 63445 

9-37756 

23 

ID.  62244 

10.01202 

9. 98798 

35 

26 

1232 

47  28 

36608 

23 

63392 

37812 

24 

62188 

01205 

98795 

34 

27 

12  24 

47  36 

36660 

24 

63340 

37868 

25 

62132 

01208 

98792 

33 

28 

12  16 

47  44 

36713 

25 

63287 

37924 

26 

62076 

01211 

98789 

32 

29 

12  8 

47  52 

36766 

25 

63234 

37980 

27 

62020 

01214 

98786 

31 

30 

10  12  0 

I  48  0 

9. 36819 

26 

10. 63181 

9- 38035 

28 

10.61965 

10. 01217 

2 

9-98783 

30 

31 

II  52 

48  8 

36871 

27 

63129 

38091 

29 

61909 

01220 

2 

98780 

29 

32 

II  44 

48  16 

36924 

28 

63076 

38147 

30 

61853 

01223 

2 

98777 

28 

33 

II  36 

48  24 

36976 

29 

63024 

38202 

31 

61798 

01226 

2 

98774 

27 

34 

II  28 

48  32 

37028 

30 

62972 

38257 

32 

61743 

01229 

2 

98771 

26 

35 

10  II  20 

I  48  40 

9.37081 

31 

ID.  62919 

9-38313 

32 

10.61687 

10.01232 

2 

9. 98768 

25 

3^ 

II  12 

48  48 

37133 

32 

62867 

38368 

33 

61632 

01235 

2 

98765 

24 

37 

II  4 

48  50 

37185 

32 

62815 

38423 

34 

61577 

01238 

2 

98762 

23 

3« 

10  56 

49  4 

37237 

33 

62763 

38479 

35 

61521 

OI24I 

2 

98759 

22 

39 

10  48 

49  12 

37289 

34 

6271 1 

38534 

36 

37 

61466 

01244 

2 

98756 

21 

40 

10  10  40 

I  49  20 

9- 37341 

35 

10.  62659 

9.38589 

10.  614II 

10.01247 

2 

9-  98753 

20 

41 

1032 

49  28 

37393 

36 

62607 

38644 

38 

61356 

01250 

2 

98750 

19 

42 

10  24 

49  36 

37445 

37 

62555 

38699 

39 

613OI 

01254 

2 

98746 

18 

43 

10  16 

49  44 

37497 

38 

62503 

38754 

40 

61246 

01257 

2 

98743 

17 

44 

45 

10  8 

49  52 

37549 

39 

62451 

38808 

41 

61 192 

01260 

2 

98740 

16 

10  10  0 

I  50  0 

9. 37600 

39 

10. 62400 

9. 38863 

42 

10. 61 137 

10.  01263 

2 

9-98737  15 

45 

952 

50  8 

37652 

40 

62348 

38918 

43 

61082 

01266 

2 

98734  14 

47 

9  44 

50  16 

37703 

41 

62297 

38972 

44 

61028 

01269 

2 

98731   13 

48 

936 

50  24 

37755 

42 

62245 

39027 

45 

60973 

01272 

2 

98728  12 

49 

9  28 

50  32 

37806 

43 

62194 

39082 

45 

60918 

01275 

2 

98725  1  II 

50 

10  9  20 

I  50  40 

9-  37858 

44 

10.62142 

9-  39136 

46 

10.  60864 

10.01278 

3 

9.  98722 

10 

51 

9  12 

50  48 

37909 

45 

62091 

39190 

47 

60810 

01281 

3 

98719 

9 

52 

9  4 

50  56 

37960 

46 

62040 

39245 

48 

60755 

01285 

3 

98715 

8 

53 

856 

51  4 

3801 1 

47 

61989 

39299 

49 

60701 

01288 

3 

98712 

7 

54 

55 

848 

51  12 

38062 

47 

61938 

39353 

50 

60647 

OI29I 

3 

9S709 

6 

10  8  40 

I  51  20 

9-38113 

48 

10.61887 

9-  39407 

51 

10.  60593 

10.01294 

3 

9. 98706 

5 

5^^ 

832 

51  28 

38164 

49 

61836 

39461 

52 

60539 

01297 

3 

98703 

4 

57 

824 

51  36 

38215 

50 

61785 

39515 

53 

60485 

01300 

3 

98700 

3 

5^ 

8  16 

51  44 

38266 

51 

61734 

39569 

54 

60431 

01303 

3 

98697 

2 

59 

8  8 

51  52 

38317 

52 

61683 

39623 

55 

60377 

01306 

3 

98694 

I 

bo 

8  0 

52  0 

38368 

53 

Diflf. 

61632 

39677 

56 

60323 

OI3IO 

3 

98690 

0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Secant. 

Cotangent. 

Diflf. 

Tangent. 

Cosecant. 

Diflf. 

Sine. 

M. 

103 

0 

A 

A 

B 

B 

C 

C    76°  1 

Seconds  of  time. 


Prop,  parts  of  cols.  ■<  H 
C 


13 
I 


20 
21 


26 
28 


33 

35 


39 

42 

2 


46 

49 

3 


TABLE  44. 

Page  421 

S'. 

V 

Log.  Sines,  Tangent-s,  and  Secants. 

G'. 

i4° 

A          A 

B 

B 

c 

C   165° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 
9- 39677 

Diff. 
0 

Cotangent. 
10.  60323 

Secant. 
10.  01310 

Diff. 
0 

Cosine. 
9. 98690 

M. 
60 

0 

10  8  0 

I  52  0 

9.  38368 

0 

10.61632 

I 

752 

52  8 

38418 

I 

61582 

39731 

I 

60269 

01313 

0 

98687 

S9 

-> 

744 

52  16 

38469 

2 

61531 

39785 

2 

60215 

01316 

0 

98684 

S8 

736 

52  24 

38519 

2 

61481 

39838 

3 

60162 

01319 

0 

98681 

S7 

4 

728 

52  32 

38570 

3 

61430 

39892 

3 

60108 

01322 

0 
0 

98678 

56 

S 

10  7  20 

I  52  40 

9. 38620 

4 

10.61380 

9- 39945 

4 

10.  60055 

10.01325 

9.  98675 

55 

b 

7  12 

52  48 

38670 

5    61330 

39999 

5 

60001 

01329 

0 

98671 

S4 

7 

7  4 

52  56 

38721 

6   ;        61279 

40052 

6 

59948 

01332 

0 

9866S 

S3 

S 

656 

53  4 

38771 

7  i   61229 

40106 

7 

59894 

01335 

0 

98665 

52 

9 

648 

53  12 

38821 
9.  38871 

7 
8 

61 1 79 

40159 

8 

59841 

01338 

0 

98662 

51 

10 

10  6  40 

I  53  20 

10. 61 129 

9.  40212 

9 

TO.  59788 

10. 01341 

9. 98659 

SO 

II 

632 

53  28 

38921 

9 

61079 

40266 

10 

59734 

01344 

98656 

49 

12 

6  24 

53  36 

38971 

10 

61029 

40319 

:io 

59681 

01348 

98652 

48 

!> 

6  16 

53  44 

39021 

II 

60979 

40372 

:ii 

59628 

01351 

98649 

47 

14 

6  8 

53  52 
I  54  0 

39071 

II 

60929 

40425 

12 
"13" 

___59575 
10. 59522 

01354 
10.01357 

98646 

46 

IS 

10  6  0 

9.39121 

12 

10. 60879 

9. 40478 

9.  98643 

4S 

i6 

552 

54  8 

39170 

13 

6o8w 

40531 

14 

59469 

01360 

98640 

44 

17 

544 

54  16 

39220 

14 

60780 

40584 

15 

59416 

01364 

98636 

43 

iS 

536 

54  24 

39270 

15 

60730 

40636 

16 

59364 

01367 

98633 

42 

19 

528 

54  32 

39319 

15 

60681 

40689 
9. 40742 

17 

593" 

01370 

98630 

41 

20 

10  5  20 

I  54  40 

9- 393^9 

16  10,60631 

17 

10. 59258 

10.01373 

9.98627 

40 

21 

5  12 

54  48 

39418 

17  :    60582 

40795 

18 

59205 

01377 

98623 

39 

22 

5  4 

54  56 

39467 

18  :      60533 

40847 

19 

59153 

01380 

98620 

38 

2', 

456 

55  4 

39517 

19  !   60483 

40900 

20 

59100 

01383 

98617 

37 

24 

448 

55  12 

39566 

20  J   60434 

40952 
9. 41005 

21 
22 

59048 
10.  58995 

01386 
10.01390 



98614 

36 

2S 

10  4  40 

I  55  20 

9-39615 

20  10. 60385 

9.98610 

35 

26 

432 

55  28 

39664 

21  1   60336 

41057 

23 

5S943 

01393 

98607 

34 

27 

424 

55  36 

39713 

22  '   60287 

41 109 

23 

58891 

01396 

98604 

33 

28 

4  16 

55  44 

39762 

23  :     60238 

41161 

24 

5^39 

01399 

2 

98601 

32 

29 

4  8 

55  52 

398 II 

24       60189 

41214 

25 

58786 

01403 

2 
2 

98597 

31 

SO 

10  4  0 

I  56  0 

9. 39860 

24    10.  60140 

9. 41266 

26 

10. 58734 

10.01406 

9- 98594 

30 

SI 

352 

56  8 

39909 

25       60091 

41318 

27 

58682 

01409 

2 

98591 

29 

^2 

344 

56  16 

39958 

26  j     60042 

41370 

28 

58630 

01412 

2 

98588 

28 

1  T 

336 

56  24 

40006 

27  1   59994 

41422  1  29 

58578 

01416 

2 

98584 

27 

34 

328 

56  32 

40055 

28 
29 

59945 

41474 

30 
30 

58526 

01419 

2 
2 

98581 

26 

SS 

10  3  20 

I  56  40 

9. 40103 

10.  59897 

9.41526 

10.  58474 

10.  01422 

9.98578 

25 

^'J 

3  12 

56  48 

40152 

29  i    59848 

41578 

31 

58422 

01426 

2 

98574 

24 

37 

3  4 

5656 

40200 

30 

59800 

41629 

32 

58371 

01429 

2 

98571 

23 

3!^ 

2  56 

57  4 

40249 

31 

59751 

41681 

33 

58319 

01432 

2 

98568 

22 

39 

248 

57  12 

40297 

32 

59703 

4173s 
9.41784 

34 
35 

58267 

01435 

10. 01439 

2 

98565 

21 

40 

10  2  40 

I  57  20 

9.  40346 

33 

10.  59654 

10.  58216 

2 

9. 98561 

20 

41 

232 

57  28 

40394 

33     59606 

41836 

36 

58164 

01442 

2 

98558 

19 

42 

2  24 

57  36 

40442 

34     59558 

41887 

36 

5^'13 

01445 

2 

98555 

18 

43 

2  16 

57  44 

40490 

35    59510 

41939 

37 

58061 

01449 

2 

9^551 

17 

44 

2  8 

57  52 

40538 

36 

59462 

41990 
9. 42041 

38 

58010 

01452 
10.01455 

2 
2 

98548 

16 

4S 

10  2  0 

I  58  0 

9. 40586 

37 

10. 59414 

39 

10.57959 

9- 98545 

15 

4b 

I  52 

58  8 

40634 

37 

59366 

42093 

40 

57907 

01459 

3 

98541 

14 

47 

I  44 

58  16 

40682 

38 

59318 

42144 

41 

57856 

01462 

3 

98538 

13 

48 

136 

58  24 

40730 

39 

59270 

42195 

42 

57805 

01465 

3 

98535 

12 

49 

I  28 

58  32 

40778 

40 

59222 

42246 

43 

57754 
10.57703 

01469 

3 
3 

98531 
9. 98528 

II 

10 

SO 

10  I  20 

I  58  40 

9. 40825 

41 

10.59175 

9. 42297 

43 

10.01472 

51 

I  12 

5848 

40873 

42 

59127 

42348 

44 

57652 

01475 

3 

98525 

9 

52 

I  4 

5856 

40921 

42 

59079 

42399 

45 

57601 

01479 

3 

98521 

8 

53 

0  56 

59  4 

40968 

43 

59032 

42450 

46 

57550 

01482 

3 

98518 

7 

54 

5S 

048 

59  12 

41016 

44 

58984 
^0.  58937 

42501 
9.  42552 

47 
48 

57499 

01485 

3 
3 

98515 

6 

10  0  40 

I  59  20 

9.  41063 

45 

10.57448 

10.01489 

9. 985 1 1 

5 

s(> 

■  032 

59  28 

41111 

46 

58889 

42603 

49 

57397 

01492 

3 

98508 

4 

57 

0  24 

59  36 

41158 

46 

58842 

42653 

50 

57347 

01495 

3 

98505 

3 

5« 

0  16 

59  44 

41205 

47 

58795 

42704 

50 

57296 

01499 

3 

98501 

2 

59 

0  8 

59  52 

41252 

48 

58748 

42755 

SI 

57245 

01502 

3 

98498 

I 

bo 

0  0 

200 

41300 

49 
Diflf 

58700 

42805 

52 

57195 

01506 

3 
Diff. 

98494 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Sine. 

104 

0 

A            A 

B 

B 

C 

C    75°  1 

Seconds  of  time 

1» 

*i" 

3" 

18 
20 

4»    5'  i  «• 

V 

1^ 
Prop,  parts  of  cols.  <  B 

|c 

6 

7 
0 

12 

13 

1 

24    31 
26    33 

2    2 

37 
39 

2 

43 
46 

3 

Page  422] 

TABLE  44. 

S'. 

Log.  Sines,  Tangents^  and  Secants. 

G'. 

15° 

A 

A 

B 

B 

C 

C   164° 

M. 

Hour  A.  M. 

Hour  P.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

10  0  0 

200 

9.41300 

0 

10.  58700 

9-  42805 

0 

10.57195 

10.01506 

0 

9.  98494 

60 

I 

95952 

0  8 

41347 

I 

58653 

42856 

I 

57144 

01509 

0 

98491 

59 

2 

59  44 

0  16 

41394 

2 

58606 

42906 

2 

57094 

OI512 

0 

98488 

S8 

3 

5936 

0  24 

4144I 

2 

58559 

42957 

2 

57043 

01516 

0 

98484 

57 

4 

5928 

0  32 

41488 

3 

58512 

43007 

3 

4 

56993 

01519 

0 

98481 

56 

5 

95920 

2  0  40 

9-41535 

4 

10. 58465 

9-43057 

10.  56943 

10.01523 

0 

9-  98477 

55 

6 

59  12 

0  48 

41582 

5 

58418 

43108 

5 

56892 

01526 

0 

98474 

54 

7 

59  4 

0  5b 

4ib28 

5 

58372 

43158 

6 

56842 

01529 

0 

98471 

5S 

8 

5^56 

I  4 

41675 

b 

58325 

43208 

7 

56792 

01533 

0 

98467 

52 

9 

5848 

I  12 

41722 

7 

58278 

43258 

7 

56742 
10.  56692 

01536 

98464 

51 

lO 

95840 

2  I  20 

9.41768 

8 

10. 58232 

9-  43308 

8 

10.01540 

9.  98460 

50 

II 

5832 

I  28 

41815 

8 

58185 

43358 

9 

56642 

01543 

98457 

49 

12 

5824 

I  36 

41861 

9 

58139 

43408 

10 

56592 

01547 

98453 

48 

'3 

58  lb 

I  44 

41908 

ID 

58092 

43458 

II 

56542 

01550 

98450 

47 

14 

58  8 

I  52 

41954 

II 

58046 

43508 

II 

56492 

01553 

98447 

46 

'5 

958  0 

220 

9. 42001 

II 

10.57999 

9-43558 

12 

10.  56442 

10.01557 

9.  98443 

45 

It) 

5752 

2  8 

42047 

12 

57953 

43607 

13 

56393 

01560 

98440 

44 

17 

57  44 

2  lb 

42093 

13 

57907 

43657 

14 

56343 

01564 

98436 

43 

i8 

57  3^5 

2  24 

42140 

14 

57860 

43707 

15 

56293 

01567 

98433 

42 

19 

57  28 

2  32 

42186 

14 

57814 

43756 

16 

56244 

01571 

98429 

41 

20 

95720 

2   2  40 

9. 42232 

IS 

10.57768 

9. 43806 

16 

10,  56194 

10.01574 

9. 98426 

40 

21 

57  12 

2  48 

42278 

lb 

57722 

43855 

17 

56145 

01578 

98422 

39 

22 

57  4 

25b 

42324 

17 

57676 

43905 

18 

56095 

01581 

98419 

38 

23 

5656 

3  4 

42370 

17 

57630 

43954 

19 

56046 

01585 

98415 

37 

24 

5b  48 

3  12 

42416 

18 

57584 

44004 

20 

55996 

01588 

98412 

36 

25 

95640 

2  3  20 

9.  42461 

19 

10.57539 

9- 44053 

20 

10.  55947 

10. 01591 

9- 98409 

35 

2b 

5632 

328 

42507 

20 

57493 

44102 

21 

55898 

01595 

2 

98405 

34 

27 

5624 

3  36 

42553 

21 

57447 

44151 

22 

55849 

01598 

2 

98402 

33 

28 

56  16 

3  44 

42599 

21 

57401 

44201 

23 

55799 

01602 

2 

98398 

32 

29 
30 

5b  8 

3  52 

42644 

22 

57356 

44250 

24 

55750 

01605 

2 

98395 

31 

956  0 

240 

9. 42690 

23 

10.57310 

9- 44299 

25 

10.55701 

10.  01609 

2 

9.98391 

30 

31 

5552 

4  8 

4273s 

24 

57265 

44348 

25 

55652 

01612 

2 

98388 

29 

32 

55  44 

4  16 

42781 

24 

57219 

44397 

26 

55603 

01616 

2 

98384 

28 

33 

55  36 

4  24 

42826 

2S 

57174 

44446 

27 

55554 

01619 

2 

98^81 

27 

34 
35 

5528 
9  55  20 

4  32 
2  4  40 

42872 
9.42917 

26 

57128 

44495 

28 

55505 

01623 
10.01627^ 

2 

98377 

26 

27 

10.57083 

9-44544 

29 

10.55456 

2 

9-98373 

25 

3(^ 

55  12 

4  48 

42962 

27 

57038 

44592 

29 

55408 

01630 

2 

98370 

24 

37 

55  4 

4  56 

43008 

28 

56992 

44641 

30 

55359 

01634 

2 

98366 

23 

3'^ 

5456 

5  4 

43053 

29 

56947 

44690 

31 

55310 

01637 

2 

98363 

22 

39 
40 

5448 

5  12 

43098 

30 
30 

56902 

44738 

32 

55262 

01641 

2 

98359 

21 

95440 

2  5  20 

9- 43 '43 

10.56857 

9-44787 

33 

10.55213 

10. 01644 

2 

9- 98356 

20 

41 

5432 

5  28 

43188 

31 

56812 

44836 

34 

55164 

01648 

2 

98352 

19 

42 

54  24 

5  36 

43233 

32 

56767 

44884 

34 

55116 

OI65I 

2 

98349 

18 

43 

54  16 

5  44 

43278 

33 

56722 

44933 

35 

55067 

01655 

3 

98345 

17 

44 

54  8 

5  52 

43323 

33 

56677 

44981 

36 

55019 

01658 

3 

98342 

16 

45 

9  54  0 

2  b  0 

9-43367 

34 

10.  56633 
56588 

9.  45029 

37 

10.54971 

10.  01662 

3 

9- 98338 

15 

4b 

5352 

b  8 

43412 

3S 

45078 

38 

54922 

01666 

3 

98334 

14 

47 

53  44 

6  lb 

43457 

36 

56543 
56498 

45126 

38 

54874 

01669 

3 

98331 

13 

48 

5336 

6  24 

43502 

36 

45174 

39 

54826 

01673 

3 

98327 

12 

49 

5328 

6  32 

43546 

37 
'38 

S6454 

45222 

40 

54778 

01676 

3 

98324 

11 

5" 

9  53  20 

2  6  40 

9-43591 

10.  56409 

9- 45271 

41 

10. 54729 

10.  01680 

3 

9- 98320 

10 

51 

53  12 

6  48 

43635 

39 

56365 

45319 

42 

54681 

01683 

3 

98317 

9 

52 

53  4 

b  5b 

43680 

39 

56320 

45367 

43 

54633 

01687 

3 

98313 

8 

53 

52  56 

7  4 

43724 

40 

56276 

45415  i  43 

54585 

OI69I 

3 

98309 

7 

54 

55 

5248 

7  12 

43769 

41 

56231 

45463 

44 

54537 

01694 

3 

98306 

6 

95240 

2  7  20 

9-43813 

42 

10.  56187 

9.45511 

45 

10.  54489 

10.01698 

3 

9-  98302 

5 

5^ 

5232 

7  28 

43857 

43 

56143 

45559 

4b 

54441 

OI70I 

3 

98299 

4 

57 

5224 

7  36 

43901 

43 

56009 

45606 

47 

54394 

01705 

3 

98295 

n 
J 

5« 

52  16 

7  44 

43946 

44 

56054 

45654  47 

54346 

01709 

3 

98291 

2 

59 

52  8 

7  52 

43990 

45 

56010 

45702  48 

54298 

01712 

3 

98288 

I 

bo 

52  0 

8  0 

44034 

46 

55966 

45750 

49 

54250 

01716 

4 

98284 

0 

M. 

105 

Hour  H.  M. 

HourA.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

D 

A 

A 

B 

B 

c 

C   74°  1 

Secontis  of  time 

V 

•2» 

3» 

P 

5- 

()» 

T» 

Prop,  parts  of  cols. 

6 
C 
0 

II 
12 

I 

17 
18 

I 

23 

25 
2 

28 

31 
2 

34 

37 

3 

40 

43 

3 

TABLE  44. 

Page  423 

S'. 

V 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

16° 

A 

A 

B 

B 

C 

C   163° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

DiflF. 

Cosecant. 

Tangent. 

Diff., 
0  ' 

Cotangent, 

10.  54250 

Secant. 

Diflf. 

Cosinq. 

M. 

o 

9  52  0 

280 

9.  44034 

0 

10. 55966 

9-45750 

10. 01716 

0 

9. 98284 

60 

I 

51  52 

8  8 

44078 

I 

55922 

45797   I 

54203 

01719 

0 

98281 

59 

■J 

51  44 

8  16 

44122 

I 

55878 

45845   2 

54155 

01723 

0 

98277 

58 

51  36     8  24 

44166 

2 

55834 

45892   2 

54108 

01727 

0 

98273 

57 

4 

51  28     8  32 

44210 

3 

55790 

45940 

-3_ 
4 

54060 

01730 

0 

98270 

5b 

s 

9  51  20  2  8  40 

9-44253 

4 

10.55747 

9- 45987 

10.54013 

10.01734 

0 

9. 98266 

55 

0 

51  12  ,    8  48 

44297 

4 

55703 

46035   5 

53965 

01738 

0 

98262 

54 

7 

51  4     8  56 

44341 

.S 

55659 

46082   5 

53918 

01 741 

0 

98259 

53 

8 

50  56     9  4 

44385 

6 

55615 

46130 

6 

53870 

01745 

0 

98255 

52 

9 

50  48  I    9  12 

44428 

6 

7 

55572 
10.  55528 

46177 
9. 46224 

7 
8 

53823 

01749 

98251 
9. 98248 

51 
50 

lO 

9  50  40  2  9  20 

9.  44472 

10.  53776 

10.01752 

II 

50  32     9  28 

44516 

8 

55484 

46271 

9 

53729 

01756 

98244 

49 

12 

50  24 

9  36 

44559 

9 

55441 

46319 

9 

53681 

01760 

98240 

48 

I,> 

50  16 

9  44 

44602 

9 

55398 

46366  j  10 

53634 

01763 

98237 

47 

14 

50  8 

9  52 

44646 

10 

55354 
10.55311 

46413 

II 

53587 

01767 

98233 

46 

15 

9  50  0  2  10  0 

9. 44689 

II 

9. 46460 

12 

10. 53540 

10.01771 

9. 98229 

45 

it> 

49  52    10  8 

44733 

II 

55267 

46507 

12 

53493 

01774 

98226 

44 

17 

49  44    10  16 

44776 

12 

55224 

46554 

13 

5344tJ 

01778 

98222 

43 

iS 

49  36    10  24 

44819 

1,3 

55181 

46601   14 

53399 

01782 

98218 

42 

19 

49  28 

10  32 

44862 

14 

55138 

46648 

15 

53352 
10.  53306 

01785 

98215 

41 

20 

9  49  20 

2  10  40 

9- 44905 

14 

10. 55095 

9- 46694 

15 

10.01789 

9.  982 1 1 

40 

21 

49  12  i   10  48 

44948 

15 

55052 

46741 

16 

53259 

01793 

98207 

39 

22 

49  4    10  56 

44992  1  16 

55008 

46788 

17 

53212 

01796 

98204 

38 

2;> 

48  56    II  4 

45035 

16 

54965 

46835 

18 

53165 

01800 

98200 

37 

24 

48  48    II  12 

45077 

17 

54923 

46881 

19 

19 

531 19 
10.  53072 

01804 

I 

98196 

3b 

2S 

9  48  40  2  II  20 

9.45120  1  18 

10. 54880 

9.  46928 

10.01808 

2 

9.98192 

35 

26 

48  32    1 1  28 

45163  ;  18 

54837 

46975  20 

53025 

01811 

2 

98189 

34 

27 

48  24 

II  36 

45206 

19 

54794 

47021 

21 

52979 

01815 

2 

98185 

33 

28 

48  16 

II  44 

45249 

20 

54751 

47068 

22 

52932 

01819 

2 

98181 

32 

29 

48  8 

II  52 

45292 

21 

54708 

^47ii_4_ 

9. 47160 

22 
23 

528S6 

01823 

2 

98177 

31 

30 

9  48  0 

2  12  0 

9-  45334 

21 

10.  54666 

10.  52840 

10.01826 

2 

9.98174 

30 

31 

47  52 

12  8 

45377 

22 

54623 

47207 

24 

52793 

01830 

2 

98170 

29 

32 

47  44    12  16 

45419 

23 

54581 

47253 

25 

52747 

01834 

2 

98166 

28 

0.1 

47  36    12  24 

45462 

23 

54538 

47299 

26 

52701 

01838 

2 

98162 

27 

34 

3,S 

47  28  1   12  32 

45504 

24 

54496 

47346 

26 

52654 

01841 

2 
2 

98159 

26 

9  47  20 

2  12  40 

9-  45547 

25 

10.  54453 

9-  47392 

27 

10.  52608 

10.01845 

9-98155 

25 

3b 

47  12 

12  48 

45589 

26 

5441 1 

47438 

28 

52562 

01849 

2 

98151 

24 

37 

47  4 

12  56 

45632 

26 

54368 

47484 

29 

52516 

01853 

2 

98147 

23 

3« 

46  56 

13  4 

45674 
45716 

27 

54326 

47530 

29 

52470 

01856 

2 

98144 

22 

39 
40 

46  48 

13  12 

2a 

54284 

4y'576 

30 

52424 

01860 

2 

98140 

21 

9  46  40 

2  13  20 

9-45758 

28 

10, 54242 

9. 47622 

31 

10.  52378 

10.01864 

2 

9.98136 

20 

41 

46  32 

13  28 

45801 

29 

54199 

47668 

32 

52332 

01868 

3 

98132 

19 

42 

46  24 

13  36 

45843 

30 

54157 

47714 

32 

52286 

01871 

'J 

3 

9S129 

18 

43 

46  16 

13  44 

45885  31 

54115 

47760 

33 

52240 

01875 

-> 

.1 

98125 

17 

44 

46  8 

13  52 

45927  31 
9. 45969  32 

54073 

47806 

34 

52194 
10.  52148 

01879 
10. 01883 

3 

98121 

16 

45 

9  46  0  2  14  0 

10. 54031 

9.  47852 

35 

3 

9.  981 1 7 

15 

46 

45  52    14  8 

460 1 1  ^^ 

53989 

47897 

36 

52103 

01887 

3 

981 13 

14 

47 

45  44    14  16 

46053  33 

53947 

47943 

36 

52057 

01890 

3 

981 10 

13 

48 

45  36    14  24 

46095  34 

53905 

47989 

37 

5201 1 

01894 

3 

98106 

12 

49 

45  28  ,   14  32 

46136 

35 
36 

53864 
10.  53822 

48035 

38 
39 

51965 

01898 

3 

98102 

11 

50 

9  45  20  2  14  40 

9.46178 

9. 48080 

10.  51920 

10.01902 

3 

9. 98098 

10 

51 

45  12    14  48 

46220  !  36 

53780 

48126 

39 

51874 

01906 

3 

98094 

9 

52 

45  4  ,   14  56 

46262   37 

53738 

481 71 

40 

51829 

01910 

3 

98090 

8 

53 

44  56  !   15  4 

46303   38 

53697 

48217 

41 

51783 

01913 

3 

980S7 

7 

54 

44  48    15  12 

46345   38 

53655 

48262 
9.48307 

42 
43 

51738 

01917 

3 

980S3 

t> 

5 

55 

9  44  40  1  2  15  20 

9.  46386   39 

10.53614 

10.51693 

10.01921 

-3 

9- 98079 

S^ 

44  32 

15  28 

46428   40 

53572 

48353 

43 

51647 

01925 

3 

98075 

4 

57 

44  24 

15  36 

46469   41 

53531 

48398 

44 

51602 

01929 

4 

98071 

-t 
J 

5« 

44  16  ;   15  44 

465 1 1 

41 

53489 

48443 

45 

51557 

01933 

4 

98067 

0 

59 

44  8    15  52 

4^552 

42 

5344« 

48489 

46 

51511 

01937 

4 

98063 

I 

bo 

44  0    16  0 

46594 

43 

53406 

48534 

46 

51466 

01940 

4 

98060 

0 

M. 

Hour  P.M.  Hour  A.M. 

Cosine. 

DifF. 

Secant. 

Cotangent. 

Difr. 

Tangent. 

Cosecant. 

DiflF. 

Sine. 

M. 

106 

0 

A 

A 

R 

B 

C 

C   73°  1 

Seconds  of  time 

I'        2» 

3' 

16 

17 

I 

4»    5» 

21    27 

23    29 

2    2 

6' 

I» 

Prop,  parts  of  cols.  <  B 

5  II 

6  12 
0     I 

32 

35 

3 

37 

41 

3 

Page  424] 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

ir 

A 

A 

B 

B 

C 

C   162° 

M. 
O 

Hour  A.M. 

Hour  p.  M. 

Sine. 

DifF. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M.  ' 

9  44  0 

2  16  0 

9-  46594 

0 

ID.  53406 

9-  48534 

0 

10. 51466 

10.  01940 

0 

9. 98060 

60 

I 

43  52 

16  8 

46635 

I 

53365 

48579 

I 

51421 

01944 

0 

98056 

59 

2 

43  44 

16  16 

46676 

I 

53324 

48624 

I 

5137(5 

01948 

0 

98052 

58 

3 

43  36 

16  24 

46717 

2 

53283 

48669 

2 

51331 

01952 

0 

98048 

57 

4 

43  28 

16  32 

46758 

3 

53242 

48714 

3 

51286 

01956 

0 

98044 

56 

S 

9  43  20 

2  16  40 

9.  46800 

3 

10.  53200 

9-  48759 

4 

10.  51241 

10.01960 

0 

9.  98040 

55 

6 

43  12 

16  48 

46841 

4 

53159 

48804 

4 

5 1 196 

01964 

0 

98036 

54 

7 

43  4 

16  56 

46882 

5 

53118 

48849 

5 

51151 

01968 

0 

98032 

53 

8 

42  56 

17  4 

46923 

5 

53077 

48894 

6 

5 1 106 

01971 

98029 

52 

9 

42  48 

17  12 

46964 

6 

53036 

48939 

7 

51061 

01975 

98025 

51 

10 

9  42  40 

2  17  20 

9.  47005 

7 

10.  52995 

9.  48984 

7 

10.  51016 

10.01979 

9.  9802 1 

50 

u 

42  32  ; 

17  28 

47045 

7 

52955 

49029 

8 

50971 

01983 

98017 

49 

12 

42  24 

17  36 

47086 

8 

52914 

49073 

9 

50927 

01987 

98013 

48 

1.3 

42  16 

17  44 

47127 

9 

52873 

491 18 

10 

50882 

01991 

98009 

47 

14 

15 

42  8 

17  52 

47168 

9 

52832 

49163 

ID 

50837 
10.  50793 

01995 

98005 

46 

9  42  0 

2  18  0 

9.  47209 

10 

10. 52791 

9. 49207 

II 

10.  01999 

9. 98001 

45 

lb 

41  52 

18  8 

47249 

II 

52751 

49252 

12 

50748 

02003 

97997 

44 

17 

41  44 

18  16 

47290 

II 

52710 

49296 

12 

50704 

02007 

97993 

43 

iS 

41  36 

18  24 

47330 

12 

52670 

49341 

13 

50659 

0201 1 

97989 

42 

19 

41  28 

18  32 

47371 

13 

52629 

49385   14 

50615 

02014 

97986 

41 

20 

9  41  20 

2  18  40 

9.  474 II 

13 

10. 52589 

9.49430  '  15 

10. 50570 

10.02018 

9.97982 

40 

21 

41  12 

18  48 

47452 

14 

52548 

49474  '  15 

50526 

02022 

97978 

39 

22 

41  4 

18  56 

47492 

15 

52508 

49519   16 

50481 

02026 

97974 

38 

23 

40  56 

19  4 

47533 

15 

52467 

49563   17 

50437 

02030 

2 

97970 

37 

24 

2^ 

40  48 

19  12 

47573 

16 

52427 

49607 

18 

iS 

50393 

02034 

2 

97966 

36 

9  40  40 

2  19  20 

9.47613 

17 

10.52387 

9. 49652 

10.  50348 

10.02038 

2 

9.  97962 

35 

26 

40  32 

19  28 

47654 

17 

52346 

49696  ;  19 

50304 

02042 

2 

97958 

34 

27 

40  24 

19  36 

47694 

18 

52306 

49740  20 

50260 

02046 

2 

97954 

33 

28 

40  16 

19  44 

47734 

19 

52266 

49784 

21 

50216 

02050 

2 

97950 

32 

29 

40  8 

19  52 

47774 

19 

52226 

49828 

21 

50172 

02054 

2 

97946 

31 

30 

9  40  0 

2  20  0 

9.47814 

20 

10.  52186 

9. 49872 

22 

10. 50128 

10.  02058 

2 

9. 97942 

30 

SI 

39  52 

20  8 

47854 

21 

52146 

49916  j  23 

500S4 

02062 

2 

97938 

29 

32 

39  44 

20  16 

47894 

21 

52106 

49960  24 

50040 

02066 

2 

97934 

28 

33 

39  36 

20  24 

47934 

22 

52066 

50004  \   24 

49996 

02070 

2 

97930 

27 

34 

3928 

20  32 

47974 

23 

23 

52026 

50048 

25 

49952 

02074 

2 

97926 

25 

3S 

9  39  20 

2  20  40 

9.  48014 

10. 51986 

9. 50092 

26 

10.  49908 

10.02078 

2 

9. 97922 

25 

36 

39  12 

20  48 

48054 

24 

51946 

50136 

26 

49864 

02082 

2 

97918 

24 

37 

39  4 

20  56 

48094 

25 

51906 

50180  1  27 

49820 

02086 

2 

97914 

23 

3« 

3856 

21  4 

48133 

25 

51867 

50223  28 

49777 

02090 

3 

97910 

22 

■39 

3848 

21  12 

48173 

26 

27 

51827 

•  50267 

29 
29 

__  49733. 
10. 49689 

02094 
10.  02098 

3 
3 

97906 

21 

40 

9  38  40 

2  21  20 

9.48213 

10.51787 

9-50311 

9. 97902 

20 

41 

38  32 

21  28 

48252 

27 

51748 

50355 

30 

49645 

02102 

3 

97898 

19 

42 

38  24 

21  36 

48292 

28 

51708 

50398 

31 

49602 

02106 

3 

97894 

18 

4S 

38  16 

21  44 

48332 

29 

51668 

50442 

32 

49558 

02110 

3 

97890 

17 

44 

38  8 

21  52 

48371 

29 
30 

51629 
10.  51589 

50485 
9.  50529 

32 

33 

49515 
10. 49471 

021 14 

3 

97S86 

16 

4.S 

9  38  0 

2  22  0 

9.  4841 1 

10.02118 

3 

9.  97882 

15 

46 

37  52 

22  8 

48450 

31 

51550 

50572 

34 

49428 

02122 

3 

97878 

14 

47 

37  44 

22  16 

48490 

31 

51510 

50616 

35 

49384 

02126 

3 

97874 

13 

48 

37  36 

22  24 

48529 

32 

51471 

50659 

35 

49341 

02130 

3 

97870 

12 

49 

37  28 

22  32 

48568 

33 
33 

51432 

50703 

36 

49297 

02134 

3 

97866 

II 

50 

9  37  20 

2  22  40 

9. 48607 

10.51393 

9. 50746 

37 

10. 49254 

10.02139 

3 

9.  97861 

10 

SI 

37  12 

22  48 

48647 

34 

51353 

50789 

37 

492 II 

02143 

3 

97857 

9 

52 

37  4 

22  56 

48686 

35 

51314 

50833 

38 

49167 

02147 

3 

97853 

8 

53 

3656 

23  4 

48725 

35 

51275 

50876 

39 

49124 

021 5 1 

4 

97849 

7 

54 
55 

36  48 
9  36  40 

23  12 
2  23  20 

48764 
9.  48803 

36 

51236 

50919 

40 
40 

49081 
10. 49038 

02155 

4 

97845 

6 

37 

IO.51197 

9. 50962 

10.02159 

4 

9.  97841 

5 

5^ 

36  32 

23  28 

48842 

37 

51158 

51005 

41 

48995 

02163 

4 

97S37 

4 

57 

36  24 

23  36 

48881 

38 

51119 

51048 

42 

48952 

02167 

4 

97833 

5« 

36  16 

23  44 

48920 

39 

51080 

51092 

43 

48908 

02171 

4 

97829 

2 

59 

36  8 

23  52 

48959 

39 

51041 

51135 

43 

48865 

02175 

4 

97825 

I 

60 
M. 

36  0 
Hour  P.M. 

24  0 

48998 

40 
DiflF. 

51002 

51 1 78 

44 
Diff. 

48822 

02179 

4 

97821 

0 

Hour  A.M. 

Cosine. 

Secant. 

Cotangent. 

Tangent. 

Cosecant. 

DiflF. 

Sine. 

M. 

10^ 

0 

A 

A 

B 

B 

C 

C 

72° 

Seconds  of  time 

1' 

5 
6 
0 

2' 

3. 

p 

5> 

6' 

30 

33 
3 

7- 

35 
39 

Prop,  parts  of  cols.  -;  H 

10 
II 

I 

IS 

17 

I 

20 

22 

2 

25 
28 

2 

TABLE  44. 

Page  425 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

18^ 
M. 

A          A 

B 

B 

C 

C   161° 

Hour  A.M. 

Hour  p.  M.  1 

Sine.   Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 
10.02179 

Diff. 

Cosine. 

M. 

o 

9  36  0 

2  24  0 

9. 48998 

0 

10.  51002 

9.51178 

0 

10.  48822 

0 

9.97821 

60 

I 

35  52 

24  8 

49037 

I 

50963 

51221 

I 

48779 

02183 

0 

97817 

59 

2 

35  44 

24  16 

49076 

I 

50924 

51264 

I 

48736 

02188 

0 

97812 

58 

^ 

35  36 

24  24 

49"5 

2 

50885 

51306 

2 

48694 

02192 

0 

97808 

57 

4 

35  28 

24  32 

49153 

3 

50847 

51349 

3 

48651 

02196 

0 

97804 

56 

S 

9  35  20 

2  24  40 

9.49192 

3 

10.  50808 

9-51392 

3 

10.  48608 

10.  02200 

0 

9. 97800 

55 

6 

35  12 

24  48 

49231  !  4 

50769 

5143s 

4 

48565 

02204 

0 

97796 

54 

7 

35  4 

24  56 

49269   4 

50731 

51478 

5 

48522 

02208 

0 

97792 

53 

s 

34  56 

25  4 

49308   5 

50692 

51520 

6 

48480 

02212 

97788 

52 

9 

34  48 

25  12 

49347 

6 

50653 

51563^ 

6 

48437 

02216 

97784 

51 

\o 

9  34  40 

2  25  20 

9- 493S5 

6 

10.  50615 

9.  51606 

7 

10. 48394 

10.02221 

9-97779 

50 

II 

34  32 

25  28 

49424 

7 

50576 

51648 

8 

48352 

02225 

97775 

49 

12 

34  24 

25  36 

49462 

8 

50538 

51691 

8 

48309 

02229 

97771 

48 

1,1 

34  16 

25  44 

49500 

8 

50500 

51734 

9 

48266 

02233 

97767 

47 

U 

IS 

34  8 

25  52 

49539 

9 

50461 

51776 

10 

48224 

02237 

97763 

46 

9  34  0 

2  26   0 

9-49577 

9 

10. 50423 

9-51819 

10 

I0.48I8I 

10.02241 

9-97759 

45 

lb 

33  52 

26  8 

49615 

10 

503S5 

51861 

II 

48139 

02246 

97754 

44 

17 

2,-,   44 

26  16 

49654  !  II 

50346 

51903 

12 

48097 

02250 

97750 

4^ 

iS 

y^  36 

26  24 

49692  1  II 

50308 

51946 

13 

48054 

02254 

97746 

42 

'9 

3328  , 

26  32 

49730  12 

50270 

51988 

13 

48012 

02258 

97742 

41 

20 

9  33  20  ! 

2  26  40 

9. 49768  13 

10.  50232 

9. 52031 

14 

10. 47969 

10.  02262 

9-97738 

40 

21 

33  12 

26  48 

49806  1  13 

50194 

52073 

15 

47927 

02266 

97734 

39 

22 

32,    4 

26  56 

49844  '   14 

50156 

52115 

15 

47885 

02271 

2 

97729 

38 

-J 

32  56 

27  4 

49882   14  ;     501 18 

52157 

16 

47843 

02275 

2 

97725 

37 

^4 
^5 

32  48 

27  12 

49920 

I 5     50080 

52200 

17 

47800 

10.47758 

02279 
10.02283 

2 

97721 

36 

9  32  40 

2  27  20 

9. 49958 

16 

10.  50042 

9. 52242 

17 

2 

9.97717 

35 

2b 

32  32 

27  28 

49996  ;  16 

50004 

52284 

18 

47716 

02287 

2 

97713 

34 

27 

32  24 

27  36 

50034  !  17 

49966 

52326 

19 

47674 

02292 

2 

97708 

28 

32  16 

27  44 

50072  ,18     49928 

52368 

20 

47632 

02296 

2 

97704 

32 

29 

32  8 

27  52 

50110 

18     49890 

52410 

20 

47590 

02300 

2 
2 

97700 
9. 97696 

31 
30 

30 

9  32  0 

2  28  0 

9.  50148 

19 

10. 49852 

9- 52452 

21 

10. 47548 

10.  02304 

31 

31  52 

28  8 

50185 

20 

49815 

52494 

22 

47506 

02309 

2 

97691 

29 

32 

31  44 

28  16 

50223 

20 

49777 

52536 

22 

47464 

02313 

2 

97687 

28 

"1  -» 

3'  36 

28  24 

50261   21 

49739 

52578 

23 

47422 

02317 

2 

97683 

27 

34 

31  28 

28  32 

50298 

21 

49702 

52620 

24 

47380 

02321 

2 
2 

97679 
9-  97674 

26 
25 

3.S 

9  31  20 

2  28  40 

9-  50336 

22 

10. 49664 

9.  52661 

24 

10. 47339 

10.  02326 

3(> 

31  12 

28  48 

50374  \   23  I    49626 

52703 

25 

47297 

02330 

3 

97670 

24 

37 

31  4 

28  56 

5041 1 

23  i    49589 

52745 

26 

47255 

02334 

3 

97666 

23 

3« 

30  56 

29  4 

50449 

24 

49551 

52787 

27 

47213 

02338 

3 

97662 

22 

39 

30  48 

29  12 

50486 

25 
25 

49514 
10. 49477 

52829 
9- 52870 

27 

47171 

02343 
10.02347 

3 
3 

97657 
9.97653 

21/ 
20 

40 

9  30  40 

2  29  20 

9-  50523 

28 

10.47130 

41 

30  32 

29  28 

50561 

26 

49439 

52912 

29 

47088 

02351 

3 

97649 

19 

42 

30  24 

29  36 

50598 

26 

49402 

52953 

29 

47047 

02355 

3 

97645 

18 

43 

30  16 

29  44 

50635 

27 

49365 

52995 

30 

47005 

02360 

3 

97640 

17 

44 
45 

30  8 
9  30  0 

29  52 

50673 

28 
28" 

49327 

53037 

31 

46963 

02364 

3 
3 

97636 

lb 

2  30  0 

9.50710 

10. 49290 

9- 53078 

31 

10.  46922 

10.  02368 

9-  97632 

15 

4b 

29  52 

30  8 

50747 

29 

49253 

53120 

32 

46880 

02372 

3 

97628 

14 

47 

29  44 

30  16 

50784 

30 

49216 

53161 

33 

46839 

02377 

3 

97623 

13 

48 

29  36 

30  24 

50821 

30 

49179 

53202 

34 

46798 

02381 

3 

97619 

12 

49 

50 

29  28 

30  32 

50858 

31 

49142 

53244 

34 

46756 

02385 

3 
4 

97615 

II 

9  29  20 

2  30  40 

9. 50896 

31 

10.49104 

9- 53285 

35 

10.46715 

10.02390 

9.  97610 

10 

5' 

29  12 

30  48 

50933 

32 

49067 

53327 

36 

46673 

02394 

4 

97606 

9 

S2 

29  4 

30  56 

50970 

33 

49030 

53368 

36 

46632 

02398 

4 

97602 

s 

53 

28  56 

31  4 

51007 

33 

48993 

53409 

37 

46591 

02403 

4 

97597 

7 

54 

28  48 

31  12 

51043 

34 

35 

48957 
10.48920 

53450 
9- 53492 

38 

46550 

02407 

4 

97593 

6 

S 

55 

9  28  40 

2  31  20 

9.  51080 

38 

10.46508 

10.  0241 1 

4 

9-  975S9 

5*' 

28  32 

31  28 

51117 

35 

48883 

53533 

39 

46467 

02416 

4 

97584 

4 

57 

28  24 

31  3^ 

51154 

36 

48846 

53574 

40 

46426 

02420 

4 

97580 

3 

S^ 

28  16 

31  44 

51191 

37 

48809 

53615 

41 

46385 

02424 

4 

97576 

-> 

59 

28  8 

31  52 

51227 

37 

48773 

53656 

41 

46344 

02429 

4 

97571 

1 

00 

28  0 

32  0 

51264 

38 

48736 

53697 

42 

46303 

02433 

4 

97567 

0 

M. 

Hour  P.M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

lOS 

0 

A           A 

B 

B 

C 

c     n°\ 

Seconds  of  time 

P 

2» 

3» 

4' 

.5» 

6» 

7' 

Prop,  parts  of  cols.  <  B 

5 
5 

I 

9 
10 

I 

14 

16 

2 

'9 

21 

2 

24 
26 

3 

28 

31 

3 

33 

37 

4 

Page  426 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

19° 

A 

A 

B 

B 

C 

C   160° 

M. 

Hour  A.M. 

Hour  P.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 

9  28  0 

2  32   0 

9.51264 

0 

10.  48736 

9-  53697 

0 

10.46303 

10.  02433 

0 

9-97567 

60 

I 

27  52 

32  8 

51301 

I 

48699 

53738 

I 

46262 

02437 

0 

97563 

59 

2 

27  44 

32  16 

51338 

I 

48662 

53779 

I 

46221 

02442 

0 

97558 

58 

J 

27  36 

32  24 

51374 

2 

48626 

53820 

2 

46180 

02446 

0 

97554 

57 

4 

27  28 

32  32 

514" 

2. 

48589 

53861 

3 

46139 

02450 

0 

97550 

56 

5 

9  27  20 

2  32  40 

9-51447 

3 

10.  48553 

9- 53902 

3 

10.  46098 

10.  02455 

0 

9-  97545 

55 

6 

27  12 

32  48 

51484 

4 

48516 

53943 

4 

46057 

02459 

0 

97541 

54 

7 

27  4 

32  56 

51520 

4 

48480 

53984 

5 

46016 

02464 

97536 

53 

S 

26  56 

33  4 

51557 

5 

48443 

54025 

5 

45975 

02468 

97532 

52 

9 

10 

26  48 

33  12 

51593 

5 
6 

48407 

54065 

6 

45935 

02472 

97528 

51 
50 

9  26  40 

2  33  20 

9.51629 

10.48371 

9. 54106 

7 

10. 45894 

10.02477 

9.97523 

1 1 

26  32 

33  28 

51666 

7 

48334 

54147 

7 

45853 

02481 

97519 

49 

12 

26  24 

33  36 

51702 

7 

48298 

54187 

8 

45813 

02485 

97515 

48 

13 

26  16 

33  44 

51738 

8 

48262 

54228 

9 

45772 

02490 

97510 

47 

•4 

26  8 

33  52 

51774 

8 

48226 

54269 

9 

45731 

02494 

97506 

46 

1 5 

9  26  0 

2  34  0 

9. 51811 

9 

10.48189 

9  54309 

10 

10.45691 

10.02499 

9.97501 

45 

10 

25  52 

34  8 

5 '^^7 

10 

48153 

54350 

II 

45650 

02503 

97497 

44 

17 

25  44 

34  16 

51883 

10 

48117 

54390 

II 

45610 

02508 

97492 

43 

i8 

25  36 

34  24 

51919 

II 

48081 

54431 

12 

45569 

02512 

97488 

42 

19 

20 

25  28 

34  32 
2  34  40 

51955 

II 

48045 
10. 48009 

54471 
9.54512 

13 

45529 

02516 

97484 

41 

9  25  20 

9-51991 

12 

13 

10.  45488 

10.02521 

9-  97479 

40 

21 

25  12 

34  48 

52027 

12 

47973 

54552 

14 

45448 

02525 

2 

97475 

39 

22 

25  4 

34  56 

52063 

13 

47937 

54593 

15 

45407 

02530 

2 

97470 

38 

23 

24  56 

35  4 

52099 

14 

47901 

54633 

15 

45367 

02534 

2 

97466 

37 

24 

24  48 

35  12 

52135 

14 

47865 

54673 

16 

45327 

02539 
10.02543 

2 

97461 

36 

25 

9  24  40 

2  35  20 

9-52171 

15 

10. 47829 

9-54714 

17 

10. 45286 

2 

9-97457 

35 

2b 

24  32 

35  28 

52207 

15 

47793 

54754 

17 

45246 

02547 

2 

97453 

34 

27 

24  24 

35  36 

52242  16 

47758 

54794 

18 

45206 

02552 

2 

97448 

33 

28 

24  16 

35  44 

52278 

17 

47722 

54835 

19 

45165 

02556 

2 

97444 

32 

29 

24  8 

35  52 

52314 
9- 52350 

17 

18 

47686 

54875 

19 

45125 

02561 

2 

97439 

31 

30 

9  24  0 

2  36  0 

10. 47650 

9-54915 

20 

10.45085 

10.  02565 

2 

9-  97435 

30 

31 

23  52 

36  8 

52385 

18 

47615 

54955 

21 

45045 

02570 

2 

97430 

29 

32 

23  44 

36  16 

52421 

19 

47579 

54995 

21 

45005 

02574 

2 

97426 

28 

33 

23  36 

36  24 

52456 

20 

47544 

55035 

22 

44965 

02579 

2 

97421 

27 

34 

35 

23  28 

36  32 

52492 
9.52527 

20 

47508 

55075 

23 

44925 

02583 

3 

97417 

26 

9  23  20 

2  36  40 

21 

10.  47473 

9-55"5 

23 

10. 44885 

10.02588 

3 

9.97412 

25 

3& 

23  12 

36  48 

52563 

21 

47437 

55155 

24 

44845 

02592 

3 

97408 

24 

37 

23  4 

36  56 

52598 

22 

47402 

55195 

25 

44805 

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3 

97403 

23 

3« 

22  56 

37  4 

52634 

23 

47366 

55235 

25 

44765 

02601 

^ 

97399 

22 

'39 

22  48 

37  12 

52669 

23 
24 

47331 

55275 
9-55315 

26 

~2'7" 

44725 

02606 

3 

97394 

21 

40 

9  22  40 

2  37  20 

9-  52705 

10. 47295 

10. 44685 

10. 02610 

3 

9-  97390 

20 

41 

22  32 

37  28 

52740 

24 

47260 

55355 

27 

44645 

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3 

97385 

19 

42 

22  24 

n   3b 

52775 

25 

47225 

55395 

28 

44605 

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3 

97381 

18 

43 

22  16 

37  44 

5281 1 

26 

47189 

55434 

29 

44566 

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3 

97376 

17 

44 

22  8 

37  52 

52846 
9.  52881 

26 

47154 

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29 

44526 

02628 

3 

97372 

16 
"15 

45 

9  22  0 

2  38  0 

27 

10. 47119 

9-55514 

30 

10. 44486 

10.02633 

3 

9.97367 

46 

21  52 

38  8 

52916 

27 

47084 

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31 

44446 

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3 

97363 

14 

47 

21  44 

38  16 

52951 

28 

47049 

55593 

31 

44407 

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3 

97358 

13 

48 

21  36 

38  24 

52986 

29 

47014 

55633 

32 

44367 

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4 

97353 

12 

49 

21  28 

3832 

53021 

29 

46979 

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33 

44327 

02651 

4 

97349 

II 
10 

50 

9  21  20 

2  38  40 

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30 

10. 46944 

9-55712 

33 

10.44288 

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4 

9- 97344 

51 

21  12 

38  48 

53092 

30 

46908 

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34 

44248 

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4 

97340 

9 

52 

21  4 

38  56 

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31 

46874 

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35 

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4 

97335 

8 

53 

20  56 

39  4 

53161 

32 

46839 

55831 

35 

44169 

02669 

4 

97331 

7 

54 

55 

20  48 

39  12 

53196 

32 

46804 

55870 

36 

44130 

02674 

4 

97326 

6 

5 

9  20  40 

2  39  20 

9.53231 

33 

10. 46769 

9- 55910 

37 

10. 44090 

10.02678 

4 

9.  97322 

5b 

20  32 

39  28 

53266 

33 

46734 

55949 

37 

44051 

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4 

97317 

4 

57 

20  24 

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34 

46699 

55989 

38 

440 1 1 

0268S 

4 

97312 

3 

5^S 

20  16 

39  44 

53336 

34 

46664 

56028 

39 

43972 

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4 

97308 

2 

59 

20  8 

39  52 

53370 

35 

46630 

56067 

39 

43933 

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4 

97303 

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60 

20  0 

40  0 

53405 

36 

46595 

56107 

40 

43893 

02701 

4 

97299 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine . 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

109 

3 

A 

A 

B 

B 

c 

C   70°  1 

Seconds  of  time. 


Prop,  parts  of  cols.  >  K  ; 


(' 


9 
10 


13 
2 


18 

20 

2 


22 

25 

3 


27 

30 

3 


31 

35 
4 


TABLE  44. 

[Page  427 

S'. 

^ 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

20° 

A 

A 

B 

B 

C 

C   159° 

M. 

Hour  A.  M. 

Hour  r.  m. 

Sine. 

Diff. 
0 

Cosecant. 

Tangent. 

^Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 

9  20  0   2  40  0 

9- 53405 

10.  46595 

9.  56107 

0 

ID.  43893 

10.  02701 

0. 

9- 97299 

60 

I 

19  52    40  8 

53440 

I 

46560 

56146 

I 

43854 

02706 

0 

97294 

59 

'> 

19  44    40  16 

53475 

I 

46525 

56185 

I 

43815 

0271 1 

0 

97289 

S8 

19  36    40  24 

53509 

2 

46491 

56224 

2 

43776 

02715 

0 

97285 

S7 

4 

19  28  :  40  32 

53544 

2 

46456 

56264 

3 

43736 

02720 

0 

97280 

56 
55 

5 

9  19  20  ]  2  40  40 

9-53578 

3 

10.  46422 

9- 56303 

3 

10.  43697 

10.02724 

0 

9.97276 

b 

19  12   40  48 

53613  1  3 

46387 

56342 

4 

43658 

02729 

jO 

97271 

54 

7 

19  4   40  56 

53647  i  4 

46353 

56381 

4 

43619 

02734 

97266 

5^1 

S 

18  56- 

41   4 

53682 

5 

46318 

56420 

5 

43580 

02738 

97262 

52 

9 

18  48 

'41  12 

53716 

5 

46284 

56459 

6 

43541 

02743 

97257 

51 

lO 

9  18  40 

2  41  20 

9-53751 

6 

10.  46249 

9- 56498 

6 

10.  43502 

10.  02748 

9.97252 

50 

II 

18  32  1  41  28 

53785 

6 

46215 

56537 

7 

43463 

02752 

97248 

49 

12 

18  24  1  41  36 

53819 

7 

46181 

56576 

8 

43424 

02757 

97243 

48 

i;^ 

18  16  1  41  44 

53854 

7 

46146 

56615 

8 

43385 

02762 

97238 

47 

14 
1.S 

18  8 

41  52 

53888 

8 
8 

46112 
10. 46078 

56654 
9. 56693 

9 

43346 

02766 

97234 

46 

9  18  0 

2  42   0 

9- 53922 

10 

10.43307 

10.02771 

9- 97229 

45 

16 

17  52 

42  8 

53957 

9 

46043 

56732 

10 

43268 

02776 

I 

97224 

44 

17 

17  44  1   42  16 

53991 

10 

46009 

56771 

II 

43229 

02780 

97220 

43 

i8 

17  36  1   42  24 

54025 

10 

45975 

56810 

12 

43190 

02785 

97215 

42 

•9 

17  28 

42  32^ 

2  42  40 

54059 
9- 54093 

II 

45941 

56849 

12 

43151 

02790 

97210 

41 

20 

9  17  20 

II 

ID.  45907 

9- 56887 

13 

IO.43113 

10.02794 

2 

9.  97206 

40 

21 

17  12    42  48 

54127 

12 

45873 

56926 

13 

43074 

02799 

2 

97201 

39 

O  T 

17  4    42  56 

54161 

12 

45839 

56965 

14 

43035 

02804 

2 

9719b 

38 

23 

16  56    43  4 

54195 

13 

45805 

57004 

15 

42996 

02808 

2 

97192 

37 

24 
2.S 

16  48 
9  16  40 

43  12 

54229 

14 
14 

45771 
10.45737 

57042 

15 
16 

42958 

02813 
10.02818 

2 

97187 

36 

2  43  20 

9-  54263 

9.57081 

10.42919 

2 

9.97182 

35 

2b 

16  32 

43  28 

54297 

IS 

45703 

57120 

17 

42880 

02822 

2 

97178 

34 

27 

16  24 

43  36 

54331 

IS 

45669 

57158 

17 

42842 

02827 

2 

97173 

28 

16  16    43  44 

54365 

16 

45635 

57197 

18 

42803 

02832 

2 

97168 

.32 

29 

16  8    43  52 

54399 

16 

45601 

57235 

19 
19 

42765 
10.42726 

0283  7_ 

10.02841 

2 
2' 

97163 

31 

30 

9  16  0  2  44  0 

9- 54433 

17 

10.45567 

9- 57274 

9-97159 

30 

31 

15  52    44  8 

54466 

17 

45534 

57312 

20 

42688 

02846 

2 

97154 

29 

32 

15  44  1   44  16 

54500 

18 

45500 

57351 

21 

42649 

02851 

3 

97149 

28 

15  36    44  24 

54534 

19 

45466 

57389 

21 

4261 1 

02855 

3 

97145 

27 

34 

15  28 

44  32 

__  54567_ 
9. 54601 

19 

45433 

57428 
9.57466 

22 
22^ 

42572 

02860 

3 

97140 

20 

3,S 

9  15  20 

2  44  40 

20 

10. 45399 

10.  42534 

10.02865 

3 

9-97135 

25 

30 

15  12 

44  48 

54635 

20 

45365 

57504 

23 

42496 

02870 

3 

97130 

24 

^Z 

'5  i 

44  56 

54668 

21 

45332 

57543 

24 

42457 

02874 

3 

97126 

23 

3^ 

14  56    45  4 

54702 

21 

45298 

57581 

24 

42419 

02879 

3 

97121 

22 

39 

14  48  1   45  12 

54735 

22 

45265 

57619 
9.57658 

25 
26 

42381 

02884 

3 

97116 

21.. 

40 

9  14  40  2  45  20 

9- 54769 

23 

10.45231 

10.42342 

10.  02889 

3 

9.97111 

20 

41 

14  32    45  28 

54802 

23 

45198 

57696 

26 

42304 

02893 

3 

97107 

19 

42 

14  24    45  36 

54836 

24 

45164 

57734 

27 

42266 

02898 

-1 

97102 

18 

43 

14  16 

45  44 

54869 

24 

45131 

57772 

28 

42228 

02903 

3 

97097 

17 

44 

14  8 

45  52 

54903 

25 

45097 

57810 

28 
29 

42190 

02908 

3 

97092 

lb 

45 

9  14  0  1  2  46  0 

9-  54936 

25 

10. 45064 

9-57849 

10. 4215 1 

10.02913 

4 

9.97087 

15 

4b 

13  52    46  8 

54969 

26 

45031 

57887 

30 

42113 

02917 

4 

97083 

14 

47 

13  44  1   46  16 

55003 

26 

44997 

57925 

30 

42075 

02922 

4 

97078 

13 

48 

13  36  j   46  24 

55036 

27 

.  44964 

57963 

31 

42037 

02927 

4 

97073 

12 

49 

50 

13  28  \      46  32 

55069 

28 

44931 

58001 

31 

41999 

02932 

4 

97068 

ir 

9  13  20  2  46  40 

9. 55102  28 

10.44898 

9- 58039 

32 

10.  4I961 

10.02937 

4 

9. 97063 

10 

^i 

13  12    46  48 

55136  29 

44S64 

58077 

33 

41923 

02941 

4 

97059 

9 

52 

13  4    46  56 

55169  29 

44831 

5811S 

33 

41885 

02946 

4 

97054 

8 

53 

12  56    47  4 

55202 

30 

44798 

58153 

34 

41847 

02951 

4 

97049 

7 

54 

12  48    47  12 

55235 

30 

44765 

58191 

35 

41809 

02956 

4 

97044 

b 

55 

9  12  40   2  47  20 

9. 55268 

31 

10. 44732 

9. 58229 

35 

IO.41771  j 

xo.  02961 

4 

9- 97039 

5 

5b 

12  32     47  28 

55301 

32 

44699 

58267 

36 

41733  1 

02965 

4 

97035 

4 

57 

12  24     47  36 

55334 

32 

44666 

58304 

37 

41696  1 

02970 

4 

97030 

5« 

12  16     47  44 

55367 

33 

44633 

58342 

37 

41658  I 

02975 

5 

97025 

2 

59 

12  8    47  52 

55400 

33 

44600 

58380 

38 

41620 

02980 

5 

97020 

I 

bo 

12   0 

48  o| 

55433 

34 

44567 

58418 

39 

41582 

02985 

5 

97015 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant,  j 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

110' 

> 

A 

A 

B 

B 

C 

C    69°  1 

Seconds  of  time 1     1' 

2» 

3- 

4, 

5» 

21 

24 
3 

()' 

7» 

(A   4 

Prop,  parts  of  cols.  -<  B   5 

(C   1 

8 
10 

1 

13 

2 

17 

2 

25 
29 

4 

30 

34 
4 

Page  428 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

21° 

A 

A 

B 

B 

C 

C   158° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

9  12  0 

2  48  0 

9-  55433 

0 

10.  44567 

9. 58418 

0 

10,41582 

ID.  02985 

0 

9.97015 

60 

I 

II  52 

48  8 

55466 

I 

44534 

58455 

I 

41545 

02990 

0 

97010 

59 

2 

II  44 

48  16 

55499 

I 

44501 

58493 

I 

41507 

02995 

0 

97005 

58 

'^ 
J 

II  36 

48  24 

55532 

2 

44468 

58531 

2 

41469 

02999 

0 

97001 

S7 

4 

II  28 

48  32 

55564 

2 

44436 

58569 

2 

4143I 

03004 

0 

96996 

56 

9  II  20 

2  48  40 

9-55597 

3 

10.44403 

9.  58606 

3 

10.41394 

10.  03009 

0 

9.96991 

55 

6 

II  12 

48  48 

55630 

3 

44370 

58644 

4 

41356 

03014 

0 

96986 

54 

7 

II   4 

48  56 

55663 

4 

44337 

58681 

4 

413I9 

03019 

96981 

53 

8 

10  56 

49  4 

55695 

4 

44305 

58719 

5 

41281 

03024 

96976 

S2 

9 

10  48 

49  12 

55728 

5 

44272 

58757 

6 

41243 

03029 

96971 

51 

10 

9  10  40 

2  49  20 

9-55761 

5 

10. 44239 

9- 58794 

6 

10.41206 

10. 03034 

9. 96966 

50 

II 

10  32 

49  28 

55793 

6 

44207 

58832 

7 

41 168 

03038 

96962 

49 

12 

10  24 

49  36 

55826 

6 

44174 

58869 

7 

4II31 

03043 

96957 

48 

1,3 

10  16 

49  44 

55858 

7 

44142 

58907 

8 

41093 

03048 

96952 

47 

H 

10  8 

49  52 

55891 

7 
8 

44109 

58944 

9 

41056 

03053 

96947 

46 

IS 

9  10  0 

2  50  0 

9- 55923 

10.  44077. 

9. 58981 

9 

10.  41019 

10.  03058 

9. 96942 

45 

i6 

9  52 

50  8 

55956 

9 

44044 

59019 

10 

40981 

03063 

96937 

44 

17 

9  44 

50  16 

55988 

9 

44012 

59056 

10 

40944 

03068 

96932 

43 

i8 

9  36 

50  24 

56021 

10 

43979 

59094 

II 

40906 

03073 

96927 

42 

19 

9  28 

_.5o_32 
2  50  40 

56053 

10 

43947 

59131 

12 

40869 

03078 

2 

96922 

41 

20 

9  9  20 

9. 56085 

II 

10.43915 

9.59168 

12 

10. 40832 

10.  03083 

2 

9.96917 

40 

21 

9  12 

50  48 

56118 

II 

43882 

59205 

13 

40795 

03088 

2 

96912 

39 

22 

9  4 

50  56 

56150 

12 

43850 

59243 

14 

40757 

03093 

2 

96907 

38 

2,S 

8  56 

51  4 

56182 

12 

43818 

59280 

14 

40720 

03097 

2 

96903 

37 

24 

8  48 

51  12 

56215 

13 

13 

43785 

59317 

15 

40683 

03102 

2 

96898 

36 

2S 

9  8  40 

2  51  20 

9.  56247 

10.43753 

9- 59354 

15 

10.  40646 

10.03107 

2 

9.  96893 

35 

26 

832 

51  28 

56279 

14 

43721 

59391 

16 

40609 

031 12 

2 

96888 

34 

27 

8  24 

51  36 

563" 

14 

43689 

59429 

17 

40571 

031 17 

2 

96883 

33 

28 

8  16 

51  44 

56343 

IS 

43657 

59466 

17 

40534 

03122 

2 

96878 

32 

29 

8  8 

51  52 

56375 

16 

43625 

59503 

18 

40497 
10. 40460 

03127 

2 

96873 

31 

30 

980 

2  52  0 

9. 56408 

16 

10. 43592 

9. 59540 

19 

10.  03132 

2 

9.  96868 

30 

31 

7  52 

52  8 

56440 

17 

43560 

59577 

19 

40423 

03137 

3 

96863 

29 

32 

7  44 

52  16 

56472 

17 

43528 

59614 

20 

40386 

03142 

3 

96858 

28 

33 

7  36 

52  24 

56504 

18 

43496 

59651 

20 

40349 

03147 

3 

96853 

27 

34 

7  28 

52  32 

56536 

18 
19 

43464 

59688 

21 

40312 

03152 

3 
3 

96848 

26 

3S 

9  7  20 

2  52  40 

9.  56568 

10. 43432 

9-  59725 

22 

10.40275 

10.03157 

9.  96843 

25 

3& 

7  12 

52  48 

56599 

19 

43401 

59762 

22 

40238 

03162 

3 

96838 

24 

37 

7  4 

52  56 

56631 

20 

43369 

59799 

23 

40201 

03167 

3 

96833 

23 

3!^ 

6  56 

53  4 

56663 

20 

43337 

59835 

23 

40165 

03172 

3 

96828 

22 

39 

6  48 

53  12 

56695 

21 

43305 

59872 

24 

40128 

03177 

3 

96823 

21 

40 

9  6  40 

2  53  20 

9-  56727 

21 

10.43273 

9- 59909 

25 

10.40091 

10.03182 

3 

9.96818 

20 

41 

632 

53  28 

56759 

22 

43241 

59946 

25 

40054 

03187 

3 

96813 

19 

42 

6  24 

53  36 

56790 

22 

43210 

59983 

26 

40017 

03192 

3 

96808 

18 

43 

6  16 

53  44 

56822 

23 

43178 

60019 

27 

39981 

03197 

4 

96803 

17 

44 

6  8 

53  52 

56854 

24 

43146 

60056 

27 

39944 

03202 

4 

96798 

16 

45 

960 

2  54  0 

9.  56886 

24 

10.  431 14 

9.  60093 

28 

10.  39907 

10.  03207 

4 

9-  96793 

15 

46 

5  52 

54  8 

56917 

2S 

43083 

60130 

28 

39870 

03212 

4 

96788 

14 

47 

5  44 

54  16 

56949 

25 

43051 

60166 

29 

39834 

03217 

4 

96783 

13 

48 

5  3b 

54  24 

56980 

26 

43020 

60203 

.30, 

39797 

03222 

4 

96778 

12 

49 

5  28 

54  32 

57012 

26 

42988 

60240 

30 

39760 

03228 

4 

96772 

II 

SO 

9  5  20 

2  54  40 

9-57044 

27 

10. 42956 

9.60276 

31 

10.  39724 

10.03233 

4 

9.  96767 

10 

51 

5  12 

54  48 

57075 

27 

42925 

60313 

31 

39687 

03238 

4 

96762 

9 

52 

5  4 

54  56 

57107 

28 

42893 

60349 

32 

39651 

03243 

4 

96757 

8 

.S3 

4  5^^ 

55  4 

57138 

28 

42862 

60386 

33 

39614 

03248 

4 

96752 

7 

54 

448 

55  12 

57169 

29 

42831 

60422 

33 

39578 

03253 

4 

96747 

6 

55 

9  4  40 

2  55  20 

9.57201 

29 

10.42799 

9- 60459 

34 

10.39541 

10.03258 

5 

9-  96742 

5 

5^ 

4  32 

55  28 

57232 

30 

42768 

60495 

3S 

39505 

03263 

5 

96737 

4 

57 

4  24 

55  36 

57264 

30 

42736 

60532 

35 

39468 

03268 

5 

96732 

3 

5« 

4  16 

55  44 

57295 

31 

42705 

60568 

36 

39432 

03273 

5 

96727 

2 

59 

4  8 

55  52 

57326 

32 

42674 

60605 

36 

39395 

03278 

5 

96722 

I 

60 

4  0 

56  0 

57358 

32 

42642 

60641 

37 
Diff. 

39359 

03283 

5 

96717 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

Ill 

0 

A 

A 

B 

B 

c 

C    68°  1 

Seconds  of  time 

1' 

2» 

3« 

4- 

5' 

«• 

!• 

Prop,  parts  of  cols.  <  H 

4 
5 

I 

8 

9 

I 

12 

14 
2 

16 

19 
2 

20 

23 

3 

24 
28 

4 

28 

32 

4 

TABLE  44. 

Page  429 

S'. 

» 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

22° 

M. 

A 

A 

B          B 

c 

C   1 

57° 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 
0 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 

940 

2  56  0 

9.57358 

10. 42642 

9.  60641 

0 

10.39359 

10.03283 

0 

9.96717 

60 

I 

3  52 

5f  f 

57389 

I 

4261 1 

60677 

I 

39323 

03289 

0 

96711 

59 

2 

3  44 

56  16 

57420 

I 

42580 

60714 

I 

39286 

03294 

0 

96706 

5^ 

,1 

3  36 

56  24 

57451 

2 

42549 

60750 

2 

39250 

03299 

0 

96701 

57 

4 

328 

56  32 

57482 

9-57514 

2 

~3' 

42518 

60786 

2 

39214 

03304 
10. 03309 

0 

96696 

56 

s 

9  3  20 

2  56  40 

10. 424S6 

9.  60823 

3 

10.39177 

0 

9.96691 

55 

0 

3  12 

5648 

57545 

3 

42455 

60859 

4 

39141 

03314 

96686 

54 

/ 

3  4 

50  5^ 

57576 

4 

42424 

60895 

4 

39105 

03319 

96681 

53 

8 

2  56 

57  4 

57607 

4 

42393 

60931 

5 

39069 

03324 

96676 

52 

9 

2  48 

57  12 

57638 

5 

42362 
10.42331 

60967 
9.61004 

5 
6 

39033 
10.  38996 

03330 
10.03335 

96670 
9.  96665 

51 

50 

10 

9  2  40 

2  57  20 

9.57669 

5 

II 

2  32 

57  28 

57700 

b 

42300 

61040 

7 

38960 

03340 

96660 

49 

12 

2  24 

57  36 

57731 

6 

42269 

61076 

7 

38924 

03345 

96655 

48 

1,3 

2  16 

57  44 

57762 

7 

42238 

61112 

8 

38888 

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38852 
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20 

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58  32 

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42053 

10. 42022 

61328 
9. 61364 

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12 

38672 

03381 

2 
2 

96619 
9.96614 

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40 

9  I  20 

2  58  40 

9.57978 

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10. 38636 

10.03386 

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58  48 

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13 

38600 

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2 

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56  8 

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30 

40842 

62750 

35 

37250 

03592 

5 

96408 

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56  0 

4  0 

59188 

31 

40812 

62785 
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36 

37215 

03597 
Cosecant. 

5 

Diff. 

96403 
Sine. 

0 
M. 

M. 

Hour  P.M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Diff. 

Tangent. 

112 

3 

A 

A 

B          B 

C 

C    67°  1 

Seconds  of  time. . 

1» 

2> 

3- 

4"  1  5» 

6< 

27 

31 
5 

Prop,  parts  of  cols. 

1^ 

4 
4 

I 

8 

9 

I 

II 

13 

2 

IS    19 

18  -1  22 

3     3 

23 
27 

4 

Page  430 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

23° 

M. 
0 

A 

A 

B 

B 

c 

C   l.>«° 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

60 

8  56  0 

340 

9.59188 

0 

10.40812 

9.62785 

0 

10.37215 

10.03597 

0 

9.  96403 

I 

's  52 

4  8 

59218 

0 

!      40782 

62820 

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37180 

03603 

0 

96397 

59 

2 

55  44 

4  16 

59247 

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40753 

62855 

I 

37145 

03608 

0 

96392 

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55  36 

4  24 

59277 

I 

40723 

62890 

2 

37110 

03613 

0 

96387 

S7 

4 

55  28 
8  55  20 

4  32 

59307 

2 

2 

40693 
10.40664 

62926 

2 

37074 

03619 

0 

96381 

50 

3  4  40 

9-  59336 

9.  62961 

3 

10. 37039 

10.  03624 

0 

9.96376 

ss 

6 

55  12 

448 

59366 

3 

40634 

62996  !  3 

37004 

03630 

96370 

S4 

7 

55  4 

4  56 

59396 

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40604 

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36969 

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96365 

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8 

54  56 

5  4 

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4 

40575 

63066  :    5 

36934 

03640 

96360 

52 

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10 

54  48 

8  54  40 

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4 
5 

40545 
10.40516 

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36899 
10.  36865 

03646 

96354 

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3  5  20 

9.  59484 

10.03651 

9-  96349 

50 

II 

54  32 

5  28 

59514 

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4O4S6 

63170   6 

3*^830 

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40 

12 

54  24 

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96338 

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13 

54  i(> 

5  44 

59573  ,  6 

40427 

63240      7 

36760 

03667 

96333 

47 

14 
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54  8 
8  54  0 

5  52 
360 

59602  :    7 
9-  59632      7 

40398 

10.40368 

63275  1  8 
9.63310  1  9 

36725 
10.  36690 

03673 



96327 

46 

10.03678 

9.  96322 

4S 

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53  52 

6  8 

59661   8 

4"339 

63345   9 

36655 

03684 

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44 

17 

53  44 

6  16 

59690   8 

40310 

63379  10 

36621 

03689 

2 

963 1 1 

43 

i8 

53  36 

6  24 

59720  ;    9 

40280 

63414  10 

36586 

03695 

2 

96305 

42 

J9_ 

20 

5328 
8  53  20 

6  32 

59749 

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ID 

40251 

63449  1 1 

36551 

03700 

2 

2 

96300 
9.  96294 

41 

40 

3  6  40 

9.  59778 

10. 40222 

9. 63484  12 

10. 36516 

10.  03706 

21 

53  12 

6  48 

59808  10 

40192 

63519  12 

36481 

03711 

2 

96289 

39 

22 

53  4 

6  56 

59S37  II 

40163 

63553   13 

36447 

03716 

2 

96284 

38 

2^ 

52  56 

7  4 

59866  1  II 

40134 

63588 

13 

36412 

03722 

2 

96278 

37 

24 
2^ 

52  48 
8  52  40 

7  12 

3  7  20 

59895 
9- 59924 

12 

40105 

63623 

14 

36377 

03727 

2 

96273 

36 

12 

10.40076 

9-63657 

14 

10. 36343 

10.03733 

2 

9.96267 

35 

26 

52  3- 

728 

59954 

13 

40046 

63692 

15 

3630S 

03738 

2 

96262 

34 

27 

52  24 

736 

59983 

13 

40017 

63726 

16 

36274 

03744 

2 

96256 

33 

2S 

S2  16 

7  44 

60012 

14 

39988 

63761 

16 

36239 

03749 

3 

96251 

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29 

30 

52  8 
8  52  0 

7  52 

60041 

14 

39959 

63796 

17 
17 

36204 

03755 

3 

96245 

31 

3  8  0 

9.  60070 

IS 

10.  39930 

9. 63830 

10.36170 

10.03760 

3 

9.  96240 

30 

31 

51  52 

8  8 

60099 

IS 

39901 

63865   18 

36135 

03766 

3 

96234 

29 

32 

51  44 

8  16 

60128 

15 

39872 

63899  '  18 

36101 

03771 

3 

96229 

28 

0  T 

51  36 

824 

60157 

16 

39843 

63934  '  19 

36066 

03777 

3 

96223 

27 

34 

3S 

51  28 

832 
3  8  40 

60186 
9.  60215 

16 

39814 

63968  20 

36032 

03782 

3 

96218 

26 

8  51  20 

17 

10.  39785 

9.64003  1  20 

10.35997 

10.  03788 

3 

9.96212 

25 

3t> 

51  12 

8  48 

60244 

17 

39756 

64037  1  21 

35963 

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3 

96207 

24 

37 

51  4 

8  56 

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18 

39727 

64072  ;  21 

35928 

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3 

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50  56 

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60302 

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39698 

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35894 

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3 

96196 

22 

39 
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50  48 
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9  12 

60331 

19 

39669 
10.39641 

64140   22 

35860 

03810 

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96190 

21 

3  9  20 

9-  60359 

19 

9-64175 

23 

10.  35825 

10.03815 

9.96185 

20 

41 

53  32 

9  28 

60388 

20 

39612 

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24 

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03821 

4 

96179 

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50  24 

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39583 

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39554 

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25 

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17 

44 
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50  8 
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21 

39526 

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4 
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96162 
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3  10  0 

9.  60503 

22 

10.  39497 

9.  64346 

10.35654 

10.  03843 

46 

49  52 

10  8 

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22 

39468 

64381   26 

35619 

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4 

96151 

14 

47 

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10  16 

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23 

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13 

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4 

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12 

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10  32 

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9. 60646  24 

10.39354 

9.64517  I  29 

lo-  35483 

10.  03871 

s 

9.96129 

10 

SI 

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96123 

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52 

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26 

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27 

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29 

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5 

96079 

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^0 

48  0 

12  0 

60931 

29 

39069 

64858 

35 

35142 

03927 

6 

96073 

0 

M. 

Hour  I'.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

113^ 

) 

A 

A 

B 

B 

C 

c      m'\ 

Seconds  of  time 

1» 

2» 

3» 

4,    5. 

«» 

7» 

Prop,  parts  of  cols.  <   H 

4 

4 

I 

7 
9 
I 

II 

13 
2 

IS    18 
17    22 

3     3 

22 

26 

4 

25 

31 

5 

TABLE  44. 

Page  431 

S'. 

» 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

24= 

A 

A 

B 

B 

C 

C 

155° 

Hour  A.M. 

Hour  I'.  M. 

Sine. 

Diff 

Cosecant. 

Tangent. 

Diff 

Cotangent. 
10.35142 

Secant. 

10.  03927 

Diff 
0 

Cosine. 

M. 
60 

11 

cS  48   0 

3120 

9.60931 

0 

10.  39069 

9. 64858 

0 

9.96073 

I 

47  52 

12   S 

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0 

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9. 95960 

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3 

95897 

29 

32 

43  44 

16  16 

61S28  , 

15 

38172 

65937  1  18 

34063 

04109 

3 

95891 

2S 

43  36 

16  24 

61856 

15 

38 1 44 

65971   18 

34029 

041 15 

3 

95885 

27 

34 

43  28 

16  32 

61883 

16 

38117 

66004  19 

33996 

04121 

3 

95879 

26 

35 

8  43  20 

3  16  40 

9.61911   16 

10.  38089 

9. 66038 

20 

10.  33962 

10.  04127 

3 

9-  95873 

25 

3'^ 

43  12 

16  48 

61939  17 

38061 

66071 

20 

33929 

04132 

3 

95868 

24 

37 

43  4  ' 

16  56 

61966   17 

38034 

66104  '  21 

33896 

04138 

4 

95862 

2^ 

3« 

42  56 

17  4 

61994 

18 

38006 

66138  21 

33862 

04144 

4 

95856 

22 

_39__ 

40 

42  48 

17  12 

62021 

18 

37979  1 

66171  22 

33829 

04150 
10.04156 

4 

95850 

21 

20 

8  42  40 

3  17  20 

9. 62049 

18 

10.37951 

9. 66204  22 

10.33796 

4 

9.  95844 

41 

42  32 

17  28 

62076  19 

37924 

66238  23 

33762 

04161 

4 

95839 

19 

42 

42  24 

17  36 

62104 

19 

37896 

66271  23 

33729 

04167 

4 

95833 

18 

43 

42  16 

17  44 

62131 

20 

37869 

66304  24 

33696 

04173 

4 

95827 

17 

44 

42  8  1 

17  52 

62159 

20 

37841 

66337 

25  1 

25'! 

33663 

04179 

4 

95821 

16 

45 

8  42  0  : 

3  18  0 

9.62186  j  21 

10.37814 

9.66371 

10.  33629 

10.04185 

4 

9.95815 

15 

40 

41  52 

18  8 

62214  21 

37786 

66404  ,  26 

33596 

04190 

4 

95810 

14 

47 

41  44 

18  16 

62241  22 

37759 

66437  :  26 

33563 

04196 

5 

95804 

13 

4S 

41  3'3 

18  24 

62268  22 

37732 

66470  !  27 

33530 

04202 

5 

95798 

12 

49 
50 

41  28 

18  32 

62296  23 

37704 

66503  !  27 

33497 

04208 

S 

95792 

II 

8  41  20 

3  18  40 

9.62323  i  23 

10.37677 

9.66537  i  28 

10. 33463 

10.04214 

5 

9-95786 

10 

51 

41  12 

18  48 

62350  24 

37650 

66570    28  ' 

33430 

04220 

5 

95780 

9 

52 

41  4 

iS  56 

62377 

24 

37623 

66603  1 

29  ! 

33397 

04225 

5 

95775 

8 

53 

40  56 

19  4 

62405 

24 

37595 

66636 

30 

33364 

04231 

5 

95769 

7 

54 

40  48 

19  12 

62432 

25 

37568 

66669 

30 

33331 

04237 

5 

95763 

6 

5 

55 

8  40  40 

3  19  2; 

9-62459  i 

25 

10.  37541 

9.66702  i 

31 

10.  33298 

10.  04243 

5 

9-95757 

5'^ 

40  32 

19  28 

62486  :  26 

37514 

66735 

31 

33265 

04249 

5 

95751 

4 

57  i 

40  24 

19  36 

62513  j  26 

37487 

66768 

32 

33232 

04255 

5 

95745 

5-^ 

40  16 

19  44 

62541  27 

37459 

66801 

32 

33199 

04261 

6 

95739 

2 

59 

40  8 

19  52 

62568  27 

37432 

66834 

33 

33166 

04267 

6 

95733 

I 

60  3 

M.  j 

40  0 

20  0 

62595  1  28 

37405 

66867 

33 

.  33133 

04272 

6 

95728 

0 
M. 

Hour  p.  M. 

Hour  A.M. 

Cosine.   Diff. 

Secant. 

Cotangent.!  Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

114° 

A 

A 

B 

B 

C 

C    65°  1 

Seconds  of  time. . 

I' 

3 

4 

I 

2' 

3" 

4. 

5' 

B' 

7' 

Prop,  parts  of  cols. 

I 

7 
8 

I 

10 

2 

14 

3 

17 
21 

4 

21 

4 

24 
29 

S 

Page  432 

S'. 
25° 

A 

TABLE  44. 
Log.  Sines,  Tangents,  and  Secants. 
A       B          B 

C 

G'. 
C   154° 

M. 

HourA.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diflf. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 

I 

2 

3 
4 

8  40  0 
39  52 
39  44 
39  36 
3928 

3  20  0 
20  8 
20  16 
20  24 
20  32 

3  20^40" 
20  48 

20  56 

21  4 
21  12 

9.  62595 
62622 
62649 
62676 
62703 

9. 62730 

62757 
62784 
628 1 1 
62838 

0 
0 

I 
I 

2 
2 
3 

3 
4 
4 

10.  37405 
37378 
37351 
37324 
37297 

9. 66867 
66900 

66933 
66966 

66999 

0 
I 
I 
2 
2 

10.33133 
33100 
33067 

33034 
33001 

10.04272 
04278 
04284 
04290 
04296 

0 
0 
0 
0 
0 

9.95728 
95722 
95716 
95710 
95704 

9.  95698 
95692 
956S6 
95680 
95674 

60 

5'» 

5^ 
57 
5" 

I 

7 
8 

9 

8  39  20 
39  12 
39  4 
3856 
3848 

10.  37270 

37243 
37216 

37189 
37162 

9.  67032 
67065 
67098 

67131 
67163 

3 
3 
4 
4 
5 

10. 32968 

32935 
32902 

32869 
32837 

10.  04302 
04308 

04314 
04320 
04326 
10.04332 
04337 
04343 
04349 
04355 

55 
54 
53 
5- 
5' 

lO 

II 

12 

13 
14 

15 
16 

17 
18 

19 

8  38  40 
3832 
38  24 
38  16 
38  8 
"8  38^0 
37  52 
37  44 
37  36 
37  28 

^  21  20 
21  28 

21  36 
21  44 
21  52 

9.  62865 
62892 
62918 
62945 
62972 

4 
5 
5 
6 
6 

10.37135 

37108 

37082 

37055 
37028 

9.67196 
67229 
67262 

67295 
67^.27 

5 
6 

7 
7 
8 

10. 32804 

32771 
32738 
32705 
32673 

9.  95668 
95663 
95657 
95651 
95645 

5'"' 
4<J 
48 

47 
46 

3  22   0 
22   8 
22  16 
22  24 
22  32 

9.  62999 
63026 
63052 
63079 
63106 

7 
7 
8 
8 
8 

10.37001 

36974 
36948 
36921 
36894 

9.  07360 

67393 
67426 

67458 
67491 

8 

9 

9 

10 

10 

10.32640 
32607 

32574 
32542 
32509 

10.  04361 
04367 
04373 
04379 
04385 

10.  04391 

04397 
04403 
04409 

04415 

2 
2 
2 
2 
2 

9-  95639 

95633 
95627 
95621 

95615 

45 
44 
43 
42 
41 

20 
21 
22 

23 
24 

8  37  20 
37   12 
37    4 
3656 
36  48 

3  22  40 
22  48 

22  56 

23  4 

23  12 

9-  63133 

63213 
63239 

9 

9 

10 

10 

II 

10.  36867 
36841 
36814 
36787 
36761 

9.  67524 

67556 

67589 
67622 

67654 

II 
II 
12 
12 

13 

10. 32476 

32444 
324 II 

32378 

32346 

2 

2 
2 

2 

2 

9. 95609 
95603 
95597 
95591 
95585 

40 
39 

38 
37 
36 

25 
26 

'^ 

29 

30 
31 

32 
33 
34 

35 
36 
37 
38 
39 
40 

41 
42 

43 
44 

45 
46 

47 
48 

49 
50 
51 

52 
53 

54 

5| 
56 

57 
58 

59 
60 

8  36  40 
36  32 
36  24 
36  16 
36  8 

3  23  20 
23  28 

23  36 
23  44 
23  52 

9. 63266 
63292 
63319 
63345 
63372 

II 
II 
12 
12 
13 

10. 36734 

36708 
36681 

36655 
36628 

9. 67687 
67719 
67752 
67785 
67817 

14 

14 

15 

15 
16 
16 
17 
17 
18 
18 

10.32313 
32281 

32248 

32215 
32183 

10.32150 

32II8 

32085 

32053 

32020 

10.04421 
04427 

04433 
04439 
04445 

10.04451 

04457 
04463 
04469 

04475 

3 

3 

3 
3 
3 

9-95579 
95573 
95567 
95561 
95555 

35 
34 
33 
32 

_3' 

30 
29 
28 

27 
26 

8  36  0 

35  52 
35  44 
35  36 
35  28 

3  24  0 

24  8 
24  16 
24  24 
24  32 

9- 63398 
63425 
63451 
63478 
63504 

13 
14 
14 
IS 
15 

10. 36602 

36575 
36549 
36522 
36496 

9.  67850 
67882 
67915 
67947 
67980 

3 
3 
3 
3 
3 

9-  95549 

95543 
95537 
95531 
95525 

8  35  20 
35  12 
35  4 
34  56 
34  48 

3  2440 
24  48 

24  56 

25  4 
25  12 

9-  63531 
63557 

63610 
63636 

15 
-16 

16 
17 
17 
18 
18 
19 
19 
19 

10. 36469 

36443 
36417 
36390 

36364 
10. 36338 

363 1 1 

36285 

36259 
36233 

9.  68012 
68044 
68077 
68109 
68142 

19 
20 

20 

21 

21 

10.  31988 

31956 

31923 
3I89I 

31858 

10.04481 
04487 

04493 
04500 
04506 

4  !  9-95519 

4  1   95513 
4    95507 
4  1   95500 
4  !   95494 

25 
24 
23 
22 
21 

8  34  40 
34  32 
34  24 
34  16 
34  8 

8  34  0 
33  52 
33   44 
33   36 
33   28 

8  33  20 
33  12 
33  4 
32  56 
32  48 

3  25  20 
25  28 
25  36 
25  44 
25  52 

9. 63662 

63689 

63715 
63741 
63767 

9.68174 
68206 
68239 
68271 
68303 

22 
22 

23 
23 
24 

10.31826 

31794 
3I76I 
31729 
31697 

10.  04512 
04518 
04524 
04530 
04536 

4 

4 
4 
4 
4 

9.  95488 
95482 
95476 
95470 
95464 

20 

19 
iS 

17 
16 

3  26  0 
26  8 
26  16 
26  24 
26  32 

9- 63794 
63820 
63846 
63872 
63898 

20 
20 
21 
21 
22 

10. 36206 

36180 

36154 
36128 

36102 

9. 68336 
68368 
68400 
68432 
68465 

24 
25 

26 

27 

10.31664 

31632 

31600 

31568 
31535 

10.  04542 
04548 

04554 
04560 
04566 

5 
5 
5 
5 
5 
5 
5 
5 
5 
5 

9-  95458 
95452 
95446 
95440 
95434 

IS 

14 
13 

12 

n 

3  26  40 
26  48 

26  56 

27  4 
27  12 

9.  63924 

63950 
63976 
64002 
64028 

22 

23 

23 

23 
24 

10.  36076 
36050 
36024 

35998 
35972 

9. 68497 
68529 
68561 

68593 
68626 

27 
28 
28 

29 
29 

10.31503 
3I47I 
31439 
31407 
31374 

10.04573 

04579 
04585 
04591 

04597 

9- 95427 
95421 
95415 
95409 
95403 

10 

9 

S 

7 
6 

8  32  40 
32  32 
32  24 
32  16 
32  8 
32  0 

3  27  20 
27  28 
27  36 

27  44 

27  52 

28  0 

9.  64054 
64080 
64106 
64132 
64158 
64184 

24 
25 

^I 
26 

26 

26 

10. 35946 
35920 

35894 
35868 
35842 

35816 

9.  68658 
68690 
68722 

68754 
68786 

68818 

30 
30 
31 
31 
32 
33 

10.31342 
3I3IO 
31278 

31246 
3I2I4 
3II82 

10.04603 
04609 
04616 
04622 
04628 
04634 

6 
6 
6 
6 
6 
6 

9-  95397 
95391 
95384 
953  78 
95372 
95366 

5 

4 

3 
2 

I 
0 

M. 

Hour  p.  M. 

HourA.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

115 

0 

A 

A 

R 

B 

C 

C    64°  1 

Seconds  of  time 

1» 

2»    3» 

4s 

5'  1  «» 

T 

Prop,  parts  of  cols.K  B 

3 
4 

I 

7 
8 

2 

10 

12 

2 

?6 

3 

17 
20 

4 

20 

24 

5 

23 

1 

i 


TABLE  44- 

Page  433 

S'. 

> 

Log 

.  Sines,  Tangents,  and  Secants. 

G'. 

2<5° 

A 

A 

R 

B 

C 

C   153° 

M. 

Hour  A.  M. 

Hour  r.  m. 

Sine. 

Diff. 

Cosecant.  | 

Tangent.  Diflf. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

S  32  0 

3  28  0 

9.  64184 

0 

10.  S5816 

9.68818 

0 

IO.31182 

10.04634 

0 

9. 95366 

60 

I 

31  52 

28  8 

64210 

0 

35790 

68850 

I 

31150 

04640 

0 

95360 

59 

2 

31  44 

28  16 

64236 

I 

35764 

6S882 

I 

31118 

04646 

0 

95354 

58 

] 

3'  36 

28  24 

64262    I 

35738 

68914 

2 

31086 

04652 

0 

95348 

57 

4 

31  28 

28  32 

64288  ;  2 

35712 

68946 

2 

31054 

04659_ 

0 

95341 

56 

S 

8  31  20 

3  28  40 

9-64313    2 

10.35687 

9. 68978 

3 

10.31022 

10.04665 

9-  95335 

55 

0 

31  12 

28  48 

64339   3 

35661 

69010 

3 

30990 

04671 

95329 

54 

7 

31  4 

28  56 

64365   3 

35635 

69042 

4 

30958 

04677 

95323 

53 

S 

30  56 

29  4 

64391   3 

35609 

69074 

4 

30926 

04683 

I      95317  1 

52 

9 

3048 

29  12 

64417   4 

35583 

69106 

-  5 

30894 
10.  30862 

04690 

95310 

51 

lO 

8  30  40 

3  29  20 

9. 64442   4 

10.35558 

9.69138 

5 

10. 04696 

9- 95304 

50 

1 1 

30  32 

29  28 

64468   5 

35532 

69170   6 

30830 

04702 

95298 

49 

12 

30  24 

29  36 

64494 

S 

35500 

69202  !  6 

30798 

04708 

95292 

48 

I'-, 

30  16 

29  44 

64519 

5 

35481 

69234   7 

30766 

04714 

95286 

47 

14 

30  8 

29  52 

64545 

6 

35455 

69266   7 

30734 

04721 

95279 

40 

IS 

8  30  0 

3  30  0 

9-64571 

6 

10.35429 

9. 69298   8 

10. 30702 

10. 04727 

2 

9-95273 

45 

lb 

29  52 

30  8 

64596 

/ 

35404 

69329   8 

30671 

04733 

2 

95267 

44 

I? 

29  44 

30  16 

64622 

7 

35378 

69361  i  9 

30639 

04739 

2 

95261 

43 

i8 

29  36 

30  24 

64647 

8 

35353 

69393   9 

30607 

04746 

2 

95254 

42 

19 

29  28 

30  32 

64673 

8 
8 

35327 
10.  35302 

69425   10 
9.69457  1  II 

30575 
10. 30543 

04752 

2 

95248 

41 

20 

8  29  20 

3  30  40 

9. 64698 

10.04758 

2 

9- 95242 

40 

21 

29  12 

30  48 

64724 

9 

35276 

69488  '   II 

30512 

04764 

2 

95236 

^2 

22 

29  4 

30  56 

64749 

9 

35251 

69520  1  12 

30480 

04771 

2 

95229 

38 

2^. 

2856 

31  4 

f'4775 

10 

35225 

69552 

12 

30448 

04777 

2 

95223 

37 

24 

28  4'. 

31  12 

64800 

10 

35200 

69584 

13 

30416 

04783 

3  i   95217  1 

36 

2S 

8  28  40 

3  31  20 

9. 64826 

II 

10.35174 

9.69615 

13 

10. 30385 

10.  04789 

3 

9.  9521 1 

35 

26 

28  32 

31  28 

64851 

II 

35149 

69647 

14 

30353 

04796 

3 

95204 

34 

27 

28  24 

31  36 

64S77 

II 

35123 

69679 

14 

30321 

04802 

3 

95198 

33 

28 

28  16 

51  44 

64902 

12 

35098 

69710 

i.S 

30290 

04808 

3 

95192 

32 

29 

28  8 

31  52 

64927 

12 

35073 

69742 

15 

30258 

04815 

3 

95185 

31 

so 

8  28  0 

3  32  0 

9- 64953 

13 

10. 35047 

9.69774  j  16 

10. 30226 

10.04821 

3 

9.95179 

30 

V 

27  52 

32  8 

64978 

13 

35022 

69805   16 

30195 

04^27 

3 

95173 

29 

0" 

27  44 

32  16 

65003 

14 

34997 

69837   17 

30163 

04833 

3    95167 

28 

Vi 

27  36 

j2  24 

65029 

14 

34971 

69868  ,  17 

30132 

04840 

3  •      95160 

27 

34 

27  28 

32  32 

65054 

14 
15 

34946 
10. 34921 

69900  i  18 
9.69932   18 

30100 
10. 30068 

04846 
10.04852 

4    95154 

2b 

,iS 

8  27  20 

3  32  40 

9-  65079 

4 

9.95148 

25 

S6 

27  12 

32  48 

65104 

IS 

34896 

69963   19 

30037 

04859 

4 

95141 

24 

S7 

27  4 

32  56 

65130 

16 

34870 

69995  20 

30005 

04865 

4 

95135 

23 

S8 

26  56 

33    4 

65155 

16 

34845 

70026  20 

29974 

04871 

4 

95129 

22 

39 

26  48 

33   12 

65180 

16 
17 

34820 
10.34795 

70058  21 
9.  70089  21 

29942 

10. 29911 

04878 
1 0. 04884 

4 

95122 

21 

40 

8  26  40 

3  33   20 

9. 65205 

4 

9.95116 

20 

4! 

26  32 

33   28 

65230 

17 

34770 

70121   22 

29879 

04890 

4 

95110 

19 

42 

26  24 

33  36 

65255 

18 

34745 

70152  22 

29848 

04897 

4 

95103 

18 

4^ 

26  16 

33   44 

65281 

18 

34719 

70184  23 

29816 

04903 

5 

95097 

17 

44 

26  8 

33  52 

65306 

19 

19 

34694 

70215  23 

29785 

04910 

5 

95090 

16 
15 

4> 

8  26  0 

3  34  0 

9-65331 

10.  34669 

9.  70247  24 

10.29753 

10.04916 

5 

9- 95084 

4'' 

25  52 

34  8 

65356 

19 

34644 

70278  24 

29722 

04922 

5 

95078 

14 

47 

25  44 

34  16 

65381 

20 

34619 

70309  25 

29691 

04929 

5 

95071 

13 

4S 

25  36 

34  24 

65406 

20 

34594 

70341  '   25 

29659 

04935 

5 

95065 

12 

49 
S" 

25  28 

8  25  20 

34  32 

65431 

21 
21 

34569 

70372 

26 

26 

29628 
10. 29596 

04941 

5 

95059 

II 

3  34  40 

9-  65456 

10.34544 

9- 70404 

10. 04948 

5 

9.  95052 

10 

SI 

25  12 

34  48 

65481 

22 

34519 

70435  27 

29565 

04954 

5 

95046 

9 

S2 

25  4 

34  56 

65506 

22 

34494 

70466  27 

29534 

04961 

5 

95039 

8 

s^^ 

24  56 

35  4 

65531   22 

34469 

70498  28 

29502 

04967 

6 

95033 

7 

54 

ss 

2448 

35  12 

65556  23 

34444 

70529  i  28 

29471 

_°4973_ 
10.04980 

b 

6 

95027 

b 

8  24  40 

3  35  20 

9. 65580 

23 

10.34420 

9.  70560  29 

10. 29440 

9-  95020 

5 

.S6 

24  32 

3528 

65605 

24 

34395 

70592  30 

29408 

04986 

6 

95014 

4 

S7 

24  24 

35  3^ 

65630 

24 

34370 

70623 

30 

29377 

04993 

6 

95007 

3 

S'^ 

24  16 

35  44 

65655 

2S 

1    34345 

70654 

31 

29346 

04999 

6 

95001 

2 

SO 

24  8 

35  52 

65680 

25 

34320 

70685 

31 

29315 

05005 

6 

94995 

1 

60 
M. 

116 

24  0 

36  0 

65705 

25 

34295 

70717 

32 

29283 

05012 

6 

9498S 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

0 

A 

A 

B 

B 

C 

C    63°  1 

3S    B 


Secoiuls  of  time 

1" 

2' 

3' 

4' 

3 

5» 

16 
20 

4 

24 

5 

7» 

22 

28 
6 

(A 
Prop,  parts  of  cols.  <  B 

(c 

3 
4 

I 

6 

8 

10 

12 

2 

I 


Page  434 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

2:° 

A 

A 

B 

B 

C 

C 

152° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difr. 

Cotangent. 

Secant. 

Diff 

Cosine. 

M. 

0 
I 

2 

4 

S  24  0 
23  52 
23  44 
23  36 
23  28 

1  3  36  0 
36  8 

I   36  16 
36  24 

3632 

3  36  40 

36  48 
3656 

37  4 
37  12 

9.65705 

65729 

65754 

65779 
65804 

9.  65828" 

65853 
65878 
65902 
65927 

0 

0 

I 

I 

2 

2. 

2 

I 

10.  34295 
.34271 
34246 

34221 
34196 

9.70717 
70748 
70779 
70810 
70841 

0 

I 

I 

2 

2 

10.  29283 
29252 
29221 
29190 

29159 

10.  05012 
05018 

05025 
05031 
05038 

0 
0 
0 
0 
0 

9.  94988 
949S2 

94975 
'   94969 

!    94962 

9-94956" 
94949 

94943 
94936 
94930 

9-  94923 
94917 
94911 

94904 
94898 

60 

59 

57 
5'' 
55 
54 
53 
52 
51 
50 

49 
48 

47 
46 

45 
44 
43 
42 
41 

1 

7 
8 

9 

8  23  20 
23  12 
23  4 
22  56 
22  48 

10.34172 

34147 
34122 
34098 

34073 

9.  70873 
70904 

70935 
70966 

70997 

3 

3 
4 
4 

5 

5 
6 
6 

7 
7 
8 
8 
9 
9 
10 

10. 29127 
29096 
29065 

29034 
29003 

10. 28972 

28941 

28910 

28879 
28847 

10.05044 

05051 
05057 

05064 
05070 

10 
II 

12 

13 
H 

15 

16 

17 
18 

19 

8  22  40 
22  32 
22  24 
22  16 
22  8 

8  22  0 
21  52 
21  44 
21  36 
21  28 

3  37  20 
37  28 
37  3^ 
37  44 
37   52 

y-  65952 
65976 
66001 
66025 
66050 

4 
4 

'  5 

i 

6 
6 

7 

7 
8 

10.  34048 

34024 

33999 
33975 
33950 

10.  33925 
33901 
33876 
33852 
33827 

9.  71028 

71059 
71090 

71121 

71153 

9.  71 184 
71215 
71246 
71277 
71308 

10.  05077 
05083 
05089 
05096 
05102 

2 

3  38  0 
38  8 
38  16 
38  24 
38  32 

9. 66075 
66099 
66x24 
66148 
66173 

10.28816 

28785 

28754 
28723 
28692 

10. 05109 

05II5 

05122 
05129 

05135 

2 
2 
2 
2 
2 

9.  94891 
94885 
94878 
94871 
94865 

20 
21 
22 

23 
24 

25 
2b 

27 
28 

29 
30 
31 

32 

34 

35 

3' 

M 

3^ 

39_ 

40 

41 
42 
43 
44 

8  21  20 
21  12 
21  4 
20  56 
20  48 

8  20  40 
20  32 
20  24 
20  16 
20  8 

8  20  0 

19  52 
19  44 

19  36 
19  28 

8  19  20 
19  12 
19  4 
18  56 
18  48 

3  38  40 
38  48 

38  56 

39  4 
39  12 

9.66197 
66221 
66246 
66270 
66295 

8 
8 

9 
9 

ID 

lo.  33803 
33779 
33754 
33730 
33705 

9-  71339 
71370 
71401 

71 43 1 
71462 

10 
II 
II 
12 
12 

10. 28661 
2S630 

28599 

28569 

_____  28538 

10. 28507 

28476 

28445. 
28414 

28383 

10.  28352 

28321 

28291 

28260 

28229 

10.  28198 

2SI67 
28137 

28106 

28075 

10.  28045 
28014 

27983 

27952 

27922 

10.05142 

05148 

05155 

05161 

05168 

10.  051747 
05IS1 

05187 
05194 

05201 

10.  05207 

05214 

05220 

05227 

_o53_3_ 
10.  05240 

05247 

05253 
05260 
05266 

2 
2 
2 
3 
3' 

9.  94858 
94852 
94845 
94839 
94832 

40 
39 
38 
37 
36 

35 
34 
33 
32 
31 
30 

29 

28 

27 
26 

3  39  20 
39  28 
39  3'' 
39  44 
39  52 

9.66319 

66343 
66368 
66392 
66416 

10 
II 
II 
II 
12 

10.  33681 

33657 
33632 
33608 

33584 

9-  71493 
71524 
71555 
71586 
71617 

13 

13 
14 
14 
15 

11 

16 
17 
17 
18 
19 
19 
20 
20 
21 
21 
22 
22 
23 

3 
3 
3 
3 
3 
3 
3 
4 
4 
4 

4 
4 
4 
4 
4 

9.  94826 
94819 

94813 
94806 

94799 

9-  94793 
94786 
94780 

94773 
94767 

3  40  0 
40  8 
40  16 
40  24 
40  32 

3  40  40 
40  48 

40  56 

41  4 
41  12 

9. 66441 
66465 
66489 
66513 
66537 

12 
13 
13 
13 

H 

10.33559 
33535 
335 1 1 
33487 
33463 

9.  71648 
71679 
71709 
71740 
71771 

9. 66562 
66586 
66610 
66634 
66658 

14 
IS 
IS 

10. 33438 
33414 
33390 
33366 
33342 

9.  71802 

71833 
71863 
71894 
71925 

9.  94760 

94753 
94747 
94740 
94734 

25 
24 

23 
22 

21 

20 

19 

18 

17 
16 

15 
14 

13 
12 

u 

8  18  40 

1832 
18  24 
18  16 
18  8 

3  41  20 

41  28 

41  36 

41  44 

41  52 

9. 66682 
66706 
66731 

^^755 
66779 

16 

17 
17 
17 
18 

10.33318 
33294 
33269 

33245 
33221 

9-  71955 
71986 
72017 
72048 
72078 

10.05273 
05280 
05286 

05293 
05300 

4 

4 
5 
5 
5 
5 
5 
5 
5 
5 

9.94727 

94720 

94714 

94707 

94700 

9- 94694 
94687 
94680 
94674 
94667 

45 
4' 
47 
48 

49 

8  18  0 

17  52 
17  44 
1736 
17  28 

3  42  0 
42  8 
42  16 
42  24 
42  32 

9. 66803 

66827 
66851 
66875 
66899 

18 
19 
19 
19 
20 

20 

21  { 

21  : 

21 

22 

10.33197 
33173 
33149 
33125 
33  loi 

9.  72109 
72140 
72170 
72201 
72231 

23 

24 

24 
25 
25 

ID. 2  78qi 

27860 
27830 
27799 
27769 

10.  05306 

05313 
05320 
05326 

05333 

50 
51 
52 

53 
54 

8  17  20 
17  12 

17  4  i 
16  56 
16  48 

3  42  40 
42  48 

42  56 

43  4 
43  12 

9.  66922 
66946 
66970 
66994 
67018 

10.33078 

33054 
33030 
33006 
32982 

9.  72262 

72293 
72323 
72354 
72384 

26 
26 
27 
27 
28 

10.27738 

27707 
27677 

27646 
27616 

10.27585 

27555 
27524 
27494 

27463 
27433 

10.  05340 

05346 

05353 
05360 

05366 

1 

6 
6 
6 

9.  94660 

94654 
94647 
94640 
94634 

10 

7 
6 

55 
5'^ 
57 
58 

59  i 

60  1 

8  16  40 
1632 
16  24 
16  16 
16  8 
16  0 

3  43  20 
43  28 
43  36 

43  44 

43  52 

44  0 

9. 67042 
67066 
67090 
67113 

67137 
67161 

22 

23 
23 

23 
24 

24 

10.  32958 

32934 
32910 

32887 

32863 

32839 

9.  72415 

72445 
72476 
72506 

72537 
72567 

28 
29 
29 
30 
30 
31 

10.05373 
05380 
05386 

05393 
05400 

05407 

6 
6 
6 
6 
6 
7 

9.94627 
94620 
94614 
94607 
94600 

94593 

5 
4 

3 

2 

I 

0 

M.  j 

Hour  p.  M. 

Hour  A.M. 

Cosine . 

Diff.j 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

in° 

A 

A 

B 

B 

C 

C    62°  1 

Seconds  of  time 

1'  1  2' 

3"  i  4» 

5» 

6' 

7» 

(A 
Prop,  parts  of  cols.  ■<  B 

\c 

3  6 

4  8 
I     2 

g    12 
12    IS 

^     1   3 

IS 

19 

4 

18 
23 

5 

21 

27 
6 

TABLE  44. 

Page  435 

S'. 

» 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

28° 

A 

A 

B 

B 

C 

C   151° 

M. 

Hour  A.  M. 

Hour  1'.  iM. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

iDiflf. 

Cotangent. 

Secant. 

Diff. 

("osine. 

M. 

0 

8  16  0 

3  44  0 

9. 67161 

0 

10.  32S39 

9.  72567 

0 

10-  27433 

10.  05407 

0 

9. 94593 

60 

I 

15  52 

44  S 

67185 

0 

32815 

72598 

I 

27402 

05413 

0 

945S7 

59 

2^ 

15  44 

44  16 

67208 

I 

32792 

72628 

I 

27372 

05420 

0 

94580 

58 

-> 

15  36 

'   44  24 

67232 

I 

32768 

72659 

2 

27341 

05427 

0 

94573 

57 

4 

15  28 

44  32 
3  44  40 

67256 
9.  67280 

2 
2 

32744 
10.  32720 

72689 

2 

27311 

05433 
10.  05440 

0 

_  94567 

56 

5 

8  15  20 

9.  72720" 

3 

10. 27280 

"1" 

9-  94560 

55 

6 

15  12 

44  48 

67303 

2 

32697 

72750 

3 

27250 

05447 

94553 

54 

7 

15  4 

1   44  56 

67327 

0 

J 

32673 

72780 

1  4 

27220 

05454 

94546 

53 

8 

14  56 

45  4 

67350 

3 

32650 

7281 1 

4 

27189 

05460 

94540 

52 

9_ 

14  48 

45  12 

3  45  20 

67374 
9.  67398 

3 
4 

32626 
10.  52602 

72841 
9.  72872 

5 

5 

_     27159 

10.  27I2S 

05467 
10.05474 

94533 

51 

10 

8  14  40 

9- 94526 

50 

1 1 

14  32 

45  28 

67421 

4 

32579 

72902 

6 

27098 

05481 

94519 

49 

12 

14  24 

45  36 

67445 

5 

32555 

72932 

6 

27068 

05487 

94513 

48 

13 

14  16 

45  44 

67468 

5 

32532 

72963 

7 

27037 

05494 

94506 

47 

H 

14  8 

45  52 
3  46  0 

67492 
9-67515 

I 

32508 
10.  32485 

72993 
9.  73023 

7 
'.     8 

27007 

05501 

2 

94499 

46 

'5 

8  14  0 

10.  26977 

10.  05508 

2 

9.  94492 

45 

Ih 

I 

13  52 

46  8 

67539 

6 

32461 

73054 

8 

26946 

05515 

2 

94485 

44 

•7 

13  44 

46  16 

67562 

7 

32438 

73084 

9 

26916 

05521 

2 

94479 

43 

i8 

13  36 

46  24 

67586 

7 

32414 

73 1 14 

9 

26886 

05528 

2 

94472 

42 

.'9_ 

13  28 

46  32 
3  46  40 

67609 
9- 67633 

7 
8 

32391 
10.  32367 

73M4 

J^ 

26856 

05535 

2 
2 

94465 

41 

20 

8  13  20 

9-73175 

10 

10.  26825 

10.05542 

9.  94458" 

40 

21 

13  12 

40  48 

67656 

8 

32344 

73205 

II 

26795 

05549 

2 

94451 

39 

2  ^ 

13  4 

46  56 

67680 

9 

32320 

73235 

II 

26765 

05555 

3 

94445 

38 

1  -» 
-J 

12  56 

47  4 

67703 

9 

32297 

73265 

12 

26735 

05562 

'3 

94438 

1,1 

24 

12  48 

47  12 

67726 

9 
10 

32274 
10.32250 

73295 
9-  73326 

12 

26705 

05569 

3 

9443i_ 

36 

25 

8  12  40 

3  47  20 

9.67750 

13 

10. 26674 

10.  05576 

3 

9-  94424 

35 

26 

12  31 

47  28 

67773 

IQ 

32227 

73356 

13 

26644 

05583 

3 

94417 

34 

27 

12  24 

47  3f' 

67796  10 

32204 

73386 

14 

26614 

05590 

3 

94410 

33 

28 

12  16 

47  44 

67820 

II 

32180 

73416 

14 

26584 

05596 

3 

94404 

32 

29 

12  8 

47  52 

67843 

II 

32157 

73446 
9-  73476 

15 

26554 

05603 

3 
3 

94397 

31 

^8  12  0 

3  48  0 

9.67866   12 

10.32134 

15 

10. 26524 

10. 05610 

9. 94390 

30 

J  3' 

II  52 

48  8 

67890  ;  12 

32110 

73507 

16 

26493 

05617 

4 

94383 

29 

32 

II  44 

48  16 

67913 

12 

32087 

73537 

16 

26463 

05624 

4 

94376 

28 

II  36 

48  24 

67936 

13 

32064 

73567 

17 

26433 

05631 

4 

94360 

27 

34 

II  28 

48  32 
3  48  40 

67959 
9. 67982 

*3 

14 

32041 
10.  32018 

73597 

17 

26403 

05638 

4 

94362 

26 

35 

8  II  20 

9-  73627 

18 

10.26373 

10.05645 

4 

9- 94355 

25 

36 

11  12 

48  48 

68006 

1 

14  1 

31994 

73657 

18 

26343 

05651 

4 

94349 

24 

^:,7 

II  4 

48  56 

68029    14 

31971 

73687 

19 

26313 

05658 

4 

94342 

23 

3S 

10  56 

49  4 

68052    15 

31948 

73717 

19 

26283 

05665 

4 

94335 

22 

39 

ID  48 

49  12 

68075 

15 

31925 
10.31902 

73747 

20 

__  26253 

05672 
10.05679 

4 

94328 

21 

40 

8  TO  40 

3  49  20 

9.68098 

I6n 

9-  73777 

20 

10. 26223 

5 

9.94321 

20 

41 

10  32 

49  28 

68121 

16 

31879 

73807 

21 

26193 

05686 

5 

94314 

19 

42 

10  24 

49  36 

68144    16 

31856 

73837 

21 

26163 

05693 

5 

94307 

18 

43 

10  16 

49  44 

68167    17 

31833 

73867 

22 

26133 

05700 

5 

94300 

17 

44 
45^ 

10  8 
8  10  0  ; 

49  52 

68190 

17 

31810 
10.31787 

73897 
9- 73927 

22 
23 

26103 

05707 

5 

5 

94293 
9. 94286 

16 
15 

3  50  0 

9.68213 

17 

10. 26073 

10.  05714 

46 

9  52 

50  8 

68237 

18 

31763 

73957 

23 

26043 

05721 

5 

94279 

14 

47 

9  44 

50  16 

68260  1  18 

31740 

73987 

24 

26013 

05727 

5 

94273 

13 

48 

9  36 

50  24 

6S283    19 

31717 

74017 

24 

25983 

05734 

5 

94266 

12 

49 
"50^ 

9  28 

50  32 

68305  i 

19 
19 

31695 
10.31672 

74047 
9. 74077 

25 
25 

25953 

05741 

6 

94259 

II 

8  9  20 

3  50  40 

9.68328  ' 

10. -25923 

10.  05748 

6 

9- 94252 

10 

51 

9  12 

50  48 

68351  i  20 

31649 

74107 

26 

25893 

05755 

6 

94245 

9 

52 

2  "^  \ 

50  56 

68374    20 

31626 

74137 

26 

25863 

05762 

6 

94238 

8 

53 

8  56  1 

51  4 

68397  !  21 

31603 

74166 

27 

25834 

05769 

6 

94231 

7 

54 
55 

8  48  ! 

51  12 

68420 

21 
21 

31580 
10-31557 

74196 
9.  74226 

27 
28 

25804 

05776 

6 

94224 
9.94217 

6 

"  5 

8  8  40 

3  51  20" 

'9.68443  1 

"10.25774 

10.05783 

6 

5<' 

8  32  \ 

51  28 

68466  ■   22 

31534 

74256 

28 

25744 

0579T 

6 

94210 

4 

57 

8  24 

51  36 

68489   22 

31511 

74286 

29 

25714 

05797 

7 

94203 

3 

5''^ 

8  16  1 

51  44 

68512  '  22 

31488 

74316 

29 

25684 

05804 

7 

94196 

2 

59 

8  8 

51  52 

68534  1  23 

31466 

74345 

30 

25655 

05S11 

7 

94189 

I 

Oo 

8  0 

52  0 

68557  :  23 

31443 
Secant. 

74375 

30 

25625 

05818 

7 

94182 

0 

mT 

Hour  1'.  M. 

Hour  A.M. 

Cosine. 

Dtff. 

1 

Cotangent. 

Diflf. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

118= 

A 

A 

B 

B 

C 

C    61°  1 

Seconds  of  time. 


Prop,  parts  of  cols.  <  B 

(C 


9 
II 

3 


12 

15 
3 


.5' 

15 
19 

4 


17 
23 

5 


20 

26 

6 


Page  436 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

29° 

A 

A       B 

B 

c 

C   150° 

Hour  A.M. 
880 

Hour  r.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

DiflF. 

Cotangent. 

Secant. 

DifT. 
0 

Cosine. 
9.94182 

M. 
60 

3  52  0 

9.68557 

0 

10.31443 

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44 

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30455 

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9-  75705 

22 

24324 

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5 

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17 

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22 

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5 

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6 

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58  24 

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18 

30367 

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24207 

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0 

93840 

12 

49 

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58  32 

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18 

30345 

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6 

93833 

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50 

8  I  20 

3  58  40 

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19 

10. 30323 

9.  75852  i  25 

10.24148 

10.06174 

6 

9. 93826 

51 

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5848 

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19 

30301 

75881   25 

241 19 

06181 

6 

93819 

9 

52 

I  4 

5856 

69721 

19 

30279 

75910  26 

24090 

06189 

6 

9381 1 

8 

53 

0  56 

59  4 

69743 

20 

30257 

75939  26 

24061 

06196 

6 

93804 

7 

54 

55 

0  48 

59  12 

69765 

20. 

30235 

75969  27 

24031 

06203 

6 

93797 

6 

5 

8  0  40 

3  59  20 

9.  69787 

20 

10.  30213 

9. 75998  27 

10.  24002 

10.  0621 1 

7 

9-93789 

5b 

0  32 

59  28 

69809 

21 

30I9I 

76027  28 

23973 

06218 

7 

93782 

4 

57 

0  24 

59  36 

69831 

21 

30169 

•  76056  1  28 

23944 

06225 

7 

93775 

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5^ 

0  16 

59  44 

69853 

22 

30147 

76086  1  29 

23914 

06232 

7 

9376S 

2 

59 

0  8 

59  52 

69S75 

22 

30125 

761 15  29 

23885 

06240 

7 

93760 

I 

bo 

M. 

0  0 

400 

69897 
Cosine. 

22 

30103 

76144  29 

23856 

06247 

7 

93753 

0 

Hour  I'.  M. 

Hour  A.M. 

Diflf. 

Secant. 

Cotangent.:  DifF. 

Tangent. 

Cosecant. 

DiflF. 

Sine. 

M. 

119 

D 

A 

A        B 

r. 

C 

C    60°  1 

Seconds  of  time. 

3 

4 

I 

6 

7 
3 

3» 

8 

II 

3 

P 

II 

IS 
4 

5' 

«' 

7' 

Prop,  parts  of  cols. 

\t 

14 
18 

4 

17 
22 

5 

20 

26 
6 

TABLE  44. 

[Page  437 

S'. 

> 

Log 

'.  Sines,  Tangents,  and  Secants. 

G'. 

30° 

A 

A 

B 

B 

C 

C   149° 

M. 
o 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent . 

Secant. 

Diff. 

Cosine. 

M. 

800 

400 

9. 69897 

0 

10,  30103 

9-  76144 

0 

10.  23856 

10. 06247 

0 

9-  93753 

60 

I 

7  59  52 

0  8 

69919 

0 

30081 

76173 

0 

23827 

06254 

0 

93746 

52 

-7 

59  44  ! 

0  16 

69941 

I 

30059 

76202 

I 

23798 

06262 

0 

93738 

58 

J 

59  36  [ 

0  24 

69963  1   I 

30037 

76231 

I 

23769 

06269 

0 

93731 

57 

_  4_ 

5 

5928! 

0  32 

69984  i   I 

30016 

76261 
g. 76290 

2 
2 

23739 

06276 

0 

93724 

56 

7  59  20 

4  0  40 

9.  70006  '   2 

10. 29994 

10.23710 

10.  06283 

9-93717 

55 

6 

59  12 

0  48 

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29972 

76319 

3 

23681 

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93709 

54 

7 

59  4 

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29950 

76348 

3 

23652 

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53 

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58  56 

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3 

29928 

76377 

4 

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52 

9 

58  48 

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70093 

3 

29907 

76406 
9- 76435^ 

4 

23594 

06313 

93687 

51 
50 

10 

7  58  40 

4  I  20 

9-70115 

4 

10. 29885 

5 

10. 23565 

10. 06320 

9- 93680 

II 

58  32 

1  28 

70137 

4 

29863 

76464 

5 

23536 

06327 

93673 

49 

12 

58  24 

1  36 

70159 

4 

29841 

76493 

6 

23507 

06335 

93665 

48 

13 

58  16 

1  44 

70180 

5 

29820 

76522 

6 

23478 

06342 

2 

93658 

47 

14 

58  8 

I  52 

70202 

5 

29798 

76551 

7 

23449 

06350 
10.06357 

2 
2 

93650 

46 

15 

7  58  0 

420 

9.  70224 

5 

10.  29776 

9.  76580 

7 

10. 23420 

9- 93643 

45 

16 

57  52 

2  8 

70245  ;  6 

29755 

76609 

8 

23391 

06364 

2 

93636 

44 

17 

57  44 

2  16 

70267  ,  6 

29733 

76639 

8 

23361 

06372 

2 

93628 

43 

iS 

57  36 

.   2  24 

70288  1  6 

29712 

76668 

9 

23332 

06379 

2 

93621 

42 

19 

57  28 

2  32 

70310  j  7 

29690 

76697 

9 

23303 

06386 

2 

93614 

41 

20 

7  57  20 

4  2  40 

9-70332   7 

10.  29668 

9.  76725 

10 

10.23275 

10.06394 

2 

9.  93606 

40 

21 

57  12 

2  48 

70353   8 

29647 

76754 

ID 

23246 

06401 

3 

93599 

^2 

22 

57  4 

2  56 

70375 

8 

29625 

76783 

II 

23217 

06409 

3 

93591 

38 

2S 

56  56 

3  4 

70396 

8 

29604 

76812 

II 

23188 

06416 

3 

93584 

37 

24 

5648 

3  12 

70418 

9 

29582 

7684 1 

12 

23159 

06423 

3 

93577 

3^5 

35 

2S 

7  56  40 

4  3  20 

9-  70439  !  9 

10.29561 

9.  76870 

12 

10.23130 

10.06431 

3  1  9-93569 

26 

56  32 

328 

70461  1  9 

29539 

76899 

13 

23IOI 

06438 

3 

935^2 

34 

27 

56  24 

336 

70482  !  10 

29518 

76928 

13 

23072 

06446 

3 

93554 

2S 

56  16 

3  44 

70504  :  10 

29496 

76957 

13 

23043 

06453 

3 

93547 

32 

29 

56  8 

3  5^- 

70525  10 

29475 

76986 

14 

14 

230(4 

10.  22985 

06461 
10.  06468 

4 

93539 

31 

30 

7  56  0 

440 

9-70547  II 

10. 29453 

9.77015 

4 

9-  93532 

30 

31 

55  52 

4  8 

70568  II 

29432 

77044 

15 

22956 

06475 

4 

93525 

29 

32 

55  44 

4  16 

70590  II 

29410 

77073 

15 

22927 

06483 

4 

93517 

28 

55  36 

4  24 

7061 1  12 

29389 

77101 

16 

22899 

06490 

4 

93510 

27 

34 

55  28 

4  32 

70633 

12 

29367 

77130 

16 

22870 

06498 

4 

93502 

2b 

3S 

7  55  20 

4  4  40 

9.  70654 

13 

10. 29346 

9-77159 

17 

10. 22841 

10.  06505 

4 

9- 93495 

25 

36 

55  12 

448 

70675 

13 

29325 

77188 

17 

•  22812 

06513 

4 

93487 

24 

37 

55  4 

4  56 

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13 

29303 

77217 

18 

22783 

06520 

5 

93480 

23 

3!^ 

54  56 

5  4 

70718 

14 

29282 

77246 

18 

22754 

06528 

5 

93472 

22 

39 

54  48 

5  12 

70739 

14 

29261 

77274 

19 

22726 

06535 

5 

93465 

21 

40 

7  54  40 

4  5  20 

9. 70761 

14 

10. 29239 

9- 77303 

19 

10. 22697 

10.  06543 

5 

9-93457 

20 

41 

54  32 

5  28 

70782 

15 

29218 

77332 

20 

22668 

06550 

5 

93450 

'9 

42 

54  24 

5  36 

70803 

15 

29197 

77361 

20 

22639 

06558 

5 

93442 

iS 

4i 

54  16 

5  44 

70824 

15 

29176 

77390 

21 

22610 

06565 

5 

93435 

17 

44 

54  8 

5  52 

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16 

29154,. 
10.29133 

77418 

21 

22582 

065 73_ 
10.  06580 

5 

93427 

16 

4S 

7  54  0 

460 

9.  70867 

16 

9- 77447 

22 

10. 22553 

6 

9.  93420 

15 

46 

53  52 

!    6  8 

70888 

10 

29II2 

77476 

22 

22524 

06588 

6 

93412 

14 

47 

53  44 

6  16 

70909 

17 

29091 

77505 

23 

22495 

06595 

6 

93405 

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48 

53  36 

:   6  24 

70931 

17 

29069 

77533 

23 

22467 

06603 

b 

93397 

12 

49 

5328 

1   6  32 

70952 

18 
18 

29048 

77562 

24 

:      22438 

06610 

b 

93390 

II 

SO 

7  53  20 

4  6  40 

9- 70973 

ID.  29027 

9- 77591 

24 

10. 22409 

10.06618 

6 

9- 93382 

10 

51 

53  12 

6  48 

70994 

18 

29006 

77619 

25 

22381 

06625 

b 

93375 

9 

S2 

53  4 

6  56 

71015 

19 

28985 

77648 

25 

22352 

06633 

b 

93367 

8 

S3 

52  56 

7  4 

71036 

19 

28964 

77677 

26 

22323 

06640 

7 

93360 

7 

54 

55 

52  48 

7  12 

71058 
9.  71079 

19 

28942 

77706 

26 

22294 
10.  22266 

06648 

7 

93352 

6 

7  52  40 

4  7  20 

20 

10.  28921 

9- 77734 

26 

10. 06656 

7 

9- 93344 

5 

56 

52  32 

728 

71 100 

20 

28900 

77763 

27 

22237 

06663 

7 

93337 

4 

57 

52  24 

7  36 

71121 

20 

28879 

77791 

27 

22209 

06671 

7 

93329 

J 

58 

52  16 

7  44 

71 142 

21 

28858 

77820 

28 

22180 

06678 

7 

93322 

2 

59 

52  8 

7  52 

71 163 

21 

28837 

77849 

28 

22  I  5  I 

06686 

7 

93314 

I 

60 

52  0 

8  0 
Hour  A.M. 

71184 

21 

28816 

77877 

29 

22123 

06693 

7 

93307 

0 

M. 

M. 

Hour  p.  M. 

Cosine . 

Diff 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

120 

° 

A 

A 

B 

B 

c 

C    59° 

Seconds  of  time 

1" 

2'    3- 

4- 

5- 

«■ 

16 

22 

6 

7" 

25 

7 

(  A   3 
Prop,  parts  of  cols.  •<  B  j   4 

5     8 

7  1  " 
2  \       3 

II 

14 
4 

13 
18 

5 

Page  438 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

31° 

A 

A       B 

B 

C 

C   148° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent.  Diff. 

Cotangent . 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  52  0 

480 

9.  71 184 

0 

10.28816 

9. 77877 

0 

10.  22123 

16.  06693 

0 

9-  93307 

60 

I 

51  52 

8  8 

71205 

0 

28795 

77906 

0 

22094 

06701 

0 

93299 

59 

7 

51  44 

8  16 

71226 

I 

28774 

77935 

22065 

06709 

0 

93291 

58 

7 
51  36 

8  24 

71247 

1 

28753 

77963 

I 

22037 

06716 

0 

93284 

57 

4 

51  28 

832 

71268 

I 

28732 

^    77992 

2  i 

22008 

06724 

93276 

56 

^ 

7  51  20 

4  8  40 

9.  71289 

2 

10.  2871 1 

9.  78020 

2 

10.  21980 

10.06731 

9.  93269 

55 

6 

51  12 

8  48 

71310 

2 

28690 

78049 

3 

21951 

06739 

93261 

54  ■ 

7 

5'  4 

8  56 

71331 

2 

28669 

78077 

3 

21923 

06747 

93253 

53 

S 

50  56 

9  4 

71352 

3 

28648 

78106 

4 

21894 

06754 

93246 

52 

9_ 

lO 

50  48 
7  50  40 

9  12 

71373 

3 

28627 

78135 

4 
5 

21865 

06762 

93238 

51 

4  9  20 

9-  71393 

3 

10.  28607 

9. 78163 

10.21837 

10.06770 

9-  93230 

50 

II 

50  32 

9  28 

71414 

4 

28586 

78192 

5 

21808 

06777 

93223 

49 

12 

50  24 

9  36 

71435 

4 

28565 

78220 

6 

21780 

06785 

2 

93215 

48 

I^, 

50  16 

9  44 

71456 

4 

28544 

78249 

6 

21751 

06793 

2 

93207 

47 

14 

50  8 

9  52 

71477 

5 
S 

28523 

78277 

7 

21723 

06800 

2 

93200 

46 

15 

7  50  0 

4  10  0 

9.  71498 

10.  28502 

9. 78306 

7 

10. 21694 

10.  06808 

2 

9.  93192 

45 

16 

49  52 

10  8 

71519 

S 

28481 

78334 

8 

21666 

06816 

2 

93184 

44 

17 

49  44 

10  16 

71539 

6 

28461 

78363 

8 

21637 

06823 

2 

93177 

43 

18 

49  36 

10  24 

71560 

6 

28440 

78391 

9 

21609 

06831 

2 

93169 

42 

iq 

49  28 

10  32 

71581 

7 

28419 

78419 

9 

21581 

06839 

2* 

93161 

41 

20 

7  49  20 

4  10  40 

9.  71602 

7 

10.  28398 

9. 78448 

9 

10.  21552 

10.06846 

3 

9-93154 

40 

21 

49  12 

10  48 

71622 

7 

28378 

78476 

10 

21524 

06854 

3 

93146 

39 

22 

49  4 

10  56 

71643 

8 

28357 

78505 

10 

21495 

06862 

3 

93138 

38 

23 

48  56 

II  4 

71664 

8 

28336 

78533 

II 

21467 

06869 

3 

93131 

37 

24 

48  48 

II  12 

4  1 1  20~ 

71685 

8 

28315 

78562 

II 

21438 

06877 

3 

93123 

36 

25 

7  48  40 

9.71705 

9 

10.  28295 

9. 78590 

12 

10. 21410 

10.06885 

3 

9-93115 

35 

26 

48  32 

II  28 

71726 

9 

28274 

78618 

12 

21382 

06892 

3 

93108 

34 

27 

48  24 

II  36 

71747 

9 

28253 

78647 

13 

21353 

06900 

3 

93100 

33 

28 

48  16 

II  44 

71767 

ID 

28233 

78675 

13 

21325 

06908 

4 

93092 

32 

29 

48  8 

II  52 

71788 

10 

28212 

78704 

14 

21296 
10. 21268 

06916 

4 

93084 

31 

30 

7  48  0 

4  12   0 

9.  71809 

10 

10.  28191 

9. 78732 

14 

10.06923 

4 

9-  93077 

30 

31 

47  52 

12   8 

71829 

II 

28171 

78760- 

15 

21240 

06931 

4 

93069 

29 

32 

47  44 

12  16 

71850 

II 

28150 

78789 

15 

2I2II 

06939 

4 

93061 

28 

->  "> 

47  36 

12  24 

71870 

II 

28130 

78817 

16 

21  183 

06947 

4 

93053 

27 

34 

47  28 

12  32 

71891 

12 

28109 

78845 

16 

17 

2II55 

06954 

4 

93046 

2b 

^S 

7  47  20 

4  12  40 

9-71911 

12 

10. 28089 

9. 78874 

10. 21126 

10. 06962 

5 

9-  93038 

25 

36 

47  12 

12  48 

71932 

12 

28068 

78902 

17 

21098 

06970 

5 

93030 

24 

37 

47  4 

12  56 

71952 

13 

28048 

78930 

17 

21070 

06978 

5 

93022 

23 

ss 

46  56 

13  4 

71973 

13 

28027 

78959 

18 

2IO4I 

06986 

5 

93014 

22 

39 

46  48 

13  12 

71994 

13 

28006 

78987 

18 

2IOI3 

06993 

5 

93007 

21 

40 

7  46  40 

4  13  20 

9.  72014 

14 

10.  27986 

9. 79015 

19 

10.  20985 

10. 07001 

5 

9. 92999 

20 

41 

46  32 

13  28 

72034 

14 

27966 

79043 

19 

20957 

07009 

5 

92991 

19 

42 

46  24 

13  36 

72055 

14 

•  27945 

79072 

20 

20928 

07017 

5 

92983 

18 

4> 

46  16 

13  44 

72075 

15 

27925 

79100 

20 

20900 

0707.4 

b 

92976 

17 

44 

46  8 

13  52_ 
4  14  0 

72096 
9.  721 16 

IS 

27904 

79128 

21 

20872 

07032 

6 

92968 

lb 

4S 

7  46  0 

15 

10.  27884 

9. 79156 

21 

10. 20844 

10.  07040 

6 

9.  92960 

15 

46 

45  52 

14  8 

72137 

16 

27863 

79185 

22 

20815 

07048 

b 

92952 

14 

47 

45  44 

14  16 

72157 

16 

27843 

79213 

22 

20787 

07056 

6 

92944 

13 

48 

45  36 

14  24 

72177 

16 

27823 

79241 

23 

20759 

07064 

6 

92936 

12 

49 

SO 

45  28 

14  32 

72198 

17 

27802 

79269 

23 

24 

20731 

07071 

b 

92929 

II 

7  45  20 

4  14  40 

q.  72218 

17 

10.27782 

9. 79297 

10. 20703 

10.07079 

6 

9.92921 

10 

SI 

45  12 

14  48 

72238 

18 

27762 

79320 

24 

20674 

07087 

7 

92913 

9 

S2 

45  4 

14  56 

72259 

18 

27741 

79354 

25 

20646 

07095 

7 

92905 

8 

S^> 

44  56 

15  4 

72279 

18 

27721 

79382 

25 

20618 

07103 

7 

92897 

7 

,S4 

44  48 

15  12 

72299 

19 

27701 

79410 

26 
26 

1      20590 

07111 

7 

92889 

6 

ss 

7  44  40 

1  4  15  20 

9.  72320 

19 

10. 27680 

9-  79438 

'   10. 20562 

10. 07119 

7 

9.92881 

5 

S6 

44  32 

15  28 

72340 

19 

27660 

79466 

26 

20534 

07126 

7 

92874 

4 

S7 

44  24 

'5  36 

72360 

20 

27640 

79495 

27 

i      20505 

07134 

7 

92866 

:> 

ss 

44  16 

15  44 

72381 

20 

27619 

79523 

27 

!    20477 

07142 

7 

9285S 

2 

S9 

44  8 

15  52 

72401 

20 

27599 

79551 

28 

20449 

07150 

8 

92850 

I 

60 

44  0 

16  0 

72421 

21 

27579 

79579 

28 

20421 

07158 

8 

92842 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

.Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

121 

0 

A 

A       B 

B 

c 

C 

58° 

Seconds  of  time 

1» 

2' 

3' 

P 

5» 

fi» 

7» 

(A 
Prop .  parts  of  cols.  ■<  B 

3 
4 

I 

5 
7 
2 

8 

II 

3 

10 

14 

4 

13 
18 

5 

15 
21 

6 

18 
25 

7 

TABLE  44 

. 

Page  439 

S'. 

Log.  Siues,  Tangents,  and  Secants. 

G'. 

32° 

A 

A 

li 

B        C 

C   141° 

M. 

Hour  A.M. 

Hourp.-M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent.   Secant. 

Diff. 

Cosine. 

M. 

o 
I 

4 

7  44  0 
43  52 
43  44 
43  36 
43  28 

4  16  0 
16  8 
16  16 
16  24 
16  32 

9.  72421 
72441 
72461 
72482 
72502 

0 
0 

I 
I 
I 

10.27579 

27559 
27539 
27518 
27498 

9-  79579 
79607 

79035 
79663 

79691 

0 
0 

I 
I 
2 

10.20421   10.07158 
20393     07166 
20365     07174 
20337     07182 
20309     07190 

0 
0 
0 
0 

9.  92842 
92834 
92S2O 
928 1 8 
92810 

60 

59 

58 
57 
56 

5 
6 

7 
8 

9 

7  43  20 
43  12 

43  4 
42  56 
42  48 

4  16  40 
16  48 

16  56 

17  4 
J7  12 

9.  72522 

72542 
72562 
72582 
72602 

2 

2 
2 

3 
3 

ID.  27478 

2745S 
27438 
27418 

27398 

9.  79719 

79747 
79776 
79804 
79832 

2 

3 
3 
4 
4 
5 

1 

6 
7 

10.  20281 

20253 
20224 
20196 
20168 

10.07197 
07205 
07213 
07221 
07229 

9. 92803 

92795 

92787 

92779 
92771 

55 
54 
53 
52 
51 
50 
49 
48 
47 
46 

45 
44 
43 
42 
41 

lo 
11 

12 

13 
14 

7  42  40 
42  32 
42  24 
42  16 
42  8 

4  17  20 
17  28 
17  36 
17  44 
17  52 

9.  72622 

72643 
72663 
72683 

72703 

3 
4 
4 
4 
5 

10.27378 

27357 
27337 
27317 
27297 

9. 79860 
79888 
79916 

79944 
79972 

10. 20140 

20II2 
200S4 
20056 
20028 

10.07237 
07245 

07253 
07261 

07269 

2 
2 
2 

9. 92763 

92755 
92747 
92739 
92731 

15 
16 

17 
18 

19 

7  42  0 

41  52 
41  44 

41  36 
41  28 

4  18  0 
18  8 
18  16 
18  24 

18  32 

9. 72723 

72743 
72763 

72783 
72803 

5 

5 
6 

6 

6 

10.27277 
27257 
27237 
27217 
27197 

9. 80000 
80028 
80056 
80084 
801 12 

7 
7 
8 
8. 
9 

10.  20000 

19972 
19944 
19916 
19888 

10.07277 
07285 
07293 
07301 
07309 

2 
2 

2 
2 

3 

9.92723 

92715 
92707 

92699 

92691 

20 
21 

22 

23 
24 

7  41  20 
41  12 
41  4 
40  56 
40  48 

4  18  40 
18  48 

18  56 

19  4 
19  12 

9.  72823 

72843 

f   72863 

72883 

72902 

7 
7 
7 
8 
8 

10.27177 
27157 

27137 
27117 

27098 

9. 80140 
80168 
So  195 
80223 
80251 

9 
10 
10 
II 
II 

10.  19860 

19832 
19805 

19777 
19749 

10.07317 
07325 
07333 
07341 
07349 

3 
3 
3 
3 
3 

9. 92683 
92675 
92667 
92659 
92651 

40 
39 
38 
37 
36 

25 
26 

27 
28 

29 

7  40  40 
40  32 
40  24 
40  16 
40  8 

4  19  20 
19  28 
19  36 
19  44 

19  52 

9.  72922 

72942 
72962 
72982 
73002 

8 
9 

9 

9 

10 

ID.  27078 
27058 
27038 
27018 
26998 

9. 80279 
80307 

80335 
80363 
80391 

12 
12 
13 
13 
13 

10.  I972I 
19693 
19665 

19637 
19609 

10.07357 
07365 
07373 
07381 
07389 

3 

4 
4 
4 

9. 92643 

92635 
92627 

92619 

9261 1 

35 
34 

32 
31 

30 
31 
32 
OJ) 

34 

35 
36 

37 
38 
39 

7  40  0 
39  52 
39  44 
39  36 
39  28 

4  20  0 
20  8 
20  16 
20  24 
20  32 

9.  73022 

73041 
73061 
73081 
73101 

10 
10 

IX 

II 

10.  26978 

26959 
26939 
26919 

26899 

9.  80419 
80447 

80474 
80502 

80530 

14 
14 
15 
15 
16 

10. 19581 

19553 
191^26 

19498 

19470 

10.  07397 
07405 

07413 
07421 

07429 

4 

4 
4 
4 
5 

9. 92603 

92595 
92587 
92579 
92571 
9-  92563 

92555 
92546 

92538 

__  92530 

9. 92522 

92514 
92506 
92498 
92490 

30 
29 
28 

27 
26 

25 
24 

23 
22 

21 

20 

19 
18 

17 
16 

7  39  20 
39  12 

39  4 
38  56 
38  48 

4  20  40 
20  48 

20  56 

21  4 
21  12 

9.  73121 

73140 
73160 
73180 
73200 

12 
12 
12 
13 
13 

10.  26879 
26860 
26840 
26820 
26800 

9. 80558 
80586 
80614 
80642 
80669 

16 

17 
17 
18 
18 

10. 19442 
19414 
19386 
19358 
I933I 

10.  07437 

07445 
07454 
07462 
07470 

5 

5 
5 
5 
5 

I 

6 
6 
6 

40 

41 

42 

43 
44 

7  38  40 
38  32 
38  24 
38  16 
38  8 

4  21  20 
21  28 
21  36 

21  44 
21  52 

9.  73219 
73239 
73259 
73278 
73298 

13 
14 
14 
14 
15 

10.  26781 
26761 

26741 
26722 
26702 

9. 80697 
80725 

80753 
80781 

80808 

19 
19 

20 

20 
20 
21 
21 
22 
22 
23 

10.  19303 

19275 
19247 

I92I9 

19192 

10.  0747S 
07486 

07494 
07502 
07510 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

7  38  0 
37  52 
37  44 
37  36 
37  28 

4  22   0 
22   8 
22  16 
22  24 
22  32 

9-  73318 

73357 
73377 
73396 

15 

;i 

16 
16 

10.  26682 

26663 

26643 
26623 
26604 

9. 80836 
S0864 
80892 
80919 
80947 

10.  19104 
19136 
19108 
1 908 1 

19053 

10.07518 
0752/ 
07535 
07543 
07551 

6 
6 
6 
6 

7 

9. 924S2 

92473 

92465 

92457 
92449 

15 
14 
13 

12 
II 
10 

9 

8 

7 
6 

7  37  20 
37  12 
37  4 
36  56 
36  48 

4  22  40 
22  48 

22  56 

23  4 
23  12 

9- 734  <  6 
73435 
73455 
73474 
73494 

17 
17 
17 
18 
18 

10. ^6584 

26565 
26545 

26526 
26506 

9. 80975 
81003 
81030 
81058 
81086 

23 
24 
24 
25 
25 

10. 19025 

18997 

18970 
18942 
IS9I4 

10.07559 
07567 
07575 
07584 
07592 

7 
7 

7 
7 
7 

9.92441 

92433 
92425 

92416 

92408 

55 
56 

57 
58 

59 
60 

7  36  40 
36  32 
36  24 
36  16 
36  8 
36  0 

4  23  20 
23  28 
23  36 
23  44 

23  52 

24  0 

9-  73513 
73533 
73552 
73572 

73591 
73611 

18 
19 
19 
19 
20 
20 

10.  26487 
26467 
26448 
26428 
26409 

26389 

9-81113 
81141 
81 169 
81 196 
81224 
81252 

26 
26 
26 
27 

27 
28 

Diff! 

10. 18887 
18859 
18831 
18804 

18776 

18748 

10.07600 
07608 
07616 
07624 

07633 
07641 

7 
8 
8 
8 
8 
8 

9. 92400 
92392 
92384 
92376 
92367 

92359 

5 
4 

3 
2 

I 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

122 

0 

A 

A 

B 

B        C 

C    57°  1 

Seconds  of 

time. 

1» 

1 

•2»    3» 

4, 

5»    6» 

7' 

Prop,  parts 

of  CO 

S     7 
7    10 

2     3 

10 

4 

12 

5 

15 

21 

6 

17 

24 

7 

Page  440 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

33° 

A 

A 

B 

B 

C 

C   146° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

0 
0 
I 

I 
I 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant.- 

Diff. 

Cosine. 

M. 

60 

59 

58 
57 
56 

o 
I 

2 

3 
4 

7  36  0 

35  52 
35  44 
35  36 
35  28 

4  24  0 
24  8 

24  16 
24  24 
24  32 

9.  736 II 

73630 
73(550 
73669 

73689 

10.  26389 
26370 
26350 

26331 
2631 1 

9.81252 
81279 
81307 

81335 
81362 

0 
0 

I 
I 

2 

10. 18748 
18721 
18693 
18665 
18638 

10.  07641 
07649 

07657 
07665 

07674 

0 
0 
0 
0 

9-  92359 
92351 
92343 
92335 
92326 

5 

6 

7 
8 

9 

7  35  20 
35  12 
35  4 
34  56 
3448 

4  24  40 
24  48 

24  56 

25  4 
25  12 

•  9-  73708 

73727 
73747 
73766 

73785 

2 
2 
2 

3 
3 

10.  26292 
26273 
26253 
26234 
26215 

9.  81390 
81418 
81445 
81473 
81500 

2 
3 

3 
4 
4 

5 
5 
5 
6 
6 

10. 18610 
18582 

18555 
18527 
18500 

10.07682 
07690 
07698 
07707 
07715 

9.  92318 
92310 
92302 
92293 
92285 

55 
54 
53 
52 
51 

lO 

II 

12 

'3 
14 

15 

16 

17 
18 

19 

20 
21 
22 

23 
24 

7  34  40 
34  32 
34  24 
34  It- 
34  8 

4  25  20 
25  28 

25  36 
25  44 
25  52 

9-  73805 
73824 

73843 
73863 
73882 

3 
3 
4 
4 
4 

10.  26195 
26176 
26157 
26137 
261 18 

9.81528 
81556 

81583 
81611 
81638 

10.  18472 
18444 
18417 
18389 
18362 

10.07723 

07731 
07740 
07748 
07756 

2 

2 
2 
2 

9. 92277 
92269 
92260 
92252 
92244 

50 
49 

48 
47 
46 

7  34  0 
35   52 
33  44 
3336 
33  28 

4  26  0 
26  8 
26  16 
26  24 
26  32 

9.  73901 
73921 
73940 
73959 
73978 

5 

5 

5 
6 

6 

10. 26099 
26079 
26060 
26041 
26022 

9.  81666 
81693 
81721 
81748 
81776 

7 
7 
8 
8 

9 

10.  18334 
18307 
1 82  79 

18252 

18224 

10.  07765 

07773 
07781 

07789 
07798 

2 
2 
2 

3 
3 

9.  92235 
92227 
92219 
9221 1 
92202 

45 
44 
43 
42 
41 

7  33  20 
33  12 
33  4 
32  56 
32-48 

4  26  40 
26  48 

26  56 

27  4 
27  12 

9-  73997 
74017 

74036 
7405  s 
74074 

6 

7 
7 
7 
8 

10.  26003 

25983 
25964 

25945 
25926 

9.81803 
8183I 
81858 
81886 
81913 

9 
10 

10 

II 

II 

10. 18197 

I8I69 

I8I42 
I8II4 

18087 

10. 07806 
07814 
07823 
07831 
07839 

3 
3 
3 
3 
3 

9.  92194 
92186 
92177 
92169 
92161 

40 

39 
38 
37 
36 

25 
26 

27 

28 

29 

30 
31 

32 

->  -> 

34 

35 
36 
37 
38 
39 

7  32  40 
32  32 
32  24 
32  16 
32  8 

7  32  0 
31  52 
31  44 
31  36 
31  28 

4  27  20 
27  28 
27  36 
27  44 

27  52^ 
4  28  0 

28  8 
28  16 
28  24 
28  32 

4  28  40 
28  48 

28  56 

29  4 
29  12 

9-  74093 
741 13 
74132 

74151 
74170 

9.  74189 
74208 
74227 
74246 
74265 

9.  74284 

74303 
74322 

74341 
74360 

8 

8 

9 

9 
_9_ 
10 
10 
10 
10 
II 
II 
II 
12 
12 
12 

10.  25907 
25887 
25868 

25849 
25830 

9. 8194I 
81968 
81996 
82023 
82051 

II 
12 
12 
13 
13 
14 
14 
15 
15 
16 

10. 18059 
18032 
18004 

17977 
17949 

10. 07848 
07856 
07864 
07873 
07881 

3 
4 
4 
4 
4 

9.92152 
92144 
92136 
92127 
92119 

35 
34 
33 
32 
31 

10.  2581 1 
25792 

25773 
25754 
25735 

9.  82078 
•82106 

82 1 33 
82161 

82188 

10. 17922 

17894 

17867 

17839 
I78I2 

10.  07889 

07898 

07906 

07914 
07923 

4 
4 
4 
5 
5 

9.  921 1 1 
92102 

92094 
92086 
92077 

30 
29 

28 

27 
26 

7  31  20 
31  12 

31  4 
30  56 
30  48 

10.25716 
25697 
25678 

25659 
25640 

9.82215 
82243 
82270 
82298 
82325 

16 
16 
17 
17 
18 

18 
19 

19 
20 
20 

10.  17785 

I77S7 
17730 
17702 

17675 

10.  17648 

17620 

17593 
17565 
17538 

10.07931 

07940 
07948 
07956 

07965 

5 
5 
5 
5 
5 

9.  92069 
92060 
92052 
92044 
92035 

25 
24 

23 
22 

21 

40 

41 
42 
43 
44 

7  30  4" 
30  32 
30  24 
30  16 
30  8 

4  29  20 

29  28 

29  36 
29  44 

29  52 

9-  74379 
74398 
74417 
74436 
74455 

13 
13 
13 
14 
14 

10.  25621 
25602 

25583 
25564 
25545 

9.  82352 
82380 
82407 

82435 
82462 

10. 07973 
07982 
07990 

07998 
08007 

6 
6 

6 
6 
6 
6 
6 
7 
7 
7 

9.92027 
92018 
92010 
92002 
91993 

20 

19 
18 

17 

16 

45 
46 

47 
48 

49 

7  30  0 

29  52 

29  44 
29  36 
29  28 

4  30  0 
30  8 
30  16 
30  24 
30  32 

9-  74474 
74493 
74512 

74531 
74549 

.14 
15 
15 
15 
16 

10.  25526 

25507 
25488 

25469 
25451 

9.  82489 
82517 
82544 
82571 
82599 

21 
21 
22 
22 
22 

10.  1 75 1 1 

17483 
17456 
17429 
1 740 1 

10.  08015 
08024 
08032 
08041 
08049 

9.  91985 
91976 
91968 
91959 
91951 

15 
14 

13 
12 

II 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 

7  29  20 
29  12 

29  4 
28  56 
28  48 
7  28  40 
28  32 
28  24 
28  16 
28  8 
28  0 

4  30  40 

30  48 

30  56 

31  4 
31  12 

9.  74568 

74587 
74606 

74625 
74644 

16 
16 
17 
17 
17 

17 
18 
18 
18 
19 
19 

Diff. 

10.  25432 

25413 
25394 
25375 
25356 

9.  82626 
82653 
82681 
82708 

82735 

23 
23 

24 

24 
25 

10.17374 
17347 

17319 

17292 

17265 

10. 08058 
08066 
08075 
08083 

08092 

7 

7 

7 

7 
8 

8^ 

8 

8 

8 

8 

8 

9.  91942 
91934 
91925 
91917 
91908 

10 

i 

7 

6 

4  31  20 

31  28 

31  36 
31  44 

31  52 

32  0 

9.  74662 
74681 
74700 
74719 

74737 
74756 

10.  25338 

25319 
25300 
25281 
25263 

25244 

9.  82762 
82790 
82817 
82844 
82871 
82899 

25 
26 

26 

27 
27 
27 

10.  17238 
17210 

17183 
17156 
17129 
17101 

10.08100 
08109 
081 1 7 
08126 
08134 
08143 

9.  91900 
91891 
91883 
91874 
91866 
91857 

5 
4 

3 
2 
I 

0 

M. 

Hour  F.  M. 

Hour  A.M. 

Cosine. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

123 

3 

A 

A 

B 

B 

c 

C 

56° 

Seconds  of  time. . . 

1- 

2» 

3» 

4, 

5" 

12 
17 

5 

6> 

14 

21 

6 

7» 

Prop,  parts  of  cols. 

i^ 

2 

3 
I 

5 
I 

7 
10 

3 

10 

14 

4 

17 
24 

7 

TABLE  44. 

Page  441 

S'. 

V 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

A 

A 

B           B 

c 

C   145° 

Hour  A.M. 

j  Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  28  0 

4  32  0 

9-  74756 

0 

ID.  25244 

9.  82899 

0 

ID.  17101 

10.08143 

0 

9.91857 

60 

I 

27  52 

32  8 

74775 

0 

25225 

82926 

0 

17074 

081 5 1 

0 

91849 

59 

-> 

27  44 

32  16 

74794 

I 

25206 

82953 

I 

17047 

08160 

0 

91840 

58 

3 

27  36 

32  24 

74812 

I 

25188 

82980 

I 

17020 

08168 

0 

91832 

57 

4 

27  28 

32  32 

74831 

I 

25169 

83008 

2 

16992 

08177 

I 

91823 
9.91815 

5<' 

55 

S 

7  27  20 

4  32  40 

9.  74850 

2 

10.25150 

9.  8303s 

2 

10. 16965 

10.08185 

0 

27  12 

32  48 

74868 

2 

25132 

83062 

3 

16938 

0S194 

I 

91806 

54 

7 

27  4 

32  56 

74887 

2 

25113 

83089 

3 

16911 

08202 

91798 

5i 

S 

26  56 

33  4 

74906 

2 

25094 

831 1 7 

4 

16883 

082 1 1 

917*9 

52 

0 

26  48 

7  26  40 

33   12 
4  33   20 

74924 

3 

2 

5076 

5057 

83144 

4 

16856 

oS 
10.  oJ: 

>2I9 

91781 

51 

9-  74943 

10.  2 

9-83171 

S 

ID.  16829 

)228 

9.91772 

50 

I  I 

26  32 

33   28 

74961 

25039 

83198   5     16802 

08237 

2 

91763 

49 

12 

26  24 

33  36 

74980 

4 

25020 

83225  1  5  ,    16775 

08245 

2 

91755 

48 

I^. 

26  16 

33   44 

74999 

4 

25001 

83252 

6 

16748 

08254 

2 

91746 

47 

14 

26  8 

33   52 

75017 

4 

24983 

83280 

6 

16720 

08262 

2 

91738 

46 

K 

7  26  0 

4  34  0 

9-  75036 

5 

1 0.  24964 

9. 83307 

7  10.  16693 

10.  08271 

2 

9.91729 

45 

i6 

25  52 

34  8 

75054 

5 

24946 

83334 

7     16666 

08280 

2 

91720 

44 

17 

25  44 

34  16 

75073 

5 

24927 

833&1 

8  1    16639 

08288 

2 

91712 

43 

iS 

25  36 

34  24 

75091 

6 

24909 

83388 

8 

i66i2 

08297 

3 

91703 

42 

It) 

20 

25  28 
7  25  20 

_^34  32^ 
4  34  40 

75110 
9.75128 

6 

2 

4890 

4872^ 

83415 
9. 83442 

9 
9 

16585 

08305 

3 

91695 

41 

6 

10.  2 

10.  16558 

10. 08314 

3 

9.91686 

40 

21 

25  i^ 

34  48 

75147 

6 

24853 

83470 

9  ;      16530 

08323 

3 

91677 

39 

22 

25  4 

34  56 

75165 

7 

24835 

83497 

10  1      16503 

08331 

3 

91669 

38 

2,1 

24  56 

oS  4 

75184 

7 

24816 

83524 

10        16476 

08340 

3 

91660 

37 

24 
2.S 

24  48 
7  24  40 

35  '2 

4  35  20 

75202 

7 

24798 

83551 
9.83578 

II        16449 
II    10. 16422 

08349 
10.08357 

3 

91651 

36 
35 

9.  75221 

8 

10.  24779 

4 

9.  91643 

26 

24  32 

35  28 

75239 

8 

24761 

83605  12     16395 

08366 

4 

91634 

34 

27 

24  24 

35  3^ 

75258 

8 

24742 

83632  12     16368 

08375 

4 

91625 

2S 

24  16 

35  44 

75276 

9 

24724 

83659 

13        16341 

08383 

4 

91617 

32 

29 

30 

24  8 
7  24  0 

35  52 
4  36  0 

75294 
9-  75313 

9 
9 

24706 

83686 

13 

14 

16314 

08392 

4 

91608 

31 

10.  24687 

9-83713 

10.  16287 

10.  0840J 

4 

9.91599 

30 

,ii 

23  52 

36  8 

75331 

9 

24669 

83740  '  14     16260 

08409 

4 

91591 

29 

.l2 

23  44 

36  16 

75350 

10 

24650 

83768  '  14     16232 

08418 

S 

91582 

28 

33 

23  3& 

36  24 

753^8 

10 

24632 

83795  15  ,    16205 

08427 

5 

91573 

27 

34 
35 

23  28 
7  23  20 

36  32_ 
4  36  40 

7538*5 
9-  75405 

10 
II 

24614 

83822 

15 
16 

16178 

08435^ 
10.  08444 

5 

S 

91565 

26 

10. 24595 

9. 83849 

10.  16151 

9-91556 

25 

3b 

23  12 

36  48 

75423 

II 

24577 

83876 

16 

16124 

08453 

5 

91547 

24 

23  4 

36  56 

75441 

II 

24559 

83903 

17 

16097 

08462 

5 

91538 

23 

3'^ 

22  56 

37  4 

75459 

12 

24541 

83930 

17  i      16070 

08470 

S 

91530 

22 

39 

22  48 

37  12 

75478 

12 

24522 

83957 
9-  83984 

18  j      16043 

08479 

6 

91521 

21 

4" 

7  22  40 

4  37   20 

9-  75496 

12 

10. 24504 

18    10. 16016 

10.08488 

6 

9.91512 

20 

41 

22  32 

37  28 

75514 

13 

24486 

S4011 

18        15989 

08496 

6 

91504 

19 

42 

22  24 

37  36 

75533 

13 

24467 

84038 

19        15962 

08505 

6 

91495 

18 

43 

22  16 

37  44 

75551 

13 

24449 

84065 

19        15935 

08514 

6 

91486 

17 

44 

22  8 

37  52 
4  38  0 

75569 

13 

24431 

8/ 
'9.8. 

t092 

20 

15908 

08523 

6 

91477 

16 

45 

/  22  0 

9-  75587 

14 

10.24413 

^II9 

20 

10.  15881  1 

10.  08531 

7 

9. 91469 

15 

46 

21  52 

38  8 

75605 

14 

24395 

S4146  i  21     15854 

08540 

7 

91460 

14 

47 

21  44 

38  16 

75024 

14 

24376 

84173  21     15827 

08549 

7 

91451 

13 

4S 

21  36 

38  24 

75642 

15 

24358 

84200  22     15800 

08558 

7 

91442 

12 

49 
50 

21  28 

3832 

75660 

15 

2 
10.2 

4340 

84227 

22  1      15773  1 

08567 

7 

91433 

II 

7  21  20 

4  38  40 

9.  75678 

15 

4322 

9. 84254 

2.3 

10. 15746 

10.08575 

7 

9.91425 

10 

51 

21  12 

38  48 

75696 

16 

24304 

84280 

23 

15720 

08584 

7 

91416 

9 

52 

21  4 

38  56 

75714 

16 

24286 

84307 

23 

15693 

08593 

8 

91407 

8 

53 

20  56 

39  4 

75733 

16 

24267 

84334 

24 

15666 

08602 

8 

91398 

7 

54 

20  48 

39  12 

75751 

17 

24249 

84361 

24 

15639 

0861 1 

8 

91389 

6 

55 

7  20  40 

4  39  20 

9.  75769 

17 

10.24231 

9. 84388 

25 

10.  15612 

10.08619 

8 

9.91381 

5 

5'' 

20  32 

39  28 

75787 

17 

24213 

84415 

25 

15585 

08628 

8 

91372 

4 

57 

20  24 

39  36 

75805 

17 

24195 

84442 

20 

15558 

08637 

8 

913*53 

5-S 

20  16 

39  44 

75823 

18 

24177 

84469 

26 

15531 

08646 

8 

91354 

2 

59 

20  8 

39  52 

75841 

18 

24159 

84496 

27 

15504 

08655 

9 

91345 

I 

60 

20  0 

40  0 

75859 

18 

24I4I 

84523 

27 

15477 

08664 

9 

91336 

0 

Hour  F.  M. 

Hour  A.M. 

Cosine. 

DiflF, 

Secant. 

Cotangent. 

Difr. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

> 

A 

A 

B           B 

C 

C    55°  1 

Seconds  of  time 

1» 

2» 

3' 

4» 

.5' 

II 

6» 

14 

I' 

s.^  B 

2 

5 

7 

9 

16 

Prop,  parts 

of  CO 

3 

7 

10 

14 

17 

20 

24 

(C   I 

2 

3 

4 

5 

7 

8 

\ 


Page  442 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

35° 

A 

A 

B 

B 

C 

C   144° 

M. 

Hour  A.M. 

i  Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotang'ent. 

Secant. 

Diff. 

Cosine. 

M.  \ 

o 

7  20  0 

i  4  40  0 

9-  75859 

0 

10.  24141 

9-  84523 

0 

10. 15477 

10.  o8bb4 

0 

9-91336 

bo  I 

I 

19  52 

40  8 

75877 

0 

24123 

84550 

0 

15450 

08b  72 

0 

91328 

5Q  1 

2 

19  44 

40  lb 

75895 

I 

24105 

84576  '     1 

15424 

08681 

0 

91319 

^8 

1 

J) 

19  36 

40  24 

75913 

I 

24087 

84603   I 

15397 

08690 

0 

91310 

4 

19  28 

40  32 

75931 

I 

24069 

84b30  1  2 

15370 

08699 

91301 

5b  1 

5 

7  19  20 

4  40  40 

9-  75949 

I 

ID.  2405 1 

9. 84b57   2 

10.  15343 

10.  08708 

9.91292 

5S  1 

6 

19  12 

40  48 

75967 

2 

24033 

84684   3 

15316 

08717 

91283 

54  i 

7 

19  4 

40  56 

75985 

2 

24015 

8471 1  '  3 

15289 

0872b 

91274 

5^  1 

S 

1855 

41  4 

76003 

2 

23997 

84738  '  4 

I52b2 

08734 

9i2b6 

9 

'O 

iS  4^ 

41  12 

7bo2i 

3 

23979 

84764   4 

15236 

08743 

91257 

51  1 

7  1^  40 

4  41  20 

9.  7b039 

3 

10.  239b I 

9. 84791 

4 

10.  15209 

10.  08752 

2- 

9.91248 

SO 

II 

18  32 

41  28 

76057 

3 

23943 

84818 

5 

15182 

o87bi 

2 

91239 

49 

12 

18  24 

41  36 

76075 

4 

23925 

84845  '  5 

I5I55 

08770 

2 

91230 

48 

13 

18  lb 

41  44 

76093 

4 

23907 

84872  j  b 

15128 

08779 

2 

91221 

47 

14 

18  8 

41  52 

7biii 

4 

23889 

84899 

b 

I5IOI 

08788 

2 

91212 

46 

15 

7  18  0 

4  42  0 

9.  7bi29 

4 

10.23871 

9.  84925 

7 

10.  15075 

10.  08797 

2 

9.  91203 

45 

lb 

17  52 

42  8 

7b  1 4b 

5 

23854 

84952 

7 

15048 

08806 

2 

91194 

44 

17 

17  44 

42  lb 

7bib4 

5 

23836 

84979  i  8 

15021 

08815 

3 

91185 

4", 

18 

17  3b 

42  24 

7b  182 

5 

23818 

8500b 

8 

14994 

08824 

3 

9117b 

42 

19 
20 

1728 
7  17  20 

42  32 

7b200 

6 

23800 

85033 

8 

14967 

08833 

3 

9iib7 

41 

4  42  40 

9.  7b2i8 

b 

10.23782 

9. 85059   9 

10.  14941 

10.  08842 

3 

9-91158 

40 

21 

17  12 

42  48 

7623b 

b 

23764 

8508b   9 

14914 

08851 

3 

91149 

39 

22 

17  4 

42  56 

76253 

b 

23747 

85113   10 

14887 

08859 

3 

91141 

38 

23 

'^56 

43  4 

7b27i 

7 

23729 

85140  10 

i48bo 

o88b8 

3 

91132 

37 

24 

25 

16  48 

43  12 

7b289 

7 

23711 

8516b  II 

14834 

08877 

4 

91123 

36 

7  lb  40 

4  43  20 

9.  7b307 

7 

10.  23b93 

9.85193  '  II 

10. 14807 

10.  0888b 

4 

9.91114 

35 

2b 

lb  32 

43  28 

76324 

8 

23676 

85220   12 

14780 

08895 

4 

91105 

34 

27 

lb  24 

43  3« 

76342 

8 

23658 

85247  12 

14753 

08904 

4 

9109b 

33 

28 

lb  16 

43  44 

76360 

8 

23640 

85273   12 

14727 

08913 

4 

91087 

32 

29 

lb  8 

43  52 

76378 

9 

23b22 

85300  13 

14700 

08922 

4 

91078 

31 

30 

7  lb  0 

4  44  •  0 

9-  76395 

9 

10.  23bo5 

9-85327  '  13 

10.  I4b73 

10.  08931 

5 

9. 9iob9 

30 

31 

15  52 

44  8 

76413 

9 

23587 

85354   14 

i4b4b 

08940 

5 

91060 

29 

32 

15  44 

44  16 

76431 

9 

23569 

85380  14 

I4b20 

08949 

5 

91051 

28 

3i 

153b 

44  24 

76448 

10 

-  23552 

85407  ,  15 

14593 

08958 

5 

91042 

27 

34 
35 

15  28 

44  32 

764bb 

10 

23534 

85434  1  15 

1 45  bb 

089b  7 

5 

91033 

2b 

7  15  20 

4  44  40 

9.  7b484 

10 

10.2351b 

9. 85460  1  16 

10.  14540 

10.08977 

5 

9.91023 

25 

3b 

15  12 

44  48 

76501 

II 

23499 

85487  16 

14513 

0898b 

5 

91014 

24 

37 

15  4 

44  56 

76519 

II 

23481 

85514  16 

1448b 

08995 

6 

91005 

23 

3« 

14  5b 

45  4 

76537 

II 

23463 

85540  1  17 

14460 

09004 

6 

90996 

22 

39 
40 

14  48 

45  12 

76554 

12 

23446 

85567 

17 

18 

14433 

09013 

6 

90987 

21 

7  14  40 

4  45  20 

9.  7b572 

12 

10. 23428 

9- 85594 

10.  1440b 

10.  09022 

b 

9. 90978 

20 

41 

14  32 

45  28 

76590 

12 

23410 

85b2o  ,  18 

14380 

09031 

b 

90969 

19 

42 

14  24 

45  36 

7bbo7 

12 

23393 

85647  :  19 

14353 

09040 

6 

90960 

18 

43 

14  lb 

45  44 

76625 

13 

23375 

85674  '  19 

1432b 

09049 

b 

90951 

17 

44 
45 

14  8 

45  52 

7bb42 

13 

23358 

85700 

20 

14300 

09058 

7 

90942 

lb 

7  14  0 

4  4b  0 

9.  7bbbo 

13 

10.  23340 

9.85727 

20 

10.  14273 

10.  090b 7 

7 

9-  90933 

15 

4b 

13  52 

4b  8 

76677 

14 

23323 

85754  20 

1424b 

0907b 

7 

90924 

14 

47 

13  44 

4b  lb 

76695 

14 

23305 

85  780  2 1 

14220 

09085 

7 

90915 

13 

48 

1336 

46  24 

7b7i2 

14 

23288 

85807  :  21 

14193 

09094 

7 

9090b 

12 

49 
50 

13  28 

46  32 

76730 

14 

23270 

85834  j  22 

I4ibb 

09104 

7 

9089b 

II 

7  13  20 

4  4b  40 

9. 7b747 

15 

10.23253 

9.  85860  i  22 

10.  14140 

10.  091 13 

8 

9. 90887 

10 

51 

13  12 

4b  48 

76765 

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23235 

85887  :  23 

14113 

09122 

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90878 

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52 

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46  56 

7b782 

15 

23218 

85913   23 

,  14087 

09131 

8 

9o8b9 

8 

53 

12  5b 

47  4 

7b8oo 

lb 

23200 

85940   24 

i4obo 

09140 

8 

9o8bo 

7 

54 

55 

12  48 

47  12 

7b8i7 

lb 

23183 

85967 

24 

14033 

09149 

8 

90.85 1 

6 

7  12  40 

4  47  20 

9-  76835 

16 

10.  23ib5 

9-  85993 

24 

10. 14007 

10.  09158 

8 

9.  90842 

5 

5b 

12  32 

47  28 

76852 

17 

23148 

8bo2o  25 

13980 

09ib8 

8 

90832 

4 

57 

12  24 

47  36 

7b87o 

17 

23130 

8bo4b   25 

13954 

09177 

9 

90823 

J 

5« 

12  lb 

47  44 

7b887 

17 

23113 

86073 

2b 

13927 

0918b 

9 

90814 

2 

59 

12  8 

47  52 

76904 

17 

23096 

86100 

2b 

13900 

09195 

9 

90805 

I 

bo 

12  0 

48  0 

7b922 

18 

23078 

86126 

27 

13874 

09204 

9 

9079b 

0 

M. 

Hourp.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine.    M. 

125< 

> 

A 

A 

B 

B 

C 

C    54° 

Seconds  of  time 

V 

2» 

3" 

4, 

5' 

fi" 

13 
20 

7 

7» 

Prop,  parts  of  cols  <  H 

2 

3 
1 

4 
7 
2 

7 
10 

3 

9 
13 

S 

II 

17 
6 

16 

23 

8 

TABLE  44. 

Page  443 

S'. 

Log.  Sines,  Ta 

ngents,  and  .Secants. 

G'. 

•M)° 

^ 

A 

A 

B 

B 

C 

C   143° 

M. 
0 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

7  12  0 

4  48  0 

9.  76922    0 

10.  23078 

9. 86126 

0 

10.  13874 

10.  09204 

0 

9. 90796 

~6o" 

I 

U  ^2 

48  8 

76939   0 

23061 

86153 

0 

13847 

09213 

0 

90787 

59 

■> 

II  44 

4S  16 

76957    I 

23043 

86179 

I 

13821 

09223 

0 

90777 

58 

3 

II  30 

48  24 

76974    I 

23026 

86206 

I 

13794 

09232 

0 

90768 

57 

4 
5 

II  28 

7  1 1  20 

^J^J-^ 

76991    I 

23009 

ID.  22991 

86232^ 

9.  86259 

2 
2 

13768 

09241 

90759 

56 

4  48  40 

9-  77009  1  I 

10. 13741 

10.  09250 

9.  90750 

55 

6 

1 1  12 

48  48 

77026   2 

22974 

86285 

3 

I37I5 

09259 

90741 

54 

/ 

II  4 

48  56 

77043  :   2 

22957 

86312 

3 

13688 

09269 

90731 

53 

s 

10  56 

49  4 

77061     2 

22939 

86338 

4 

13662 

09278 

90722 

52 

lu 

10  48 
7  10  40 

49  12 
4  49  20 

77078  ,  3 
9-  77095   3 

22922 

86365 

_4 

13635 

10.  13608 

09287 
10.09296 

2 

^__  90713, 
9.  90704 

51 
50 

10.  22905 

9. 86392 

4 

II 

10  32 

49  28 

77112   3 

22888 

86418 

5 

13582 

09306 

2 

90694 

49 

12 

10  24 

49  36 

77130  !  3 

22870 

86445 

5 

13555 

09315 

2 

90685 

48 

'3 

10  16 

49  44 

77147   4 

22853 

86471 

6 

13529 

09324 

2 

9067b 

•47 

14 

10  8 

49  52 

77164   4 

22836 

86498 

6 

13502 

09333 

2 

90667 

46 

15 

7  10  0 

4  50  0 

9-77i"8i  1  4 

10.  22819 

9. 86524 

> 

10. 13476 

10. 09343 

2 

9.90657" 

45 

16 

9  52 

50  8 

77199  1  5 

22801 

86551 

7 

13449 

09352 

2 

90648 

44 

17 

9  44 

50  16 

77216  1  5 

22784 

86577 

7 

13423 

09361 

^ 

J 

90639 

43 

iS 

9  36 

50  24 

77233   5 

22767 

86603 

8 

13397 

09370 

3 

90630 

42 

_'9_. 

9  28 

50  32 
4  50  40 

77250   S 

22750 

86630 

8 
9 

13370 

09380 

3 
3 

90620 
9.  9061 1 

41 
40 

20 

7  9  20 

9. 77268   6 

10. 22732 

9.  86656^ 

10. 13344 

10.  09389 

21 

9  12 

50  48 

77285   6 

22715 

86683 

9 

13317 

09398 

3 

90602 

39 

■-»  -> 

9  4 

50  56 

77302   6 

22698 

86709 

10 

1 329 1 

09408 

•^ 

J 

90592 

38 

23 

8  56 

51  4 

77319   7 

22681 

86736 

ID 

13264 

09417 

4 

90583 

37 

24 

8  48 

51  12 
4  5120 

77336   7 
9.77353  '  7 

22664 

86762 

II 

13238 

09426 

4 
4 

90574 
9- 90565 

36 
35 

25" 

7  8  40' 

10.  22647 

9.  86789 

II 

10.  I32II 

10.09435 

26 

832 

51  28 

77370  '  7 

22630 

86815 

II 

I3I85 

09445 

4 

90555 

34 

27 

8  24 

51  36 

77387   8 

22613 

86842 

12 

I3I58 

09454 

4 

90546 

28 

8  16 

51  44 

77405   8 

22595 

86868 

12 

I3I32 

09^63 

4 

90537 

32 

29 
30 

8  8 

51  52 

77422   8 

22578 

86894 
9. 86921 

13 
13 

I3I06 

_  09473_ 

5 

90527 
9.  90518 

31 

30 

780 

4  52  0 

9-  77439   9 

10.  22561 

10.  13079 

10.  09482 

5 

31 

7  52 

52  8 

77456   9 

22544 

86947 

14 

13053 

09491 

5 

90509 

29 

32 

7  44 

52  16 

77473  ,  9 

22527 

86974 

14 

13026 

09501 

5 

90499 

28 

33 

7  3t> 

52  24 

77490 

9 

22510 

87000 

15 

13000 

09510 

5 

90490 

27 

34 
35 

728 

7  7  20 

52  32 

4  52  40 

77507 

10 

22493 

87027 

15 
15 

12973 

10.  12947 

09520 
10.09529 

5 

5 

90480 

26 

9-  77524  10 

10. 22476 

9-  87053 

9.90471 

25 

3*^ 

7  12 

52  48 

77541   10 

22459 

87079 

16 

1 292 1 

09538 

6 

90462 

24 

37 

7  4 

52  56 

77558  II 

22442 

87106 

16 

12894 

09548 

6 

90452 

23 

3ii 

6  56 

53  4 

77575   II 

27^  ?5 

87132 

17 

12868 

09557 

6 

90443 

22 

39 

6  48 

53  12 

77592   II 

22408 

87158 

17 
18 

12842 

09566 

6 
6 

90434 
9.  90424 

21 

20 

40 

7  6  40 

4  53  20 

9.77609   II 

10.  22391 

9.87185 

10.  I28I5 

10.  09576 

41 

632 

53  28 

77626  12 

22374 

8721 1 

18 

12789 

09585 

6 

90415 

19 

42 

6  24 

53  36 

77643   12 

22357 

87238 

18 

12762 

09595 

7 

90405 

18 

43 

6  16 

53  44 

77660  12 

22340 

87264 

19 

12736 

09604 

7 

90396 

17 

44 
45" 

6  8 

760 

53  52 

77677 

'3 
13 

_   22323 

87290 

19 

I27IO 

09614 

7 

90386 

16 

i   54  0 

9.  77694 

10.  22306 

9- 87317^  "20" 

10.  12683 

10.  09623 

7 

9.90377 

15 

46 

5  52 

54  8 

7771 1   0 

22289 

87343  20 

12657 

09632 

7 

90368 

14 

47 

5  44 

54  16 

77728 

13 

22272 

87369  1  21 

1 263 1 

09642 

7 

90358 

13 

48 

536 

54  24 

77744 

14 

22256 

87396  21 

12604 

09651 

7 

90349 

12 

40 
50 

5  28 

/  5  20 

54  32 

4  54  40 

77761 

9-  77778 

14 
14 

22239 

87422  22 

12578 

09661 
10.  09670 

8 
8 

__  90339^ 

II 

10.22222 

9. 87448   22 

10. 12552 

9-  90330 

10 

51 

5  '2 

54  48 

77795 

15 

22205 

87475  i  22 

12525 

096S0 

8 

90320 

9 

^2 

5  4 

SA   56 

77812 

15 

22X88 

87501 

23 

12499 

09689 

8 

90311 

8 

53 

4  56 

55  4 

77829 

15 

22I71 

87527 

•23 

12473 

09699 

8 

90301 

7 

54 

55 

448 

55  12 

77846 

15 

22154 

87554 
9.  87580 

24 
24 

12446 
10. 12420 

09708 

8 

90292 

6 

7  4  40 

4  55  20 

9.  77862 

16 

10.  22138 

10.  09718 

9" 

9. 90282 

5 

5'J 

4  32 

55  28 

77879 

16 

22I2I 

87606  ;  25 

12394 

09727 

9 

90273 

4 

57 

4  24 

55  36 

77896 

16 

22104 

87633  25 

12367 

09737 

9 

90263 

5S 

4  16 

55  44 

77913 

16 

22087 

87659  26 

I234I 

09746 

9 

90254 

2 

59 

4  8 

55  52 

77930 

17 

22070 

87685  26 

12315 

09756 

9 

90244 

I 

60 

4  0 

56  0 

77946 

17 
Diff. 

22054 

87711  1  26 

12289 

09765 

9 

90235 

0 

M. 
126 

Hour  1'.  M. 

Hour  A.  M. 

Cosine. 

Secant. 

Cotangent.  Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

3 

A 

A 

B 

B 

C 

C    53°  1 

Seconds  of  time 

1'    •>■ 

3    7 
I    2 

3- 

6 

10 

4 

P 

.)•    6- 

7'' 

1^ 

Prop,  parts  of  cols.  -<  B 

9 

5 

H   :   13 
17      20 

6  1  7 

IS 

23 

8 

Page  444 

TABLE  44. 

ft..aa^ 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

sr 

A 

A                B 

B 

C 

C       142° 

M. 

o 

I 

2 
■3 

4 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine.       M. 

740 

3  52 
3  44 
3  36 
328 

4  56     0 
56     8 
56   16 
56  24 
56  32 

9.  77946 

77963 
77980 

77997 
78013 

0 

I 
I 
I 

10. 22054 
22037 
22020 
22003 
21987 

9.87711 

87738 
87764 
87790 
87817 

0 
0 

1 
I 
2 

10.  12289 
12262 
12236 
12210 
12183 

10.  09765 

09775 
09784 

09794 

09803 

0 

0 
0 
0 

9-  90235 
90225 
90216 
90206 
90197 

60 
59 
58 
57 
56 

55 
54 
53 

S2 
51 

I 

7 
8 

_9_ 

lO 

II 

12 

13 
14 

\i 

17 
i8 

19 

7    3  20 
3  12 

3    4 
256 
2  48 

4  56  40 
56  48 

56  56 

57  4 
57  12 

9.  78030 

78047 
78063 
78080 
78097 

I 

2 
2 

2 
2 

10.21970 
21953 

21937 
21920 
21903 

9- 87843 
87869 

87895 
87922 

87948 

2 

3 
3 
3 
4 

10. 12157 
12131 
12105 
12078 
12052 

10.09813 
09822 
09832 
09841 
09851 

9.  90187 
90178 
90168 

90159 
90149 

7    2  40 
2  32 
2  24 
2  16 
2     8 

4  57  20 
5728 
57  36 
57  44 
57  52 

9-78113 
78130 
78147 
78163 
78 1 80 

3 

3 

3 
4 
4 

10.21887 
21870 

21853 
21837 
21820 

9.  87974 
88000 
88027 
88053 
88079 

4 
5 

I 
6 

10. 12026 
12000 

1 1973 
11947 

11921 

10.  09861 
09870 
09880 
09889 
09899 

2 
2 

2 
2  . 
2 

9.90139 
90130 
90120 
901 1 1 
90101 

50 

49 
48 
47 
46 

720 

I  52 
I  44 

I  30 
I  28 

4  58    0 
58    8 
58  16 
58  24 
5832 

9.78197 
78213 
78230 
78246 
78263 

4 
4 
5 
5 
5 

10. 21803 

21787 
21770 
21754 

21737 

9.  88105 
88131 
88158 
88184 
88210 

7 
7 
7 
8 
8 

10. 11895 

1 1 869 
1 1842 
I18I6 
1 1 790 

10.  09909 
09918 
09928 

09937 
09947 

2 

3 
3 
3 
3 

9.  90091 
90082 
90072 
90063 
90053 

45 
44 
43 
42 
41 

20 
21 
22 
23 
24 

25 
26 

27 

28 
29 

7     I  20 
I   12 

I     4 
0  56 
0  48 

4  58  40 
58  48 

58  56 

59  4 
59  12 

9.  78280 
78296 

78313 
78329 
78346 

i 

6 
6 

7 

10.  21720 
31704 
21687 
21671 
11654 

9. 88236 
88262 
88289 

88315 
88341 

9 

9 

10 

10 

10 

10. 1 1 764 

11738 
117II 
11685 
11659 

10.09957 
09966 
09976 
09986 
09995 

3 
3 
4 
4 
4 

9.  90043 
90034 
90024 
90014 
90005 

40 

39 
38 
37 
36 

35 
34 
33 
32 
31 
30 

29 

28 

27 
26 

7    0  40 
0  32 
0  24 
0  16 
0    8 

4  59  20 
59  28 
59  36 
59  44 
59  52 

9.  78362 
78379 

78395 
78412 

78428 

7 
7 
7 
8 
8 

10.  21638 
21621 
21605 

21588 
21572 

9. 88367 

88393 
88420 
88446 
88472 

11 
11 
12 
12 

13 

10.11633 

1 1607 

11580 

1 1554 
1 1 528 

10.  10005 
10015 
10024 
10034 
10044 

4 
4 
4 
5 
5 

9.  89995 
89985 
89976 
89966 
89956 

9. 89947 

89937 
89927 
89918 
89908 

30 
31 
32 

33 
34 

700 

6  59  52 
59  44 
59  36 
59  28 

500 
0    8 
0  16 
0  24 
0  32 

9-  78445 
78461 

78478 

78494 
78510 

8 
9 
9 
9 
9 

10-21555 
21539 
21522 
21506 
21490 

9. 88498 
88524 
88550 
88577 
88603 

13 
14 
14 
14 
IS 

10.  11502 

11476 

,     1 1450 
11423 

"397 

10.  10053 
10063 
10073 
10082 
10092 

I 

5 
5 

35 
36 

11 

39 

6  59  20 

59  12 

59    4 
58  56 

5848 

5     0  4" 
0  48 

0  56 

1  4 
I   12 

9. 78527 

78543 
78560 

78576 
78592 

10 
10 
10 
10 
II 

10.21473 

21457 
21440 
21424 
21408 

9. 88629 
88655 
88681 
88707 
88733 

15 

16 
16 
17 
17 

10.  11371 

1 1345 

11319 
11293 
11267 

10.  10102 
10112 
10121 
10131 
10141 

6 
6 
6 
6 
6 

9. 89898 

89SSS 
89879 
89S69 
89859 

25 
24 

23 
22 
21 

40 

41 
42 
43 
44 

6  58  40 

5832 
58  24 
58  16 
58    8 

5     I  20 

I  28 

I  36 
I  44 

I  52 

9.  78609 
78625 
78642 
78658 
78674 

11 
II 
12 
12 
12 

10. 21391 

21375 
21358 
21342 
21326 

9.88759 
88786 
88812 
88838 
88864 

17 
18 
18 
19 
19 

10. 11241 
11214 
11188 
11162 
11136 

10.  10151 
10160 
10170 
10180 
10190 

6 

7 
7 
7 
7 

9. 89S49 
89840 
89830 
80820 
89810 

20 

19 
18 

17 
16 

45 
46 

47 

48 

49 

6  58    0 

57  52 
57  44 
57  36 
57  28 

520 
2     8 
2  16 
2  24 
2  32 

9.  78691 
78707 
78723 
78739 
78756 

12 
13 
13 
13 
13 

10.  21309 
21293 
21277 
21261 
21244 

9. 88890 
88916 
88942 
88968 
88994 

20 
20 
20 
21 
21 

10.  1 11 10 

11084 
11058 
11032 
11006 

10.  10199 
10209 
10219 
10229 
10239 

7 

7 
8 
8 
8 

9.89801 
89791 
89  78 1 
89771 
89761 

15 
14 

13 
12 

II 

50 
51 
52 
53 
54 

6  57  20  1  5     2  40 
57  12  ,        2  48 
57    4  1        2  56 
56  56           3     4 
56  48           3  12 

9.  78772 
78  788 
78805 
78821 
78837 

14 
14 
14 
15 
15 

10.  21228 
21212 
21195 
21 1 79 
21 163 

10.  21147 
21131 
21114 
21098 
21082 
21066 

9. 89020 
89046 

89073 
8goq9 

89125 

22 
22 
23 
23 
24 

10.  10980 

10954 
10927 
10901 
10875 

10. 10248 
10258 
10268 
10278 
10288 

8 
8 
8 

9 
9 

9. 89752 
89742 

89732 
89722 
89712 

10 

9 

8 

7 
6 

11 

57 
58 
59 
60 

6  56  40 

56  32 
56  24 
56  16 
56    8 
56    0 

5    3  20 
3  28 
336 
3  44 

3  52 

4  0 

9-  78853 
78869 
78886 
78902 
78918 
78934 

15 

;i 

16 
16 
16 

9.89151 
89177 
89203 
89229 

89255 
89281 

24 

24 

25 

25 
26 

26 

10.  10849 
10823 
10797 
10771 
10745 
10719 

10.  10298 
10307 
10317 
10327 
10337 
10347 

9 
9 
9 
9 
10 
10 

9.  89702 
89693 
89683 

89673 
89663 

89653 

5 
4 

J 

2 
I 
0 

M. 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

12^ 

3 

A 

A                   B 

B 

c 

C         52°  1 

Seconds  of  time 

1» 

2s        3»         4' 

5» 

6» 

7s 

Prop,  parts  of  cols.  ■<  B 

(c 

2 

3 

I 

4           6           8         10 

7            to            13            16 

2             4             56 

12 
20 

7 

14 

23 

8 

TABLE  44. 

Page  445 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

38° 

A 

A       B 

B 

C 

C   141° 

y\. 

Hour  A.  M. 

Hour  p.  M. 

540 

Sine. 

DiflF. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

DiflF. 

Cosine. 
9- 89653 

M. 
60 

o 

6  1^6  0 

9-  78934 

0 

10.  21066 

9.  S9281 

0 

10.  10719 

10.  10347 

0 

I 

55  52 

4  8 

78950 

0 

21050 

89307  :  0 

10693 

10357 

0 

89643 

59 

2 

55  44 

4  16 

78967 

I 

21033 

89333    I 

10667 

10367 

0 

89633 

S8 

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55  3^ 

4  24 

78983 

I 

21017 

89359 

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1 064 1 

10376 

89624 

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4 

55  28 

4  32 

78999 

I 

21001 

89385 

2 

I0615 

10386 

89614 

56 

S 

6  55  20 

5  4  40 

9.  79015 

I 

10.  20985 

9.  8941 1    2 

10. 10589 

10.  10396 

9. 89604 

S5 

6 

55  12 

448 

79031 

2 

20969 

89437   3 

105(53 

10406 

89594 

54 

7 

55  4 

4  56 

79047 

2 

20953 

89463  :  3 

10537 

10416 

89584 

SS 

8 

54  56 

5  4 

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2 

20937 

89489  3 

IO51I 

10426 

89574 

52 

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lo 

5448 

5  12 

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2 

20921 

89515  \    4 

10485 

10436 

2 

89564 

51 
SO 

6  54  40 

5  5  20 

9-  79095 

1 
J) 

10.  20905 

9. 89541   4 

10.  10459 

10.  10446 

2 

9-  89554 

II 

54  32 

5  28 

791 1 1 

J) 

208S9 

895^7   5 

10433 

10456 

2 

89544 

49 

12 

54  24 

5  36 

79128 

3 

20872 

89593   5 

10407 

10466 

2 

89534 

48 

IS 

54  i(^ 

5  44 

79144 

3 

20856 

89619   6 

1 038 1 

10476 

2 

89524 

47 

14 

54  8 

5  52 

79160 

4 

20840 

89645   6 

10355 

10486 

2 

3 

89514 

46 

IS 

6  54  0 

560 

9.79176 

4 

10. 20824 

9.89671   6 

10.  10329 

10.  10496 

9.  89504 

45 

i6 

53  52 

6  8 

79192 

4 

20808 

89697 

7 

10303 

10505 

3 

89495 

44 

17 

53  44 

6  16 

79208 

5 

20792 

89723 

7 

10277 

10515 

3 

89485 

4,1 

i8 

53  36 

6  24 

79224 

5 

20776 

89749 

8 

1025  I 

10525 

3 

89475 

42 

19 

5328 

6  32 

79240 

5 

20760 

89775 

8 
9 

10225 
10.  IOI99 

1053s 
10.  10545 

3 

89465 

41 

40 

20 

6  53  20 

5  6  40 

9.  79256 

5 

10. 20744 

9. 89801 

3 

9- 89455 

21 

53  12 

6  48 

79272 

6 

20728 

89827   9 

IOI73 

10555 

4 

89445 

39 

22  i 

53  4 

6  56 

79288 

6 

20712 

89S53  '   10 

IOI47 

10565 

4 

89435 

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2^! 

52  56 

7  4 

79304 

6 

20696 

89879   10 

IOI2I 

10575 

4 

89425 

V 

24  1 

52  48 

7  12 

79319 

6 

20681 

89905   10 

10095 

10585 

4 
4 

89415 
9. 89405 

36 

ss 

2S 

6  52  40 

5  7  20 

9-  79335 

7 

10.  20665 

9.89931  '  II 

ID.  10069 

10.  10595 

26 

52  32 

728 

79351 

7 

20649 

89957  ,  II 

10043 

10605 

4 

89395 

34 

27  • 

52  24 

736 

79367 

7 

20633 

89983  1  12 

IOOI7 

10615 

5 

89385 

33 

28  f 

52  16 

7  44 

79383 

7 

20617 

90009  12 

09991 

10625 

5 

89375 

32 

29  i 

52  8 

7  52 

79399 

8 

20601 

90035  i  13 

09965 

10636 

S 

89364 

31 
30 

■  30  i 

6  52  0 

580 

9-  79415 

8 

10. 20585 

9.90061   13 

10.  09939 

10.  10646 

5 

9- 89354 

•'5'  ! 

51  52 

8  8 

79431 

8 

20569 

90086  13 

09914 

10656 

5 

89344 

29 

:.2* 

51  44 

8  16 

79447 

8 

20553 

901 12  *  14 

^     O9S88 

10666 

5 

89334 

28 

3^  . 

51  36 

8  24 

79463 

9 

20537 

90138  :  14 

09862 

10676 

6 

89324 

27 

134  I 
•3S 

51  28 
6  SI  20 

8  32 

79478 

9 

20522 
10.  20506 

90164  !  15 
9.90190  15 

09836 
10.09810 

10686 
10.  10696 

6 
6 

89314 
9. 89304 

26 

'2s 

5  8  40 

9.  79494 

9 

3^'  i 

51  12 

8  48 

79510 

10 

20490 

90216  16 

09784 

10706 

6 

89294 

24 

K37 

51  4 

8  56 

79526 

10 

20474 

90242  16 

09758 

10716 

6 

89284 

23 

3« 

50  56 

9  4 

79542 

10 

20458 

90268  1  16 

09732 

10726 

6 

89274 

22 

39 

50  48 

9  12 

5  9  20 

79558 

10 

20442 

90294 
9. 90320 

17 
17 

09706 

10736 

7 

89264 

21 

40 

6  50  40 

9-  79573 

11 

ID.  20427 

10.  09680 

10.  10746 

7 

9. 89254 

20 

41 

50  32 

9  28 

79589 

II 

2041 1 

9034b  1  18 

09654 

10756 

7 

89244 

19 

42 

50  24 

9  36 

79605 

II 

20395 

90371 

18 

09629 

10767 

7 

89233 

18 

43 

50  16 

9  44 

79621 

II 

20379 

90397 

19 

09603 

10777 

7 

89223 

17 

44 

50  8 
6  50  0 

9  52 

79636 

12 

20364 

90423 

19 

09577 

io787_ 
10. 10797 

7 
8 

89213 

16 

45  , 

5  10  0 

9. 79652 

12 

10.  20348 

9. 90449 

19 

10.09551 

9.  89203 

15 

4b 

49  52 

10  8 

79668 

12 

20332 

90475 

20 

09525 

10807 

8 

89193 

14 

47 

49  44 

10  16 

79684 

12 

20316 

90501  1  20 

09499 

10817 

8 

89183 

13 

48 

49  36 

10  24 

79699 

13 

20301 

90527  21 

09473 

10827 

8 

89173 

12 

49 

49  28 

10  32 

79715 

13 

20285 

90553  i  21 

09447 

10838 

8 

89162 

II 

50 

6  49  20 

5  10  40 

9-  79731 

13 

10.  20269 

9.90578 

22 

10.  09422 

10. 10848 

8 

9.89152 

10 

51 

49  12 

ID  48 

79746 

14 

20254 

90604 

22 

09396 

10858 

9 

89142 

9 

52 

49  4 

10  56 

79762 

14 

20238 

90630 

22 

09370 

1086S 

9 

89132 

S 

53 

48  56 

II  4 

79778 

14 

20222 

90656 

23 

09344 

10878 

9 

89122 

7 

54 

5S 

48  48 
6  4S  40 

II  12 

79793 

14 

20207 

90682  23 

09318 

10888 
10.  10899 

9 
9 

891 12 
9. 89101 

(> 

S 

5  II  20 

9.  79809 

15 

10.  2OI9I 

9. 90708  i  24 

10.  09292 

5(> 

48  32 

II  28 

79825 

15 

20175 

90734  24 

09266 

10909 

9 

89091 

4 

57 

48  24 

II  36 

79840 

15 

20160 

90759  25 

09241 

10919 

10 

89081 

3 

5« 

48  16 

II  44 

79856 

15 

20144 

90785  ,  25 

09215 

10929 

10 

89071 

2 

59 

48  8 

II  52 

79872 

16 

20128 

908 1 1 

26 

09189 

10940 

10 

89060 

1 

bo 

1   48  0 

12  0 

79887 

16 

201  13 

90837 

26 

09163 

10950 

10 

89050 

0 

u. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

DiflF. 

Secant. 

Cotangent.  DiflF. 

Tangent. 

Cosecant. 

DiflF. 

Sine. 

M. 

128° 

A 

A        B 

B 

c 

C    51°  1 

Seconds  of  time. .. 

!■ 

2- 

3' 

4. 

5» 

«• 

7^ 

Prop,  parts  of  cols 

\t 

2 

3 

I 

4 

6 

3 

6 
10 

4 

8 

13 

5 

xo 

1 

12 

8 

14 
23 

9 

Page  446 

TABLE  44. 

S'. 

• 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

39° 

A 

A 

B 

B 

C 

C   140° 

M. 

Hour  A.  M.  Hour  p.  m. 

Sine. 

DiflF. 

Cosecant. 

Tangent. 

Diff. 

Cotangent.  | 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  48  05 

12   0 

9. 79887 

0 

10.  201 13 

9. 90837 

0 

10.09163  ' 

10.  10950 

0 

9.  89050 

60 

I 

47  52 

12   8 

79903 

0 

20097 

90863 

0 

09137 

10960 

0 

89040 

59 

2 

47  44 

13  16 

79918 

I 

20082 

90889 

I 

091 1 1 

10970 

0 

89030 

5^ 

J 

47  36 

12  24 

79934 

I 

20066 

90914 

I 

09086 

10980 

89020 

57 

4 

47  28 

12  32 

79950 

I 

20050 

90940 

2 

09060 

1 099 1 

89009 

5<3 

S 

6  47  20  !  5 

12  40 

9.  79965 

I 

10. 20035 

9. 90966 

2 

10.  09034 

10.  IIOOI 

9.  88999 

55 

6 

47  12 

12  48 

79981 

2 

20019 

90992 

3 

09008 

lion 

88989 

54 

7 

47  4 

12  56 

79996 

2 

20004 

91018 

3 

08982 

1 1022 

88978 

53 

8 

46  56 

13  4 

80012 

2 

19988 

91043 

3 

08957 

1 1032 

88968 

52 

9 

46  48   • 

13  12 

80027 

2 

19973 

91069 

4 

08931 

1 1042  ! 

2 
2 

88958 
9.  88948 

51 

50 

10 

6  46  40  5 

13  20 

9.  80043 

3 

10. 19957 

9.91095 

4 

10.  08905 

10. 1 1052 

II 

46  32  ^ 

1328 

80058 

3 

19942 

91 121    5 

08879 

1 1 063 

2 

88937 

49 

12 

46  24 

n  ^6 

80074 

3 

19926 

91147 

5 

08853 

1 1073 

2 

88927 

48 

n 

46  16 

13  44 

80089 

3 

19911 

91 172 

6 

08828 

11083 

2 

88917 

47 

14 

15 

46  8 

13  52 

80105 

4 

19895 

91 198 

6 

08802 

1 1094 

2 

88906 

4b 

6  46  0  5 

14   0 

9.  80120 

4 

10.  19880 

9.91224 

6 

10.  08776 

10. 1 1 104 

3 

9.  88896 

45 

i6 

45  52 

14  8 

80136 

4 

19864 

91250 

7 

08750 

11114 

3 

8S886 

44 

17 

45  44 

14  16 

801 5 1 

4 

19849 

91276 

7 

08724 

11125 

3 

^^^75 

4.S 

18 

45  3 'J 

14  24 

80166 

5 

19834 

9I30I 

8 

08699 

"135 

88865 

42 

'9_ 

20 

45  28 

14  32 

80182 

5 

19818 

91327 

8 

08673 

1 1 145 

3 
3 

88855 

41 

6  45  20  5 

14  40 

9. 80107 

5 

10. 19803 

9-91353 

9 

10. 08647 

10.  II 156 

9.  88844 

40 

21 

45  12 

14  48 

80213 

5 

19787 

91379 

9 

08621 

1 1 166 

4 

88834 

39 

22 

45  4  i 

14  5^^ 

80228 

6 

19772 

91404 

9 

08596 

1 1 176 

4 

88824 

38 

2^. 

44  56 

15  4 

80244 

6 

19756 

91430 

10 

08570 

11187 

4 

88813 

37 

24 

2S 

44  48 

IS  12 

80259 

6 

19741 

91456 

10 

08544 

11197 

4 

88803 

36 

6  44  40  1  5 

i:;  20 

9.  80274 

6 

10.  19726 

9.  91482 

II 

10.08518 

10. 11207 

4 

9-  88793 

35 

2  > 

44  32 

IS  28 

80290 

7 

19710 

91507 

II 

08493 

11218 

5 

88782 

34 

27 

44  24 

15  36 

80305 

7 

19695 

91533 

12 

08467 

1122S 

5 

88772 

33 

2S 

44  16 

15  44 

80320 

7 

19680 

91559 

12 

08441 

1 1239 

5 

88761 

32 

2-) 

44  S 

15  52 

80336 

7 

19664 
10. 19649 

91585 

9.  9I6IO 

12 
13 

08415 
10.  08390 

II 249 
10. 1 1259 

5 
5 

88751 

31 

0  44  0   5 

16  0 

9.80351 

8 

9.  88741 

30 

,>I 

43  52 

16  8 

80366 

8 

19634 

91636 

13 

08364 

1 1270 

5 

88730 

29 

->  > 

43  44 

16  16 

80382 

8 

19618 

91662 

14 

08338 

1 1280 

b 

88720 

28 

J*  J 

43  36 

16  24 

80397 

8 

19603 

91688 

14 

08312 

11291 

6 

88709 

27 

3V 
^>5 

43  28  . 
6  43  20  5 

1632 

80412 

9 

19588 

9I7I3 

15 

08287 

11301 

6 

88699 
9.'88688 

2b 

25 

16  40 

9.  80428 

9 

10. 19572 

9.91739 

15 

10. 08261 

10. 11312 

6 

^.6 

43  12 

16  48 

80443 

9 

19557 

91765 

15 

08235 

1 1322 

6 

88678 

24 

>7 

43  4 

16  56 

80458 

9 

19542 

91 791 

16 

08209 

1 1332 

6 

88668 

23 

ss 

42  56 

17  4 

80473 

10 

19527 

9I8I6 

16 

08184 

"343 

7 

■  88657 

22 

40 

42  48 

17  12 

80489 

10 

19511 

91842 

17 
17 

08158 

"353 

7 

88647 

21 

6  42  40  5 

17  20 

9.  80504 

10 

10.  19496 

9.91868 

10.  08132 

10. 1 1364 

7 

9.  88636. 

20 

■fl 

42  32 

17  28 

80519 

10 

1 948 1 

91893 

18 

08107 

"374 

7 

88626 

19 

•  T 

42  24 

17  ^.6 

80534 

II 

19466 

9I9I9 

18 

08081 

"385 

7 

88615 

18 

1-J 

42  16 

17  44 

80550 

II 

19450 

91945 

18 

08055 

"395 

7 

88605 

17 

44_ 

45 

42  8 

0  42  0  t; 

17  52 

18  0 

80565 

II 

19435 

9I97I 

19 

08029 

1 1406 

8 

88594 

lb 

0.  80580 

12 

10. 19420 

9. 91996 

19 

10. 08004 

10.  11416 

8 

9.  88584 

15 

46 

42  52 

iS  8 

80595 

12 

19405 

92022 

20 

07978 

1 1427 

8 

88573 

14 

47 

41  44 

18  16 

80610 

12 

19390 

92048 

20 

07952 

"437 

8 

88563 

13 

4'' 

41  3'^ 

18  24 

■  80625 

12 

19375 

92073 

21 

07927 

11448 

8 

88552 

12 

49 
5^ 

41  28 

6  41  23   5 

18  32 

80641 

13 

19359 

92099 

21 

07901 

1 1458 

9 

88542 

II 

iS  40 

9.  80656 

13 

10.  19344 

9.92125 

21 

10. 07875 

10. 1 1469 

9 

9.88531 

10 

51 

41  12 

18  48 

80671 

13 

19329 

92150 

22 

07850 

"479 

9 

88521 

9 

52 

41   4 

18  0 

80686 

13 

19314 

92176 

22 

07824 

1 1490 

9 

88510 

8 

5S 

40  56 

19  4 

80701 

14 

19299 

92202 

23 

07798 

11501 

9 

88499 

7 

54 
55 

40  48 

6  40  40  5 

19  12 

80716 

14 

19284 

92227 

23 
24 

07773_ 
10.  07747 

"5"„ 
10. 11522 

9 
10 

88489 
'9788478 

b 

"  5^ 

19  20 

9.  80731 

14 

10.  19269 

9-92253 

56 

40  32 

19  28 

80746 

14 

19254 

92279 

24 

07721 

"532 

10 

88468 

4 

57 

40  24 

19  36 

80762 

15 

19238 

92304 

24 

07696 

"543 

10 

88457 

J 

5^ 

40  16 

19  44 

80777 

15 

19223 

92330 

25 

07670 

"553 

10 

88447 

2 

50 

40  8 

19  52 

80792 

15 

19208 

92356 

25 

07644 

II 564 

10 

88436 

I 

Oo 
M. 

40  0 

20  0 

80807 

15 

19193 

92381 

26 

07619 

"575 

10 

88425 

0 

Hour  P.M.  H( 

jurA.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

129 

0 

A 

A 

B 

B 

c 

C 

50° 

Seconds  of  time 

1> 

2» 

3« 

4» 

5" 

6» 

T 

I  A 
Prop,  parts  of  cols.  <  B 

( c 

2 

3 

I 

4 
6 

3 

6 

lO 

4 

8 
J3 

5 

10 
16 

7 

12 

19 

8 

13 

23 

9 

TABLE  44. 

Page  447 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

40° 

A         A 

B          B       C 

C   139° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DiflF. 

Cosecant. 

Tangent. 

DifF. 

Cotangent. 

Secant. 

DiflF. 

Cosine. 

M. 

o 
I 

,■> 

4 

5 
6 

/ 
S 

9 

6  40  0 

39  52 
39  44 
39  36 
3928 

6  39  20 
39  12 

39  4 
38  56 
3848 

5  20  0 
20  8 
20  16 
20  24 
20  32 

9. 80807 
S0822 
80837 
S0S52 
80867 

0 
0 
0 
I 
I 

10. 19193 

19178 
19163 
19148 
19133 

9.92381 

92407 

92433 
92458 
92484 

0 
0 

I 
I 
2 

10.07619 

07593 
07567 
07542 
07516 

10. 11575 

1 1585 
11596 
11606 
I1617 

0 
0 
0 

9. 88425 
88415 
88404 

88394 
8838-, 

60 

59 

58 
57 
56 

5  20  40 
20  48 

20  56 

21  4 
21  12 

9. 80882 
80897 
S0912 
80927 
80942 

I 
I 
2 
2 

2 

10.  19118 

19103 
19088 

19073 
19058 

9.92510 

92535 
92561 

92587 
92612 

2 

3 
3 

3 

4 

10.  07490 

07465 
07439 
07413 
07388 

10.  1 1628 

1 1638 
II 649 

11660 
11670 

2 

9- 88372 
88362 

88351 
88340 

88330 

55 
54 
53 
52 
51 

10 

I ; 
14 

6  38  40 
38  32 
38  24 
38  16 
38  8 

5  21  20 
21  28 
21  36 
21  44 
21  52 

9.80957  j   2    10.19043 
80972  '   3       19028 

80987  1  3     19013 
81002   3     18998 

81OI7  ;   3  1      18983 

9. 92638 
92663 
92689 

92715 
92740 

4 

5 

i 

6 

10.  07362 

07337 
07311 
07285 
07260 

10.  1I68I 
11692 
1 1 702 

II7I3 
11724 

2 

2 
2 
2 

3 

9.88319 

88308 
88298 
88287 
88276 

50 

49 
48 

47 
46 

15 

16 

17 

iS 

19 

6  38  0 
37  52 
37  44 
37  36 
37  28 

5  22  0 

22  8 
22  16 
22  24 
22  32 

9.81032 
81047 
8I06I 
81076 
81O9I 

4   10. 18968 
4     18953 
4     18939 

4  18924 

5  !    18909 

9. 92766 
92792 
92817 

92843 
92868 

6 

7 

7 
8 
8 

10. 07234 
07208 

07183 

07157 
07132 

10.  11 

11 
11 
11 
11 

734 

745 
756 
766 

777 
788 

799 
809 
820 
8^1 

3 

3 
3 
3 
3 

9. 88266 
88255 
88244 
88234 
88223 

45 
44 
43 
42 
41 

20 
21 

22 

-J 

24 

6  37  20 
37  12 

37  4 
3656 
36  48 

5  22  40 
22  48 

22  56 

23  4 
23  12 

9.  81 106 
81I2I 
81  136 
81I5I 
81  166 

5  10. 18894 
5     18879 

5  '    18864 

6  188.19 
6  1    18834 

9.  92894 
92920 

92945 
92971 

92996 

9 

9 

9 

10 

10 

10. 07106 

07080 

07055 

07029 
07004 

10.  11 
11 
11 
II 
11 

4 

4 
4 
4 
4 

9. 88212 
88201 
88191 
88180 
88169 

40 
39 

38 
37 
36 
35 
34 

32 
31 

25 
26 

27 
28 
29 
30 
31 
32 
J.I 
34 

;? 

37 
38 
39 
40 

41 

42 

43 
44 

45 
46 
47 
48 
49 

6  36  40 

3^  32 
36  24 
36  16 
36  8 

5  23  20 
23  28 
23  36 
23  44 
23  52 

9.  81  180 
81I95 
812IO 
81225 
81240 

6 
6 

7 
7 
7 

10.  18820 
18805 
18790 

18775 
18760 

9. 93022 
93048 

93073 
93099 
93124 

II 
II 
12 
12 
12 

10.06978 
06952 
06927 
06901 

06876 

10.  1 1842 

II852 
11863 
11874 
11885 

4 
5 
5 
5 
5 

9.88158 
88148 
88137 
88 1 26 
881 15 

6  36  0 
35  52 
35  44 
35  36 
35  28 

5  24  0 
24  8 
24  16 

24  24 
24  32 

9. 81254 
81269 
812S4 
81299 
813I4 

7  10. 18746 

8  !    18731 
8     18716 
8     18701 
8     18686 

9-93150 

93175 
93201 

93227 
93252 

13 
13 
14 
14 
14 

10. 06850 

06825 
06799 
06773 

06748 

10.  11895 
11906 

II9I7 
11928 

1 1939 

5 
6 
6 
6 
6 

9.88105 
88094 
88083 
88072 
88061 

30 

29 

28 

27 
26 

6  35  20 
35  12 
35  4 
34  56 
34  48 

5  24  40 
2448 

24  56 

25  4 
25  12 

9.81328 

81343 
81358 

81372 

81387 

I 

9 
9 

ID 

10. 18672 

18657 
18642 
18628 
18613 

9.93278 

93303 
93329 
93354 
93380 
9. 93406 

93431 
93457 
93482 
93508 

15 

'I 

16 
17 

10. 06722 
06697 
06671 
06646 
06620 

10.  11949 
11960 

11971 
1 1982 

"993 

6 
6 

7 
7 
7 

9.88051 
88040 
88029 
88018 
88007 

25 

24 

23 
22 

21 

6  34  40 
34  32 
34  24 
34  16 
34  8 

5  25  20 
25  28 
25  36 
25  44 
25  52 

9. 81402 
8I4I7 
8143I 
81446 
8146I 

10 
10 
10 
II 
II 

10.  18598 

18583 
18569 

18554 
18539 

17 
17 
18 
18 

19 

10.06 
06 
06 
06 
06 

10.06 

06 
06 
06 
06 

594 
569 
543 
518 
492 

10. 12004 
12015 
12025 
12036 
12047 

7 
7 
8 
8 
8 

9. 87996 
87985 
87975 
87964 
87953 

20 

19 

18 

17 
16 

6  34  0 

33   52 
33  44 
33  36 
33  28 

5  26  0 
26  8 
26  16 
26  24 
26  32 

9.81475 
81490 
8,505 
815I9 

81534 

II 
II 
12 
12 
12 

10.  18525 
18510 

18495 

1 848 1 

18466 

9-  93533 
93559 
93584 
93610 

93636 

19 
20 

20 

20 

21 

467 
441 
416 
390 
364 

10.  1205S 
12069 
12080 
12091 
12102 

8 
8 
8 
9 
9 

9.  87942 

87931 
87920 

87909 
87898 

15 
14 

13 
12 

II 

50 
51 

52 
53 
54 

6  33  20 
33  12 
33  4 
32  56 
32  48 

6  26  40 
26  48 

26  56 

27  4 
27  12  1 

9.81549 
81563 

8i57§ 
81592 
81607 

12 

13 
13 
13 
13 

10. 18451 

18437 
18422 
18408 

18393 

9.  93661 

93687 
93712 
93738 
93763 

21 
22 
22 
23 
23 
23 
24 
24 

25 
25 
26 

10. 06339 

06313 

06288 

06262 

06237 

10.  12113 
12123 
12134 
12145 
12156 

9 

9 

9 

10 

10 

9.  87887 

87877 
87866 

87855 
87844 

10 

9 

8 

7 
6 

55 

11 

59 
60 

6  32  40 
32  32 
32  24 
32  16 
32  8 
32  0 

5  27  20 
27  28 
27  36 
27  44 

27  52 

28  0 

9.  81622 
81636 
81651 
81665 
8j68o 
81694 

14  1  10. 18378 

14  '     18364 
14  1     18349 

14  1     18335 

15  '     18320 

15       18306 

9-93789 
93814 
93840 

93865 
93891 
93916 

10. 062 1 1 
06186 
06160 

06135 

06109 
06084 

10.  12167 
121 78 
121S9 
12200 
12211 
12222 

10 
10 
10 
10 
II 
II 

9-87833 
87822 
8781 1 
87800 
87789 
87778 

5 
4 

3 

2 

I 

(1 

Hour  P.M. 

Hour  A.M. 

Cosine. 

Diff.i  Secant. 

Cotangent.  DiflF. 

Tangent.  | 

Cosecant. 

DiflF. 

Sine. 

M. 

130' 

3 

A           A 

B            B        C 

C    49°  1 

Seconds  of  time. 

Is 

•i'          li'          4"     .i»    «»  '   7" 

[   ' 

(A 
Prop,  parts  of  cols.  <  B 

2 

3 

I 

4     6 
6    10 
3     4 

7 
13 

S 

16 
7 

II 
8 

13 
22 

9 

Page  448 

TABLE  44. 

i 

S'. 

Log 

;.  Sines,  Tangents,  and  Secants. 

- 

G'. 

41° 

A 

A 

B 

B 

c 

C   138° 

M. 

Hour  A.M. 

Hour  P.M. 

Sine. 

DifF. 

Cosecant. 

Tangent. 

DiflF. 

Cotangent. 

Secant. 

DiflF. 

Cosine. 

M. 

60 

() 

6  32  0 

S  28  0 

9. 81694 

0 

10.  18306 

9.93916 

0 

10. 06084 

10.  12222 

0 

9.  87778 

I 

31  52 

28  8 

81709 

0 

1 829 1 

93942 

0 

06058 

12233  i 

0 

87767 

59 

2 

31  44 

28  16 

81723 

0 

18277 

93967 

1 

06033 

12244 

0 

87756 

58 

3 

31  36 

28  24 

81738 

I 

18262 

93993 

1 

06007 

12255 

87745 

57 

4 

31  28 

28  32 

81752 

I 

18248 

94018 

2 

05982 

12266 



87734 
9.  87723 

56 

S5 

5 

6  31  20 

5  28  40 

9.81767 

I 

10.  18233 

9.  94044 

2 

10.05956 

10.  12277 

6 

31  12 

28  48 

81781 

I 

1 82 1 9 

94069 

3 

05931 

12288 

87712 

54 

7 

31  4 

28  56 

81796 

2 

18204 

94095 

3     05905 

12299 

87701 

53 

8 

30  56  1 

29  4 

81810 

2 

18190 

94120 

3     05880 

12310 

87690 

52 

9 

30  48 

29  12 

81825 

2 

18175 

94 1 40 

9.94171 

4     05854^ 
4   10.05829 

1 232 1 

10.  12332 

2 

87679 

51 

10 

6  30  40 

c  29  20 

9.81839 

2 

10.  18161 

2 

9.  87668 

50 

1 1 

30  32 

29  28 

81854 

^ 
J 

18146 

94197 

5    05803 

12343 

2 

87657 

49 

12 

10  24 

29  36 

81868 

18132 

94222 

5  1   0577S 

12354 

2 

87646 

4S 

13 

30  16 

29  44 

81882 

3 

18118 

94248 

6    05752 

12365 

2 

87635 

47 

14 

IS 

30  8 

29  52 

81897 

3 

18103 

94273  j 

6 

05727 

i2376_ 
10.  12387 

3 
3 

87624 

46 

6  30  0 

5  30  0 

9.  81911 

4 

10.  18089 

9.94299  ! 

6 

10.05701 

9.87613 

45 

16 

29  52 

30  8 

81926 

4 

18074 

94324 

7 

05676 

12399  1 

3 

87601 

44 

17 

29  44 

30  16 

81940 

4 

18060 

94350 

7 

05650 

I24IO 

3 

87590 

43 

iS 

29  36 

30  24 

81955 

4 

18045 

94375 

8 

05625 

12421 

3 

87579 

42 

iq 

29  28 

30  32 

81969 

5 

1 803 1 

94401  1 

8 

05599 

12432 

4 

87568 

41 

20 

6  29  20 

5  30  40 

9.81983 

5 

10.  18017 

9.94426  \ 

8 

10.05574 

10. 12443 

4 

9.87557 

40 

21 

29  12 

30  48 

81998 

S 

18002 

94452 

9 

05548 

12454 

4 

87546 

39 

22 

29  4 

30  5*3 

82012 

5 

17988 

94477 

9 

05523 

12465 

4 

87535 

38 

23 

28  56 

31  4 

82026 

5 

17974 

94503 

10 

05497 

12476 

4 

87524 

37 

24 

2S 

28  48 

31  12 

82041 

6 

17959 

94528 

10 

05472 

12487 

4 

87513 

36 

6  28  40 

5  31  20 

9.  82055 

6 

10.17945 

9-  94554  ' 

II 

10.  0544b 

10. 12499 

5 

9.87501 

35 

26 

28  32 

31  28 

82069 

6 

17931 

94579 

II 

05421 

12510 

5 

87490 

34 

27 

28  24 

31  36 

82084 

6 

17916 

94604 

II 

05396 

12521 

5 

87479 

33 

28 

28  16 

31  44 

82098 

7 

17902 

94630 

12     05370 

12532 

5 

87468 

32 

30 

28  8 

31  52 

82112 
9.  82126 

7 

17888 

94655 

12 

05345 

12543 

5 

87457 

31 

6  28  0 

5  32  0 

7 

10.  17874 

9. 94681 

13 

10.05319 

10. 12554 

6 

9. 87446 

30 

3' 

27  52 

32  8 

82141 

7 

17859 

94706 

13 

05294 

12566 

6 

87434 

29 

'l2 

27  44 

32  16 

82155 

8 

17845 

94732 

14 

05268 

12577 

6 

87423 

28 

33 

27  36 

32  24 

82169 

8 

1 783 1 

947s  7 

14 

05243 

12588 

6 

87412 

27 

34 

3S 

27  28 

32  32 

82184 

8 

17816 

94783 

14 

05217 

12599 

6 

87401 

26 

6  27  20 

5  32  40 

9.82198 

8 

10.  17802 

9.  94808 

15 

10.05192 

10.  12610 

7 

9.  87390 

25 

3^ 

27  12 

3248 

82212 

9 

17788 

94834 

15 

05106 

12622 

J 

87378 

24 

37 

27  4 

32  56 

82226 

9 

17774 

94859 

16 

05141 

12633 

^7 

87367 

23 

S« 

26  S6 

33  4 

82  240 

9 

17760 

94884 

16 

05116 

12644 

7 

87356 

0? 

39 
45 

26  48 
6  2J  40 

33   12 

82255 

__9_ 
10 

17745 

94910 

17 
17 

05090 

12655 

7 
7 

87345 
9-  87334 

21 
20 

5  33  20 

9.  82269 

10.  1 7731 

9- 94935 

10.05065 

10.  12666 

41 

25  32 

33  28 

S2283 

10 

17717 

94961 

17 

05039 

12678 

8 

87322 

19 

4- 

25  24 

33  36 

82297 

10 

17703 

94986 

18 

05014 

12689 

•  8 

87311 

18 

43 

26  16 

33  44 

823 1 1 

10 

17689 

95012 

18 

04988 

12700 

8 

^73°o 

17 

44 

26  8 

33  52 

82326 

10 

17674 

95037 

19 
19 

04963 
10. 04938 

12712 

8 

87288 

lb 

4S 

6  26  0 

5  34  0 

9.  82340 

II 

10.  17660 

q. 95062 

10. 12723 

8 

9.87277 

15 

46 

25  52 

34  8 

82354 

II 

17646 

95088 

20 

04912 

12734 

9 

87266 

14 

47 

25  44 

34  16 

82368 

II 

17632 

95113 

20 

04887 

12745 

9 

87255 

13 

48 

25  36 

34  24 

82382 

II 

17618 

95139 

20 

04861 

12757 

9 

87243 

12 

49 
SO 

25  28 
6  25  20 

34  32 
5  34  40 

82396 

12 

17604 

95164 

21 

04836 

12768 

9 

87232 

1 1 

10 

9.  82410 

12 

10. 17590 

9.95190 

21 

10. G4810 

10.  12779 

9 

9.  87221 

SI 

25  12 

34  48 

82424 

12 

17576 

95215 

22 

04785 

I279I 

10 

87209 

0 

S2 

25  4 

34  56 

82439 

12 

17561 

95240 

22 

04760 

12802 

10 

87198 

s 

S'l 

24  S*'^ 

35  4 

82453 

13 

17547 

95266 

22 

04734 

12813 

10 

87187 

T 

54 
SS 

24  4L 
6  24  40 

35  12 

82467 

13 

17533 

95291 

1  ^^ 

j    04709 

12825 

10 

87175 

b 

5  35  20 

9. 82481 

13 

1  10. 17519 

9-95317 

23 

10.  04683 

10.  12836 

10 

9.87164 

5 

S(' 

24  32 

1   35  28 

82495 

»3 

17505 

95342 

!  24 

04658 

12847 

10 

87153 

■  4 

S7 

24  24 

;  35  36 

82509 

14 

1    17491 

95368 

24 

04632 

12859 

II 

87141 

J 

S'S 

24  16 

35  44 

82523 

14 

17477 

95393 

25 

04607 

12870 

II 

87130 

2 

S9 

24  8 

35  52 

82537 

14 

17463 

95418 

25 

1    04582 

12881 

II 

87119 

I 

60 

24  0 

36  0 

82551 

14 

17449 

95444 

25 
j  DiflF. 

04556 

12893 

II 

87107 

0 

M. 

Houri-  M. 

Hour  A.  M. 

Cosine. 

DiflF 

Secant. 

Cotangent. 

Tangent. 

Cosecant. 

DiflF. 

1 

Sine. 

M. 

131 

0 

A 

A 

B 

B 

C 

C    48° 

Seconds  of  time 

1" 

2" 

3> 

4. 

5» 

«» 

7» 

Prop,  parts  of  cols.  -(  B 

2 

3 

I 

4 
6 

3 

5 

lO 

4 

7 
13 

6 

7 

II 

8 

12 
22 
10 

TABLE  44. 

Page  449 

S'. 

» 

Log.  Sines,  Tangents,  and  Secants. 

Cx'. 

42° 

A 

A 

B 

B 

C 

C   137° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DiflF. 

Cosecant. 

Tangent. 

Diflf. 

Cotangent. 

Secant. 

DiflF. 

Cosine. 

M. 

o 

6  24  0 

5  36  0 

9.82551 

0 

10.  17449 

9-  95444 

0 

10.  04556 

10.  12893 

0 

9.87107 

60 

I 

23  52 

36  8 

82565 

0 

17435 

95469 

0 

04531 

12904 

0 

87096 

59 

2 

23  44 

36  16 

82579 

0 

17421 

95495 

I 

04505 

12915 

0 

87085 

58 

> 

23  36 

36  24 

-"52593 

I 

17407 

95520 

I 

04480 

12927 

87073 

57 

4 

23  28 

36  32 

82607 

I 

17393 

95545 

2 

04455 

12938 

87062 

50 

S 

6  23  20 

S  36  40 

9. 82621 

I 

10.17379 

9-95571 

2 

10.  04429 

10.  12950 

9-  87050 

55 

6 

23  12    36  48 

82635 

I 

17365 

95596 

3 

04404 

1 296 1 

87039 

54 

7 

23  4 

36  56 

82649 

2 

1 735 1 

95622 

3 

04378 

12972 

87028 

53 

S 

22  56 

37  4 

82663 

2 

17337 

95647 

3 

04353 

12984 

2 

87016 

52 

9 

22  48 

37  12 

82677 

2 

17323 

95672 

4 

04328 

12995 

2 

87005 

51 

lO 

6  22  40  ;  5  37  20 

9. 82691 

2 

10.  17309 

9. 95698 

4 

10.  04302 

10. 13007 

2 

9-  86993 

50 

II 

22  32     37  28 

82705 

3 

17295 

95723 

5 

04277 

13018 

2 

86982 

49 

12 

22  24     i^   36 

82719 

3 

1 728 1 

95748 

5 

04252 

13030 

2 

86970 

48 

IS 

22  16  ;   37  44 

82733 

3 

17267 

95774 

5 

04226 

1 304 1 

86959 

47 

14 

22  8  t   37  52 

82747 

3 

17253 

93799 

6 

04201 

13053 

3 

86947 

46 

IS 

6  22   0   5  38   0 

9.82761 

3 

10. 17239 

9.  95825 

6 

10.04175 

10. 13064 

3 

9. 86936 

45 

i6 

21  52    3«  8 

82775 

4 

17225 

95850 

7 

04150 

13076 

3 

86924 

44 

17 

21  44  :     38  16 

82788 

4 

17212 

95875 

7 

04125 

13087 

3 

86913 

43 

i8 

21  36  I    38  24 

82802 

4 

17198 

95901 

S' 

04099 

13098 

3 

86902 

42 

_L9_ 

20 

21  28     38  32 

82816 

4 

5 

1 7184 

95926 

8 

04074 

13110 

4 

86890 

41 

6  21  20  5  38  40 

9. 82830 

10.  1 71 70 

9-  95952 

8 

10. 04048 

10. 13121 

4 

9. 86879 

40 

21 

21  12  :   38  48 

82844 

S 

17156 

95977 

9 

04023 

13133 

4 

86867 

39 

22 

21   4  I    38  56 

82858 

S 

1 7142 

96002 

9 

03998 

13145 

4 

86855 

38 

2> 

20  56    39  4 

82872 

S 

17128 

96028. 

10 

03972 

13156 

4 

86844 

37 

24 

20  48 

39  12 

S  39  20 

82885 

6 

17115 

96053 

10 

03947 

13168 

5 

86832 

36 

2S 

6  20  40 

9.  82899 

6 

10.  17101 

9. 96078 

II 

10. 03922 

10.  13179 

5 

9.86821 

35 

26 

20  32    39  28 

S2913 

6 

17087 

96104 

II 

03896 

13191 

5 

86S09 

34 

27 

20  24    39  36 

82927 

6 

17073 

96129 

II 

03871 

13202 

5 

86798 

-1  -> 

28 

20  16    39  44 

82941 

6 

17059 

96155 

12 

03845 

13214 

5 

86786 

32 

29 

20  8    39  52 

82955 

7 

17045 

96180  1  12 

03820 

13225 

6 

.  86775 

31 

SO 

6  20  0   5  40  0 

9. 82968 

7 

10. 17032 

9. 96205 

13 

10.03795 

10. 13237 

6 

9.86763 

30 

SI 

19  52    40  8 

82982 

7 

17018 

96231   13 

03769 

13248 

6 

86752 

29 

S2 

19  44    40  16 

82996 

7 

17004 

96256  14 

03744 

13260 

6 

86740 

28 

ss 

19  36    40  24 

83010 

8 

16990 

96281  '  14 

03719 

13272 

6 

86728 

27 

34 

19  28    40  32 

83023 

8 

16977 

96307 

14 
15 

03693 

13283 

7 

86717 

26 

ss 

6  19  20  5  40  40 

9-  S3037 

8 

10.  16963 

9- 96332 

10.03668 

10.  13295 

7 

9.  86705 

25 

S6 

19  12    40  48 

8305-1 

8 

16949 

96357   15 

03643 

13306 

7 

86694 

24 

S7 

19  4    40  56 

83065 

8 

16935 

96383   16 

03617 

13318 

7 

86682 

23 

ss 

18  56    41  4 

83078 

9 

16922 

96408   16 

03592 

13330 

7 

86670 

22 

39 

18  48    41  12 

83092 

9 

16908 

96433   16 

03567 

1 334 1 

8 

8 

86659 
9.  86647 

21 

20 

40 

6  iS  40   5  41  20 

9. 83106 

9 

10. 16894 

9.96459  ;  17 

10.03541 

10.  13353 

41 

18  32    41  28 

83120 

9 

16880 

96484  !  17 

03516 

13365 

8 

86635 

19 

42 

iS  24    41  36 

83133 

10 

16867 

96510  i  18 

03490 

13376 

8 

86624 

18 

4S 

18  16    41  44 

83147 

10 

16853 

90535 

18 

03465 

13388 

8 

86612 

17 

44 

18  8    41  52 

83161 

10 

16839 

96560 

19 
19 

03440 

13400 

8 
9 

86600 

lb 

4S 

6  18  0   5  42  0 

9-83174 

10 

10.  16826 

9.  96586 

10. 03414 

10. 13411 

9. 86589 

15 

46 

17  52    42  8 

83188 

II 

16812 

9661 1   19 

03389 

13423 

9 

86577 

14 

47 

17  44    42  16 

83202 

II 

16798 

96636  20 

03364 

13435 

9 

86565 

13 

48 

17  36 

42  24 

83215 

II 

16785 

96662  20 

03338 

13446 

9 

86554 

12 

49 

1728 

42  32 

83229 
9.  83242 

II 

16771 

96687  1  21 

03313 

13458 

9 

10 

86542 

II 

SO 

6  17  20 

5  42  40 

II 

10.  16758 

9.96712  21 

10. 03288 

10. 13470 

9. 86530 

10 

SI 

17  12    42  48 

83256 

12 

16744 

967^8  22 

03262 

13482 

10 

86518 

9 

S2 

17  4    42  56 

83270 

12 

16730 

96763  22 

03237 

13493 

10 

86507 

8 

ss 

16  56 

43  4 

83283 

12 

16717 

96788    ;     22 

03212 

13505 

10 

86495 

7 

54 

16  48 

43  12 

83297 

12 

16703 

96814 

23 

23 

03186 

10. 03I6I 

13517 

10 

86483 

6 

SS 

6  16  40 

5  43  20 • 

9.83310 

13 

10.  16690 

9.   96839 

10.  13528 

II 

9.  86472 

5 

S6 

16  32 

43  28 

83324 

IS 

16676 

96864        24 

03136 

13540 

II 

86460 

4 

S7 

16  24 

43  36 

83338 

13 

1 6662 

96890        24 

031 10 

13552 

II 

8644S 

3 

S« 

16  16 

43  44 

83351 

13 

16641) 

96915         25 

03085 

13564 

II 

86436 

2 

S9 

16  8 

43  52 

83365 

14 

16635 

1)6940         25 

03060 

13575 

II 

86425 

1 

(>o 

i()  0 

44  0 

83378 

14 

16622 

Secant. 

96966         25 

Cotangent.  Diff. 

03034 

Tangent. 

•3587 

12 

86413 

0 

M. 

Hour  !•  M. 

Hour.\.  M. 

Cosine. 

Diff. 

Cosecant. 

Diflf. 

Sine. 

M. 

132 

□ 

A 

A 

B 

B 

c 

c      4r| 

k 


29      T: 


Seconds  of  time {• 

•>'    -A'         4'    5'    (>'    7' 

1 

t  A 
Prop,  parts  of  cols.  <  B 

2 

3 

I 

3     5 
6    10 

3     4 

7 
'I 

7 

10 
'9 

9 

12 
22 
10 

Page  450 

TABLE  44. 

S'. 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

43° 

A 

A 

B 

B 

c 

C   136^ 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

DifF. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 
I 

2 

4 

6  16  0 
15  52 
15  44 
15  36 
15  28 

5  44  0 
44  8 
44  16 
44  24 
44  32 

9-  83378 
83392 
83405 
83419 
83432 

0 
0 
0 
I 
I 

10.  16622 
16608 

16595 
16581 
16568 

9. 96966 
96991 
97016 
97042 
97067 

0 
0 
I 
I 

2 

10.  03034 
03009 
02984 
02958 
02933 

10- 13587 
13599 
13611 
13623 
13634 

0 
0 
0 

9.  86413 

86401 

86389 

86377 
86366 

60 
59 
58 
57 
5<J 
\55 
54 
53 
52 
51 

5 
6 

7 
8 

9 

6  15  20  5  44  40 
15  12    44  48 
15  4  I   44  56 
14  56  ]   45  4 
14  48    45  12 

9.  S3446 

83459 
83473 
83486 

83500 

I 
I 

2 
2 

2 

ID.  16554 
16541 
16527 
16514 
16500 

9.  97092 
97118 

97143 
97168 

97193 

2 

3 
3 
3 
4 

10. 02908 
02882 
02857 
02832 
02807 

10.  13646 
13658 
13670 
13682 
13694 

2 
2 

9- 86354 
86342 
86330 
86318 
86306 

10 

II 

12 

13 
14 

6  14  40 

'4  32 
14  24 
14  16 
14  8 

5  45  20 
45  28 
45  36 
45  44 
45  52 

9-83513 
83527 
83540 
83554 
83567 

2 
2 

3 
3 

3 

10. 16487 

16473 

16460 
16446 

16433 

9.97219 

97244 
97269 

97295 
97320 

4 
5 
5 

6 
7 
7 
8 
8 
8 
9 
9 
10 
10 

10.02781 

02756 

02731 
02705 
02680 

10.  13705 
i37'7 
13729 
13741 
13753 

2 
2 
2 

3 
3 

3 
3 
3 
4 
4 

9. 86295 
86283 
86271 
86259 
86247 

9-  86235 
86223 
8621 1 
86200 
86188 

9.86176 
86164 
86152 
86140 
86128 

50 
49 
48 

47 
46 

45 
44 

43 
42 

41 
'40 
39 
38 
37 
36 

15 
16 

18 
19 

6  14  0  5  46  0 

13  52  ;    46  8 

13  44    46  16 
13  36    46  24 
13  28    46  32 

9.  83581 

83594 
83608 
83621 
83634 

3 
4 
4 
4 
4 

10.  16419 
16406 
16392 

16379 
16366 

9-  97345 
97371 
97396 
97421 

97447 

10. 02655 

02629 
02604 
02579 
02553 

10.  13765 
13777 
'3789 
13800 
13812 

20 
21 
22 

23 

24 

6  13  20 
13  12 

13  4 
12  56 
12  48 

5  46  40 
46  48 

46  56 

47  4 
47  12 

9.  83648 
83661 

83674 
83688 
83701 

4 
5 
5 
5 

5 

10. 16352 
16339 

16326 

16312 
16299 

9.  97472 
97497 
97523 
97548 
97573 

10.02528 
02503 
02477 
02452 
02427 

10.  02402 
02376 
02351 
02326 
02300 

10.  13824 
13836 
13848 
13860 
13872 

4 
4 
4 
5 
5 

26 
27 
28 
29 

6  12  40 
12  32 
12  24 
12  16 
12  8 

5  47  20 
47  28 
47  36 
47  44 
47  52 

9-83715 

83728 

83741 
83755 
83768 

6 
6 
6 
6 
6 

10.  16285 
16272 
16259 

16245 
16232 

9-97598 
97624 

97649 
97674 

97700 

II 
II 
II 
12 
12 

10. 13884 

13896 
13908 
13920 
13932 
10.  13944 
13956 
13968 
13980 
13992 

5 
5 
5 
6 

6 
6 
6 
6 

9.  861 16 

86104 
86092 
86080 
86068 

35 
34 
33 
32 
3' 

30 
31 
32 
JJ 

34_ 

35 
.^6 

37 
3^ 
39 

6  12  0 
II  52 
II  44 
II  3b 
II  28 

0  II  20 
II  12 
II  4 
10  56 
10  48 

5  48  0 
48  8 
48  16 
48  24 
48  32 

5  48  40 
48  48 

48  56 

49  4 
49  12 

5  49  20 
49  28 

49  36 
49  4i 
49  52 

9-  83781 

83795 
83808 
83821 
83834 

9-  83848 
83861 

83874 
83887 
83901 

9.  83914 

83927 
83940 
83954 
83967 
9- 83980 

83993 
84006 

84020 
84033 

7 
7 

I 

10. 16219 
16205 
I6I92 

16179 
I6I66 

9-97725 
97750 
97776 
97801 
97826 

13 
13 
13 
14 
14 

15 
15 
16 
16 
16 

10.  02275 
02250 
02224 
02199 
02174 

10.  02149 
02123 
02098 
02073 
02047 

9. 86056 
86044 
86032 
86020 
86008 

30 
29 
28 

27 
26 

8 
8 

I 

9 

9 

9 

9 
10 

10 

10.  I6I52 

16139 

I6I26 

16113 

16099 

ID.  16086 
16073 
16060 
16046 
16033 

9.97851 

97877 
97902 

97927 
97953 
9. 97978 
98003 
98029 

98054 
98079 

10.  14004 
14016 
14028 
14040 
14052 

8 
8 

9. 85996 

85984 
85972 
85960 
85948 

25 
24 

23 
22 

21 

40 

41 

42 

43 
44 

6  10  40 
ID  32 
10  24 

ID  16 

10  8 

17 
17 
18 
18 
19 

10. 02022 

01907 
OI97I 

01946 
OI92I 

10.  14064 
14076 
14088 
14100 
141 12 

8 
8 
8 
9 
9 

9.  85936 

85924 
85912 
85900 
85888 
9.85876 
85864 

85851 
85839 
85827 

9-85815 
85S03 

85791 
85779 
85766 

20 

19 

18 

'7 
16 

15 
14 

13 
12 

II 
10 

9 

8 

7 
6 

45 

46 

47 
48 

49 

6  10  0 

9  52 
9  44 
9  36 
9  28 

5  50  0 
50  S 
50  16 
50  24 
50  32 

10 
10 
10 
II 
II 

10.  16020 
16007 

15994 

15980 

15967 

9.98104 
98130 

98155 
98180 

98206 

19 
19 

20 

20 
21 

10.  01896 
01870 
01845 
01820 

01794 

10.  14124 

14136 

14149 
14161 

14173 

9 
9 
9 
10 
10 
10 
10 
10 
II 
II 

50 
51 

52 
53 
54 

b  9  20 
9  12 

9  4 
8  56 

8  48 

5  50  40 
50  48 

50  56 

51  4 
51  12 

5  51  20 
51  28 

51  36 
5'  44 

51  52 

52  0 

9. 84046 

84059 
84072 
84085 
84098 
9.  841 12 
84125 
84138 
84151 
84164 
84177 

II 

12 
12 
12 
12 
12 
13 
13 
13 
13 

10. 15954 
15941 
15928 

15915 
15902 

9.98231 
98256 
98281 
98307 
98332 

21 

22 
22 
22 
23 

10.01769 

01744 
01719 

01693 

01668 

10.  14185 
14197 
14209 
14221 
14234 

55 
56 
57 
58 

59 
60 

6  8  40 
832 
8  24 
8  16 
8  8 
8  0 

10. 15888 

15862 
15849 

15836 
15823 

9-98357 
98383 
98408 

98433 
98458 
98484 

Cotangent. 

23 

24 

24 
24 
25 
25 

Diff. 

10. 01643 
OI6I7 

01592 
01567 
01542 

OI5I6 

10. 14246 
14258 
14270 
14282 
14294 
14307 

II 
II 
II 
12 
12 
12 

Diff. 

9-85754 

85742 
85730 
85718 
85706 
85693 

5 

4 
3 
2 
I 
0 

M. 

Hour  i>.  M. 

Hour  A.M. 

Cosine. 

DiflF. 

Secant. 

Tangent. 

Cosecant. 

Sine. 

u. 

133 

0 

A 

A 

B 

1! 

C 

C    46°  1 

Seconds  of  time 1' 

2> 

I 
3 

3» 

4" 

.")» 

«>  i  7»  1 

(A   2 

Prop,  parts  of  cols.  -^  B  1   3 

(  C  '   2 

S 
9 

5 

7 

1 

8 

16 

8 

10 

9 

12 
22 
II 

TABLE  44. 

Page  451 

S'. 

^ 

Log.  Sines,  Tangents,  and  Secants. 

G'. 

£4° 

M. 

A          A 

B 

B 

c 

C   135° 

Hour  A.M. 

Hour  r.  m. 

Sine. 

DiflF. 

Cosecant. 

Tangent. 

DiflF. 

Cotangent. 

Secant. 

DiflF 

Cosine. 

»M. 

o 

I 

2 

3 

4 

680 

7  52 
7  44 
736 
728 

5  52  0 
52  8 
52  16 
52  24 
52  32 

9.84177 
84190 
84203 
84216 
84229 

0 
0 
0 
I 
I 

10.  15823 
15810 
15797 
15784 
15771 

9.98484 
98509 

98534 
98560 

98585 

0 
0 
I 

I 
2 

IO.O1516 
01491 
01466 
01440 

01415 

10.  14307 
14319 
14331 
14343 
14355 

0 
0 
0 

T 

9- 85693 
85681 
85669 

85657 
85645 

60 

59 

58 
57 
56 

5 
() 

7 

S 

_.  9_ 

10 

II 

12 

'3 
14 

6  7  20 
7  12 

7  4 
6  56 
6  48 

5  52  40 
52  48 

52  56 

53  4 
53  12 

9.  84242 

84255 
84269 

84282 
84295 

I 

I 

2 
2 
2 

10.  15758 
15745 
15731 
15718 
15705 

9.98610 

98635 
98661 
98686 
9871 1 

2 

3 
3 

4 

10.01390 

01365 

01339 

01314 
01289 

10.  14368 
14380 

14392 
14404 

14417 

2 
2 

9- 85632 
85620 
85608 
85596 
85583 

55 
54 
53 
52 
51 

6  6  40 
632 
6  24 
6  16 
6  8 

5  53  20 
53  28 
53  36 
53  44 
53  52 

9. 84308 
84321 
84334 
84347 
84360 

2 

2 

3 

3 
3 

10. 15692 

15679 
15666 

15653 

15640 

9-98737 
98762 

98787 

98812 

98838 

4 

5 
5 

I 

6 

7 
7 
8 
8 

10.01263 
01238 
01213 
01 188 
01 162 

10.  14429 
14441 

14453 
14466 

14478 

2 
2 
2 

3 

3 

9-85571 
85559 
85547 
85534 
85522 

50 
49 
48 

47 
46 

15 
16 

17 

iS 

19 

660 

5  52 
5  44 
5  36 
5  28 

5  54  0 
54  8 
54  16 
54  24 
54  32 

9- 84373 
84385 
84398 
84411 
84424 

3 
3 
4 
4 
4 

10.  15627 

I56I5 

15602 

15589 
15576 

9.98863 
98888 

98913 
98939 
98964 

10. 01 137 
OIII2 
01087 
OI061 
01036 

10.  14490 
14503 
14515 
14527 
14540 

3 

3 
4 
4 
4 

9.85510 

85497 

85485 

85473 
85460 

45 
44 
43 
42 
41 

20 
21 

22 

23 
24 

6  5  20 
5  12 

5  1 
4  56 

448 

5  54  40 
5448 

54  56 

55  4 
55  12 

9- 84437 
84450 

84463 
84476 
84489 

4 

5 
5 
5 
5 

10. 15563 
15550 

15537 
15524 
I55II 

9.98989 

99015 
99040 

99065 
99090 

8 
9 

9 
10 
10 
II 
II 
II 
12 
12 

10.  OIOII 

00985 
00960 

00935 
00910 

10.  14552 

14564 
14577 
14589 

1 460 1 

4 
4 

5 

•5 

5 

9.  85448 
85436 
85423 
85411 
85399 

40 
39 
38 
37 
36 

25 

26 

27 
28 

29 

6  4  40 
4  32 
4  24 
4  16 
4  8 

5  55  20 
55  28 
55  36 
55  44 
55  52 

9.  84502 

84515 
84528 
84540 
84553 
9. 84566 

84579 
84592 
84605 
84618 

5 
6 

6 

6 

6 

10. 15498 

15485 
15472 

15460 

15447 

9.991 16 

99141 
99166 

99191 
99217 

10.  00884 
00859 
00834 
00809 
00783 

10.  I46I4 
14626 

14639 
14651 
14663 

5 

6 
6 

9- 85386 
85374 
85361 
85349 
85337 

9-  85324 
85312 
85299 
85287 
85274 

35 
34 
33 
32 
31 

30 
31 

32 

-1  -» 

34 

640 

3  52 
3  44 
336 
328 

5  56  0 
56  8 
56  16 
56  24 
56  32 

6 

7 
7 
7 
7 

10. 15434 
1 542 1 

15408 

15395 

15382 

9.99242 
99267 

99293 
99318 
99343 

13 

13 
14 
14 

10.  00758 

00733 
00707 

00682 

00657 

10.  14676 

14688 

14701 

I47I3 
14726 

6 
6 

7 
7 
7 
7 
7 
8 
8 
8 
8 
8 
9 
9 
9 

9 

10 
10 
10 
10 

30 
29 
28 

27 
26 

35 
36 
37 
3S 
39 

6  3  20 
3  12 

3  4 
2  56 
2  48 

5  56  40 

56  48 

5656 

57  4 
57  12 

9.  84630 
84643 
84656 
84669 
84682 

8 
8 
8 
8 
8 

9 
9 
9 
9 
9 

10. 15370 

15357 
15344 

1 533 1 
15318 

10.  15306 

15293 
15280 
15267 

15255 

9.99368 
99394 
99419 
99444 
99469 

9-99495 
99520 

99545 
99570 
99596 
9.99621 
99646 
99672 

99697 
99722 

15 

15 
16 

16 

16 

17 
17 
18 
18 

19 

19 
19 
20 
20 
21 

10.  00632 
00606 
00581 
00556 
00531 

10. 14738 

14750 

14763 

14775 
14788 

9.  85262 

85250 

85237 
85225 
85212 

25 
24 

23 
22 
21 

40 

41 
42 
43 

44 

6  2  40 
2  32 
2  24 
2  16 
2  8 

5  57  20 
57  28 
57  36 
57  44 
57  52 

9.  84694 
84707 
84720 

84733 
84745 

10.00505 
00480 

00455 
00430 

00404 

10. 14800 

14813 
14825 

14838 

14850 

9. 85200 
85187 

85175 
85162 

85150 

20 

19 

18 

17 
16 

45 
46 

47 
48 

49 

50 

SI 

52 
53 
54 

620 

1  52 

I  44 

I  36 
I  28 

5  58  0 
58  8 
58  16 
58  24 
5832 

9.  84758 
84771 
84784 
84796 
84809 

10 
10 
10 

ID 
II 

10.  15242 
15229 
15216 
15204 

15191 

10. 00379 

00354 

00328 
00303 
00278 

10. 14863 

14875 
14888 

14900 

14913 

9-85137 
85125 
851 12 
85100 
85087 

15 

14 

13 

12 

II 

6  I  20 
I  12 

1  4 
0  56 
0  48 

5  58  40 

58  48 
5856 

59  4 
59  12 

9.  84822 

84835 
84847 
84860 

84873 

11 
II 
II 
1  I 
12 
12 
12 
12 
12 

13 
13 

10.  15178 
15165 

15153 
15140 
15127 

9-99747 
99773 
99798 
99823 
99848 

21 
21 
22 
22 

23 

23 

24 

24 
24 
25 
25 

DiflF. 

10.  00253 
00227 
00202 

00177 

00152 

10.  14926 

14938 

14951 
14963 
14975 

10 
II 
II 
II 
II 

9-  85074 
85062 

85049 
85037 
85024 

10 

9 

8 

7 
6 

55 

5'^ 
57 
5«'i 

59 
60 

6  0  40 

0  32 
0  24 
0  16 
0  8 
0  0 

5  59  20 

59  28 
59  36 
59  44 
59  52 
600 

Hour  A.  M. 

9. 84885 
84898 
849 II 

84923 
84936 

84949 

10. 15115 
15102 

15089 

15077 
15064 

15051 

9.99874 
99899 
99924 
99949 

99975 
10.00000 

10.  00126 

OOIOI 

00076 
00051 
00025 
00000 

10.  14988 
1 500 1 
15014 

15026 

15039 
15051 

II 
12 
12 
12 
12 
12 

9.85012 
84999 
84986 

S4974 
84961 
84949 

5 
4 

3 

2 

I 
0 

M. 

Hour  P.M. 

Cosine. 

DiflF. 

Secant. 

Cotangent, 

Tangent. 

Cosecant. 

DiflF. 

Sine. 

M. 

i:U 

0 

A           A 

B 

r. 

C 

C    45°  1 

Seconds  of  time 

1« 

2 
3 

2» 

3» 

s 

9 

5 

4, 

5» 

«» 

7' 

Prop,  parts  of  cols.  J.  B 

I 

6 

13 

6 

8 
16 

8 

10 

"9 

9 

II 
22 
II 

Page  452 

TABLE  45 

• 

Proportional  Logarithms. 

Sv 

o 

h.    m. 

h.    m. 

h .    jn . 

h.   m. 

h.   in. 

k.    m. 

k.   m. 

h,  m. 

h.    m. 

S. 

0°  0' 

0°  V 

0°  V 

0°  3' 

0°  4' 

0°  5' 

0°  6^ 

0°  V 

0°  8' 

2.2553 

I > 9542 

I.  7782 

1.6532 

1-5563 

I.  4771 

1. 4102 

1.3522 

0 

I 

4-  0334 

2481 

9506 

7757 

6514 

5549 

4759 

4091 

3513 

I 

2 

3-  7324 

2410 

9471 

7734 

6496 

5534 

4747 

4081 

3504 

2 

3 

5563 

2341 

9435 

7710 

6478 

5520 

4735 

4071 

3495 

3 

4 

5 

4314 
o-  3345 

2272 

2.  2205 

9400 

7686 

6460 

_  5506 

4723 
1.4711 

4061 
1.4050 

3486 

1-3477 

4 

1.9365 

I.  7663 

^176443" 

I. 5491 

5  i 

6 

2139 

9331 

7639 

6425 

5477 

4699 

4040 

3468 

6 

7 

1883 

2073 

9296 

7616 

6407 

5463 

4688 

4030 

3459 

7 

8 

1303 

2009 

9262 

7593 

6390 

5449 

4676 

4020 

3450 

8 

9 

lO 

0792 
3-  0334 

1946 
2.  1883 

9228 

7570 

6372 

5435 
I.  5421 

4664 

4010 

3441 
1-3432 

9 
10 

'"1.9195 

I.  7547 

1.6355 

1.4652 

1 . 4000 

II 

2.  9920 

1822 

9162 

7524 

6338 

5407 

4640 

3989 

3423 

II 

12 

9542 

1 761 

9128 

7501 

6320 

5393 

4629 

3979 

3415 

12 

13 

9195 

1 701 

9096 

7479 

6303 

5379 

4617 

3969 

3406 

13 

14 

8873 

1642 

9063- 

7456^ 

6286 

5365 

4606 

3959 

3397 
1.3388 

14 
15 

15 

2.8573 

2.  1584 

I.  9031 

I.  7434 

1.6269 

I- 5351 

1.4594 

1-3949 

i6 

8293 

1526 

8999 

7412 

6252 

5337 

4582 

3939 

3379 

16 

17 

8030 

1469 

8967 

7390 

6235 

5324 

4571 

3929 

3371 

17 

i8 

7782 

I4I3 

8935 

7368 

6218 

5310 

4559 

3919 

3362 

18 

19 

7547 
2.  7324 

1358 

8904 

7346 

6201 

5296 

4548 

3910 

3353 

19 

20 

2.  1303 

1.8873 

I-  7324 

1. 6185 

1-5283 

1.4536 

I . 3900 

1-3345 

20 

21 

7112 

1249 

8842 

7302 

6168 

5269 

4525 

3890 

3336 

21 

22 

6910 

II96 

8811 

7281 

6151 

5256 

4514 

3880 

3327 

22 

23 

6717 

"43 

8781 

7259 

6135 

5242 

4502 

3870 

3319 

23 

24 
25 

6532 

1091 

8751 

7238 

6118 

5229 

4491 

3860 

3310 

24 

2. 6355 

2.  1040 

1. 8721 

I.  7217 

1. 6102 

1-5215 

I.  4480 

1-3851 

I- 3301 

25 

26 

6185 

0989 

8691 

7196 

6085 

5202 

4468 

3841 

3293 

26 

27 

6021 

0930 

8661 

7175 

6069 

5189 

4457 

3831 

3284 

27 

28 

5863 

0889 

8632 

7154 

6053 

5175 

4446 

3821 

3276 

28 

29 
30 

5710 
2.  5563 

0840 

8602 

7133 

6037 

5162 

4435 
1.4424 

3812 
1.3802 

3267 
1-3259 

29 
30 

2.  0792 

1-8573 

I.  7112 

1. 6021 

1-5^49 

31 

5421 

0744 

8544 

7091 

6005 

5136 

4412 

3792 

3250 

31 

32 

5283 

0696 

8516 

7071 

5989 

5123 

4401 

3783 

3242 

32 

33 

5149 

0649 

8487 

7050 

5973 

5110 

4390 

3773 

3233 

7>1, 

34 

5019 

0603 
2.o557~ 

8459 

7030 

5957 

5097 

4379 

3764 

3225 

34 

35 

2. 4894 

I.  8431 

I.  7010 

1-5941 

I.  5084 

1.4368 

1-3754 

I.  3216 

35 

36 

4771 

0512 

8403 

6990 

5925 

5071 

4357 

3745 

3208 

36 

37 

4652 

0467 

8375 

6970 

5909 

5058 

4346 

3735 

3199 

37 

38 

4536 

0422 

8348 

6950 

5894 

5045 

4335 

3726 

3191 

38 

39 

4424 

0378 
2. 0334 

8320 

6930 

5878 
~  1-5863 

5032 
I.  5019 

4325 
1-4314 

3716 
1-3707 

3 '83 
1-3174 

39 
40 

40 

2.4314 

1.8293 

I.  6910 

41 

4206 

0291 

8266 

6890 

5847 

5007 

4303 

3^97 

3,66 

41 

42 

4102 

0248 

8239 

6871 

5832 

4994 

4292 

3688 

3'58 

42 

43 

4000 

0206 

8212 

6851 

5816 

4981 

4281 

3678 

3149 

43 

44 

3900 

0164 

8186 
I.  81 59 

6832 
1. 6812 

5801 
^  I.  5786" 

4969 
1.4956 

4270 
I.  4260 

3669, 
I . 3660 

3'4i 

44 

45 

2.  3802 

2.0122 

I- 3133 

45 

46 

3707 

0081 

8133 

6793 

5771 

4943 

4249 

3650 

3124 

46 

47 

3613 

0040 

8107 

6774 

5755 

4931 

4238 

3641 

3116 

47 

48 

3522 

0000 

8081 

6755 

5740 

4918 

4228 

3632 

3108 

48 

49 

3432 

1 .  9960 

8055 

6736 

5725 

4906 
1.4894 

4217 
1.4206 

3623 
I- 3613 

3100 
1.3091" 

49 
50 

50 

2-  3345 

I . 9920 

1.8030 

I. 6717 

I.  5710 

51 

3259 

9881 

8004 

6698 

5695 

4881 

4196 

3604 

3083 

51 

52 

3174 

9842 

7979 

6679 

5680 

4869 

4185 

3595 

3075 

52 

53 

3091 

9803 

7954 

6661 

5666 

4856 

4175 

3586 

3067 

53 

54 

3010 

9765 

7929 

6642 

5651 
I.  5636 

4844 
1.4832 

4164 
1. 4154 

3576 
1-3567 

3059 

54 

55 

2.2931 

1.9727 

I.  7904 

1.6624 

I- 3051 

55 

56 

2852 

9690 

7879 

6605 

5621 

4820 

4143 

3558 

3043 

56 

57 

2775 

9652 

7855 

6587 

5607 

4808 

4133 

3549 

3034 

57 

58 

2700 

9615 

7830 

6568 

5592 

4795 

4122 

3540 

3026 

58 

59 

2626 

9579 

7806 

6550 

5578 

4783 

4112 
0°  6' 

3531 

3018 

59 

S. 

0°  0' 

0°  V 

0°  1' 

0°  V 

0°  4' 

0°  5' 

0°  8' 

S. 

4 


TABLE  45. 

(Page 

453 

% 

Proportional  Logarithms. 

s. 

h.     fft. 

h.     m. 

h.     )>!. 

k.     w.     h,     in. 

h .     »! . 

h.     m. 

It .     m . 

h.     111. 

s. 

0°  9' 

0°  10^ 

0°  11' 

0°  12'   0°  13' 

0^  11' 

0°  15' 

0°  16' 

0°  w 

o 

1. 3010 

I-  2553 

1. 2139 

1. 1761 

I.  I4I3 

I.  I09I 

1.0792 

1. 0512 

1.0248 

0 

I 

3002 

2545 

2132 

1755 

I40S 

1086 

0787 

0507 

0244 

I 

2 

2994 

2538 

2126 

1749 

1402 

I08I 

0782 

0502 

0240 

2 

1 

J 

2986 

2531 

2II9 

1743 

1397 

1076 

0777 

0498 

0235 

-> 

4 

2978 

2524 

2II3 

1737 

I39I 

I07I 

0773 

0493 

0231 

4 

5 

1 . 2970 

1.2517 

1. 2106 

1-1731 

1. 1386 

1. 1066 

1.0768 

1.0489 

1.0227 

5 

0 

2962 

2510 

2099 

1725 

1380 

I06I 

0763 

0484 

0223 

6 

7 

2954 

2502 

2093 

1719 

1374 

1055 

0758 

0480 

0219 

7 

s 

2946 

2495 

2086 

1713 

1369 

1050 

0753 

0475 

0214 

8 

9 

2939 

2488 

2080 

1707 

1363 

1045 

0749 

0471 

0210 

9 

10 

1-2931 

1. 2481 

1.2073 

1. 1 701 

1. 1358 

1. 1040 

1.0744 

1.0467 

r.  0206 

10 

II 

2923 

2474 

2067 

'^§5 

1352 

1035 

0739 

0462 

0202 

II 

12 

2915 

2467 

2061 

1689 

1347 

1030 

0734 

0458 

0197 

12 

13 

2907 

2460 

2054 

1683 

1342 

1025 

0730 

0453 

0193 

13 

14 

2S99 

2453 

2048 

1677 

1336 

1020 

0725 

0449 

0189 

14 

15 

1. 2891 

1.2445 

1. 2041 

1. 1671 

I-  I33I 

I.  IOI5 

1.0720 

i.o44t 

1. 0185 

15 

16 

2883 

2438 

2035 

1665    1325 

1009 

0715 

0440 

0181 

16 

17 

2876 

2431 

2028 

1660    1320 

1004 

0711 

0435 

0176 

17 

iS 

2868 

2424 

2022 

1654  !   1314 

0999 

0706 

0431 

qi72 

18 

19 

2860 

2417 

2016 

1648  1   1309 

0994 

0701 

0426 

0168 

19 

20 

1. 2852 

1. 2410 

1.2009 

1. 1642   1. 1303 

1.0989 

I.  0696 

1 .  0422 

1. 0164 

20 

21 

2845 

2403 

2003 

1636    1298 

0984 

0692 

0418 

0160 

21 

22 

2837 

2396 

1996 

1630    1292 

0979 

0687 

0413 

0156 

22 

23 

2829 

2389 

1990 

1624  i   1287 

0974 

0682 

0409 

0151 

23 

24 

2821 

2382 

1984 

1619 

1282 

0969 
I . 0964 

0678 
1.0673 

0404 

0147 

24 

25 

1. 2814 

I-  2375 

1. 1977 

1. 1613 

I.  127b 

1 .  0400 

1-0143 

25 

26 

2806 

2368 

I97I 

'  1607 

I27I 

0959 

0668 

0395 

0139 

26 

27 

2798 

2362 

1965 

1 601 

1266 

0954 

0663 

0391 

0135 

27 

2S 

2791 

2355 

1958 

1595 

1260 

0949 

0659 

0387 

0131 

28 

29 

2783 

2348 

1952 

1589 

1255 

0944 
1. 0939 

0654 
I.  0649 

0382 
1.0378 

0126 

29 

30 

1-2775 

1. 2341 

1. 1946 

I. 1584 

1. 1249 

1. 0122 

30 

31 

2768 

2334 

1939 

1578 

1244 

0934 

0645 

0374 

0118 

31 

32 

2760 

2327 

1933 

1572 

1239 

0929 

0640 

0369 

0114 

32 

2753 

2320 

1927 

1566 

1233 

0924 

0635 

0365 

Olio 

33 

34 

2745 

2313 

I92I 

1561 

1228 

0919 

0631 

0360 

0106 

34 

35 

1.2738 

1.2307 

I.I9I4 

I- 1555 

1. 1223 

1. 0914 

1.0626 

1.0356 

I.  0102 

35 

36 

2730 

2300 

1908 

1549 

I2I7 

0909 

0621 

0352 

0098 

3b 

2722 

2293 

1902 

1543 

I2I2 

0904 

0617 

0347 

0093 

37 

3'S 

2715 

2286 

1896 

1538 

1207 

0899 

0612 

0343 

0089 

38 

39 

2707 

2279 

1889 

1532 

I20I 

0894 

0608 

0339 

0085 

39 

40 

I.  2700 

1.2272 

1. 1883 

1. 1526   1. 1196 

1.0889 

1 .  0603 

1-0334 

I.  0081 

40 

41 

2692 

2266 

1877 

1520    1191 

0884 

0598 

0330 

0077 

41 

42 

2685 

2259 

I87I 

1515 

II86 

0880 

0594 

0326 

0073 

42 

43 

2678 

2252 

1865 

1509 

I180 

0875 

0589 

0321 

0069 

43 

44 

45 

2670 
1.2663 

2245_ 

1.2239 

1859 

1503 

1 175 

0870 

0585 

0317 

0065 

44 
45 

1. 1852 

1. 1498   1. 1 1 70 

1.0865 

1.0580 

1-0313 

I.  0061 

46 

2655 

2232 

1846 

1492    1 164 

0860 

0575 

0308 

0057 

4b 

47 

2648 

2225 

1840 

i486    1 159 

0855 

0571 

0304 

0053 

47 

48 

2640 

2218 

1834 

1481    1 154 

0850 

0566 

0300 

0049 

48 

49 
50 

2633 
I.  2626 

2212 

1828 

1475     "49 

0845 

0562 

0295 
I.  0291 

ooz}4 

49 

I.  2205 

1. 1822 

I.  1469   I.  1 143 

1 .  0S40 

1-0557 

1 .  0040 

50 

51 

2618 

2198 

I8I6 

1464     1138 

0835 

0552 

0287 

0036 

51 

52 

261 1 

2192 

1809 

1458     1 133 

0831 

0548 

0282 

0032 

52 

53 

2604 

2185 

1803 

1452     1128 

0826 

0543 

0278 

0028 

53 

54 

2596 

2178 

1797 

1447     1 123 

0821 

0539 

0274 

0024 

54 

55 

1.2589 

I.  2172 

1-1791 

I. 1441    I.  1117 

i.c8i6 

1-0534 

1.0270 

I . 0020 

55 

56 

2582 

2165 

I7S5 

1436     1 1 12 

081 1 

0530 

0265 

0016 

56 

57 

2574 

2159 

1779 

1430 

II07 

0806 

0525 

0261 

0012 

57 

5« 

..567 

2152 

1773 

1424 

1 102 

0801 

0521 

0257 

0008 

58 

59 

2560 

2145 

i7fa^ 

1419 

1097 

0797 

0516 

0252 

0004 

59 

S. 

0°  9' 

0°  10' 

0°  11' 

0°  w 

0°  13' 

0°  14' 

0°  15' 

0°  16' 

0°  ir 

S. 

Page  454 

TABLE  45. 

Proportional 

logarithms. 

s. 

h .      in . 

// .  m . 

h.     71!. 

h .    nt . 

A .    m . 

/t,    m . 

h .    m . 

h.    tn. 

h .    in . 

h.    vt. 

h.    m. 

h.    in. 

s. 

0°  18^ 

0°  19' 

0°20' 

0°  21' 

0°  22' 

0°23' 

0°  24' 

0°  25' 

0°  26' 

8403 

0°  27' 

0=^  28' 

0°  29' 

o 

1. 0000 

9765 

9542 

9331 

9128 

8935 

8751 

8573 

8239 

8081 

7929 

0 

I 

9996 

9761 

9539 

9327 

9125 

8932 

8748 

8570 

8400 

8236 

8079 

7926 

I 

2 

9992 

9758 

9535 

9324 

9122 

8929 

8745 

8568 

8397 

8234 

8076 

7924 

2 

3 

9988 

9754 

9532 

9320 

9119 

8926 

8742 

8565 

8395 

8231 

8073 

7921 

1 
J 

4 

5 

9984 
9980 

9750 
9746 

9528 

9317 

9115 

^  ^^123 

8739 
8736 

8562 
8559 

8392 
8389 

8228 
8226 

8071 
8068 

7919 
7916 

4 
5 

9524 

9'3i3 

9112 

8920 

6 

9976 

9742 

952' 

9310 

9109 

8917 

8733 

8556 

8386 

8223 

8066 

7914 

6 

7 

9972 

9739 

9517 

9306 

9106 

8913 

8730 

8553 

Vb 

8220 

8063 

791 1 

7 

8 

9968 

9735 

9514 

9303 

9102 

8910 

8727 

8550 

8381 

8218 

8061 

7909 

8 

9 

9964 

9731 

9510 

9300 

9099 
9096 

8907 
8904 

8724 
8721 

8547 
8544 

8378 
8375 

8215 
8212 

8058 
8055 

7906 

9_ 

lO 

9960 

9727 

9506 

9296 

7904 

10 

II 

9956 

9723 

9503 

9293 

9092 

8901 

8718 

8542 

8372 

8210 

8053 

7901 

II 

12 

9952 

9720 

9499 

9289 

9089 

8898 

8715 

8539 

8370 

8207 

8050 

7899 

12 

13 

9948 

9716 

9496 

9286 

9086 

8895 

8712 

8536 

8367 

8204 

8048 

7896 

13 

14 
15 

9944 
9940 

9712 
9708 

9492 

9283 

9083 

8892 

8709 
8706 

8533 
8530 

8364 
8361 

8202 
8199 

8045 
8043 

7894 
7891 

14 
15 

9488 

9279 

9079 

8888 

16 

9936 

9705 

9485 

9276 

9076 

8885 

8703 

8527 

8359 

8196 

8040 

7889 

16 

17 

9932 

9701 

9481 

9272 

9073 

8882 

8700 

8524 

8356 

8194 

8037 

7887 

17 

18 

9928 

9697 

9478 

9269 

9070 

8879 

8697 

8522 

8353 

8191 

8035 

7884 

18 

19 

9924 

9693 

9474 

9266 

9066 

8876 

8694 

8519 

8350 
8348 

8188 
8 1 86^ 

803^ 
8030 

7882 
"  7879 

_^9_ 
20 

20 

9920 

9690 

9471 

9262 

9063^ 

8873' 

869T 

"8516' 

21 

9916 

9686 

9467 

9259 

9060 

8870 

8688 

8513 

8345 

8183 

8027 

7877 

21 

22 

9912 

9682 

9464 

9255 

9057 

8867 

8685 

8510 

8342 

8181 

8025 

7874 

22 

23 

9908 

.  9678 

9460 

9252 

9053 

8864 

8682 

8507 

8339 

8178 

8022 

7872 

23 

24 

9905 

9675 
9671 

_9456_ 

9249 

9050 
9047 

8861 
8857 

8679 
8676 

8504 
8502 

8337 
8334 

8175 
8173 

8020 
8017 

7869 

24 

25 

9901 

9453 

9245 

7867 

25 

26 

9897 

9667 

9449 

9242 

9044 

8854 

8673 

8499 

«33i 

8170 

8014 

7864 

26 

27 

9«93 

9664 

9446 

9238 

9041 

8851 

8670 

8496 

8328 

8167 

8012 

7862 

27 

28 

9889 

9660 

9442 

9235 

9037 

8848 

8667 

8493 

8326 

8165 

8009 

7859 

28 

29 
30 

9885 
9881 

9656 

9439 

9232 

9034 

8845 

8664 
8661 

8490 
8487 

8323 
8320 

8162 
8159 

8007 
8004 

7857 
785^5 

29 
30 

9652 

9435 

9228 

9031 

8842 

31 

9877 

9649 

9432 

9225 

9028 

8839 

8658 

8484 

8318 

8157 

8002 

7852 

31 

32 

9873 

9645 

9428 

9222 

9024 

8836 

8655 

8482 

8315 

8154 

7999 

7850 

32 

33 

9869 

9641 

9425 

9218 

9021 

8833 

8652 

8479 

8312 

8152 

7997 

7847 

33 

34 

9865 
9861 

9638 

9421 

^9215 

9018 

8830 

8649 
8646 

8476 
"  8473 

8309 
8307 

8149 
8146 

7994 

7992 

7845 
'   7842 

34 
35 

35 

9634 

9418 

9212 

9015^ 

8827 

36 

9858 

9630 

9414 

9208 

9012 

8824 

8643 

8470 

8304 

8144 

7989 

7840 

36 

37 

9854 

9626 

941 1 

9205 

9008 

8821 

8640 

8467 

8301 

8141 

7987 

7837 

37 

38 

9850 

9623 

9407 

9201 

9005 

8817 

8637 

8465 

8298 

8138 

7984 

7835 

38 

39 

9846 

9619 
9615 

9404 

9198 

9002 

8814 
'88 II 

8635 
8632 

8462 
"8459" 

8296 
8293 

8136 
8133 

7981 
7979 

7832 
7830 

39 
40 

40 

9842 

9400 

9195 

8999 

41 

9838 

9612 

9397 

9191 

8996 

8808 

8629 

8456 

8290 

8131 

7976 

7828 

41 

42 

9834 

9608 

9393 

9188 

8992 

8805 

8626 

8453 

8288 

8128 

7974 

7825 

42 

43 

9830 

9604 

9390 

9185 

8989 

8802 

8623 

8451 

8285 

8125 

7971 

7823 

43 

44 

9827 

9601 

9386 

9181 

8986 

8799 
8796 

8620 
8617 

8448 
8445 

8282 
8279 

8123 
8120 

7969 
7966 

7820 
7818 

44 
45 

45 

9823 

9597 

9383 

9178 

8983 

46 

9819 

9593 

9379 

9175 

8980 

8793 

8614 

8442 

8277 

8117 

7964 

781-5 

46 

47 

9815 

9590 

9376 

9171 

8977 

8790 

861 1 

8439 

8274 

8115 

7961 

7813 

47 

48 

981 1 

9586 

9372 

9168 

8973 

8787 

8608 

8437 

8271 

8112 

7959 

781 1 

48 

49 

50 

9807 
9803 

9582 

9369 

9165 
9162 

8970 
8967 

8784 
8781 

8605 
8602 

8434 
8431 

8269 
8266 

8110 
8107 

7956 
7954 

7808 
7806" 

49 
50 

9579 

9365 

5' 

9800 

9575 

9362 

9158 

8964 

8778 

8599 

8428 

8263 

8104 

7951 

7803 

51 

52 

9796 

9571 

9358 

9155 

8961 

8775 

8597 

8425 

8261 

8102 

7949 

7801 

52 

53 

9792 

9568 

9355 

9152 

8958 

8772 

8594 

8423 

8258 

8099 

7946 

7798 

53 

54 

55 

9788 
9784 

9564 
9561 

9351 

9148 

8954 

8769 

8591 

8420 

8255 
8253 

8097 
8094 

7944 

7796 

54 

9348 

9145 

8951 

8766 

8588 

8417 

7941 

7794 

55 

56 

9780 

9557 

9344 

9142 

8948 

8763 

8585 

8414 

8250 

8091 

7939 

7791 

56 

57 

9777 

9553 

9341 

9138 

8945 

8760 

8582 

841 1 

8247 

8089 

7936 

7789 

57 

5« 

9773 

9550 

9337 

9135 

8942 

8757 

8579 

8409 

8244 

8086 

7934 

7786 

58 

59 

9769 

9546 

9334 

9132 
0°  21' 

8939 

8754 

8576 

8406 

8242 

8084 

7931 

7784 

59 

S.  ; 

S. 

0°  18' 

0°  19' 

0°  20' 

0°  22' 

0°23' 

0°  24' 

0°  25' 

0°26' 

o°2r 

0°  28' 

0°  29' 

1 


TABLE  45. 

Page  455  | 

% 

Proportional  Logarith 

ns. 

/e.     m. 

A .    >« . 

A.    >«. 

h.    m. 

h.    tn. 

h.    m. 

h .    in . 

h.    m. 

k.      7H. 

h.    m. 

h .    m . 

h .    m , 

s. 

0°30^ 

0°3r 

0°  32^ 

0°  33' 

0°34' 

0°35' 

0°36' 

o°3r 

0°38' 

o°3r 

OMO' 

6532 

0°41^ 

0 

7782 

7639 

7501 

7368 

7238 

7112 

6990 

6871 

6755 

6642 

6425 

0 

I 

7779 

7637 

7499 

7365 

7236 

7110 

6988 

6869 

6753 

6640 

6530 

6423 

X 

2 

Tin 

7634 

7497 

7363 

7234 

7108 

6986 

6867 

6751 

6638 

6529 

6421 

2 

3 

7774 

7632 

7494 

7361 

7232 

7106 

6984 

6865 

6749 

6637 

6527 

6420 

•^ 

0 

4 

7772 

7630 

7492 

7359 

7229 

7104 

6982 

6863 

6747 

6635 
6633 

6525 

6523 

6418 

4 

^ 

7769 

7627 

7490 

7357 

7227 

7102 

6980 

6861 

6745 

64x6 

5 

0 

7767 

7625 

748S 

7354 

•   7225 

7100 

6978 

6859 

6743 

6631 

652/ 

6414 

b 

7 

7765 

7623 

7485 

7352 

7223 

7098 

6976 

68S7 

6742 

6629 

6519 

6413 

7 

8 

^^e2 

7620 

7483 

7350 

7221 

7096 

6974 

68S5 

6740 

6627 

6518 

64XX 

8 

9 

7760 

7618 

7481 

7348 

7219 

7093 

6972 

6853 

6738 

6625 

6516 
6514 

6409 

9 

lO 

7757 

7616 

7479 

7346 

7217 

7091 

6970 

6851 

6736 

6624 

6407 

10 

II 

7755 

7613 

7476 

7344 

7215 

7089 

696S 

6849 

6734 

6622 

6512 

6406 

II 

12 

7753 

7611 

7474 

7341 

7212 

7087 

6966 

6847 

6732 

6620 

6510 

6404 

12 

i;i 

7750 

7609 

7472 

7339 

7210 

7085 

6964 

6845 

6730 

6618 

6509 

6402 

n 

14 
IS 

7748 

7607 

7470 

7337 

7208 

7083 

6962 

6843 

6728 

66x6 
6614 

6507 
6505 

6400 
15398" 

14 

15 

7745 

7604 

7467 

7335 

7206 

7081 

6960 

6841 

6726 

i6 

7743 

7602 

7465 

7333 

7204 

7079 

6958 

6840 

6725 

66x2 

6503 

6397 

16 

17 

7741 

7600 

7463 

7330 

7202 

7077 

6956 

6838 

6723 

661 1 

650  X 

6395 

17 

18 

7738 

7597 

7461 

7328 

720Q 

7075 

6954 

6836 

6721 

6609 

6500 

6393 

iS 

19 

7736 

7595 

7458 

7326 

7198 

7073 
7071 

6952 

6834 

6719 

6607 

6498 
6496 

6391 

19 

20 

7734 

7593 

7456 

7324 

7196 

6950 

6832 

6717 

6605 

6390 

20 

21 

7731 

7590 

7454 

7322 

7193 

7069 

6948 

6830 

6715 

6603 

6494 

6388 

21 

22 

7729 

7588 

7452 

7320 

7191 

7067 

6946 

6828 

6713 

6601 

6492 

6386 

22 

2-, 

7726 

7586 

7450 

7317 

7189 

7065 

6944 

6826 

6711 

6600 

649  X 

6384 

2S 

24 

7724 

7583 

7447 

7315 

7187 

7063 

6942 

6824 

6709 
6708 

6598 

6489 

6383 

24 

2S 

25 

7722 

7581 

7445 

7313 

7185 

7061 

6940 

6822 

6596 

6487 

638  X 

26 

7719 

7579 

7443 

731 1 

7183 

7059 

6938 

6820 

6706 

6594 

648s 

6379 

26 

27 

7717 

7577 

7441 

7309 

7181 

7057 

6936 

6818 

6704 

6592 

6484 

6377 

27 

28 

7714 

7574 

7438 

7307 

7179 

7055 

6934 

6816 

6702 

6590 

6482 

6376 

28 

29 

7712 

7572 

7436 

7304 

7177 

7052 

6932 

6814 

6700 

6589 

6480 

6374 

29 

30 

7710 

7570 

7434 

7302 

7175 

7050 

6930 

6812 

6698 

6587 

6478 

6372 

30 

■SI 

7707 

7567 

7432 

7300 

7172 

7048 

6928 

6810 

6696 

658s 

6476 

6371 

31 

32 

7705 

7565 

7429 

7298 

7170 

7046 

6926 

6809 

6694 

6583 

6475 

6369 

32 

7703 

7563 

7427 

7296 

7168 

7044 

6924 

6807 

6692 

6581 

6473 

6367 

3;> 

34 

7700 

7560 

7425 

7294 

7166 

7042 

6922 

6805 

6691 

6579 
6s  78 

6471 

6365 

34 

35 

7698 

7558 

7423 

7291 

7164 

7040 

6920 

6803 

6689 

6469 

6364 

35 

36 

7696 

7556 

7421 

72S9 

7162 

7038 

6918 

6801 

6687 

6576 

6467 

6362 

S6 

37 

7693 

7554 

7418 

7287 

7160 

7036 

6916 

6799 

6685 

6574 

6466 

6360 

37 

3« 

7691 

7551 

7416 

7285 

7158 

7034 

6914 

6797 

6683 

6572 

6464 

6358 

S8 

39 

7688 

7549 

7414 

7283 

7156 

7032 

6912 

6795 

6681 

6570 
6568 

6462 
6460 

6357 

39 

40 

7686 

7547 

7412 

7281 

7154 

7030 

6910 

6793 

6679 

6355 

40 

41 

7684 

7544 

7409 

7279 

7152 

7028 

6908 

6791 

6677 

6S67 

6459 

6353 

41 

42 

7681 

7542 

7407 

7276 

7149 

7026 

6906 

6789 

6676 

6565 

6457 

6351 

42 

43 

7679 

7540 

7405 

7274 

7147 

7024 

6904 

6787 

6674 

65^3 

6455 

6350 

4i 

44 

7677 

7538 

7403 

7272 

7145 
7143 

7022 
7020 

6902 
6900 

6785 

6672 

6561 

6453 

6348 

44 

45 

7674 

7535 

7401 

7270 

6784 

6670 

6559 

6451 

6346 

45 

46 

7672 

7533 

7398 

7268 

7141 

7018 

6898 

6782 

6668 

6ss8 

6450 

6344 

46 

47 

7670 

7531 

7396 

7266 

7139 

7016 

6896 

6780 

6666 

6556 

6448 

6343 

47 

48 

7667 

7528 

7394 

7264 

7137 

7014 

6894 

6778 

6664 

6554 

6446 

6341 

48 

49 

7665 

7526 

7392 

7261 

7135 
7133 

7012 
7010 

6892 
6890 

6776 
6774 

6663 

6552 

6444 

6339 

49 

50 

7663 

7524 

7390 

7259 

6661 

6550 

6443 

6338 

50 

51 

7660 

7522 

7387 

7257 

7131 

7008 

6888 

6772 

6659 

6548 

644  X 

(^:y^(^ 

51 

52 

7658 

7519 

7385 

7255 

7129 

7006 

6886 

6770 

6657 

6547 

6439 

6334 

52 

53 

7655 

7517 

7383 

7253 

7127 

7004 

6884 

6768 

66S5 

6545 

6437 

6332 

5^. 

54 
55 

7653 

•/^5i 

7515 

7381 

7251 

7124 

7002 

6882 

6766 
■  6764" 

6653 
6651 

6543 
6541 

_643_5„ 
6434 

6331 

54 

7513 

7379 

7249 

7122 

7000 

6881 

6329 

55 

5^^ 

7  48 

7510 

7376 

7246 

7120 

6998 

6879 

6763 

6650 

6539 

6432 

6327 

5^> 

57 

7046 

7508 

7374 

7244 

7118 

6996 

6877 

6761 

66^8 

6538 

6430 

6325 

S7 

5« 

7044 

7506 

7372 

7242 

7116 

6994 

6875 

6759 

6646 

6536 

6428 

6324 

58 

59 

S. 

7641 

7503 

7370 

7240 

7114 

6992 

6873 

6757 

6644 

6534 

6427 

6322 

59 

0°30' 

0°31' 

0°  32' 

0°  33' 

0°34' 

0°  35' 

0°36' 

0°37' 

0°38' 

0°39' 

0°40' 

0°41' 

S. 

Page  466j 

TABLE 

45- 

Proportional  Logarith 

ms. 

o 

/; .  Ill . 

k .     in . 

h.    m. 

h .    m . 

/i .   Ill . 

A .    m . 

h .    m . 

h.    m. 

11 ,    m . 

h.    m. 

h .    VI . 

h .    m , 

S. 

b. 

«°  42' 

0°43' 

0044/ 

0°45' 

0°46' 

0°4r 

0°48^ 

0°49' 

0°50' 

5563 

0°51' 

5477 

0°  52' 

5393 

0°53^ 

o' 

6320 

6218 

6xx8 

602  X 

5925 

5832 

5740 

5651 

5310 

0 

I 

6319 

6216 

6x17 

6019 

5924 

5830 

5739 

5649 

5562 

5476 

5391 

5309 

I 

2 

6317 

6215 

6115 

6017 

5922 

5829 

5737 

5648 

5560 

5474 

5390 

5307 

2 

3 

6315 

6213 

6x13 

60x6 

5920 

5827 

5736 

5646 

5559 

5473 

5389 

5306 

3 

4 

5 

^i^i 

62 1 1 

6112 

60x4 

5919 
5917 

5826 
5824 

5734 
5733 

5645 
5643 

5557 
5556 

5471 
5470 

5387 

5305 

4 

6312 

6210 

61x0 

6013 

"  5386 

5303 

5 

6 

6310 

6208 

6108 

60x1 

5916 

5823 

5731 

5642 

5554 

5469 

5384 

5302 

6 

7 

6308 

6206 

6107 

6009 

5914 

5821 

5730 

5640 

5553 

5467 

5383 

5300 

7 

8 

6306 

6205 

6105 

6008 

5913 

^In 

5728 

5639 

5551 

5466 

5382 

5299 

8 

9_ 

10 

6305 
6303 

6203 

6103 

6006 

591 L 

58x8 

5727 

5637 

5550 

5464 
5463 

5380 
5379 

5298 
5296 

_9^ 
xo 

6201 

6102 

6005 

5909 

58x6 

5725 

5636 

5549 

II 

6301 

6200 

6100 

6003 

5908 

5815 

5724 

5635 

5547 

5461 

5377 

5295 

II 

12 

6300 

6198 

6099 

600  X 

5906 

5813 

5722 

5633 

5546 

5460 

5376 

5294 

12 

13 

6298 

6196 

6097 

6000 

5905 

58x2 

5721 

5632 

5544 

5459 

5375 

5292 

13 

14 
15 

6296 
6294 

6195 

_6o95 

5998 

5903 

5810 

5719 

5630 

5543 

5457 
5456 

5373 
5372 

5291 

14 
15 

6193 

6094 

5997 

5902 

5809 

5718 

5629 

5541 

5290 

16 

6293 

6191 

6092 

5995 

5900 

5807 

5716 

5627 

5540 

5454 

5370 

5288 

16 

17 

6291 

6190 

6090 

5993 

5898 

5806 

5715 

5626 

5538 

5453 

5369 

5287 

17 

18 

6289 

6188 

6089 

5992 

5897 

5804 

5713 

5624 

5537 

5452 

5368 

5285 

18 

19 

6288 

6186 

6087 

5990 

5895 

5803 

5712 

5623 

5536 

5450 
5449 

5366 

5284 

J9_ 

20 

6286 

6185 

6085 

5989 

5894 

5801 

5710 

562  X 

5534 

5365 

5283 

20 

21 

6284 

6183 

6084 

5987 

5892 

5800 

5709 

5620 

5533 

5447 

5364 

5281 

21 

22 

6282 

6181 

6082 

5985 

5891 

5798 

5707 

56x8 

5531 

5446 

5362 

5280 

22 

23 

6281 

6179 

6081 

5984 

5889 

5796 

5706 

5617 

5530 

5445 

53&I 

5279 

23 

24 

6279 

6178 

6079 

5982 

5888 

5795 
5793 

5704 
5703 

5615 
5614 

5528 
5527 

5443 
5442 

5359 
5358 

5277 

24 

25 

6277 

6176" 

6077 

5981 

5^^^ 

5276 

^5 

26 

6276 

6174 

6076 

5979 

5^^ 

5792 

5701 

5613 

5526 

5440 

5357 

5275 

26 

27 

6274 

6173 

6074 

■5977 

5883 

5790 

5700 

561 1 

5524 

5439 

5355 

5273 

27 

28 

6272 

6171 

6072 

5976 

5881 

5789 

5698 

56x0 

5523 

5437 

5354 

5272 

28 

29 
30 

6271 
6269 

6169 

6071 

5974 

5880 

5787 

5697 

5608 

5521 

5436 

5353 

5271 

29 

6x68 

6069 

5973 

5878 

5786 

5695 

5607 

5520 

5435 

5351 

5269 

30 

31 

6267 

6x66 

6067 

5971 

5877 

5784 

5694 

5605 

5518 

5433 

5350 

5268 

31 

32 

6265 

6165 

6066 

5969 

5875 

5783 

5692 

5604 

5517 

5432 

5348 

5266 

32 

33 

6264 

6163 

6064 

5968 

5874 

5781 

5691 

5602 

5516 

5430 

5347 

5265 

33 

34 

6262 

6161 

6063 

5966 

5872 

5780 
5778 

5689 
5688 

5601 

5514 

5429 

5346 

5264 

34 

35 

6260 

6x60 

606  X 

5965 

5870 

5599 

5513 

5428 

5344 

5262 

35 

36 

6259 

6158 

6059 

5963 

5869 

5777 

5686 

5598 

55" 

5426 

5343 

5261 

36 

H 

6257 

6156 

6058 

5961 

S!^7 

5775 

5685 

5596 

5510 

5425 

5341 

5260 

37 

38 

6255 

6155 

6056 

5960 

5866 

5774 

5683 

5595 

5508 

5423 

5340 

5258 

38 

39 

6254 

6153 

6055 

5958 

5864 

5772 
5771 

5682 

5594 

5507 

5422 
5421 

5339 

5257 

39 

40 

6252 

6151 

6053 

5957 

5863 

5680 

5592 

5506 

5337 

5256 

40 

41 

6250 

6150 

6051 

5955 

5861 

5769 

5679 

5591 

5504 

5419 

5336 

5254 

41 

42 

6248 

6148 

6050 

5954 

5860 

5768 

5677 

55^9 

5503 

5418 

5335 

5253 

42 

43 

6247 

6146 

6048 

5952 

5858 

5766 

5676 

5588 

5501 

5416 

5333 

5252 

43 

44 

6245 

6x45 

6046 

5950 

5856 

5765 
5763 

5674 
5673 

5586 
"  5585" 

5500 
5498 

5415 
5414 

5332 

5250 

44 

45 

6243 

6143 

6045 

5949 

5855 

5331 

^5249^ 

45 

46 

6242 

6141 

6043 

5947 

5853 

5761 

5671 

5583 

5497 

5412 

5329 

5248 

46 

47 

6240 

6140 

6042 

5946 

5852 

5760 

5670 

5582 

5496 

54" 

5328 

5246 

47 

48 

6238 

6138 

6040 

5944 

5850 

5758 

5669 

5580 

5494 

5409 

5326 

5245 

48 

49 

6237 

6136 

6038 

5942 

5849 

5757 

5667 

5579 

5493 

5408 

5325 

5244 

49 

50 

6235 

6135 

6037 

5941 

5!47' 

5755 

5666 

5578 

5491 

5407 

5324 

5242 

50 

51 

6233 

6133 

6035 

5939 

5846 

5754 

5664 

5576 

5490 

5405 

5322 

5241 

51 

52 

6232 

6131 

6033 

5938 

5844 

5752 

5663 

5575 

5488 

5404 

5321 

5240 

52 

53 

6230 

6x30 

6032 

5936 

5843 

5751 

5661 

5573 

5487 

5402 

5320 

5238 

53 

54 

55 

6228 
6226 

6x28 
6126 

6030 

5935 

5841 

5749 
5748 

5660 
5658 

5572 

5486 

5401 

531.8 

5237 
5235 

54 
55 

6029 

5933 

5839 

5570 

5484 

5400 

5317 

56 

6225 

6125 

6027 

5931 

5838 

5746 

5fJ57 

5569 

5483 

5398 

53'5 

5234 

5'> 

57 

6223 

6123 

6025 

5930 

5836 

5745 

5655 

5567 

5481 

5397 

5314 

5233 

57 

5^ 

6221 

6121 

6024 

5928 

5835 

5743 

5654 

5566 

5480 

5395 

5313 

5231 

58 

59 

s. 

6220 

6120 

6022 

5927 

5833 

5742 

5652 

5564 



5478 
0°  50^ 

5394 
0°51' 

53" 
0°  52' 

5230 

50 

0°42' 

0°  43' 

0°44° 

0°45' 

0°46' 

0047/ 

0°48' 

0°49^ 

0°53' 

S. 

TABLE  45. 

Page  457 

k. 

Proportional  Logarithms. 

* 

s. 

o 

h  ,     ifi  . 

A  .    Ill  . 

// .  ;// . 

/t .  Ill . 

// .  ;// . 

// .  ;;/ . 

h .   Ill . 

!  A.  m. 

h.  m. 

h.   m. 

!i .  Ill . 

1  , 

/i .    in . 

0°  54' 

5229 

0°  55' 

5 149 

0°56' 

0°57' 

4994 

0°  5S' 

4918 

0°  59' 

4844 

1°0' 

4771 

1  1°1' 
4699 

1°2' 

4629 

1°3' 

4559 

r4' 

1°5' 

s. 

i  5071 

4491 

4424 

0 

I 

5227 

5148 

5070 

1  4993 

4917 

4843 

4770 

4698 

4628 

4558 

4490 

4422 

I 

"> 

S22() 

5146 

5068 

4991 

4916 

4842 

4769 

4697 

4626 

4557 

4489 

4421 

2 

.■> 

5225 

5145 

5067 

4990 

4915 

4841 

4768 

•  4696 

;  4625 

4556 

4488 

4420 

•> 

4_ 

5 

5223 
5222 

5144 
5143 

5066 
5064 

4989 
498S 

4913 
4912 

4839 

4766 

4695 
4693 

1  4624 
4623 

4555 
4554 

4486 
4485 

4419 
4418" 

4 

5 

4838 

4765 

0 

5221 

5^41 

S°('i 

4986 

491 1 

4837 

4764 

4692 

4622 

4552 

4484 

4417 

6 

i 

5219 

5140 

5062 

4985 

4910 

4836 

4763 

4691 

4621 

4551 

4483 

4416 

7 

s 

5218 

5139 

5061 

4984 

4908 

4834 

4762 

4690 

4619 

4550 

4482 

4415 

8 

0 
10 

5217 

5137 

5059 

4983 
4981 

4907 
4906 

4833 
4832 

4760 

4759 

4689 
4688 

4618 

4549 

_448i 

4414^ 

_9^ 

5215 

5136 

5058 

4617" 

4548 

4480 

4412' 

ID 

1 1 

5214 

5135 

5057 

4980 

4905 

4831 

4758 

4686 

4616 

4547 

4479 

441 1 

II 

12 

5213 

5133 

5055 

4979 

4903 

4830 

4757 

4685 

4615 

4546 

4477 

4410 

12 

13 

52II 

5132 

5054 

4977 

4902 

4828 

4756 

4684 

4614 

4544 

4476 

4409 

13 

14 

5210 

5131 
5129 

5053 
5051 

4976 
4975 

_490i 
4900 

4827 
4826 

4754 
4753 

4683 
4682 

4612 
461 1 

_4543 

4542 

4475 
4474 

440S 
4407 

14 
15 

15 

"5209 

10 

5207 

512S 

5050 

4974 

4899 

4825 

4752 

4680 

4610 

4541 

4473 

4406 

16 

17 

5206 

5127 

5049 

4972 

4897 

4823 

4751 

4679 

4609 

4540 

4472 

4405 

17 

iS 

5205 

5125 

5048 

4971 

4896 

4822 

4750 

4678 

4608 

4539 

4471 

4404 

18 

_'9^ 

5203_ 

5124 

5046 

4970 

^4895 
4894 

4821 
4820 

4748 

4677 

4607 
4606 

4538 

4469 

4402 

J9_ 

20 

5202 

5123 

5C'45 

4969 

4747 

4676 

"  4536 

4468 

4401 

20 

21 

5201 

5122 

5044 

4967 

4892 

4819 

4746 

4675 

4604 

4535 

4467 

4400 

21 

22 

5199 

5120 

5043 

4966 

4891 

4817 

4745 

4673 

4603 

4534 

4466 

4399 

22 

23 

5 '98 

5119 

5041 

4965 

4890 

4816 

4744 

4672 

4602 

4533 

4465 

4398 

23 

24 

25 

5197 

5118 

5040 

4964 

4889 

4815 

4742 

4671 
4670 

z;6oi 
4600 

4532 
4531 

4464 

4397 

24 

5195 

5116 

5039 

4962 

4887 

4814 

4741 

4463 

4396 

25 

26 

5194 

5i>5 

5037 

4961 

4886 

4812 

4740 

4669 

4599 

4530 

4462 

4395 

26 

27 

5193 

5114 

5036 

4960 

4^^5 

481 1 

4739 

4668 

4597 

4528 

4460 

4394 

27 

2S 

519' 

5112 

5035 

4959 

4884 

4S10 

4738 

4666 

4596 

4527 

4459 

4393 

28 

29 
30 

5190 
5189 

5"i 

5034 

4957 
4956 

4882 
4881 

4809 
4808 

4736 
4735 

4665 
4664 

_4595 
4594 

4526  1 
4525 

4458 

4391 

J9_ 
30 

5110 

5032 

4457 

4390 

31 

5187 

5108 

5031 

4955 

4880 

4806 

4734 

4663 

4593 

4524 

4456 

4389 

31 

32 

5186 

5107 

5030 

4954 

4879 

4805 

4733 

4662 

4592 

4523 

4455 

4388 

32 

11 

5185 

5106 

5028 

4952 

4877  , 

4804 

4732 

4660 

4590 

4522 

4454 

4387 

■J  t 

34 
35 

5183 
5182 

5105 

5027 

4951 

4876  , 

4803 

4730 

4659 
4658 

4589 
4588 

4520  [ 

4453 

4386 
4385 

34 
35 

5103 

5026  , 

4950 

4875 ! 

4801 

4729 

4519 

4452 

36 

5181 

5102 

5025 

4949 

4874 

4800 

4728 

4657 

4587 

4518 

4450 

4384 

36 

37 

5179 

5101 

5023 

4947 

4873 

4799 

4727 

4656 

4586 

4517 

4449 

4383 

37 

38 

5178 

5099 

5022 

4946  j 

4871 , 

4798 

4726 

4655 

4585 

4516  i 

4448 

4381 

38 

.39_ 
40 

5177 
5175 

5098 
5097 

5021  1 

4945  : 
4943 

4870 1 
4869 

4797 

4724 

4653 
4652 

4584 
4582 

4515  . 
4514 

4447 
4446 

4380 

J9 
40 

5019 

4795 

4723  1 

4379 

41 

5174 

5095  1 

5018 

4942 

4868 

4794 

4722 

4651 

4581 

4512 

4445 

4378 

41 

42 

5173 

5094 

5017 

4941 

4866 

4793 

4721 

4650 

4580 

4511 

4444 

4377 

42 

43 

5'72 

5093 

5016 

4940 

4865 

4792 

4720 

4649 

4579 

45JO 

4443 

4376 

43 

44 
45 

5170 
5169 

5092 

5014 

4938 
4937 

4864 , 

4791 

4718 
4717 

4648 
4646 

4578 
4577 

4509 
4508 

4441 

__4375_ 

44 
45 

5090 

5013  ' 

4863 

4789 

4440 

4374 

46 

5168 

5°!9 

5012 

4936 

4861 

4788 

4716 

4645 

4575 

4507 

4439 

4373 

46 

47 

5166 

5088 

5011 

4935 

4860 

4787 

4715 

4644 

4574 

4506 

4438 

4372 

47 

4S 

5165  , 

5086 

5009 

4933 

4^59 

4786 

4714 

4643 

4573 

4505 

4437 

4370 

48 

_49 

5164  , 

5085 

5008 

4932 

4858 

4785 
4783 

4712 
4711 

4642 

4572 

4503 

4502  ! 

4436 
4435 

4369 
4368 

49 
50 

50 

5162  , 

5084 

5007 

4931 

4856 

4640 

4571 

51 

5161 

5082 

5005  ' 

4930 

4855 

4782 

4710 

4639 

4570 

4501 

4434 

4367 

51 

S2 

5160 

5081 

5004 

4928 

4854 

4781 

4709 

4638 

4569 

4500 

4433 

4360 

52 

53 

5158  ' 

5080 

5003 

4927 

4853 

4780 

4708 

4637 

4567 

4499 

4431 

4365 

53 

54 
55 

5157 

5079 

5002 

4926 

4852 

4778 

4707  i 

4636 

4566 

4498 
4497 

4430  , 
4429 

4364 
4363 

54 
55 

5156 

5077 

5000 

4925 

4850 

4777 

4705  : 

4635 

4565 

56 

5154  ; 

5076 

4999 

4923 

4849 

4776 

4704 

4633 

4564 

4495 

4428 

4362 

5^' 

57 

5153  ' 

5075 

4998 

4922 

4848 

4775 

4703 

4632 

4563 

4494 

4427 

4361 

57 

58 

5152 

5073 

4997 

4921 

4847 

4774 

4702 

4631 

4562 

4493 

4426 

4359 

58 

59 

5150  1 

5072 

4995 

4920 

4845 

4772 

4701 

4630 

4560 

4492 

1°3' 

4425 

4358 

59 

S. 

0°  54' 

0°  55' 

0°  56'  ' 

1 

0°  5r 

0°58' 

0°  59'  j 

1°0' 

ri' 

1°2' 

1°4' 

r5' 

i 

Page  458 

' 

FABLE  45. 

Proportional  Logarithi 

US. 

/;.  m. 

h.    m.          h.  in. 

h.   m. 

h  .    Ill  . 

/; .  in . 

h .    m . 

A.   ill. 

h .    m . 

h.    7H. 

h .    ni . 

h.    m. 

s. 

1°6' 

\°v 

l°8^ 

r9^ 

\°w 

- 
4040 

r  w 

rw 

i°w 

\°w 

\°w 

\°\r 

o 

4357 

4292 

4228 

4164 

4102 

3979 

3919 

3860 

3802 

3745 

3688 

0 

I 

4356 

4291   4227 

4163 

4IOI 

4039 

3978 

3919 

3859 

3801 

3744 

3687 

I 

2 

4355 

4290  :   4226 

4162 

4100 

4038 

3977 

3918 

3858 

3800 

3743 

3686 

2 

3 

4354 

4289  ]   4224 

4161 

4099 

4037 

3976 

3917 

3857 

3799 

3742 

3&85 

0 
J 

4 

4353 

4288    4223 

4160 

4098 

4036 

3975 

3916 

3856 

3798 

3741 

3684 

4 

4352 

4287    4222 

4159 

4097 

4035 

3974 

3915 

3856 

3797 

3740 

3683 

5 

6 

4351 

4285  1   4221 

4158 

4096 

4034 

3973 

3914 

3855 

3796 

3739 

3682 

6 

7 

4350 

4284    4220 

4157 

4095 

4033 

3972 

3913 

3854 

3795 

3738 

3681 

7 

8 

4349 

4283  1   4219 

4156 

4093 

4032 

3971 

3912 

3853 

3794 

3737 

3680 

cS 

9 

4347 

4282    4218 

4155 

4092 

4031 

3970 

39" 

3852 
3851 

3793 
3792 

3736 

3679 
3678 

^9 

10 

10 

4346 

4281    4217 

4154 

4091 

4030 

3969 

3910 

3735 

II 

4345 

4280    4216 

4153 

4090 

4029 

3968 

3909 

3850 

3792 

3734 

3677 

II 

12 

4344 

4279 

4215 

4152 

4089 

4028 

3967 

3908 

3849 

3791 

3733 

3677 

12 

I,S 

4343- 

4278 

4214 

4151 

4088 

4027 

3966 

3907 

3848 

3790 

3732 

3676 

13 

H 

4342 

4277 

4213 

4150 

4087 

4026 
4025" 

3965 
3964 

3906 

3847 

3789 

3731 

3675 

14 

i,S 

■4341 

4276 

4212 

4149 

4086 

3905 

3846 

3788 

3730 

3674 

IS 

I6 

4340 

4275  ;    421  I 

4147 

4085 

4024 

3963 

3904 

3845 

3787 

3729 

3673 

lb 

17 

4339 

4274      4210 

4146 

4084 

4023 

3962 

3903 

3844 

3786 

3728 

3672 

17 

i8 

433^ 

4273      4209 

4145 

4083 

4022 

3961 

3902 

3843 

3785 

3727 

3671 

18 

19 

4336 

4271      4207 

4144 

4082 

4021 

3960 

3901 

3842 
3841 

3784 
3783 

3727 
3726 

3670 
"3669^ 

J9 
20 

20 

4335 

4270      4206 

4143 

4081 

4020 

3959 

3900 

21 

4334 

4269      4205 

4142 

4080 

4019 

3958 

3899 

3840 

3782 

3725 

3668 

21 

22 

4333 

4268      4204 

4141 

4079 

4018 

3957 

3898 

3839 

3781 

3724 

3667 

22 

23 

4332 

4267      4203 

4140 

4078 

4017 

3956 

3897 

3838 

3780 

3723 

3666 

23 

24 
25 

4331 

4266 

4202 

4139 
4138 

4077 
4076 

•  4016 

3955 

389b 
3895 

3837 
3836 

3779 
3778 

3722 

3bb5 

24 

4330 

4265 

4201 

4015 

3954 

3721 

3664 

25 

26 

4329 

4264  :  4200 

4137 

4075 

4014 

3953 

3894 

3835 

3777 

3720 

3t'b3 

2b 

27 

4328 

4263 

4199 

4136 

4074 

4013 

3952 

3893 

3834 

3776 

3719 

3663 

27 

28 

4327 

4262 

4198 

4135 

4073 

4012 

3951 

3892 

3833 

3775 

3718 

3662 

28 

29 

4326 

4261 

4197 

4134 

4072 

4011 

3950 

3891 

3832 
3831 

3774 
3773 

3717 

3661 

29 

30 

4325 

4260 

4196 

4133 

4071 

4010 

3949 

3716 

3660 

30 

31 

4323 

4259 

4195 

4132 

4070 

4009 

3948 

3889 

3830 

3772 

3715 

3659 

31 

32 

4322 

4258  !   4194 

4131 

4069 

4008 

3947 

3888 

3829 

3771 

3714 

3^58 

32 

33 

4321 

4256     4193 

4130 

4068 

4007 

3946 

3887 

3828 

3770 

3713 

3657 

33 

34 

4320 

4255 

4192 

4129 

4067 

4006 

3945 

3886 
3885 

3827 

3769 

3712 
37" 

3655 

34 
35 

3S 

4319 

4254 

4191 

4128 

4066 

4005 

3944 

3826 

.^768 

36 

4318 

4253 

4189 

4127 

4065 

4004 

3943 

3884 

3825 

3768 

3710 

3654 

3(> 

37 

4317 

4252 

4188 

4126 

4064 

4003 

3942 

3883 

3824 

3767 

3709 

3653 

37 

3« 

4316 

4251 

4187 

4125 

4063 

4002 

3941 

3882 

3823 

3766 

3709 

3652 

38 

39 

4315 

4250 

4186 

4124 

4062 

4001 

3940 

3881 

3822 

3765 
3764 

3708 

3651 

39 

40 

4314 

4249 

4185 

4122 

4061 

4000 

3939 

3880 

3821 

3707 

3650 

40 

41 

4313 

4248 

4184 

4121 

4060 

3999 

3938 

3879 

3820 

3763 

3706 

3649 

41 

42 

431 1 

4247 

4183 

4120 

4059 

3998 

3937 

3878 

3820 

3762 

3705 

3649 

42 

43 

4310 

4246 

4182 

4119 

4058 

3997 

3936 

3877 

3819 

3761 

3704 

3648 

43 

44 
45 

4309 

4245 

4181 

4118 

4056 

3996 

3935 

3876 

3818 

3760 

3703 

3647 

44 

4308 

4244 

4180 

4117 

4055 

3995 

3934 

3875 

3817 

3759 

3702 

3646 

45 

46 

4307 

4243 

4179 

4116 

4054 

3993 

3933 

3874 

3816 

3758 

3701 

3645 

4b 

47 

4306 

4241 

4178 

4115 

4053 

3992 

3932 

3873 

3815 

3757 

3700 

3644 

47 

48 

4305 

4240     4177 

4114 

4052 

3991 

3931 

3872 

3814 

3756 

3699 

3643 

48 

49 

4304 

4239 

4176 
4175 

4113 

4051 

3990 
3989 

3930 
3929 

3871 
3870 

3813 

3755 

3698 

3642 

49 

50 

4303 

4238 

4112 

4050 

3812 

3754 

3697 

3641 

50 

51 

4302 

4237 

4174 

4111 

4049 

3988 

3928 

3869 

3811 

3753 

3696 

3640 

51 

52 

4301 

4236 

4173 

4110 

4048 

3987 

3927 

3868 

3810 

3752 

3695 

3639 

52 

53 

4300 

4235 

4172 

4109 

4047 

3986 

3926 

3867 

3809 

3751 

3694 

3638 

53 

54J 
55 

4298 

4234 

4171 

4108 

4046 

3985 

3925 

3866 

3808 

3807 

3750 

3693 

3637 
3636 

54 

4297 

4233 

4169 

4107 

4045 

3984 

3924 

3865 

3749 

3693 

55 

56 

4296 

4232 

4168 

4106 

4044 

3983 

3923 

3864 

3806 

3748 

3692 

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5b 

57 

4295 

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4167 

4105 

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57 

5« 

4294 

4230 

4166 

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4042 

3981 

3921 

3862 

3804 

3746 

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3634 

58 

59 

4293 

4229 

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4041 

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3746 

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S. 

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1°8' 

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1°10^ 

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1°12' 

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i°ir 

S. 

i 


TAliLE  45. 

Page  459 

»•• 

• 

Proportional  Logarith 

ms. 

h .  in . 

/i .    Ill . 

h .    1)1 . 

h .    II! . 

h.    tn. 

ii .  Ill . 

h .    in . 

h .    in . 

h .    in . 

/i .    m . 

A.    in. 

/i .    in . 

S. 

s. 

1°18' 

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3576 

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1°26' 

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3522 

3468 

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3362 

3310 

3259 

3208 

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3576 

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3467 

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3413 

3360 

3308 

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3156 

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3519 

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3359 

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4 

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3518 

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3558 

3306 

3255 

3204 

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3626 

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3357 

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3153 

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6 

7 

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3570 

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3462 

3408 

3356 

3304 

3253 

3202 

3152 

3102 

3053 

7 

8 

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3569 

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3461 

3408 

3355 

3303 

3252 

3201 

3151 

3101 

3052 

8 

9 

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3568 

35H 

3460 

3407 

3354 

3302 

3251 

3200 

3150 

3101 

3052 

9 

lO 

3623 

3567 

3513 

3459 

3406 

3353 

3301 

3250 

3199 

3149 

3100 

3051 

10 

1 1 

3622 

3566 

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3458 

3405 

3352 

3300 

3249 

3198 

3148 

3099 

3050 

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12 

3621 

3565 

3511 

3457 

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3351 

3300 

3248 

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3098 

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3620 

3565 

3510 

3456 

3403 

3351 

3299 

3247 

3197 

3147 

3097 

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13 

U 

3619 

3564 

3509 

3455 

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3350 

3298 
3297 

3247 
3246 

3196 

3146 

3096 

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14 

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3618 

3563 

3508 

3454 

3401 

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3195 

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16 

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3095 

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lb 

17 

3616 

3561 

3506 

3453 

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3347 

3295 

3244 

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3143 

3094 

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17 

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3615 

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3506 

3452 

3399 

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3294 

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3193 

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3093 

3044 

18 

10 

3614 

3559 

3505 

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3398 

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3293 

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3192 

3142 

3092 

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19 

20 

3613 

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3504 

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3141 

3091 

3043 

20 

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3612 

3557 

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3449 

3396 

3344 

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3241 

3190 

3140 

3091 

3042 

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22 

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3556 

3502 

3448 

3395 

3343 

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3240 

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3139 

3090 

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22 

23 

3610 

3555 

3501 

3447 

3394 

3342 

3290 

3239 

3188 

3138 

3089 

3040 

23 

24 

3610 

3555 
3554 

3500 
3499 

3446 
3446 

3393 
3393 

3341 

3289 

3238 
3237 

3188 
3187 

3138 

3088 

3039 
3039 

24 
25 

25 

3609 

3340 

3288 

3137 

3087 

25 

3608 

3553 

3498 

3445 

3392 

3339 

3288 

3236 

3186 

3i3(> 

3087 

3038 

2b 

27 

3607 

3552 

3497 

3444 

3391 

3338 

3287 

3236 

3185 

3135 

3086 

3037 

27 

28 

3606 

3551 

3497 

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3390 

3338 

3286 

3235. 

3184 

3134 

3085 

3036 

28 

29 

3605 

3550 

3496 

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3389 

3337 
3336 

3285 

3234 

3183 

3133 

3084 

3035 

29 

30 

3604 

3549 

3495 

3441 

3388 

3284 

3233 

3183 

3133 

3083 

3034 

30 

31 

3603 

3548 

3494 

3440 

3387 

3335 

3283 

3232 

3182 

3132 

3082 

3034 

31 

32 

3602 

3547 

3493 

3439 

3386 

3334 

3282 

3231 

3181 

3131 

3082 

3033 

32 

3601 

3546 

3492 

3438 

3386 

3333 

3282 

3231 

3180 

3130 

3081 

3032 

33 

34 

3600 

3545 
3545 

3491 

3438 

3385 
3384 

3332 

3281 

3230 
3229 

3179 
3178 

3129 
3129 

3080 

3031 

34 

35 

3599 

3490 

3437 

3332 

3280 

3079 

3030 

35 

3^' 

3598 

3544 

3489 

3436 

3383 

3331 

3279 

3228 

3«78 

3128 

3078 

3030 

3^ 

37 

3598 

3543 

3488 

3435 

3382 

3330 

3278 

3227 

3177 

3127 

3078 

3029 

37 

3« 

3597 

3542 

3488 

3434 

3381 

3329 

3277 

3226 

3176 

3126 

3077 

3028 

38 

39 

3596 

3541 
3540 

3487 

3433 

3380 
3379 

3328 
3327 

3276 
3276 

3225 
3225 

3175 
3174 

3125 
3124 

3076 

3027 

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40 

40 

3595 

3486 

3432 

3075 

3026 

41 

3594 

3539 

3485 

3431 

3379 

3326 

3275 

3224 

3173 

3124 

3074 

3026 

41 

42 

3593 

3538 

3484 

3431 

3378 

3325 

3274 

3223 

3173 

3123 

3073 

3025 

42 

43 

3592 

3537 

3483 

3430 

3377 

3325 

3273 

3222 

3172 

3122 

3073 

3024 

43 

44 

3591 

3536 

3482 

3429 

3376 

3324 

3272 

3221 

3171 

3121 

3072 

3023 

44 

45 

3590 

3535 

3481 

3428 

3375 

3323 

3271 

3220 

3170 

3120 

3071 

3022 

45 

4b 

3589 

3535 

3480 

3427 

3374 

3322 

3270 

3220 

3169 

3"9 

3070 

3022 

4b 

47 

3588 

3534 

3480 

3426 

3373 

3321 

3270 

3219 

3ib8 

3119 

3069 

3021 

47 

48 

3587 

3533 

3479 

3425 

3372 

3320 

3269 

3218 

3168 

3118 

3069 

3020 

48 

49 

3587 

3532 

3478 

3424 

3372 

3319 

3268 

3217 

3167 

3117 

3068 

3019 

49 
50 

50 

3586 

3531 

3477 

3423 

3371 

3319 

3267 

3216 

3166 

3116 

3°^I 

3018 

51 

3585 

3530 

3476 

3423 

3370 

3318 

3206 

3215 

3165 

3"5 

3066 

3018 

5' 

52 

35S4 

3529 

3475 

3422 

3369 

3317 

3265 

3214 

'  3164 

3114 

3065 

3017 

52 

53 

3583 

3528 

3474 

3421 

3368 

3316 

3265 

3214 

3163 

3"4 

3065 

3016 

53 

54 

3582 

3527 
3526 

3473 

3420 

3367 

3315 

3264 

3213 

3i^i 

3"3 

3064 

3015 

54 

55 

3581 

3472 

3419 

3366 

3314 

3263 

3212 

3162 

3112 

3063 

3014 

55 

5fJ 

3580 

3525 

3471 

3418 

3365 

3313 

3262 

3211 

3161 

3111 

3062 

3014 

5(^ 

57 

3579 

3525 

3471 

3417 

3365 

3313 

3261 

3210 

3160 

3110 

3061 

3013 

57 

5-^ 

3578 

3524 

3470 

3416 

3364 

3312 

3260 

3209 

3159 

3110 

3060 

3012 

58 

59 

3577 

3523 

3469 

3415 

3363 

33" 

3259 

3209 

3158 

3109 

3060 

301 1 

59 

" 

1°18' 

1°19' 

1°  m' 

1°  IV 

r  22' 

i°  23' 

1°  24' 

1°  25' 

1°26' 

1°  27' 

1°  28' 

1°  29' 

S. 

I 


Page  460 

TABLE  45. 

Proportional  Logarith 

ms. 

s. 

k.    ni. 

h.    m. 

h .    in . 

// .  /;/ . 

//.  ?«. 

A .    VI . 

h.    m. 

h.    m. 

h .    »i . 

h.    in. 

h.    ni. 

1 

h.    m.    i  c 

rw 

1°31' 

1°  32^ 

1°33' 

1°34' 

1°35' 

r36' 

i°3r 

vw 

1°39' 

\°  w 

l°4r 

0. 

o 

3010 

'   2962 

2915 

2868 

2821 

2775 

2730 

2685 

2640 

2596 

2553 

2510 

0 

I 

3009 

2962 

2914 

2867 

2821 

2775 

2729 

2684 

2640 

2596 

2552 

2509 

I 

2 

3009 

2961 

2913 

2866 

2820 

2774 

2729 

2684 

2639 

2595 

2551 

2508 

2 

3 

3008 

2960 

2912 

2866 

2819 

2773 

2728 

2683 

2638 

2594 

2551 

2507 

-> 

4 

3007 

2959 

2912 

2865 

2818 

2772 

2727 

2682 

2638 

2593 

2550 

2507 

4 
5 

5 

3006 

2958 

291 1 

2864 

2818 

2772 

2726 

2681 

2637 

2593 

2549 

2506 

6 

3005 

2958 

2910 

2863 

2817 

2771 

2725 

2681 

2636 

2592 

2548 

2505 

6 

7 

3005 

2957 

2909 

2862 

2816 

2770 

2725 

2680 

2635 

2591 

2548 

2504 

7 

8 

3004 

2956 

2909 

2862 

2815 

2769 

2724 

2679 

2635 

2591 

2547 

2504 

8 

9 

3003 

2955 

2908 

2861 

2815 

2769 

2723 

2678 

2634 

2590 

2546 

2503 

_9 

lO 

3002 

2954 

2907 

2860 

2814 

2768 

2722 

2678 

2633 

2589 

2545 

2502 

10 

II 

3001 

2954 

2906 

2859 

2813 

2767 

2722 

2677 

2632 

2588 

2545 

2502 

II 

12 

3001 

2953 

2905 

2859 

2812 

2766 

2721 

2676 

2632 

2588 

2544 

2501 

12 

13 

3000 

2952 

2905 

2858 

281 1 

2766 

2720 

2675 

2631 

2587 

2543 

2500 

13 

14 

2999 

2951 

2904 

2857 

281 1 

2765 

2719 
2719 

2675 
2674 

263o_ 
2629 

2586 

2543 

2499 

14 

15 

2998 

2950 

2903 

2856 

2810 

2764 

2585" 

2542 

2499 

15 

16 

2997 

2950 

2902 

2855 

2809 

2763 

2718 

2673 

2629 

2585 

2541 

2498 

16 

17 

2997 

2949 

2901 

2855 

2808 

2763 

2717 

2672 

2628 

2584 

2540 

2497 

17 

18 

2996 

2948 

2901 

2854 

2808 

2762 

2716 

2672 

2627 

2583 

2540 

2497 

18 

19 

2995 

2947 

2900 

2853 

2807 
2806 

2761 
2760 

2716 
2715 

2671 

2626 

2583 

2539 

2496 

J  9 

20 

2994 

2946 

2899 

2852" 

2670 

2626 

2582 

2538" 

2495^ 

20 

21 

2993 

2946 

2898 

2852 

2805 

2760 

2714 

2669 

2625 

2581 

2538 

2494 

21 

22 

2993 

2945 

2898 

2851 

2805 

2759 

2713 

2669 

2624 

2580 

2537 

2494 

22 

23 

2992 

2944 

2897 

2850 

2804 

2758 

2713 

2668 

2624 

2580 

2536 

2493 

23 

24 

2991 

2943 

2896 

2849 

2803 

2757 
2756 

2712 

2667 

2623 

2579 

2535 
2535 

2492^ 

24 

25 

2990 

2942 

2895 

2848 

2802 

27II 

2666 

2622 

2578 

2492 

25 

26 

2989 

2942 

2894 

2848 

2801 

2756 

2710 

2666 

2621 

2577 

2534 

2491 

26 

27 

2989 

2941 

2894 

2847 

2801 

2755 

2710 

2665 

2621 

2577 

2533 

2490 

27 

28 

2988 

2940 

2893 

2846 

2800 

2754 

2709 

2664 

2620 

2576 

2533 

2489 

28 

29 

2987 

2939 

2892 

2845 

2799 

2753 

2708 
2707 

2663 
2663 

2619 

26r8~ 

2575 
2574 

2532 

2489 

29 

30 

2986 

2939 

2SgT 

2845 

2798 

2753 

2531 

2488 

30 

31 

2985 

2938 

2891 

2844 

2798 

2752 

2707 

2662 

2618 

2574 

2530 

2487 

31 

32 

2985 

2937 

2890 

2843 

2797 

2751 

2706 

2661 

2617 

2573 

2530 

2487 

32 

33 

2984 

2936 

2889 

2842 

2796 

2750 

2705 

2660 

2616 

2572 

2529 

2486 

0  T 

0J> 

34 

2983 

2935 
2935 

2888 
2887 

2842 
2841 

2795 

2750 

2704 

2660 

2615 
2615 

2572 

2528 

2485 

34 

35 

2982 

2795 

2749 

2704 

2659 

2571 

2527 

2485 

35 

36 

2981 

2934 

2887 

2840 

2794 

2748 

2703 

2658 

2614 

2570 

2527 

2484 

36 

37 

2981 

2933 

2886 

2839 

2793 

2747 

2702 

2657 

2613 

2569 

2526 

2483 

n 

38 

2980 

2932 

2885 

2838 

2792 

2747 

2701 

2657 

2612 

2569 

2525 

24S2 

38 

39 

2979 

2931 
2931 

2884 

2838 

2792 

2746 
2745 

2701 
2700 

2656 
2655" 

2612 
261 1 

2568 

2525 

2482 

39 

40 

2978 

2883 

2837 

2791 

2567 

2524 

2481 

40 

41 

2977 

2930 

2883 

2836 

2790 

2744 

2699 

2655 

2610 

2566 

2523 

2480 

41 

42 

2977 

2929 

2882 

2835 

2789 

2744 

2698 

2654 

2610 

2566 

2522 

2480 

42 

43 

2976 

2928 

2881 

2835 

2788 

2743 

1698 

2653 

2609 

2565 

2522 

2479 

43 

44 
45 

2975 
2974 

2927 

2880 

2834 

2788 

2742 

269  7_ 
2696 

2652 

2608 

2564 

2521 

2478 

44 
45 

2927 

2880 

2833 

2787 

2741 

2652 

2607 

2564 

2520 

2477 

46 

2973 

2926 

2879 

2832 

2786 

2741 

2695 

2651 

2607 

2563 

2520 

2477 

46 

47 

2973 

2925 

2878 

2831 

2785 

2740 

2695 

2650 

2606 

2562 

2519 

2476 

47 

48 

2972 

2924 

2877 

2831 

2785 

2739 

2694 

2649 

2605 

2561 

2518 

2475 

48 

49 

2971 

2924 

2876 

2830 
2829 

2784 
2783 

2738 
2738 

2693 

2692 

2649 
2648 

2604 
2604 

2561 

2517 

2475_ 

49 

50 

2970 

2923 

2876 

2560 

2517 

2474 

50 

51 

2969 

2922 

2875 

2828 

2782 

2737 

2692 

2647 

2603 

2559 

2516 

2473 

51 

52 

2969 

2921 

2874 

2828 

2782 

2736 

2691 

2646 

2602 

2559 

2515 

2472 

52 

53 

2968 

2920 

2873 

2827 

2781 

2735 

2690 

2646 

2601 

2558 

2515 

2472 

53 

54 
55 

_  2967 

2920 

2873 

2826 
2825 

2780 
2779 

2735 
2734 

2689 

2689 

2645_, 
2644 

2601 
2600 

2557 

2514 

2471 

54  \ 
55 

2966 

2919 

2872 

2556 

2513 

2470 

56 

2965 

2918 

2871 

2825 

2779 

2733 

2688 

2643 

2599 

2556 

2512 

2470 

56 

57 

2965 

2917 

2870 

2824 

2778 

2732 

2687 

2643 

2599 

2555 

2512 

2469 

57 

58 

2964 

2916 

2869 

2823 

2777 

2732 

2687 

2642 

2598 

2554 

25 1 1 

2468 

58 

59 

2963 

2916 

2869 

2822 

2776 

2731 

2686 

2641 

2597 

2553 

2510 

2467 

59 

S. 

1°30' 

\°U' 

1°32' 

1°33' 

VW 

r35^ 

1°36' 

i°3r 

1°38^ 

1°  39^ 

1°40' 

i°4r 

S. 

i 


TABLE  45. 

[Page  461  | 

^ 

Proportional  Logarithms. 

1 

A.    m. 

/t.    m. 

k.    tn. 

h.    m. 

h.   m. 

A.  m. 

h.    m. 

k.    m. 

h.    m. 

h.    tn. 

h.    m. 

A.    m. 

S. 

s. 

1°42' 

i°U' 

1044/ 

1°45' 

2300 

ViV 

\°W 

\°w 

\°w 

1°51' 

1°52' 

2061 

r53' 

0 

2467 

2424 

2382 

2341 

2259 

2218 

2178 

2139 

2099 

2022 

0 

I 

2466 

2424 

2382 

2340 

2299 

2258 

2218 

2178 

2138 

2099 

2060 

2021 

I 

2 

2465 

2423 

2381 

2339 

2298 

2258 

2217 

2177 

2137 

2098 

2059 

2021 

2 

3 

2465 

2422 

2380 

2339 

2298 

2257 

2216 

2176 

2137 

2098 

2059 

2020 

3 

4 

2464 

2422 

2380 

2338 

^2291_ 

2256 

2216 

2176 

2136 

2097 
2096 

2058 
2057 

2019 
2019" 

4 
5 

5 

2463 

2421 

2379 

2337 

2296 

2256 

2215 

2175" 

2136 

6 

2462 

2420 

2378 

2337 

2296 

2255 

2214 

2174 

2135 

2096 

2057 

2018 

6 

7 

2462 

2419 

2378 

2336 

2295 

2254 

2214 

2174 

2134 

2095 

2056 

2017 

7 

S 

2461 

2419 

2377 

2335 

2294 

2253 

2213 

2173 

2134 

2094 

2055 

2017 

8 

_9_ 

2460 

2418 

2376 

2335 
2334 

2294 
2293 

_  2253 

2252 

2212 

2172 

2133 

2094 

2055 
2054 

2016 

_  9 

lO 

2460 

2417 

2375 

2212 

2172 

2132 

2093 

2016 

10 

II 

2459 

2417 

2375 

2333 

2292 

2251 

2211 

2I7I 

2132 

2092 

2053 

2015 

II 

12 

2458 

2416 

2374 

2333 

2291 

2251 

2210 

2170 

2I3I 

2092 

2053 

2014 

12 

13 

2458 

2415 

2373 

2332 

2291 

2250 

2210 

2170 

2130 

2091 

2052 

2014 

13 

14 

2457 

2415 

2373 

2331 

2290 

2249 

2209 

2169 

2130 
2129 

2090 

2052 

2013 
2012 

14 
15 

15 

2456 

2414 

2372 

2331 

2289 

2249 

2208 

2169 

2090 

^051 

i6 

2455 

2413 

2371 

2330 

2289 

2248 

2208 

2168 

2128 

2089 

2050 

2012 

16 

17 

2455 

2412 

2371 

2329 

2288 

2247 

2207 

2167 

2128 

2088 

2050 

201 1 

17 

i8 

2454 

2412 

2370 

2328 

2287 

2247 

2206 

2167 

2127 

2088 

2049 

2010 

18 

19- 

2453 

241 1 

2369 

2328 

2287 

2246 

2245" 

2206 

2166 

2126 
2126 

2087 
2086 

2048 

2010 

J9_ 

20 

2453 

2410 

2368 

2327 

2286 

2205 

2165 

2048 

2009 

20 

21 

2452 

2410 

2368 

2326 

2285 

2245 

2204 

2165 

2125 

2086 

2047 

2009 

21 

22 

2451 

2409 

2367 

2326 

2285 

2244 

2204 

2164 

2124 

2085 

2046 

2008 

22 

23 

2450 

2408 

2366 

2325 

2284 

2243 

2203 

2163 

2124 

2085 

2046 

2007 

23 

24 

2450 

2408 

2366 

2324 

2283 

2243 

2202 

_^'^3, 

2123 

2122 

2084 
2083 

2045 
2044 

2007 
2006 

24 
25 

25 

2449 

2407 

2365 

2324 

2283 

2242 

2202 

2162 

26 

2448 

2406 

2364 

2323 

2282 

2241 

2201 

2161 

2122 

2083 

2044 

2005 

26 

27 

2448 

2405 

2364 

2322 

2281 

2241 

2200 

2161 

2I2I 

2082 

2043 

2005 

27 

28 

2447 

2405 

2363 

2322 

2281 

2240 

2200 

2160 

2120 

2081 

2042 

2004 

28 

29 

2446 

2404 

2362 

2321 

2280 

2239 

2199 
2198 

2159 
2159 

2120 
21I9 

2081 

2042 

2003 
2003 

29 
30 

30 

2445 

2403 

2362 

2320" 

2279 

2239 

2080 

2041 

31 

2445 

2403 

2361 

2320 

2279 

2238 

2198 

2158 

2I18 

2079 

2041 

2002 

3« 

32 

2444 

2402 

2360 

2319 

2278 

2237 

2197 

2157 

2II8 

2079 

2040 

2001 

32 

33 

2443 

2401 

2359 

2318 

2277 

2237 

2196 

2157 

2II7 

2078 

2039 

2001 

33 

34 

2443 

2401 

2359 

2317 

2277 

2236 

2196 

2156 

2II6 
2I16 

2077 

2077 

2039 
2038 

2000 

34 

•35 

2442 

2400 

2358 

2317 

2276 

2235 

2195 

"2155^ 

2000 

35 

36 

2441 

2399 

2357 

2316 

2275 

2235 

2194 

2155 

2II5 

2076 

2037 

1999 

36 

37 

2441 

2398 

2357 

2315 

2274 

2234 

2194 

2154 

2II5 

2075 

2037 

1998 

37 

38 

2440 

2398 

2356 

2315 

2274 

2233 

2193 

2153 

2II4 

2075 

2036 

1998 

38 

39^ 

2439 

2397 

2355 

2314 

2273 

2272 

2233 
2232 

2192 

2153 

2II3 
2II3 

2074 
2073 

2035 

2035 

1997 
1996 

39 

40 

40 

2438 

2396 

2355 

2313 

2192 

2152 

41 

2438 

2396 

2354 

2313 

2272 

2231 

2I9I 

2151 

2II2 

2073 

2034 

1996 

41 

42 

2437 

2395 

2353 

2312 

2271 

2231 

2190 

2151 

2III 

2072 

2033 

1995 

42 

43 

2436 

2394 

2353 

2311 

2270 

2230 

2190 

2150 

2IH 

2072 

2033 

1994 

43 

44 

2436 

2394 

2352 

23 II 

2270 
2269 

2229 
2229 

2189 
2188" 

2i49_ 
2149 

2IIO 

2109 

2071 
2070 

2032 
2032 

1994 
1993 

44 
45 

45 

2435 

2393 

2351 

2310 

46 

2434 

2392 

2350 

2309 

2268 

2228 

2188 

2148 

2109 

2070 

2031 

1993 

46 

47 

2433 

2391 

2350 

2309 

2268 

2227 

2187 

2147 

2108 

2069 

2030 

1992 

47 

48 

2433 

2391 

2349 

2308 

2267 

2227 

2186 

2147 

2107 

2068 

2030 

1991 

48 

49 

2432 

2390 

2348 

2307 

2266 

2226 

2225 

2186 

-2185- 

2146 

'  2145 

2107 

2068 

2029 

2028 

1991 
1990 

49 

50 

50 

2431 

2389 

2348 

2307 

2266 

2106 

2067 

51 

2431 

2389 

2347 

2306 

2265 

2225 

2184 

2145 

2105 

2066 

2028 

1989 

51 

52 

2430 

2388 

2346 

2305 

2264 

2224 

2184 

2144 

2105 

2066 

2027 

1989 

52 

53 

2429 

2387 

2346 

2304. 

2264 

2223 

2183 

2143 

2104 

2065 

2026 

1988 

53 

54 

2429 

2387 

2345 

2304 

2263 

2223 

2182 

A^43 

2103 

2064 

2026 
2025 

1987 
1987" 

54 

55 

55 

2428 

2386 

2344 

2303 

2262 

22:.'2 

2182 

2142 

2103 

2064 

56 

2427 

2385 

2344 

2302 

2262 

2221 

2181 

2141 

2102 

2063 

2025 

1986 

S6 

57 

2426 

2384 

2343 

2302 

2261 

2220 

2180 

2141 

2IOI 

2062 

2024 

1986 

57 

58 

2426 

2384 

2342 

2301 

2260 

2220 

2180 

2140 

2IOI 

2062 

2023 

1985 

58 

59 

2425 

2383 

2342 

2300 

2260 

1°4G' 

2219 

2179 

2139 

2100 

2061 

2023 

r  52' 

1984 

59 

s. 

1°  42' 

1°43' 

1044/ 

r45' 

\°iV 

r48' 

r4r 

1°50' 

1°  sr 

1°53' 

S. 

Page  462]                   TABLE  45. 

Proportional  Logarithms. 

S. 

A.    m. 

k.    m. 

h.     m. 

l°5r 

h.    m. 

h.     m. 

h.  m. 

h.  m. 

TV 

k.  tn. 

2°  2' 

h.  m. 

2°  3' 

k.  m. 

2°  4' 

S. 

0 

I 
2 

3 
4 

1984 

1983 
19S2 
1982 
1981 

1946 

1945 
1944 
194.V 

1943 

1908 
1908 
1907 
1906 
1906 

1871 
1870 
1870 
1869 
1868 

1834 
1833 
1833 
1832 

I83I 

1797 
1797 
1796 
1795 
1795 

1 761 
1760 
1760 

1759 
1759 

1725 
1724 
1724 

1723 
1722 

1689 
1689 
1688 
1687 
1687 

1654 

1653 
1652 

1652 

1651 

1619 
1618 
1617 
1617 
1616 

0 
I 

2 

3 
4 

5 
6 

7 
8 

9 

1981 
(980 
1979 
1979 
1978 

1943 
1942 
1941 
1941 
1940 

1905  !   1868 
1904  '   1867 
1904  :    1867 
1903  ,    1866 
1903     1865 

I83I 
1830 

1830 
1829 
1828 

1794 
1794 
1793 
1792 
1792 

1758 
1757 
1757 
1756 
1755 

1722 
1721 
1 721 
1720 
1719 

1686 
1686 
1685 
1684 
1684 

1651 
1650 
1650 
1649 
1648 

1616 
1615 
1614 
1614 
1613 

5 
6 

7 
8 

9 

10 
II 
12 

13 

14 

1977 
1977 
1976 

1975 
1975 

1939 
1939 
1938 
1938 
1937 

1902 
1901 
1901 
1900 
1899 

1865 
1864 
1863 
1863 
1862 

1828 

1827 
1827 

1826 
1825 

1791 
I79I 
1790 

1789 
1789 

1755 
1754 
1754 
1753 
1752 

1752 
1751 
1751 
1750 
1749 

1719 
1718 
1718 
1717 
1717 

"1716 
1715 

1715 
1714 

1714 

1683 
1683 
1682 
1681 
1681 

1648 
1647 
1647 
1646 
1645 

1613 
1612 
1612 
1611 
1610 

10 
II 
12 

13 
14 

15 
16 

17 
18 

19 

1974 
1974 

1973 
1972 
1972 

1936 
1936 
1935 
1934 
1934 

1899 
1898 
1898 

1897 
1896 

1862 
1861 
i860 
i860 
1859 

1825 

1824 

1823 

1823 
1822 

1788 
1788 
1787 
1786 
1786 

1680 
1680 
1679 
1678 
1678 

1645 
1644 
1644 

1643 
1643 

1610 
1609 
1609 
1608 
1607 
1607 
1606 
1606 
1605 
1605 

15 
16 

17 
18 

19 

20 
21 

22 

23 
24 

1971 
1970 
1970 
1969 
1968 

1933 
1933 
1932 

1931 
1931 

1896     1859 
1895     1858 
1894     1857 
1894     1857 
1893     1856 

1822 
I82I 
1820 
1820 
I8I9 

1785 
1785 
1784 

1783 

1783 

1749 
1748 
1748 

1747 
1746 

1713 
1712 
1712 
1711 
1711 

1677 
1677 
1676 
1676 
1675 

1642 
1641 
1641 
1640 
1640 

20 
21 

22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

1968 
1967 
1967 
1966 

1965 
1965 
1964 
1963 

1963 
1962 

1930 
1929 
1929 
1928 
1928 

1893 
1892 
1891 
1891 
1890 

1855 
1855 
1854 
1854 
1853 

I8I9 
I8I8 

I8I7 
I8I7 

I8I6 

1782 
1 781 
1 781 
1780 
1780 

1746 
1745 
1745 
1744 
1743 

1710 
1709 
1709 
1708 
1708 

1674 
1674 

1673 
1673 

1672 

1639 
1638 
1638 
1637 
1637 

1604 
1603 
1603 
1602 
1602 

26 

27 
28 
29 

1927 
1926 
1926 

1925 
1924 

1889 
1889 
1888 
1888 
1887 

1852 
1852 
185 1 
1850 
1850 

I8I6 

I8I5 

I8I4 
I8I4 

I8I3 

1779 

1778 
1778 
1777 
1777 

1743 
1742 
1742 
1 741 
1740 

1707 
1706 
1706 
1705 
1705 

1671 
1671 
1670 
1670 
1669 

1636 

1635 
1635 
1634 
1634 

1601 
1600 
1600 
1599 
1599 
1598 
1598 
1597 
1596 
1596 

30 
31 
32 
33 
34 

35 
36 
37 
3^ 
39 

1962 
1961 
i960 
i960 
1959 

1924 

1923 
1923 
1922 
1 92 1 

1886     1849 
1886     1849 
1885     1848 
1884     1847 
1884  1    1847 

I8I2 
I8I2 
I8II 
I8II 
I8I0 

1776 

1775 
1775 
1774 
1774 

1740 
1739 
1739 
1738 
1737 

1704 
1703 
1703 
1702 
1702 

1668 
1668 
1667 
1667 
1666 

1633 

1633 
1632 

1631 

1631 

40 

41 

42 

43 
44 

45 

46 

47 
48 

49 

1958 
1958 
1957 
1956 
1956 
1955 
1955 
1954 
1953 
1953 

1921 
1920 
1919 
1919 
1918 

1883  1    1846 
1883  1    1846 
1882  1    1845 
1881     1844 
1881     1844 

1809 
1809 
1808 
1808 
1807 

1773 

1772 
1772 

I77I 
I77I 

1737 
1736 
1736 
1735 
1734 

1 701 
1700 
1700 
1699 
1699 

1665 
1665 
1664 
1664 
1663 

1630 
1630 
1629 
1628 
1628 

1595 
1595 
1594 
1593 
1593 

40 

41 
42 

43 

44 

1918 
1917 
1916 
1916 
1915 

1880  1    1843 
1880  i    1843 
1879  ,    1842 

1878  !   1841 
1878   1841 

1806 
1806 
1805 
1805 
1804 

1770 
1769 
1769 
1768 
1768 

1734 
1733 
1733 
1732 

1 731 

1698 
1697 
1697 
1696 
1696 

1663 
1662 
1661 
1661 
1660 

1627 
1627 
1626 
1626 
1625 

1592 
1592 
1591 

1591 
1590 

46 

47 
48 
49 

50 
51 

52 
53 
54 

1952 
1951 
'951 
1950 
1950 

1914 
1914 

1913 
1913 
1912 

1877   1840 
1876   1839 
1876   1839 
1875   1838 
1875  :  1838 

1803 
1803 
1802 

1802 

I80I 

1767 
1766 
1766 
1765 
1765 

1 731 

1730 

1730 
1729 

1728 

1695 
1694 
1694 
1693 
1693 

1660 
1659 
1658 
1658 
1657 

1624 
1624 
1623 
1623 
1622 

1589 
1589 

1588 
1588 
15S7 

50 
51 
52 
53 
54 

55 
56 

59 

11 

57 
58 
59 

1949 
1948 

1948 

1947 
1946 

1911 
1911 
1910 
1909 
1909 

1874 
1873 
1873 
1872 
1871 

1837 
1836 
1836 
1835 
1835 

1800 
1800 
1799 
1798 
1798 

1764 
1763 
1763 

1762 
1762 

1728 
1727 
1727 
1726 

1725 

1692 
1692 
1691 
1690 
1690 

1657 
1656 

1655 
1655 
1654 

1621 
1621 
1620 
1620 
1619 

1587 
1586 
1585 

1585 
1584 

S. 

1°  54' 

1°55' 

1°  56' 

1°57' 

1°58' 

1°59' 

2°0' 

2°!' 

2°  2' 

2°  3' 

2°  4' 

S. 

TABLE  45. 

[Page 

463 

». 

Proportional  Logarithms. 

r-i 

A.  m. 

h.  m. 

h.  m. 

h.  nt. 

h.  tn. 

h.    nt. 

h.  m. 

h.   ni. 

h.  m. 

h.   tn. 

h.   nt. 

s. 

b. 

2°  5' 

2°  6' 

TV 

2°  8' 

2°r 

2°  10^ 

2°ir 

2°  12' 

2°  13' 

2°  14' 

2°  15' 

0 

1584 

1549 

I5IS 

1481 

1447 

1413 

1380 

1347 

1314 

1282 

1249 

0 

I 

1583 

1548 

I5I4 

1480 

1446 

1413  1 

1379 

1346 

1314 

1281 

1249 

I 

-> 

1582 

1548 

I5I4 

1479 

1446 

1412  ' 

1379 

1346 

1313 

1281 

1248 

2 

J> 

1582 

1547 

I5I3 

1479 

1445 

1412 

1378 

1345 

1313 

1280 

1248 

3 

4 

I58I 

1547 

I5I2 
1512 

1478 
1478 

1445  _ 
1444 

1411 
1411 

1378 

1345 

1312 

1280 
1279 

1247 
1247 

4 
5 

5 

1 58 1  i 

1546 

1377 

1344 

13"  ! 

6 

1580 ' 

1546 

1511 

1477 

1443 

1410 

1377 

1344 

1311 

1278 

1246 

6 

7 

1580 

1545 

1511 

1477 

1443 

1409 

1376 

1343 

1310 

1278 

1246 

7 

8 

1579 

1544 

I5I0 

1476 

1442 

1409 

1376 

1343 

1310 

1277 

1245 

8 

9 

1578 

1544 

I5I0 

1476 

1442 

1408 

1375 
1374 

1342 
1342 

1309 
1309 

1277 

1245 

9 

lO 

1578 

1543 

1 509^ 

1475 

1441 

1408 

1276 

1244 

10 

II 

1577 

1543 

1508 

1474 

1441 

1407 

1374 

1341 

1308 

1276 

1243 

II 

12 

1577 

1542 

1508 

1474 

1440 

1407 

1373 

1340 

1308 

1275 

1243 

12 

J3 

1576  : 

1542 

1507 

1473 

1440 

1406 

1373 

1340 

1307 

1275 

1242 

13 

14 

1576 

1541 

1507 

1473 

1439 

1406 

1372 

1339 

1307 

1274 

1242 
1241 

14 
15 

IS 

1575  ' 

1540 

1506 

1472 

1438 

1405' 

1372 

1339 

1306 

1274 

i6 

1574 

1540 

1506 

1472 

1438 

1404 

1371 

1338 

1306 

1273 

1241 

16 

-7 

1574 

1539 

1505 

1471 

1437 

1404 

1371 

1338 

1305 

1273 

1240 

17 

i8 

1573 

1539 

1504 

1470 

1437 

1403  1 

1370 

1337 

1304 

1272 

1240 

18 

19 

1573 

1538 

1504 

1470 

1436 

._  14°3_ 

1370 

1337 

1304 

1271 

1239 

19 

20 

1572 

1538 

1503 

1469 

1436 

1402 

^3^9 

1336 

1303 

1271 

1239 

20 

21 

1571 

1537 

1503 

1469 

1435 

1402 

1368 

1335 

1303 

1270 

1238 

21 

22 

1571 

1536 

1502 

1468 

1435 

1401 

1368 

1335 

1302 

1270 

1238 

22 

^3 

1570 

1536 

1502 

1468 

1434 

1401 

1367 

1334 

1302 

1269 

1237 

23 

24 

1570 

1535 

I50I 

1467 
1467 

1433 
1433 

1400 

1367 

1334 

1301 

1269 

1237 

24 

25 

1569 

1535 

1500 

1399 

1366 

1333 

1301 

1268 

1236 

26 

1569 

1534 

1500 

1466 

1432 

1399 

1366 

nv:, 

1300 

1268 

1235 

26 

27 

1568 

1534 

1499 

1465 

1432 

1398 

1365 

1332 

1300 

1267 

1235 

27 

28 

1567 

1533 

1499 

1465 

1431 

1398 

1365 

1332 

1299 

1267 

1234 

28 

29 

1567 

1532 

1498 

1464 
1464 

143 1 

1430 

1397 

1364 

I33I 

1298 

1266 

1234 

29 

30 

1566 

1532 

1498 

1397 

1363 

I33I 

1298 

1266 

1233 

30 

31 

1566 

1531 

1497 

1463 

1429 

1396 

1363 

1330 

1297 

1265 

1233 

31 

1565 

1531 

1496 

1463 

1429 

1396 

1362 

1329 

1297 

1264 

1232 

32 

33 

1565 

1530 

1496 

1462 

1428 

1395 

1362 

1329 

1296 

1264 

1232 

33 

34 

1564 

1530 

1495 

1461 

1428 

1394 

1361 

1328 

1296 

1263 

1231 

34 

35 

1563 

1529 

1495 

1461 

1427" 

1394 

1361 

1328 

1295 

1263 

1231 

35 

36 

1563 

1528 

1494 

1460 

1427 

1393 

1360 

1327 

1295 

1262 

1230 

36 

^l 

1562 

1528 

1494 

1460 

1426 

1393 

1360 

1327 

1294 

1262 

1230 

37 

38 

1562 

1527 

1493 

1459 

1426 

1392 

1359 

1326 

1294 

1261 

1229 

38 

39 

1561 

i527_ 

1493 

1459 

1425 

1392 
1391 

1359 
1358 

1326 

1293 

1261 

1229 

39 

40 

40 

1561 

1526 

1492 

1458 

1424 

1325 

1292 

1260 

1228 

41 

1560 

1526 

149 1 

1458 

1424 

1391 

1357 

1325 

1292 

1260 

1 

1227 

41 

42 

1559 

1525 

I49I 

1457 

1423 

1390 

1357 

1324 

1291 

1  1259 

1227 

42 

43 

1559 

1524 

1490 

1456 

1423 

1389 

1356 

1323 

1291 

1259 

1226 

43 

44 

1558 

1524 

1490 

1456 

1422 

1389 

1356 

1323 

1290 

1258 

1226 

44 

45 

45 

1558 

1523 

1489 

1455 

1422 

1388 

1355 

1322 

1290 

1257 

1225 

46 

1557 

1523 

1489 

1455 

1421 

1388 

1355 

1322 

1289 

1257 

1225 

46 

47 

1556 

1522 

1488 

1454 

1421 

1387 

1354 

I32I 

1289 

'  1256 

1224 

47 

48 

1556 

1522 

1487 

1454 

1420 

1387 

1354 

I32I 

1288 

1256 

1224 

48 

49 

1555 

1521 

1487 

1453 

1419 

1386 

1353 

1320 

1288 
1287 

1255 

1255 

1223 

1223 

49 

50 

SO 

1555 

1520 

i486 

1452 

1419 

1386 

1352 

1^20 

51 

1554 

1520 

i486 

1452 

1418 

1385 

1352 

I3I9 

1287 

1254 

1222 

51 

52 

1554 

1519 

1485 

145 1 

1418 

1384 

1351 

I3I9 

1286 

1254 

1222 

52 

53 

1553 

1519 

1485 

145 1 

1417 

1384 

1351 

I3I8 

1285 

1253 

1221 

53 

54 

1552 

1518 
1518 

1484 
1483 

1450 

1417 

1383 

1350 

I3I7 
I3I7 

1285 
'1284 

1253 
1252 

1221 

1220 

54 

55 

55 

1552 

1450 

1416 

1383 

1350 

56 

1551 

1517 

1483 

1449 

1416 

1382 

1349 

1  I3I6 

1284 

1252 

1219 

56 

57 

1551 

1516 

1482 

1449 

1415 

1382 

1349 

I3I6 

12S3 

1251 

1219 

57 

58 

1550 

1516 

1482 

1448 

1414 

1381 

1348 

I3I5 

1283 

1250 

1218 

58 

59 

1550 

1515 

I48I 

1447 

1414 

1381 

1348 

I3I5 

1282 

1 

2°  13' 

1250 

- 

2°  14' 

1218 
2°  15' 

59 
S. 

S. 

2°  5^ 

2°  6' 

%°v 

2°  8^ 

2°  9^ 

2°  10' 

2°  11' 

2°  12' 

Page  464 

TABLE  45. 

Proportional  Logarithms. 

s. 

/l  .      7)1 . 

k.     m. 

h.    ;« . 

h.     m. 

h.    m. 

h.    m. 

k.   m. 

h.   m. 

h.   m. 

k.  rn. 

h.   m. 

S. 

"r  w 

2°ir 

2°  18^ 

1°W 

rw 

2°  21' 

2°  22' 

2°  23' 

2°  24' 

2°  25' 

rw 

o 

1217 

1 186 

"54 

1 123 

1091 

1061 

1030 

0999 

0969 

0939 

0909 

0 

T 

1217 

1185 

"53 

1 1 22 

1091 

1060 

!  1029 

0999 

0969 

0939 

0909 

I 

2 

1216 

1 184 

"53 

I  122 

1090 

I   1060 

1029 

0998 

0968 

0938 

0908 

2 

-> 

1216 

1 184 

1152 

II2I 

1090 

1059 

1028 

099S 

0968 

0938 

0908 

3 

4 

1215 

1 183 

1152 

1 120 

1089 

1058 

1028 
1027 

0997 
0997 

0967 

0937 

0907 

4 
5 

5 

121S 

1183 

"51 

II20 

1089 

1058 

0967 

0937 

0907 

6 

1214 

1 182 

"51 

III9 

1088 

1057 

1027 

0996 

0966 

0930 

090b 

6 

7 

1214 

1 182 

1 150 

I  I  19 

1088 

1057 

1026 

0996 

0966 

0936 

090b 

7 

8 

1213 

1.181 

1150 

II18 

1087 

1056 

1026 

0995 

0965 

0935 

0905 

8 

9 

1213 

1181 

"49 

II18 
III7 

10S7 

1056 

1025 
1025 

0995 

0965 

0935 

0905 

9 

lO 

1212 

1 180 

"49 

1086 

1055 

0994 

0964 

0934 

0904 

10 

II 

1211 

1 180 

1 148 

III7 

1086 

1055 

1024 

0994 

0964 

0934 

0904 

n 

12 

1211 

"79 

1 148 

II16 

1085 

1054 

1024 

0993 

0963 

0933 

0903 

12 

•3 

1210 

"79 

"47 

II16 

1085 

1054 

1023 

0993 

0963 

0933 

0903 

13 

H 

1210 

1 178 

"47 

III5 

1084 

1053 

1023 

0992 

0962 

0932 

0902 

14 
15 

15 

1209 

1178 

1 146 

"I5 

1084 

1053 

1022 

0992 

0962 

0932 

0902 

i6 

1209 

"77 

1 146 

1 1 14 

1083 

1052 

1022 

0991 

0961 

0931 

0901 

lb 

17 

1208 

"77 

"45 

III4 

1083 

1052 

1021 

0991 

0961 

0931 

0901 

17 

18 

1208 

1 1 76 

"45 

III3 

1082 

105 1 

1021 

0990 

0960 

0930 

0900 

18 

19 

1207 

"75 

"44 

III3 

1082 

1051 

1020 

0990 

0960 

0930 

0900 

19 

20 

1207 

"75 

"43 

III2 

1081 

1050 

1020 

0989 

0959 

0929 

0899 

20 

21 

1206 

"74 

"43 

III2 

1081 

1050 

1019 

0989 

0959 

0929 

0899 

21 

22 

1206 

"74 

1 142 

nil 

1080 

1049 

1019 

0988 

0958 

0928 

0898 

22 

23 

1205 

"73 

1 142 

nil 

1080 

1049 

1018 

0988 

0958 

0928 

0898 

23 

24 

1205 

"73 

1 141 

IIIO 

1079 

1048 

ioi8 

0987 

0957 

0927 

0897 

24 
25 

^5 

1204 

1 1 72 

1141 

IIIO 

1079 

1048 

1017 

0987 

0957 

0927 

0897 

26 

1204 

1 1 72 

1 140 

1109 

1078 

1047 

1017 

0986 

095b 

0926 

0896 

2b 

27 

1203 

1171 

1 140 

1 109 

1078 

1047 

1016 

0986 

0956 

0926 

089b 

27 

28 

1202 

1171 

"39 

II08 

1077 

1046 

1016 

0985 

0955 

0925 

0895 

28 

29 

1202 

1 1 70 

"39 
1 138 

1 108 

1 107 

1076 
1076 

1046 
1045 

1015 

0985 

0955 

0925 

0895 

29 

30 

1201 

II 70 

1015 

0984 

0954 

0924 

.  0894 

30 

3t 

1201 

1 1 69 

1 138 

1 106 

1075 

1045 

1014 

0984 

0954 

0924 

0S94     31  1 

32 

1200 

1109 

^m 

1 106 

IC7S 

1044 

1014 

0983 

0953 

0923 

0893 

32 

i3 

1200 

1 168 

"37 

1 105 

1074 

1044 

1013 

0983 

0953 

0923 

0893 

33 

34 

"99 

1 168 

1 136 

II05 

1074 

1043 

1013 
1012 

0982 

0952 

0922 

0892 

34 

35 

1 199 

1167 

II36 

1 104 

1073 

1043 

0982 

0952 

0922 

0892 

35 

3<' 

1 198 

1 167 

"35 

1 104 

1073 

1042 

1012 

0981 

0951 

09^1 

0891 

3^ 

H 

1 198 

1 166 

"35 

1 103 

1072 

1042 

ion 

09S1 

0951 

0921 

0891 

37 

3« 

"97 

1 165 

"34 

1 103 

1072 

1041 

ion 

0980 

0950 

0920 

0890 

3« 

39 

"97 

1 165 

"34 

1 102 

1071 

1041 

lOIO 

0980 

0950 

0920 
0919 

0890 
"  0889" 

39 
40 

40 

1 196 

1 164 

"33 

1 102 

1071 

1040 

1009 

0979 

0949 

41 

II 96 

1 164 

1 132 

IIOI 

1070 

1040 

1009 

0979 

0949 

0919 

0889 

41 

42 

"95 

1 1 63 

1 132 

IIOI 

1070 

1039 

1008 

0978 

0948 

0918 

0888 

42 

43 

"95 

1 163 

"31 

I  100 

1069 

1039 

1008 

0978 

0948 

0918 

0888 

43 

44 

"94 

1 162 

1131 

IIOO 

1069 

1038 

1007 

0977 

0947 

0917 

0887 

44 

45 

"93 

1 162 

1 130 

1099 

1068 

1037 

1007 

0977 

0947 

0917 

0887 

45 

4b 

"93 

1161 

1 130 

1099 

1068 

1037 

1006 

0976 

0946 

0916 

0886 

46 

47 

1 192 

1161 

1 129 

1098 

1067 

1036 

1006 

0976 

094b 

oqi6 

088b 

47 

48 

1 192 

1 160 

1 129 

1098 

1067 

1036 

1005 

0975 

0945 

0915 

0885 

48 

49 

1191 

1 160 

1 128 

1097 

1066 

1035 

1005 

0975 

0945 

0915 

0885 

49 
50 

50 

1191 

"59 

1 128 

1097 

1066 

1035 

1004 

0974 

0944 

0914 

0884 

51 

1 190 

"59 

1127 

1096 

1065 

1034 

1004 

0974 

0944 

0914 

0S84 

51 

52 

1 190 

1158 

1127 

1096 

1065 

1034 

1003 

0973 

0943 

0913 

0883 

52 

53 

1 189 

1158 

1126 

1095 

1064 

1033 

1003 

0973 

0943 

0913 

0883 

53 

54 

1 189 

"57 

1 126 

1095 

1064 

1033 

1002 

0972 

0942 

0912 

0883 

54 

55 

1 188 

"57 

1 125 

1094 

1063 

1032 

1002 

0972 

0942 

0912 

0882 

55 

50 

1 188 

1 156 

1125 

1094 

1063 

1032 

lOOI 

0971 

0941 

0911 

0882 

5(' 

57 

1 187 

1 1 56 

1 124 

1093 

1062 

103 1 

lOOI 

0971- 

0941 

0911 

0881 

57 

5« 

1187 

"55 

1 124 

1092 

1062 

103 1 

1000 

0970 

0940 

0910 

0881 

58 

59 

S. 

1 186 

"54 

1123 

1092 

1061 

1030 

1000 

0970 

0940 

0910 

0880 

59 

S. 

*>"  16' 

2°  W 

2°  18' 

2°  19' 

2°  20' 

2°  21' 

2°  22' 

2°  23' 

2°  24' 

2°  25' 

2°  26' 

TABLE  45" 

Page 

465 

% 

p 

roportional  Logari 

thms. 

// .  m . 

A.     m. 

h.     m. 

h.     m. 

h.    m. 

■h.    m. 

h.    tn. 

h.   m. 

h.   m. 

h.   m. 

h.   in. 

s. 

2°  21' 

2°  28^ 

2°  29^ 

2°  30' 

2°  31' 

2°  32' 

2°  33' 

2°  34' 

2°  35' 

2°  36' 

2°  31' 

0 

0880 

0850 

0821 

0792 

0763 

0734 

0706 

0678 

0649 

0621 

0594 

0 

I 

0879 

0850 

0820 

0791 

0762 

0734 

0705 

0677 

0649 

0621 

0593 

I 

'> 

0879 

0849 

0820 

0791 

0762 

0733 

0705 

0677 

0648 

0621 

0593 

2 

1 

0878 

0849 

0819 

0790 

0762 

0733 

0704 

0676 

0648 

0620 

0592 

J 

4 

0878 

0848 

0819 

0790 

0761 

0732 

0704 

0676 

0648 

0620 

0592 

4 

5 

0877 

0848 

0818 

0789 

0761 

0732 

0703 

0675 

0647 

0619 

0591 

5 

6 

0877 

0847 

0818 

0789 

0760 

0731 

0703 

0675 

0647 

0619 

0591 

6 

"7 
/ 

0S76 

0847 

0817 

°788 

0760 

0731 

0703 

0674 

0646 

0618 

0591 

7 

s 

0876 

0846 

0817 

0788 

0759 

0730 

0702 

0674 

0646 

0618 

0590 

8 

9 

0875 

0846 

0816 

0787 

0759 

0730 

0702 

0673 

0645 

0617 

0590 

9 

lO 

0875 

0845 

0816 

0787 

0758 

0730 

0701 

0673 

0645 

0617 

0589 

10 

II 

0874 

0845 

0816 

0787 

0758 

0729 

0701 

0672 

0644 

0616 

0589 

II 

12 

0874 

0844 

0815 

0786 

0757 

0729 

0700 

0672 

0644 

0616 

0588 

12 

13 

0873 

0844 

0815 

0786 

0757 

0728 

0700 

0671 

0643 

0615 

0588 

13 

14 

0873 

0843 

0814 

0785 

0756 

0728 

0699 

0671 

0643 

0615 

0587 

14 

IS 

0872 

0843 

0814 

0785 

0756 

0727 

0699 

0670 

0642 

0615 

0587 

15 

16 

0872 

0842 

0813 

0784 

0755 

0727 

0698 

0670 

0642 

0614 

0586 

16 

17 

0871 

0842 

0813 

0784 

0755 

0726 

0698 

0670 

0641 

0614 

0586 

17 

iS 

0871 

0841 

0812 

0783 

0754 

0726 

0697 

0669 

0641 

0613 

0585 

18 

19 

0870 

0841 

0812 

0783 

0754 

0725 

0697 

0669 

0641 

0613 

0585 

19 

20 

0870 

0840 

0811 

0782 

0753 

0725 

0696 

0668 

0640 

0612 

0585 

20 

21 

0869 

0840 

0811 

0782 

0753 

0724 

0696 

0668 

0640 

0612 

0584 

21 

22 

0869 

0839 

0810 

0781 

0752 

0724 

0695 

0667 

0639 

0611 

0584 

22 

23 

0868 

0839 

o8io 

0781 

0752 

0723 

0695 

0667 

0639 

061 1 

0583 

23 

24 

0868 

0838 

0809 

0780 

0751 

0723 

0694 

0666 

0638 

0610 

0583 

24 

25 

0867 

0838 

0809 

0780 

0751 

0722 

0694 

0666 

0638 

0610 

0582 

25 

26 

0867 

0837 

0808 

0779 

0751 

0722 

0694 

0665 

0637 

0609 

0582 

26 

27 

0866 

0837 

0808 

0779 

0750 

0721 

0693 

0665 

0637 

0609 

0581 

27 

28 

0866 

0836 

0807 

0778 

0750 

0721 

0693 

0664 

0636 

0609 

0581 

28 

29 

0865 

0836 

0807 

0778 

0749 

0721 

0692 

0664 

0636 

0608 

0580 

29 
30 

30 

0865 

0835 

0806 

0777 

0749 

0720 

0692 

0663 

0635 

0608 

0580 

31 

0864 

0835 

0806 

0777 

0748 

0720 

0691 

0663 

0635 

0607 

0579 

31 

32 

0864 

0834 

0805 

0776 

0748 

0719 

0691 

0663 

0634 

0607 

0579 

32 

33 

0863 

0834 

0805 

0776 

0747 

0719 

0690 

0662 

0634 

0606 

0579 

33 

34 

0863 

0834 

0804 

0775 

0747 

0718 

0690 

0662 

0634 

0606 

0578 

34 

35 

0862 

0833 

0804 

0775 

0746 

0718 

0689 

0661 

0633 

0605 

0578 

35 

36 

0862 

0833 

0803 

0774 

0746 

0717 

0689 

0661 

0633 

0605 

0577 

3b 

37 

0861 

0832 

0803 

0774 

0745 

0717 

0688 

0660 

0632 

0604 

0577 

31 

38 

0861 

0832 

0802 

0774 

0745 

0716 

0688 

0660 

0632 

0604 

0576 

38 

39 
40 

0860 

0831 

0802 

0773 

0744 

0716 

0687 

0659 

0631 

0603 

0576 

39 

0860 

0831 

0801 

0773 

0744 

0715 

0687 

0659 

0631 

0603 

0575 

40 

41 

0859 

0830 

0801 

0772 

0743 

0715 

0686 

0658 

0630 

0602 

0575 

41 

42 

0859 

0830 

0801 

0772 

0743 

0714 

0686 

0658 

0630 

0602 

0574 

42 

43 

0858 

0829 

0800 

0771 

0742 

0714 

0686 

0657 

0629 

0602 

0574 

43 

44 

0858 

0829 

0800 

0771 

0742 

0713 

0685 

0657 
0656 

0629 

0601 

0573 

44 

45 

0857 

•  0S28 

0799 

0770 

0741 

0713 

0685 

0628 

0601 

0573 

45 

46 

0857 

0828 

0799 

0770 

0741 

0712 

0684 

0656 

0628 

0600 

0573 

46 

47 

0856 

0827 

0798 

0769 

0740 

0712 

0684 

065s 

0628 

0600 

0572 

47 

48 

0856 

0827 

0798 

0769 

0740 

0711 

0683 

.  0655 

0627 

0599 

0572 

48 

49 

0855 

0826 

0797 

0768 

0740 

071 1 

0683 

0655 

0627 

0599 

0571 

49 

50 

0855 

0826 

0797 

0768 

0739 

0711 

0682 

0654 

0626 

0598 

0571 

50 

51 

0855 

0825 

0796 

0767 

0739 

0710 

0682 

0654 

0626 

0598 

0570 

51 

52 

0854 

0825 

0796 

0767 

0738 

0710 

0681 

0653 

0625 

0597 

0570 

52 

53 

0854 

0824 

0795 

0766 

0738 

0709 

0681 

0653 

0625 

0597 

0569 

53 

54 

0853 

0824 

0795 

0766 

0737 

0709 

0680 

0652 

0624 

0596 

0569 

54 

55 

0853 

0823 

0794 

0765 

0737 

0708 

0680 

0652 

0624 

0596" 

0568 

55 

56 

0852 

0823 

0794 

0765 

0736 

0708 

0679 

0651 

0623 

0596 

0568 

5<^ 

57 

0852 

0822 

0793 

0764 

0736 

0707 

0679 

0(351 

0623 

0595 

0568 

57 

S8 

0851 

0822 

0793 

0764 

0735 

0707 

0678 

0650 

0622 

0595 

0567 

58 

59 

0851 

0821 

0792 

0763 

0735 

0706 

0678 

0650 

0622 

0594 

0567 

59 

S. 

2°2r 

2°  28^ 

2°2r 

2°  30' 

2°  31' 

2°  32' 

2°  33' 

2°  34' 

2°  35' 

2°  36' 

2°  37' 

S. 

30    B 


n 


Page 

466 

TABLE  45. 

Proportional  Logarithms. 

s. 

A .     tn . 

A.  m. 

h.     in. 

h.    m. 

h.     m. 

'h.     fit. 

h.  m. 

h.   in. 

k.   in. 

k.   m. 

h.  m. 

S. 

2°  38^ 

2°3r 

2°  40' 

2°  41' 

2°  42' 

2°  43' 

2°  44' 

0404 

2°  45' 

2°  46' 

T  47' 

2°  48' 

o 

0566 

0539 

0512 

0484 

0458 

0431 

0378 

0352 

0326 

0300 

0 

I 

0566 

0538 

05 1 1 

0484 

0457 

0430 

0404 

0377 

0351 

0325 

0299 

i' 

2 

0565 

0538 

05 1 1 

0484 

0457 

0430 

0403 

0377 

0351 

0325 

0299 

2 

1 

J 

0565 

0537 

0510 

0483 

0456 

0430 

0403 

0377 

0350 

0324 

0298 

4 

0564 

0537 

0510 

0483 
0482 

0456 
0455 

0429 
0429 

0403 

0376 

0350 

0324 

0298 

4 

5 

0564 

0536 

0509 

0402 

0376 

0349 

0323 

0297 

5 

6 

0563 

0536 

0509 

0482 

0455 

0428 

0402 

0375 

0349 

0323 

0297 

6 

7 

0563 

0536 

0508 

0481 

0454 

0428 

0401 

0375 

0349 

0323 

0297 

/ 

8 

0562 

0535 

0508 

0481 

0454 

0427 

0401 

0374 

0348 

0322 

0296 

8 

9 

0562 

0535 

0507 

0480 

0454 

0427 

0400 

0374 

0348 

0322 

0296 

9 

lO 

0562 

0534 

0507 

0480 

0453 

0426 

0400 

0374 

0347 

0321 

0295 

10 

II 

0561 

0534 

0507 

0480 

0453 

0426 

0399 

0373 

0347 

0321 

0295 

II 

12 

0561 

0533 

0506 

0479 

0452 

0426 

0399 

0373 

0346 

0320 

0294 

12 

13 

0560 

0533 

0506 

0479 

0452 

0425 

0399 

0372 

0346 

0320 

0294 

13 

14 

0560 

0532 

0505 

0478 

0451 

0425 

0398 

0372 

0346 

0319 

0294 

14 
15 

15 

0559 

0532 

0505 

0478 

0451 

0424 

0398 

037' 

0345 

0319 

0293 

16 

0559 

0531 

0504 

0477 

0450 

0424 

0397 

0371 

0345 

0319 

0293 

16 

17 

0558 

0531 

0504 

0477 

0450 

0423 

0397 

0370 

0344 

0318 

0292 

17 

18 

0558 

0531 

0503 

0476 

0450 

0423 

0396 

0370 

0344 

0318 

0292 

18 

19 

0557 

0530 

0503 

0476 

0449 

0422 
0422 

0396 
0395 

0370 
0369 

0343 
0343 

0317 

0291 

19 

20 

0557 

0530 

0502 

0475 

0449 

0317 

0291 

20 

21 

0557 

0529 

0502 

0475 

0448 

0422 

0395 

0369 

0342 

0316 

0291 

21 

22 

0556 

0529 

0502 

0475 

0448 

0421 

0395 

0368 

0342 

0316 

0290 

22 

23 

0556 

0528 

0501 

0474 

0447 

0421 

0394 

0368 

0342 

0316 

0290 

23 

24 

0555 

0528 

0501 

0474 

0447 

0420 

0394 

0367 

0341 

0315 

0289 

24 

25 

0555 

0527 

0500 

0473 

0446 

0420 

0393 

°^^^ 

0341 

0315 

0289 

25 

26 

0554 

0527 

0500 

0473 

0446 

0419 

0393 

0366 

0340 

0314 

0288 

26 

27 

0554 

0526 

0499 

0472 

0446 

0419 

0392 

0366 

0340 

0314 

0288 

27 

28 

0553 

0526 

0499 

0472 

0445 

0418 

0392 

0366 

0339 

0313 

0288 

28 

29 

0553 

0526. 

0498 

0471 

0445 

0418 

0392 

0365 

0339 

0313 

0287 

29 

30 

0552 

0525 

0498 

0471 

0444 

0418 

0391 

0365 

0339 

0313 

0287 

30 

31 

0552 

0525 

0498 

0471 

0444 

0417 

0391 

0364 

0338 

0312 

0286 

31 

32 

0552 

0524 

0497 

0470 

0443 

0417 

0390 

0364 

0338 

0312 

0286 

32 

33 

0551 

0524 

0497 

0470 

0443 

0416 

0390 

0363 

0337 

031 1 

0285 

33 

34 

0551 

0523 

0496 

0469 

0442 

0416 

0389 

0363 

0337 

0311 
0310 

0285 

34 

35 

0550 

0523 

0496 

0469 

0442 

0415 

0389 

0363 

0336 

0285 

35 

3^ 

0550 

0522 

0495 

0468 

0442 

0415 

0388 

0362 

0336 

0310 

0284 

36 

H 

0549 

0522 

0495 

0468 

0441 

0414 

0388 

0362 

0336 

0310 

0284 

H 

3« 

0549 

0521 

0494 

0467 

0441 

0414 

0388 

0361 

0335 

0309 

0283 

38    1 

39 

0548 

0521 

0494 

0467 

0440 

0414 

0387 

036! 

0335 

0309 

0283 

39 

40 

0548 

0521 

0493 

0467 

0440 

0413 

0387 

0360 

0334 

0308 

0282 

40 

41 

0547 

0520 

0493 

0466 

0439 

0413 

0386 

0360 

0334 

0308 

0282 

41 

42 

0547 

0520 

0493 

0466 

0439 

0412 

0386 

0359 

0333 

0307 

0282 

42 

43 

0546 

0519 

0492 

0465 

0438 

0412 

0385 

0359 

0333 

0307 

0281 

43 

44 

0546 

0519 
0518 

0492 

0465 

0438 

041 1 

0385 

0359 

0333 

0307 

0281 

44    i 

45 

0546 

0491 

0464 

0438 

041 1 

0384 

0358 

0332 

0306 

0280 

45 

46 

0545 

0518 

0491 

0464 

0437 

0410 

0384 

0358 

0332 

0306 

0280 

46 

47 

0545 

0517 

0490 

0463 

0437 

0410 

0384 

0357 

0331 

0305 

0279 

47 

48 

0544 

0517 

0490 

0463 

0436 

0410 

0383 

0357 

0331 

0305 

0279 

48    ' 

49 

0544 

0517 

0489 

0462 

0436 

0409 

0383 

0356 

0330 

0304 

0279 

49 

50 

0543 

0516 

0489 

0462 

0435 

0409 

0382 

0356 

0330 

0304 

0278 

50 

51 

0543 

0516 

0489 

0462 

0435 

0408 

0382 

0356 

0329 

0304 

0278 

51 

52 

0542 

0515 

0488 

0461 

0434 

0408 

0381 

0355 

0329 

0303 

0277 

52 

53 

0542 

0515 

0488 

0461 

0434 

0407 

0381 

0355 

0329 

0303 

0277 

53 

54 

0541 

0514 

0487 

0460 

0434 

0407 

0381 

0354 

0328 

0302 

0276 

54 

55 

0541 

0514 

0487 

0460 

0433 

0406- 

0380 

0354 

0328 

0302 

0276 

55   , 

Sb 

0541 

0513 

0486 

0459 

0433 

0406 

0380 

0353 

0327 

0301 

0276 

56 

H 

0540 

0513 

0486 

0459 

0432 

0406 

0379 

0353 

0327 

0301 

0275 

H 

5^ 

0540 

0512 

0485 

0458 

0432 

0405 

0379 

0353 

0326 

0300 

0275 

58 

59 

0539 

0512 

0485 

0458 

0431 

0405 

0378 

0352 

0326 

0300 

0274 

59 

S. 

2°  38' 

2°W 

2°  40' 

2°  41' 

2°  42' 

2°  43' 

2°  44' 

2°  45' 

2°  46' 

2°  47' 

2°  48' 

s. 

TABLE  45. 

[Page 

467 

*■ 

Proportional  Logari 

thms. 

A.     m. 

A.    m. 

k.     w. 

k.    m. 

h.     m. 

h.    VI. 

h.   m. 

k.   m. 

h.  7)1. 

k.   m . 

k.   tn. 

s. 

0 

2°  49^ 

2°  50' 

2°  51' 

2°  52' 

2°  53' 

2°  54' 

2°  55' 

2°  56' 

2°  5r 
0073 

2°  58' 

2°  59' 

o 

0274 

0248 

0223 

0197 

0172 

0147 

0122 

0098 

0049 

0024 

I 

0273 

0248 

0222 

0197 

0172 

0147 

0122 

0097 

0073 

0048 

0024 

I 

■J 

0273 

0247 

0222 

0197 

0171 

0146 

0122 

0097 

0072 

0048 

0023 

2 

3 

0273 

0247 

0221 

0196 

0171 

0146 

0121 

0096 

0072 

0047 

0023 

J 

4 

0272 

0247 

0221 

0196 

0171 

0146 

0121 

0096 

0071 

0047 

0023 

4 
5 

5 

0272 

0246 

022 1 

0195 

0170 

0145 

0120 

0096 

0071 

0046 

0022 

0 

0271 

0246 

0220 

0195 

0170 

0145 

0120 

0095 

0071 

0046 

0022 

6 

7 

0271 

0245 

0220 

0194 

0169 

0144 

0119 

0095 

0070 

0046 

0021 

7 

S 

0270 

0245 

0219 

0194 

0169 

0144 

0119 

0094 

0070 

0045 

0021 

8 

9 

0270 

0244 

0219 

0194 

0169 

0143 

0119 

0094 

0069 

0045 

0021 

9 

lO 

0270 

0244 

0219 

0193 

0168 

0143 

0118 

0093 

0069 

0044 

0020 

10 

II 

0269 

0244 

0218 

0193 

0168 

0143 

0118 

0093 

0068 

0044 

0020 

II 

12 

0269 

0243 

0218 

0192 

0167 

0142 

0117 

0093 

0068 

0044 

0019 

12 

13 

0268 

0243 

0217 

0192 

0167 

0142 

0117 

0092 

0068 

0043 

0019 

13 

14 

0268 

0242 

0217 

0192 

0166 

0141 

0117 
0116 

0092 

0067 

0043 
0042 

0019 

14 

15 

0267 

0242 

0216 

0191 

0166 

0141 

0091 

0067 

0018 

15 

16 

0267 

0241 

0216 

0191 

0166 

0141 

0116 

0091 

0066 

0042 

0018 

16 

17 

0267 

0241 

0216 

0190 

0165 

0140 

0115 

0091 

0066 

0042 

0017 

17 

iS 

0266 

0241 

0215 

0190 

0165 

0140 

0115 

0090 

0066 

0041 

0017 

18 

19 

0266 

0240 

0215 

0189 

0164 

0139 

0114 

0090 

0065 

0041 

0017 

19 

20 

0265 

0240 

0214. 

0189 

0164 

0139 

0114 

0089 

0065 

0040 

0016 

20 

21 

0265 

0239 

0214 

0189 

0163 

0139 

0114 

0089 

0064 

0040 

0016 

21 

">  7 

0264 

0239 

0213 

0188 

0163 

0138 

0113 

0089 

0064 

0040 

0015 

22 

23 

0264 

0238 

0213 

0188 

0163 

0138 

0113 

0088 

0064 

0039 

0015 

23 

24 

0264 

0238 

0213 

0187 

0162 

0137 

0112 

0088 

0063 

0039 

0015 

24 

25 

0263 

0238 

02!2 

0187 

0162 

0137 

0112 

0087 

0063 

0038 

0014 

25 

26 

0263 

0237 

0212 

0187 

0161 

0136 

0112 

0087 

0062 

0038 

0014 

26 

27 

0262 

0237 

02 1 1 

0186 

0161 

0136 

GUI 

0087 

0062 

0038 

0013 

27 

28 

0262 

0236 

02 II 

0186 

0161 

0136 

GUI 

0086 

0062 

0037 

0013 

28 

29 

0261 

0236 

02 1  I 

0185 

0160 

0135 

Olio 

0086 

0061 

0037 

0012 

29 
30 

30 

0261 

023s 

0210 

0185 

0160 

0135 

Olio 

0085 

0061 

0036 

0012 

31 

0261 

0235 

0210 

0184 

0159 

0134 

Olio 

0085 

0060 

0036 

0012 

31 

32 

0260 

0235 

0209 

0184 

0159 

0134 

0109 

0084 

0060 

0036 

OOII 

32 

33 

0260 

0234 

0209 

0184 

0158 

0134 

GIO9 

0084 

0060 

0035 

OOII 

?>?> 

34 

0259 

0234 

0208 

0183 

0158 

0133 

oig8 

0084 

0059 

0035 

0010 

34 

35 

0259 

0233 

0208 

0183 

0158 

0133 

0108 

0083 

0059 

0034 

0010 

35 

36 

0258 

0233 

0208 

0182 

0157 

0132 

G107 

0083 

0058 

0034 

0010 

36 

37 

0258 

0233 

0207 

0182 

0157 

0132 

0x07 

0082 

0058 

0034 

0009 

H 

3« 

0258 

0232 

0207 

0181 

015b 

0131 

0107 

0082 

0057 

0033 

0009 

3« 

39 

0257 

0232 

0206 

0181 

0156 

0131 

0106 

0082 

0057 

0033 

0008 

39 

40 

0257 

0231 

0206 

0181 

0156 

0131 

0106 

0081 

0057 

0032 

0008 

40 

41 

0256 

0231 

0205 

0180 

0155 

0130 

0105 

0081 

0056 

0032 

0008 

41 

42 

0256 

0230 

0205 

0180 

0155 

0130 

0105 

0080 

0056 

0031 

0007 

42 

43 

0255 

0230 

0205 

0179 

0154 

0129 

0105 

0080 

0055 

0031 

0007 

43 

44 

0255 

0230 

0204 

0179 

0154 

0129 

0104 

0080 

0055 

0031 

0006 

44 

45 

0255 

0229 

0204 

0179 

0153 

0129 

0104 

0079 

0055 

0030 

0006 

45 

46 

0254 

0229 

0203 

0178 

0153 

0128 

0103 

0079 

0054 

0030 

0006 

46 

47 

0254 

0228 

0203 

0178 

0153 

0128 

0103 

0078 

0054 

0029 

0005 

47 

4« 

0253 

0228 

0202 

0177 

0152 

0127 

0103 

0078 

0053 

0029 

0005 

48 

49 

0253 

0227 

0202 

0177 

0152 

0127 

0102 

0077 

0053 

0029 

0004 

49 

50 

0252 

0227 

0202 

0176 

0151 

0126 

0102 

0077 

0053 

0028 

0004 

50 

51 

0252 

0227 

0201 

0176 

0151 

0126 

0101 

0077 

0052 

0028 

0004 

51 

52 

0252 

0226 

0201 

0176 

0151 

0126 

OIOI 

0076 

0052 

0027 

0003 

52 

53 

0251 

0226 

0200 

0175 

0150 

0125 

0100 

0076 

0051 

0027 

0003 

53 

54 

55 

0251 

0225 

0200 

0175 

0150 

0125 

0100 

0075 

0051 

0027 

0002 

54 

0250 

0225 

0200 

0174 

0149 

0124 

0100 

0075 

0051 

0026 

0002 

55 

5& 

0250 

0224 

0199 

0174 

0149 

0124 

0099 

0075 

0050 

0026 

0002 

5b 

57 

0250 

0224 

0199 

0174 

0148 

0124 

0099 

0074 

0050 

0025 

0001 

57 

5« 

0249 

0224 

0198 

0173 

0148 

0123 

0098 

0074 

0049 

0025 

0001 

5^ 

59 

0249 

0223 

0198 

0173 

0148 

0123 

0098 

0073 

0049 

0025 

0000 

59 

S. 

2°  49' 

2°  50' 

2°  51' 

2°  52' 

2°  53' 

2°  54' 

2°  55' 

2°  56' 

2°  51' 

2°  58' 

2°  59' 

S. 

Page  468J 


TIDE    TABLES 


TABLE  46. 


TIDE  TABLE  FOR  THE  COAST  OF  THE  UNITED  STATES. 
[From  the  United  States  Coast  Survey.] 

ATLANTIC    COAST. 


Place. 


Eastport  to  Long  Island. 


Eastport,  Me 

Hunniwell's  Point,  Kennebec  River,  Me 

Portland,  Me 

Portsmouth,  N.  H 

Newburyport,  Mass 

Rockport,  Mass 

Salem,  Mass 

Boston  Light,  Mass 

Boston,  Mass  . 

Plymouth,  Mass 

Wellfleet,  Mass 

Provincetown,  Mass 

Monomoy,  M  ass 

Nantucket,  Mass 

Hyannis,  Mass 

Edgartown,  Mass 

Holmes's  Hole,  Mass 

Tarpaulin  Cove,  Mass 

Wood's  Hole,  Mass.  (north  side) 

Wood's  Hole,  Mass.  (south  side) 

Menemsha  Bight,  Mass 

Quick's  Hole,  Mass.  (north  side) 

Quick's  Hole   Mass.  (south  side) 

Cuttyhunk,  Mass 

Kettle  Cove,  Mass 

Bird  Island  Light,  Mass 

New  Bedford  entrance  (Dumpling  Rock),  Mass 

Newport,  R.  I 

Pomt  Judith,  R.  I 

Block  Island,  R.I 

Montauk  Point,  Long  Island,  N.  Y 


Long  Island  Sound. 

Watch  Hill,  R.  I 

Stonington,  Conn 

Lhtle  Gull  Island,  X.  Y 

New  London,  Conn 

New  Haven,  Conn 

Bridgeport,  Conn 

Oyster  Bay,  Long  Island,  N.  Y 

Sand's  Point,  Long  Island,  N.  Y 

New  Rochelle,  N.  Y 

Throg's  Neck,  N.  Y 

New  York  Bay  and  Hudson  River. 

Sandy  Hook,  N.  Y 

New  York,  N.  Y 

Dobb's  Ferry,  N.  Y 

Tarrytown,  N.  Y 

Verplanck's  Point,  N.  Y 


Interval  between 

Moon's  Transit  and 

High  Water. 


a 


/i.  ni. 
II  8 
"   15 


25 


II 

II  23 

II  22 

10  57 

11  13 

II  27 

II  19 

II  5 

II  22 

11  58 

12  24 
12  22 
12  16 

II  43 

8  4 

7  59 
834 


45 
31 
36 

40 

48 
59 
57 
45 
32 
36 
20 


9 

0 

9 
9 
9 

7 
38 
28 

16 

II 

7 

13 

22 

20 

<U  C  oJ 

J)  cS  > 

^  -^  zL 

0)   U)  c 


^Si 


h.  III. 

0  51 

1  14 
o  44 

o  53 
o  50 
o  42 
o  50 
o  35 
o  43 

0  51 

1  13 

o  40 

o  37 
o  37 
o  30 

o  34 
o  31 
o  49 
o  53 

0  45 

1  o 

I  15 
I   10 

0  49 

1  o 
o  45 
o  41 
o  24 
0  46 

0  41 

1  II 


30 

7 

52 

8 

3 
51 
31 


o  39 


7  29 

0  47 

8  13 

0  43 

9  19 

0  44 

9  57 

0  58 

0  8 

0  34 

Rise  and  Fall. 


Feet. 

18.  I 

8.1 

8.9 
8.6 
7.8 
8.6 
9.2 

9-3 
10.  o 

10.  2 


II. 

9- 
3- 
3- 
3- 
2. 

I. 

2. 

4- 
I. 
2. 

3- 
3- 


2 
2 
8 
I 
2 
o 
7 
3 
o 
6 

7 
7 
I 

3-5 
4-3 
4.4 

3-8 

3-9 

31 
2.8 

1.9 


2.7 
2.7 

2-5 

2.6 
5-9 
6.5 
7-3 
7-7 
7.6 

7-3 


4.8 

4-3 
3-6 
3-5 
3-1 


tao 

c 


C/3 


Feet. 

20.  6 

9-3 

9-9 
9.9 

9.1 

10.  2 

10.6 

10.9 

II-3 
II. 4 
13.  2 
10.8 


2.8 

4-7 
2.0 

3-9 

4.3 

3.8 

4- 

5- 

5- 

4- 

4- 

3- 

3- 
2. 


Id 


3- 

3- 
2. 

3- 
6. 

8. 

9- 
8.9 
8.6 
9.2 


Feet. 

15.4 
7.0 
7.6 
7.2 
6.6 

7-1 

7.6 

8.  I 

8.5 
9.0 
9.2 

7-7 
2.6 

2.6 
1.8 
1.6 

1-3 
1.8 

3-1 

1.  2 

i.S 
2.9 

2-3 

2.9 
3-7 

3-5 
2.8 

3-  I 
2.6 

2.  o 
1.8 


2.4 
2.  2 

2-3 
2.  I 

5-2 
4-7 
5-4 
6.4 
6.6 
6.1 


Mean  Duration  of — 


o 
o 


m. 

3 
16 

14 
22 
16 
17 
19 
20 

13 

13 
6 

16 

25 
23 
44 
51 
41 
9 
51 
17 
14 

31 
29 

31 

17 

51 

50 
21 

12 

23 
17 


35 

15 
I 


5  56 

6  24 
6  I 
6    8 

5 
5 
5 


55 
51 
50 


6  10 
6    o 

6    5 
6    6 

5  25 


23 
II 

12 

7 
9 
9 
6 
6 

13 
17 
17 
10 

59 
44 
41 
29 
21 
17 
31 

ID 
14 

54 
55 
54 
4 
58 


5  53 

6  3 


10 
2 
7 


56 
10 
21 
26 

5 

7 

24 

30 

35 


a 


h.  m. 

o  22 
o  20 
o  21 
o  24 
o  30 
o    6 

o  15 
o    9 

o  29 
o  15 

O   21 

o  36 
o  9 
o  9 
o  24 

O    12 

o  34 
o  38 
o  59 
o    4 

o  39 
o  40 

o  39 
o  29 

o  42 

0  23 

1  o 

o  5 
o  31 


6 

IS 

6 

25 

6 

18 

6 

20 

7 

12 

o  14 

o  25 

o  37 
o  22 

o  33 
o  30 

o  25 

o  14 

O    12 

o  43 


O   21 

O  28 
o  17 

o  43 
o  16 


I 


I 


TABLE  46. 
TIDE  TABLE  FOR  THE  COAST  OF  THE  UNITED  STATES. 


[Page  469 


ATLANTIC    COAST— Continued. 


Place. 


New  York  Bay  and  Hudson  River — Cont'd. 

West  Point,  N.  Y 

Poughkeepsie,  N.  Y 

Tivoli,  N.  Y 

Stuyvesant,  N.  Y 

Castleton,  N.  Y 

Greenbush,  N.  Y 


Coast  of  New  Jersey. 


Cold  Spring  Inlet,  N.  J. . . 
Cape  May  Landing,  N.  J. 


Delaware  Bay  and  River. 

Delaware  Breakwater,  Del 

Higbee's,  Cape  May,  N.  J 

Egg  Island  Light,  N.  J , 

Mahon's  River,  Del . .". 

Newcastle,  Del 

Philadelphia,  Pa 


Chesapeake  Bay  and  Tributaries. 

Old  Point  Comfort,  Va 

Point  Lookout,  Md 

Annapolis,  Md 

Bodkin  Light,  Md 

Baltimore,  Md 

Washington,  D.  C 

James  River  (City  Point),  Va 

Richmond,  Va 

Tappahannock,  Va 


Coasts   of    North  and   South   Carolina, 
Georgia,  and  Florida. 

Hatteras  Inlet,  N.  C 

Beaufort,  N.  C , 

Bald  Head,  N.  C , 

Smith ville,  N.  C 

Wilmington,  N.  C , 

Georgetown  entrance,  S.  C , 

Bull's  Island  Bay,  S.  C 

Charleston,  S.  C.  (custom-house  wharf) 

Saint  Helena  Sound,  S.  C 

Tybee  Sound,  Ga.  (Fort  Pulaski) 

Savannah,  Ga.  (dry-dock  wharf) 

Doboy  Light- house,  Ga 

Saint  Simons,  Ga 

Fort  Clinch,  Fla 

Saint  John's  River,  Fla 

Saint  Augustine,  Fla 

Cape  Florida,  Fla 

Indian  Key,  Fla 

Sand  Kev,  Fla 

Key  West,  Fla 

Tortugas,  Fla 


Gulf  Coast  of  the  United  States. 


Charlotte  Harbor,  Fla 

Tampa  Bay  (Egmont  Key),  Fla. 
Cedar  Keys  (Depot  Key),  Fla. .. 
Saint  Mark's,  Fla 


Interval  between   I 
Moon's  Transit  and 
High  Water. 


> 

c 
c 


II 


m. 
2 


12  34 

I  24 

3  23 

4  29 

5  22 


7  32 

8  19 


9 

9 

II 

I 


8    o 

833 
4 
52 

53 
18 


8  46 
o  32 
438 

5  42 

6  33 


44 
II 
28 


o  42 


4 
26 


7  26 

19 

6 

56 
16 
26 
8 
20 

13 
33 

43 
53 
28 


»  21 

8  34 
8  23 

8  40 

9  30 
9  56 


o  43 
II  21 

0  49 

1  12 


CT3  — 
qj  C  !^ 

>      <u 

5J    71    c 


o  54 
o  51 
o  48 

o  55 
o  40 


o  51 
o  47 


o  50 

o  43 
o  51 
o  48 
o  24 
o  44 


o  52 

o  45 
o  40 
o  4S 
o  44 

0  52 

1  o 
I  6 
o  46 


o  57 
o  50 

o  34 

0  38 

1  o 
o  42 
o  57 

0  48 

1  o 
o  40 

o  51 
o  55 

0  46 

1  6 

o  48 

o  43 

o  51 
o  49 


I   15 
I  32 


I  38 
I  33 

1  55 

2  o 


Rise  and  Fall. 


FecL 
2.7 

3-2 
4.0 

3-8 
■  2.7 

2-3 


4.4 

4.8 


3-5 
4.9 


2-5 
1.4 
0.9 

I.O 

1-3 
3-0 
2.8 
2.9 
1.6 


2.0 
2.8 

4-3 

4-5 
2.7 

3-8 
4.8 

5-1 
5-9 
7.0 
6.5 
6.6 
6.8 
5-9 

4-5 
4.2 

1-5 
1.8 
I.  2 

1-3 
I.  2 


1.  I 
1.4 
2.6 

2.  2 


in 

to 

a 

'u 

a, 

(A 


Feet. 
3-2 
J- 
4- 
4- 
3- 
2. 


9 

,6 


5-4 
6.0 


4-5 
6.2 

7.0 
6.9 
6.9 
6.8 


2.2 
3-3 
5-0 
5-5 
31 
4-7 
5-7 
6.0 

7-4 
8.0 

7.6 
7.8 
8.2 
6.7 

5.5 
4.9 

1.8 

2.  2 

2.0 

1-5 

1-5 


1-3 
1.8 

3-2 
2.9 


Feet. 
2.0 

2.4 

3-2 

3-0 

2.3 
1.9 


3-6 
4-3 


2.  o 

0.7 
0.8 
0.8 
0.9 
2.6 

2.5 

2-3 

1-3 


1.8 
2.2 

3-4 
3-^ 
2.  2 


4-4 
5-9 


I.  2 

o.  6 
0.9 
0.6 


0.8 
I.  o 
1.6 
1.4 


Mean  Duration  of — 


-a 
o 
o 


7n. 
28 

41 

40 

18 
I 

26 


6    8 
6  II 


6  15 
6  26 

5  52 

6  II 

5    6 
4  52 


I 

59 
II 


5  23 


54 
37 
14 
53 


5  21 


6  7 
6  II 
6  18 
6     I 


651 


6  36 

6 

6 


.0 


45 

4 

20 

19 
13 

5  49 

5    4 


2 

10 

9 

58 

5 
o 

25 
31 

55 
43 


m. 
10 

44 

54 

2 

23 
59 


■a 


6  18 
615 


6 

o 

27 

II 

43 
6 


25 

19 

15 

8 

6  49 

6  58 

7  31 
7    6 


6  7 
6  10 
6  17 
6  26 


40 

19 
6 

7 
12 

35 
22 

20 

16 

17 
28 
II 

26 


5  59 
5  55 
5  29 
5  40 


5  35 

6  II 

12  i  6  13 
12  I  6  11 


//.  m. 
o  20 
o  22 
o  25 
o  31 
o  20 


o  19 
o  20 


o  26 
o  19 


36 

26 

47 
15 


14 
35 
32 
15 
44 


o  32 
o  35 


o  50 
o  42 
o  31 
o  26 
o  30 

o  35 
o  30 

o  33 
o  23 
o  26 
o  14 

o  20 


16 

32 

45 
19 

13 

12 


0.43 


I 


Page  470]  TABLE  46. 

TIDE  TABLE  FOR  THE  COAST  OF  THE  UNITED  STATES. 
ATLANTIC    COAST— Continued. 

The  tides  of  ports  in  the  Gulf  of  Mexico,  west  of  Cape  Saint  George,  ebb  and  flow,  as  a  rule,  but  once  in 
twenty-four  hours,  or  are  single-day  tides.  At  particular  parts  of  the  month  there  are  two  small  tides  in  the 
twenty-four  hours.  The  rise  and  fall  in  all  these  ports  is  small.  The  highest  high  and  the  lowest  low  waters 
occur  when  the  greatest  declination  of  the  moon  happens  at  full  or  change ;  the  least  tide  when  the  moon's  dec- 
lination is  nothing  at  the  first  or  last  quarter.  The  rise  and  fall  being  so  small,  the  times  and  heights  are  both 
much  influenced  by  the  winds,  and  are  thus  rendered  quite  irregular.  The  following  table  gives  the  rise  and 
fall  at  several  points : 

Rise  and  Fall  at  several  Stations  in  the  Gulf  of  Mexico. 


Stations . 


Saint  George's  Island,  Fla 

Pensacola,  Fla 

Fort  Morgan,  Mobile  Bay,  Ala. 

Cat  Island,  Miss 

Southwest  Pass,  La 

Isle  Derniere,  La 

Entrance  to  Lake  Calcasieu,  La 

Galveston,  Tex 

Aransas  Pass,  Tex 

Brazos  Santiago,  Tex 


Mean  Rise  and  Fall  of  Tides. 


Mean. 


Feet. 
I.  I 


At  Moon's  great- 
est Declination. 


Feet. 
1.8 

1-5 
1.9 

1.4 
2.2 
2.4 
1.6 
1.8 
1.2 


At  Moon's  least 
Declination. 


Feet. 
0.6 
0.4 
0.4 
0.6 

0-5 
0.7 

1-7 
0.8 
0.6 
0-5 


PACIFIC    COAST. 


Place. 


Interval  between 

Moon's  Transit  and 

High  Water 


<U   C  OJ 

4)  rt  > 

-M   -»->  4J 

(U   Cfi  e 

=S  on 

Q 


Rise  and  Fall. 


tn 

be 

.S 

D. 
C/3 


Mean  Duration  of- 


o 
o 


J3 


•a 
c 

C/3 


San  Diego,  Cal 

San  Pedro,  Cal 

Cuyler's  Harbor,  Cal 

San  Luis  Obispo,  Cal 

Monterey,  Cal 

South  Farallon,  Cal 

San  Francisco,  Cal.  (north  beach) 

Mare  Island,  Cal 

Benicia,  Cal 

Ravenswood,  Cal 

Bodega,  Cal 

Humboldt  Bay,  Cal 

Port  Orford,  Oregon 

Astoria,  Oregon , 

Nee-ah  I  larbor,  Wash 

Port  Townshend,  Wash 

Steilacoom,  Wash 

Semiahmoo  Bay,  Wash 


h. 
9 
9 
9 

10 


m. 

38 

39 

25 
8 


10  22 
10  37 
12  6 


I 
I 

o 
II 
12 
II 

o 
o 

3 
4 
4 


14 
44 
10 

17 

2 
26 
16 

7 
49 
46 

50 


m. 

35 
48 

2 

52 

49 
16 

4 

15 

o 

57 

54 

II 

6 

13 

28 

3 
6 


Feet. 
3-7 
3-7 
3-7 
3-6 
3-4 
3-6 
3-6 
4.8 

4-5 
6.3 
3.6 

4 
I 
I 
6 
6 
2 
7 


Feet. 

5-0 

4-7 

5-1 
4.8 

4-3 
4.4 

4.3 
5-2 
5-1 
7-3 
4-7 
5-5 
6.8 

7-4 

7-4 

5-5 
II.  I 

6.6 


Feet. 

2-3 

2.  2 

2.8 
2.4 


w. 

22 
18 
13 


2.  ■ 
2. 

4- 
3' 
4- 
2. 

3' 

3' 

4. 

4.8 

4.0 

7.2 

4.8 


6  25 
6  ^i 
6 
6 
6 


J' 
18 

39 
13 


6  26 
6  15 


19 
19 
19 

■^ 

20 

34 

3 
II 


m. 
o 

5 
5 

58 
2 

9 
51 

7 

59 
II 

59 
o 

7 
28 

6 

52 
25 
19 


//.  ni. 
o  30 
o  30 

o  35 
o  34 


o  39 
o  33 


o  28 
o  26 


i 


TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS. 
[Arranged  alphabetically,  with  the  Rise  of  the  Tide  at  Springs  and  Neaps.*] 


[Page  471 


(When  a  query,  thus  ?,  is  placed  after  the  Time  of  High  Water  and  the  Rise,  it  indicates  that  what  are  given 

are  approximations.) 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Abaco,  Bahamas 

Abbey  Head,  Scotland 

Abd-ul  Kuri,  Indian  Ocean 

Aberdeen,  Scotland 

Aberdovey,  Wales 

Abervrach,  France 

Aberystwyth,  Wales 

Abrolhos,  Brazil 

Abtao,  Port,  Chile 

Abii-shehr,  Persian  Gulf 

iVcajutla,  Central  America -. 

Acapulco,  Mexico,  West  Coast 

Acheen  Head,  Sumatra 

Achillbeg,  Ireland 

Adam  Bay,  Australia,  North  Coast 

Adims,  Port  (Mary  Island),  Yellow  Sea 

Adelaide,  Port,  Australia,  South  Coast 

Aden  and  adjacent  Bays,  Arabia,  Southeast  Coast 

Adenara,  Flores,  Malay  Archipelago 

Admiralty  Gulf,  Australia,  Northwest  Coast 

Adolphus  Island,  Australia,  Northwest  Coast 

Adou  Atoll,  Maldives 

Adou  Matte  Atoll,  Maldives 

Adventure  Cove,  Tierra  del  Fuego . 

Adventure,  Port,  New  Zealand 

Adventure  Sound,  Falkland  Islands 

Agadir,  or  Santa  Cruz,  Africa 

Aggerminde,  Jutland 

Agnes,  St.,  Sciliy  Isles .' 

Agulhas,  Cape,  Africa,  South  Coast 

Aillik  Bay,  Labrador 

Ailu,  Kapenuir  Island,  Marshall  Islands 

Air  Point,  River  Dee,  England 

Aix,  He  d',  Charente  River,  France 

Ajar,  Hindoostan,  West  Coast 

Akaroa  Harbor,  New  Zealand 

Akishi  Bay,  Japan ,. 

Akyab,  Aracan  River,  Bay  of  Bengal 

Al  Bida,  Persian  Gulf 

Alabat  Harbor,  1  Aizon 

Alan  Island,  Patagonia,  West  Coast 

Albany  Islands  (Port  Albany),  Australia,  East  Coast 

Albemarle  Island,  Galapagos  Islands 

Albemarle,  Port,  Falkland  Islands 

Albert  River  (Kangaroo  Point),  Australia,  North  Coast 

Alcm^ne,  Port,  Isle  of  Pines,  New  Caledonia 

Aldabra  Islands,  Mozambique 

Aldborough,  England 

Alderney,  English  Channel 

Alert  Bay,  Cormorant  Island,  Johnstone  Strait,  Vancouver  Island . 

Alexander,  Port,  Africa,  Southwest  Coast 

Alfred,  Port,  Kowie  River,  Africa,  South  Coast 

Alge9iras,  Spain 

Algoa  Bay,  Africa,  .South  Coast 

Alligator  Bay,  Flores 

Alligator  River,  Australia,  North  Coast 

Alloa,  Firth  of  Forth,  Scotland 

Altona,  Germany 

Amboyna,  Moluccas 

Ameland,  Netherlands 

Amet  Sound,  Nova  Scotia 


h.  m. 
8     o 

II  10 
8  30 
I  o 
8    o 


4 

7 

3 
I 


14 

31 
20 

18 

7  30 

2  25 

3  6 
845 

5  14 

6  o 
2    o 

4  40 

7  30  to  9  30 


Noon. 

7  30 

1  o 

3     o 

3  10 
o  20 

5  30 
o  45 

4  9 
4  30 

2  50 


4  53 

10  54 

3  20 

o  50 

3  24 

4  30 

9  45 
8  30? 

10    o 

o  31 

o  15 

2       O 

7  15 

7  30 

8  6 

5  o 
10  45 

6  46 


3    o 

3  50 
I  49 

4  o 


'5 
3  18 
5  9 
o  33 

9  30 
10  30 


Feet. 

3 

23 

6 

12 

15 

22 

13K 
6-7 
16-18 

7 
9 

;?* 

10 

8 

7 
8 

21 

4 
4 
4 
8 

SY^ 
9 
2 
16 

5 
7 
8 

25 
17 
14 

8 

5 
9 
6? 

9 
18 

ID 

6 

7 
10-13 

4 
10 

8? 
17 
15 

5 
4-5 

4 

4 

6 

15 

i7>^ 
8 

7 

6X 

8 


Feet. 

17 
10 

16 
10 


5-5>^ 
4>^ 


19 

I2>^ 
II 

6 


7 
3-8 


12X 


5 
15 


*  By  the  Rise  of  the  Tide  is  meant  its  vertical  rise  above  the  mean  low-water  level  of  Spring  Tides. 


Page  472]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.-Contmued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


tl 


Amirant^  Isles  (St.  Joseph  Island),  Indian  Ocean. 

Amlwch,  Wales 

Amoy  (Inner  Harbor),  China,  East  Coast 

Amoy,  Chiang  Chiu,  West  River 

Ampanam  Bay,  Lombock 

Amrum,  Denmark 

Amsterdam,  Indian  Ocean 

Armstrong  Channel,  Bass  Strait 

Amulgawein,  Persian  Gulf 

Amur  Strait,  Gulf  of  Tartary 

Ananga,  Japan  ,   

Andaman  Islands,  Port  Blair,  Indian  Ocean 

Andaman  Islands,  Port  Cornwallis 

Andaman  Strait,  Indian  Ocean 

Andrava  Bay,  Madagascar 

Andres,  San,  Bay,  Patagonia,  West  Coast 

Andrews,  St.,  New  Brunswick 

Anegada,  Virgin  Islands 

Aneiteum  (Port  Inyang),  South  Pacific 

Angosto,  Port,  Strait  of  Magellan 

Angoxa  River,  Africa,  East  Coast 

Angra,  Azores 

Angra,  Pequena,  Africa,  Southwest  Coast 

Angria  Bank,  Hindoostan,  West  Coast 

Anna  Pink  Bay,  Patagonia,  West  Coast 

Annan  Foot,  Scotland 

Anne,  St.,  Bay,  Cape  Breton 

Anno  Bom  Island,  Africa 

Anthony  Strait,  Newfoundland 

Anticosti  Island,  Gulf  St.  Lawrence,  East  Cape  . . 

Anticosti  Island,  Bear  Bay 

Anticosti  Island,  West  Point 

Antigonish  Harbor,  River  St.  Lawrence   

Antigua  Island  (English  Harbor),  Caribbean  Sea. 

Antongil  Bay  (Port  Choiseul),  Madagascar 

Antonio,  Cape  St.,  Cuba 

Antonio  River,  Africa,  East  Coast , 

A.ntonio,  Port  St.,  Patagonia,  East  Coast 

Antonio,  Port  St.,  Magellan  Strait 

Antonio,  San,  Rio  Plata 

(\ntrobus  Island,  Gulf  of  St.  Lawrence 

Antwerp,  Belgium , 

Aor  Pulo,  Sumatra,  Northeast  Coast 

Aotea  Harbor,  New  Zealand 

Apamama,  Gilbert  Islands 

Appeetetat  Bay,  Gulf  of  St.  Lawrence 

Appin,  Port  (Loch  Linnhe),  Scotland 

Appledore,  England 

Aquin  Bay,  St.  Domingo 

Aracan  River  (Bar),  Bay  of  Bengal,  East  Coast 

Aracati,  Brazil 

Araish,  El,  Africa,  North  Coast 

Arasaig,  Scotland 

Arauco  Bay,  Chile , 

Arbroath,  Scotland 

Arcachon,  France 

Areas  Rocks,  Gulf  of  Mexico 

Ardglass,  Ireland 

Ardintallan  (Loch  Feochan),  Scotland 

Ardrishaig,  Loch  Fyne 

Ardrossan,  Scotland 

Arenas,  Point,  San  Carlos,  Patagonia,  West  Coast. 

Argyle,  Bay  of  Fundy 

Arica  Road,  Peru 

Arichat,  Nova  Scotia 

Arinagour,  Coll  Island,  Scotland,  West  Coast 

Arkhangel,  White  Sea 


//.  111. 

5  o 

10  30 
Noon. 

3  40 
8  o 
o  30 

11  o 

8  30 
II  40 
II  40 

o  27 

9  30 
10    o 

10  24 
3  30 
o  45 

10  50 
9    o 

6  35 
o  40 


o  32 

2  30 

10  30 

0  45 

11  56 

834 

3  45 
7  10 

1  o 

1  10 

2  o 
9    o 


4    o 


3  15 
10  45 
Noon. 
10  o 
10  30 

4  25 


I 


10  o 

4  30 

11  ID 

5  26 

5  28 
rregular. 

9  45 

6  o 

I  30 

5  50 
10  15 
I 
4 


35 
37 

Noon. 

II      o 


5 
II 


31 

53 


II  45 
o  14 


27 
o 


8  10 

5 
7 


Feet. 

18? 
18K 

6 
9 
3 
3 
6 

5-6 

2-4 


39 
28 


9;4 

7 

5 
25 

iK 

4 

4 
13 

8 
9 

5 
20 
6 
5 
5 
5 

5 
6 

4 
2 

18-30 
7 

5K 
5 
IS 
5 

12 
6-0 

5?^ 
12X 

23 
2-3? 

9 

8 

9-12 

13K 
6 

14 

11^ 

^A 
16 

9 
9 

ID 

6 

12^ 

5 

5 

12X 

2% 


Feet. 


TABLE  47.  [Page  473 

»TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &C.— Continued. 


Place. 


Arklow,  Ireland , 

Arnhem  Bay,  Australia,  North  Coast , 

Arroa,  Malacca  Strait 

Arthur,  Port,  Tasmania    

Arundel,  England , 

Arundel  ( Bar) 

Asaph,  St.,  Bay,  Australia,  North  Coast 

Ascension  Island,  South  Atlantic 

Ashrafi  Islands,  Red  Sea 

Askaig,  Port,  Islay 

Assar  Point,  Hindoostan,  West  Coast , 

Atacames  Bay,  Ecuador , 

Athline,  Loch  Seaforth 

Atico  Road,  Peru 

Atkesi,  Yezo  Island 

Auckland  Harbor,  New  Zealand,  North  Island 
Auckland  Island,  South  Pacific  (Port  Ross).  ... 
Augustine,  St.,  Bay,  Madagascar,  West  Coast.. 

Aulapolay,  Hindoostan,  West  Coast 

Aulezavik  .Sound,  Lalirador 

.\ux  Cayes  Bay,  St.  Domingo 

Avatcha  Bay,  Kamchatcha , 

Avon  Isles,  .\ustralia.  East  Coast 

Avon  River,  Bigbury  Bay,  England 

Awasima  (Inland  Sea),  Japan 

Awanui  River,  New  Zealand , 

Axim,  Africa,  West  Coast 

Aylen  Bay,  Yellow  Sea 

Aymaun,  Persian  Gulf , 

Ayr,  Scotland , 

Ayr,  Point  of.  Isle  of  Man , 


Bab-el- Mandeb,  Gulf  of  Aden 

Babel  Island,  Bass  Strait 

Bachelor  River,  Magellan  Strait 

Bacuit  Bay,  China  Sea,  East  Coast 

Badas  Island,  Linga  Bay,  .Sumatra 

Badong  Bay,  Baly,  South  Coast 

Bahia,  Brazil 

Bahrein,  Persian  Gulf 

Balabac  Island,  China  Sea,  East  Coast , 

Balad  Harbor,  New  Caledonia 

Balambangan  Island,  Borneo,  North  Coast 

Balasore  River,  Bay  of  Bengal,  West  Coast 

Balbriggan,  Ireland 

Ballachulish  ( Loch  Leven),  Scotland 

Ballinacourty,  Dungarvan,  Ireland 

Ballinskellig  Bay,  Ireland 

Ballycastle  Bay,  Ireland 

Ballycottin,  Ireland 

Ballycrovane,  Kenmare  River,  Ireland 

Ballynakill  Bay,  Ireland 

Ballyness  (Bar),  Ireland 

Ballysadare  (Quay),  Ireland 

Ballyshannon  ( Bar),  Ireland 

Ballyweel,  Ireland 

Balta,  Scotland 

Baltimore,  Ireland 

Baltrum,  Germany 

Banana  Islands,  Africa,  West  Coast  

Bankot  or  Sitri  River  (entrance),  Hindoostan,  West  Coast. 

Banda,  Moluccas 

Bander  Aliileh,  Gulf  of  Aden 

Bander  Gori,  Gulf  of  Aden  

Bander  Jisseh,  Persian  Gulf 

Piander  Khairan,  Persian  Gulf 

Bander  Shaab,  Indian  Ocean 


High  Water,  Full 
and  Change. 


//.  m. 
845 
8  10 


7 
o 
II 
5 
5 
6 

4 


52 
25 
35 
45 
30 
o 

58 


Noon. 

3  37 

6  16 

853 
10    o? 

7  5 
Noon, 

4  30 
2     o 


Irregular, 

3  30 
8  30 

5  47 

7 

44 

30 
o 


o 

7 

4 

2 

II 

II 

II 


20 
50 

7 


Noon. 


10 
I 

10 
6 

II 
4 

5 
II 

6 
10 
10 


5 
40 

o 

o 

o 

26 
30 

o 

15 

o 
o 


10  40 


5 

5 

3 
6 

4 

3 

4 

5 
6 

5 
5 
9 
4 
II 
8 


43 
12 

40 

25 
54 
42 
40 
22 
o 
18 
23 
45 

23 
20 

15 


10  30 
4    o 

6  45 
845 

11  o 
II      o 

7  o 


Rise. 


Springs. 


Feet. 

4 
6 

10 

4 

16 

14 

2 


12 

13 
15 

5 

II 

3 

13 

3 

5 
2-3? 

6X 

5 
16X 

7 
4 
6 
6 


20? 

7 

7 

5 
6 

12 

9K 
8 

7 
5 

A% 
6-8 

15 

13 
II 

12 

3 

12 

I0>^ 
12ji 


I2>^ 

6 

loX 
8 

9 
II 

6? 
6 

S 
5 

7 


Neaps. 


Feef. 


IlK 


4 

8 


10 


1-2 


4X 
6? 


16? 


9% 

2 

1H 
9% 

8X 

SH 

8K 
8 

4K 
8X 


Page  474]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Bander  Feikam,  Arabia,  Southeast  Coast 

Banff,  Scotland 

Bangkok  River,  Siam 

Banjoewangie,  Java 

Banoko,  Africa,  West  Coast 

Bantam,  Java 

Bantry  Harbor,  Ireland 

Baracoa,  Cuba 

Barbados,  Caribbee  Islands 

Barbara,  Port,  Patagonia,  West  Coast 

Barbara,  Santa,  Island,  California 

Barbe,  St.,  Harbor,  Newfoundland 

Barbe,  St.,  Sumatra,  Northeast  Coast 

Barbe,  Santa,  Island,  California 

Barclay  Sound,  Island  Harbor,  Vancouver  Island 

Barclay  Sound,  Uchucklesit  Harbor,  Vancouver  Island. 

Barclay  Sound,  Stamp  Harbor,  Vancouver  Island 

Bardsey  Island,  Wales 

Barfleur,  France   .,.. 

Barmouth,  Wales .. 

Barnstaple  Bridge,  England 

Barquero  (entrance),  Spain,  North  Coast 

Barra  Island  (North  Harbor),  Scotland,  West  Coast 

Barra  Castle  Bay,  Scotland,  West  Coast 

Barra  Head,  Bernerad  Island,  Scotland,  West  Coast  . . . 

Barracouta  Harbor,  Gulf  of  Tartary 

Barragan  Bay,  Rio  de  la  Plata .. 

Barren  Island,  China  Sea,  East  Coast 

Barren  Islands,  Madagascar 

Barrow  Harbor,  Newfoundland 

Barrow  Point,  Arctic  Regions 

Barry  I  sland,  Wales 

Barton,  Port  (Bubon  Point),  China  Sea,  East  Coast 

Bas,  He  de,  France 

Basidiih,  Persian  Gulf 

Basil  Bay,  Korea,  West  Coast 

Basque  Port,  Newfoundland 

Bashrah  (Bar),  Persian  Gulf 

Basrah,  Town 

Bassein  River,  Bay  of  Bengal 

Batanes,  Bashee  Islands,  China  Sea,  East  Coast 

Batavia,  Java 

Batchian,  Gilolo,  Moluccas 

Bate  (Gulf  of  Kutch),  Hindoostan,  West  Coast 

Bateman  Bay,  Australia,  East  Coast 

Bathurst,  Gulf  of  St.  Lawrence 

Bathz,  Netherlands 

Batiscan,  River  St.  Lawrence 

Batoo  Barra,  .Sumatra .. 

Batticalao  River,  Ceylon 

Bawdsey  Haven.     (Sc'e  Woodbridge  Haven.) 

Bay  of  Harbors,  Bull  Road,  Falkland  Islands 

Bay  of  Islands  (Motu  Mea  Islet),  New  Zealand 

Bay  of  Mercy,  Banks  Land 

Bayonne  ( Bar),  France 

Bazaruto,  Cape,  Africa,  East  Coast 

Beachy  Head,  England .' 

Beagle  Bay,  Australia,  West  Coast 

Bear  Cape,  Prince  Edward  Island 

Bear  Head,  Cape  Breton  Island 

Beatrice  Islet,  Austraha,  North  Coast 

Beaubere  Island,  Gulf  of  St.  Lawrence 

Beaulieu,  England 

Beaumaris,  Wales 

Beaver  Cove,  Vancouver  Island 

Beaver  Creek,  Loughborough  Inlet,  British  Columbia . . 


//.  m. 
13     o 

0  28 
Irregular. 

1  o 
5  24 


3  47 

7  23 

3    o 
o  28 

8  o 

ID      O 
6      Q 

8    o 
Noon, 


Noon, 
7  40 
851 
7  41 
6  28 

3  15 

5  48 

5  44 

5  45 
10    o 


o 
30 
45 
13 


II  45 
6  39 

ic  55 
4  49 

Noon. 

4  15 
855 

Noon. 
6     o? 

10    o 


10  o 
r  o 
o  20 
8    o 

3  15 
3  15 

948 
2  50 

5  o 

6  o 

7  15 


3  45 

4  15 
II  20 

II  30 

9    o 
8  30 

3    o 

6  30 

10  25 

o  15 
10  32 


o 


Feet. 

8K 
io>^ 

7/^-11 
9 

5 
5 

ID 
2X 

3 
6 

Ar 
6 

12 
12 
12 

15 
17 
17 

loK 

iiK 

IIX 

iiX 
VA 

5-9 

5X 
12 


35X 
6 

23 
10 

18 

5K 

9? 
9 
4 
2 
6 
12 
4-6 

7 
14 

VA 
7-10 

2-3 

5 

9 

2 
12 
10 
20 

13-15 
6 

aYz 

8 
6 

10 

2I>^ 

15 
16 


8 


TABLE  47.  [Page  475 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Beaver  Harbor,  Vancouver  Island 

Beaver  Harbor,  Nova  Scotia 

Bedeque  Harbor,  Prince  Edward  Island 

Bedford  Bay,  Tierra  del  Fuego 

Behring  Bay,  America,  NortWest  Coast 

Belfast,  Ireland 

Belgrano,  Port,  La  Plata 

Bell  Sound,  Spitzbergen 

Belles  Amour  Bay,  Labrador 

Belligam  Bay,  Ceylon 

Bellona  Reefs  (Middle),  Australia,  East  Coast 

Bembatooka  Bay,  Madagascar,  West  Coast 

Bembridge  Point,  England 

Benbecula,  Scotland 

Bencoolen,  Sumatra 

Benevente,  Brazil 

Benguela,  Africa,  West  Coast 

Benin  River,  Africa,  South  Coast 

Berbereh  or  Burburra  (Gulf  of  Aden),  Africa,  East  Coast. 

Berbice,  tjuayana 

Bergen,  Norway 

Berkeley  Sound,  Falkland  Islands 

Bermuda,  Ireland  Island,  North  Atlantic 

Bernera,  Loch  Roag,  Lewis  Island 

Berneray  Island,  Sound  of  Harris 

Bersiap  Point,  Banka  Strait 

Bersimis  River,  Gulf  of  St.  Lawrence 

Berwick,  Scotland 

Betcheween  Harbor,  Gulf  of  St.  Lawrence 

Beypore  River  (entrance),  Hindoostan,  West  Coast 

Bhowliaree  Creek,  Hindoostan,  West  Coast 

Bias  Bay  (Tooniang  Island),  China,  East  Coast 

Bias  Bay  (Tsangchow  Island),  China,  East  Coast . .. 

Bic  Island,  Gulf  of  St.  Lawrence 

Biddah  River,  Bay  of  Bengal,  West  Coast 

Bideford,  England 

Bijouga  Islands,  Areas  Channel,  Africa,  West  Coast . 

Bijouga  Islands,  Bissao,  Africa,  West  Coast 

Bijouga  Islands,  Orango  Channel,  Africa,  West  Coast 

Bilbao  (Bar),  Spain 

Bilbao  (Town),  Spain 

Bima  Bay,  Sumljawa 

Binkang  Bay,  China  Sea,  West  Coast 

Binnic,  France 

Bintula  River,  China  Sea,  East  Coast 

Bird  Island,  Carlandagan  Islands,  Cbina  Sea,  East  Coast. 

Bird  Islands,  Africa,  South  Coast 

Blaavands  Huk,  Jutland 

Black  Ball  Harbor,  Ireland 

Black  R  ock.  Bay  of  Fundy 

Black  Point,  Australia,  South  Coast 

Black  Point  Bay,  Africa,  West  Coast 

Blacksod  Bay  (Quay),  Ireland 

Blacktoft,  River  Humber 

Blair  Harbor,  China  Sea,  West  Coast 

Blakeney,  England 

Blakeney  (  Bar),  England 

Blanche,  Port,  Streaky  Bay,  Australia,  South  Coast 

Blankenberg,  Belgium 

Blanco,  Cape,  Africa,  West  Coast 

Bias,  San,  Mexico,  West  Coast 

Bias,  San,  La  Plata 

Blasket  Islands,  Ireland 

Blauort  Sand,  Germany 

Blewfields,  Mosquito  Coast 

Bligh  .Sound,  New  Zealand 

Blind  Bay,  Nova  Scotia 


h.  III. 
o  30 

7  40 
10  15 

o  30 

o  30 

10  43 

6    o 

8  56 

9  o 
2  20 
8  30 
4  30 


II 

6 
6 
3 
3 
4 


I 

5 
7 
6 
6 
6 
2 
2 
II 
o 
4 


o 

3 
o 
o 

45 
30 

7  IS 
4  30 

30 
o 

14 
II 
II 

30 
o 

18 

32 

15 
46 

8  o 
8  30 
2  15 


10 
6 


10  10 

11  o 


10 

3 

3 
Noon. 

II  30 


o 

o 
20 


6 

5 
9 
4 
I 

3 
II 

4 

4 

4 
6 


3 

45 

30 
o 

45 
40 
29 

37 
30 
47 
59 


8  50 


30 
o 

15 


II  46 
9  41 


2 
3 


o 

-  30 

0  38 

1  50 

10  45 

7  46 


Feef. 

15^ 


Feet. 


6K 

4K 

7 

5 

VA 

9 

9/2 

8 

12 

10 

3^ 

4K 

2% 

2^r 

6 

16 

14 

10/2 

11/2 

sy2 

3-5 

5 

5-6 

7 

9 

8-10 

6 

4 

7 

4 

II 

8 

13 

9/2 

12 

12 

7 

15 

iiK 

5 

3 

4 

3H 

30 

23 

14 

8/2 

14 

12 

16 

1-14 

9 

8 

II 

13 

9 

6 

5 
30 

22>^ 

6 

6 

4-5 

7 

9^ 

7H 

36 

31 

8 

5-6 

6 

ID 

S'A 

16 

9 

9 

15 

5 

13 

10 

6 

6)4 

12 

10 

iiX 

8 

12 

2 

8 

6 

7>^ 

6 

Page  476]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  FuU 
and  Change. 


Rise. 


Bluff  Cay,  Bahamas 

Bluff  Harbor,  New  Zealand 

Blunder!  H arbor,  British  Columbia 

Bly th,  England 

Blyth  River,  Southwold,  England 

Boca  de  Varadero,  Cuba 

Boca  Grande,  Trinidad,  Caribbee  Islands — 

Boca  Mono,  Trinidad,  Caribbee  Islands 

Boddam  Cove,  Ladrone  Islands 

Boerong  Island,  China  Sea 

Bojador,  Cape,  Africa 

Bolt  Head,  England 

Bombay  Dockyard,  Hindoostan,  West  Coast 

Bonacca  Island,  Bay  of  Honduras 

Bonavista,  Newfoundland 

Bonne  Esperance  Harbor,  Gulf  of  St.  Lawrence 

Bonny  River,  Africa,  West  Coast 

Booby  Island,  Australia,  North  Coast 

Bordeaux,  France 

Boria  Bay,  Hindoostan,  West  Coast 

Borja  Bay,  Magellan  Strait 

Borkum,  West  Germany 

Borkum,  East  Germany 

Boscastle,  England 

Boston  (Sluice),  England 

Boston  (Deep  Clay  Hole),  England 

Boston,  Hob  Hole,  England 

Botany  Bay,  Australia,  East  Coast 

Boteler  River,  Madagascar 

Boucaut,  France 

Bought  on  Harbor,  Prince  Edward  Island 

Boulogne,  France 

Bourbon  Island,  Indian  Ocean.     (^See  Reunion  Island.) 

Bouro  (Cajili  Bay),  Moluccas 

Bow  Island,  Soulh  Pacific 


Bowen,  Port,  Australia,  East  Coast 

Bowling,  River  Clyde,  Scotland 

Boyanna  Bay,  Madagascar,  West  Coast 

Bradore  Bay,  Labrador 

Braha  Harbor,  Newfoundland 

Bramble  Cay,  Torres  Strait 

Brandy  Pots,  River  St.  Lawrence 

Brass  River,  Africa 

Brava,  Africa,  East  Coast 

Bray  Head,  Ireland 

Breaksea  Sound,  New  Zealand , 

Brehat,  France 

Bremerhaven,  Germany 

Brest,  France 

Bridgewater,  England 

Bridgewater  Bar,  England 

Bridlington,  England 

Bridport,  England 

Brielle,  Netherlands 

Brig  Bay,  Newfoundland 

Brighton,  England 

Brisbane  (Bar),  Australia 

Bristol  (King  Road),  England 

Bristol,  Cumberland  Dock  Gates 

Britannia  Bay,  Sumbawa 

British  Sound,  Madagascar,  East  Coast. 
Broad  Sound,  Australia,  East  Coast. . .. 


Broadhaven  Harbor,  Ireland 

Broadway  River  (entrance),  China,  East  Coast. 

Broken  Bay,  Australia,  East  Coast 

Broom  Loch  (Ullapool) 

Broughty  Ferry,  Scotland 


h.  m. 

7    o 

I  18 

Noon. 

3  15 

10  20 

839 
3  30 

3  50 
9  40 

4  45 
Noon. 

5  45 

11  40 

9    o 


7 
9 
4 
4 
6 

ID 


25 
15 
50 
30 
50 
O 


I    30 

10  43 

10  57 

5  15 

7    o 


8  10 

4  30? 

3  39 

8  40 
II  25 

1  32 

2  40 

9  35 

0  39 

4  30 

845 

7  o? 

9  15 

3  o 

4  o 

4  30 

10  45 

11  15 

5  51 

1  40 

3  47 

8  o 

6  50 
39 

5 
o 

46 
15 

22 
13 

13 
O 


4 
6 

3 

9 

1 1 

9 

7 

7 
I 


4 
II 

5 
II 

8 

6 


o 
o 
o 
o 

30 
40 

22 


Feet. 

8 
16 
15 

2 

4 
4 

7 

8? 

15? 
12-17 


5 

6 

8 

14 
10 

6 

7 

7 

22 

13 


17 

7-8 

'^\ 

^H 

5 
25 

aVz 

3 
16 

9 
15 

4 

2-3? 

12 

17 
6 

8 

12 

8 

31 
II 

19 
18 

35 
16 

iiX 

5 
5? 

40 

3i>^ 
11-12 

9% 
20-30 

5-7 
IAVz 

w/2 


Feet. 

6 

ii>^ 
II 

AYz 

2J^ 


II? 


^Y 
5 

123/ 


17 


6 

234: 

i9j^ 


10 


9Yz 


^J/2 

i3,¥ 

26K 
12 

1% 


16 

aYa 

31 


lYz 


II 


TABLE  47.  [Page  477 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Brouwershaven,  Netherlands 

Brouwershaven-gat 

Bruinisse,  Netherlands 

Bruit  River,  Borneo 

Bruni  River,  China  Sea,  East  Coast 

Brunsbuttel,  Germany 

Brunswick  Bay,  Australia,  Northwest  Coast 

Brush,  Yarmouth,  England 

Bubon  Point,  Port  Barton,  China  Sea,  East  Coast . ... 

Buctouche  River,  Gulf  of  St.  Lawrence 

Budehaven,  England 

Buenaventura,  Port,  Central  America  (Negrilla  Reef). 
Buenaventura,  Port,  Central  America  (off  the  town) ... 

Buenos  .\yres.  South  America,  East  Coast . . , 

Buffalo  River  (East  London),  Africa,  South  Coast .  ... 
Bulama  Island  (Areas  Channel),  Africa,  West  Coast  . . 

Bull  Harbor,  Goletas  Channel,  Vancouver  Island 

Bull  Island,  Newfoundland 

Bull's  Mouth  (Achill  Sound,  north  entrance),  Ireland  . 

Bulsar  Khar,  Hindoostan,  West  Coast 

Buluagan,  O'sta  Ana,  Port,  Filipinas 

Bunawe  ( Loch  Etive),  Scotland 

Buncranna,  Ireland 

Bunessan,  Scotland 

Burburra.     {ScY  Berbereh.) 

Burin  Harbor,  Newfoundland.  .. 

Burntisland,  Firth  of  Forth,  Scotland 

Burnt  Isles,  Kyles  of  Bute,  Scotland 

Burong  Island,  China  Sea 

Burrard  Inlet,  Gulf  of  Georgia,  British  Columbia 

Burry  Port,  Wales 

Busainga,  Burias  Island 

Bushire.     (.S'i'd' Abu-shehr.) 

Bussorah  River  (Bar),  Persian  Gulf 

Busuanga,  China  Sea,  East  Coast 

Biisum,  Germany    .    

Button  Islands,  Hudson  Strait 

Byron  Bay,  Australia,  East  Coast 


Cabita  Bay,  New  Granada 

Cacheo  River,  Africa,  West  Coast 

Cachipour,  Cape,  Brazil 

Cadiz,  Spain 

Caen,  France , 

Caermarthen  (Bar) 

Caernarvon,  Wales 

Cagayan  Sulu 

Caimites,  St.  Domingo 

Cairnlough,  Ireland , 

Cajeli  Bay,  Bouro 

Calais,  France 

Calandorang,  Balabac  Island 

Calbuco,  Patagonia,  West  Coast 

Calcutta,  Bengal 

Caldy  Road,  Bristol  Channel 

Calabar  River,  Africa,  West  Coast 

Calabar  River,  Old,  .\frica.  West  Coast  , 

Caledonia  Harbor,  New  Granada 

Calf  Sound,  Isle  of  Man     

Calicut  Roads,  Hindoostan,  West  Coast 

Callao  Bay,  Peru , 

Calshot  (Castle  Point),  England 

Calstock,  River  Tamar,  England 

Camaguin,  Babuyan  Islands 

Camarinas,  Port,  Spain 


/i.  ni. 

2      O 

1  O 

2  30 

3  o 

II      o 

1 58 

Noon. 


10  55 

3  30? 

5  45 

4  o 

6  o 
Noon. 

3  43 

10  10 

0  30 

7  22 

5  38 

1  45 
Noon. 

7  54 
5  40 

5  24 

845 

2  24 

11  50 

4  45 

6  o 
6  I 
o  30 

Noon. 

0  30 

1  21 

6  50 

9  45 


40 

45 
52 
23 


10  57 


5  44 

9  33 

6  10 

8    o? 
10  51 


I 
II 
II 

I 

2 

5 

4 

5 
II 
II 
12 

5 
II 

6 

6 

3 


o 

49 
o 

22 

30 
40 

5 
o 

40 

17 

15 

47 

30 
6 
o 
o 


Feet. 
10 

9X 
II 

II 

12 

9 

24 

6 

4.^ 

23 

13 

13 

3-5 

5 

14 
12K 

3K 
10^ 
18 

S% 
16 

12 

6K 


I 

10 

7 
16 

25^ 
6 


6 

12 


Cambay  (town),  Hindooostan,  West  Coast 


5  20 


12 

8 
7-10 

26 

I3X 

6 
I? 

SYa 
6 

I9>^ 

6 

15-20 

12-15 

24? 

6 

lb% 

4 

4 

13 

I2>^ 

6 

15 

Day,    23 
Night,  30 


Feet. 
8 


4X 

2>^? 
17 


VA 
II 

2 

VA 
H'A 


12^ 

8 


18K 


19K 

5 


16? 

5 
5 
I 

'3 

i% 

9K 
8j^ 


Page  478]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Cambing,  Banda  Sea 

Camden  Harbor,  Australia,  Northwest  Coast 

Cameleon  Harbor,  Nodales  Channel,  British  Columbia. 

Cameroon  River,  Africa,  West  Coast 

Campbell,  Cape,  New  Zealand 

Campbell  Island,  South  Pacific    

Campbell  Town,  Gulf  of  St.  Lawrence 

Campbellton,  Scotland .' 

Campeche.  Yucatan 

Campobello  ( Welchpool),  Bay  of  Fundy 

Cancale,  France 

Canna  Island,  Scotland,  West  Coast 

Canso  Gut  (north  entrance).  Nova  Scotia 

Canso  Gut  (Plaister  Cove),  Nova  Scotia 

Canso  Harbor,  Cape  Breton  Island 

Cantin,  Cape,  Africa 

Canton  River  (entrance),  China 

Canton  River,  Kuper  Island,  in  March 

Canton  River,  Kuper  Island,  in  May  and  June 

Cape  Coast  Castle,  Africa,  West  Coast 

Car  Nicobar,  Nicobar  Island 

Caracas  River,  Ecuador 

Caraquette  Harbor,  Gulf  of  St.  Lawrence 

Carbonear,  Newfoundland 

Cardiff  (Penarth),  Wales 

Cardigan,  Wales 

Cardigan  Bay,  Prince  Edward  Island 

Careening  Bay,  Australia,  Northwest  Coast 

Carelmapu,  Patagonia,  West  Coast 

Cargados,  Carajos  Shoals,  Indian  Ocean 

Cargreen,  River  Tamar,  England 

Caribou  Harbor,  Nova  Scotia 

Carlandagan  Islands,  Bird  Island,  Palawan,  East  Coast. 

Carleton  Point,  Gulf  of  St.  Lawrence 

Carlingford  Bar,  or  Cranfield  Point,  Ireland 

Carlisle  Port,  England 

Carlos,  San,  Port,  Patagonia,  West  Coast 

Carlos,  San,  Arenas  Point,  Patagonia,  West  Coast 

Carlos,  San,  English  Bank,  Patagonia,  West  Coast 

Carlos,  San,  Port,  Falkland  Islands 

Carenage,  Trinidad,  Caribbee  Islands 

Carnot  Bay,  Australia,  West  Coast 

Carouge  River,  River  St.  Lawrence 

Carrigaholt,  Ireland 

Carsaig,  Scotland 

Cartagena,  New  Granada 

Carteret,  France 

Carteret,  Port,  New  Ireland 

Carwar,  or  Sedashigar  Bay,  Hindoostan,  West  Coast... 

Cascumpeque  Harbor,  Prince  Edward  Island 

Cashla  Bay,  Ireland 

Casquets,  English  Channel 

Castillos,  Cape,  Rio  de  la  Plata 

Castlereagh,  Cape,  Tierra  del  Fuego 

Castletown,  Bearhaven,  Ireland 

Castletown,  Isle  of  Man 

Castletownsend,  Ireland 

Castors  Harbor,  Newfoundland 

Castri  Bay,  Gulf  of  Tartary , 

Castro,  Patagonia,  West  Coast 

Casuarina  Point,  China  Sea,  East  Coast 

Catalina  Harbor.  Newfoundland 

Catharina,  Santa,  Island,  Brazil 

Catharine,  St.,  Point,  Magellan  Strait 

Catlin  River,  New  Zealand 

Cato  Bank,  Australia,  East  Coast 

Catoche  Cape,  Yucatan 


h.  in. 
Noon. 
II  30 


o 

15 

o 


5 
6 

Noon. 

4    o 


II 

I 

II 

6 
6 
9 
9 
7 

10 

10 

2 

I 

4 

ID 


II 
O 
2 

5 
10 

9 

3 
II 

o 

II 

o 
o 

7 
4 
o 

7 
4 
5 
II 
6 


45 

45 

21 

20 

19 
15 

10 

48 

o 
o 

40 
40 
30 

o 

30 
40 

20 

56 

I 

40 

45 

50 

o 

47 
o 

30 
o 

o 
10 

15 
14 

4 

o 

20 

30 
15 

44 

28 

o 

25 


10    o 

5 
4 
6 
8 
2 

4 
II 

4 
10 

ID 
O 

9 
7 
2 
8 
2 


40 

45 
30 
50 

14 
10 

21 

50 
30 
II 

30 
O 

45 
5 

30 
o 

30 


Feet. 
6 

30 
16 


7 
8 

VA 
10 

^% 

23K 

37 
14 

4 

4K 

6^ 
10 

8 

5K 
5^ 
6 

5 

10 
6 

4X 
37X 
12 

5 

30 
10 

4 

14^ 
6 
6 
6 

14 
20 

6 

6 


4 

13-H 

16 

14 
10 

^% 

31 

6 

(>% 

3 
16 

2 

4 

9^ 
20 
1034: 

5? 

18 
634: 
6 
6 

30 

8 

-      6 


Feet. 


5 
6 


7 

6 

2 
20 
27 

9Yz 
2 

3 
4^ 


3 

3 

29 

9 


4 

4 
II 

14 


II 

\0Y7. 


5 

2 

12 


V/z 

16 

8 


4 

AYz 


TABLE  47.  [Page  479 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Cattawade  Bridge,  Stour  River,  England 

Cavalli  Islands,  New  Zealand 

Cavern  Island,  China  Sea,  East  Coast 

Cawee  Islands,  Gulf  of  St.  Lawrence 

Cayenne,  Guayana 

Cayeux,  France  

Ceara,  Brazil 

Cedeira,  Spain,  North  Coast 

Centre  Island,  Foveaux  Strait,  New  Zealand , 

Ceram,  Wahaay  Harbor,  Moluccas 

Cerros  Island,  California 

Ceuta,  Africa,  North  Coast 

Chacao  Bay,  Patagonia,  West  Coast 

Chacao  Narrows,  Patagonia,  West  Coast 

Chalky  Inlet,  New  Zealand , 

Chalmers,  Port,  America,  Northwest  Coast 

Cham^  Bay,  New  Granada 

Chamisso  Island,  America,  Northwest  Coast 

Champion  Bay,  Australia,  West  Coast 

Champlain,  River  St.  Lawrence 

Changchi  Island,  China,  East  Coast 

( "hange  Island,  Newfoundland 

Changues  Islands,  Patagonia,  West  Coast 

Chapu  Road,  Hang-chu  Bay,  China,  East  Coast , 

C  "harles  Island,  Galapagos  Islands 

Charles  Island,  Labrador , 

Charlowka  River,  Lapland 

Chateau  Bay,  Labrador    

Chatham,  England 

Chatham  Island,  Galapagos  Islands 

Chatham  Island,  Port  Hutt,  South  Pacific 

Chatham,  Port,  America,  Northwest  Coast 

Chauan  Bay,  China,  East  Coast 

Chausee  de  Sein,  France 

Chausey,  Isles  de,  France 

Cheduba,  Bay  of  Bengal , 

Chee-fow  Harbor,   Yellow  Sea.     {See  Chifu.) 

Chentabun  River,  China  Sea,  West  Coast 

Chepo  River,  New  Granada 

Chepstow,  England 

Cherbaniani  Reef,  Laccadives,  Indian  Ocean 

Cherbourg,  France , 

Chesilton,  England 

Chester  ( Crane  Wharf),  England 

Chesterfield  Islet,  Australia,  East  Coast 

Chetican,  Cape  Breton  Island 

Chichester,  England 

Chifu,  Yellow  Sea 

Chimmo  Bay,  China,  East  Coast 

Chimney  Island,  Rees  Pass,  China,  East  Coast 

Chinchu  Harbor,  China,  East  Coast 

Chin-hae,  Yung  River,  China,  East  Coast 

Ching-tau  Bay,  Yellow  Sea 

Chino  Bay,  China  Sea 

Chittagong  (Bar),  Bay  of  Bengal,  East  Coast 

Chodo  Island,  Korea,  West  Coast 

Choiseul,  Port,  Madagascar,  East  Coast 

Chosan  Harbor,  or  Tsau-liang-hai,  Japan  Sea 

Christchurch,  England 

Christianstsed,  Santa  Cruz .. 

Christmas  Island,  Indian  Ocean 

Christmas  Harbor,  Kerguelen  Island 

Chuen-pee  Point,  Canton  River 

Churruca,  Port,  Strait  of  Magellan 

Chusan  Archipelago  (Vernon  Channel),  China,  East  Coast 
Chusan  Tinghse,  China,  East  Coast 


High  Water,  Full 
and  Change. 


//.    II! . 


I 

8 

9 
I 

4 
II 

5 

3 

o  15 
6    o 


8 

o 

30 
50 
51 

5 

35 
o 


9 
2 
o 

o  50 
"     5 


10 

6 

40 


o 
o 

42 

ID 

45 

30 

20 


o  35 

Noon. 

2   10 

7  ^o 


7  35 

I 

II 

2 

6 

23 

50 

I 

0 

II 

0 

3 
6 

21 

9 

II 

30 

ID 

0 

3  40 

7  30 

10 

0 

7  49 
6  13 
0  16 

8 
8 

30 
15 

II 

30 

10 

34 

10 

20 

II 

30 

0 

25 

II 

20 

6 

0 

7 

0 

0 
6 

45 
20 

4 

0 

7  45 

9 

0 

II 

30 

7  30 

10 

0 

2 

0 

2 

0 

I 

0 

9  40 

II 

0 

Rise. 


Springs. 


Feet. 
4,¥ 
7 

5^ 
9 
7 
27K 


Neaps. 


Feet. 

5 
21 


3 

7-9 

Z% 

'A 

14 

16 

8 

4 

13X 

16 

I 

3 

2 

17 

4>^ 

3 

25 

6 

6-7 

12 

3K 

I 

18 

^A'A 

6^3 

6 

12 

6>4 

^iVz 

12 

35 

26 

« 

5K 

16 

38 

28  j^ 

7 

4 

17 

12^4 

lOX 

7 

10 

5 

3^ 

14 

II 

8 

6^ 

16 

12 

17 

12K 

12 

9 

6-7 

15 

ID 

12 

5 

7 

5 

5 

% 

2 

lU 

6 

14 

12 


Page  480]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place, 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Circular  Head,  Tasmania 

Clam  Point,  Bay  of  Fundy 

Clara,  Santa,  Island,  Ecuador 

Clare  Island,  Ireland 

Clarence,  Port,  America,  Northwest  Coast   

Clarence  Harbor,  Long  Island,  Bahamas 

Clarence  River,  South  Head' Australia,  East  Coast 

Clarke  Harbor,  Bay  of  Fundy 

Clayoquot  Sound,  Vancouver  Island 

Clear,  Cape,  Ireland  .    

Clearwfater  Point,  Gulf  of  St.  Lawrence 

Cleveland  Bay,  Australia,  East  Coast 

Cley,  England,  Northeast  Coast 

Clifden  Bay,  Ireland,  West  Coast 

Clonakilty  Bay,  Ireland 

Coacoacho  Bay,  Gulf  of  St.  Lawrence 

Cobija  Bay,  Bolivia 

Cocagne  River,  Gulf  of  St.  Lawrence 

Cochin  Harbor  and  Road,  Hindoostan,  West  Coast 

Cockburn  Island,  Antarctic  Ocean 

Cockburn,  Port,  Africa,  East  Coast 

Cockburn,  Australia,  North  Coast 

Cockburn  Sound,  Australia,  West  Coast 

Cockenzie,  Firth  of  Forth,  Scotland 

Codroy  Island,  Newfoundland 

Coghlan  Anchorage,  America,  Northwest  Coast 

Colarado,  River  La  Plata 

Colarados,  River  La  Plata 

Coleraine,  Ireland 

Collier  Bay,  Australia,  Northwest  Coast 

Colne  Point,  Colne  River,  England 

Colombilla  Cay,  Pearl  Cays,  Caribbean  Sea 

Colombo,  Ceylon 

Colonsay  ( Schallasaig),  Scotland,  West  Coast 

Comau  Inlet,  Patagonia,  West  Coast 

Comboyuro  Point,  Australia,  East  Coast 

Componce  River,  Africa,  West  Coast 

Conani  River,  Brazil 

Concarneau,  France 

Condore,  Cochin  China 

Congo  River,  Africa,  West  Coast 

Congoon  Bay,  Persian  Gulf 

Conil,  Spain 

Conquet  Road,  France  

Constitucion  Cove,  Bolivia 

Conway,  Cape,  Australia,  East  Coast 

Cook  Harbor,  Newfoundland 

Coondee.     {See  Kiidi.) 

Cooper,  Port,  New  Zealand 

Copiapo,  Chile 

Cequet  Road,  England,  East  Coast 

Coquimbo  Bay,  Chile 

Cordouan  Light-house,  France 

Corentyn  River,  Guayana   

Coringa,  or  Cocanada  Bay,  Bay  of  Bengal,  West  Coast. 

Coringa  River  (Bar),  Bay  of  Bengal,  West  Coast 

Corisco  Bay  (Elobey  Isles),  Africa,  West  Coast 

Cork  (Penrose  Quay),  Ireland 

Corn  Islands,  Bay  of  Honduras 

Corner  Inlet,  South  Australia 

Cornwall,  Cape,  England 

Corny  Point,  Australia,  South  Coast 

Corpach  ( Loch  Aber),  Scotland     

Corran  (Loch  Linnhe),  Scotland 

Corunna,  Spain 

Coudres  Island  (Prairie  Bay),  River  St.  Lawrence 

Courseulles,  France 


k.  III. 

II  40 

8  27 

4    o 

438 

4  25 

8  30 

8  30 

8  40 

Noon. 

4     o 

II  30 

7  30 


4  30 
10  30 

4  30 


54 
30? 

30 
50 
15 
45 
o 
16 


9  15 

o  30 

4     o 

3  40 
6  24 

II  45 

Noon. 

2     o 


I 

5 
I 

9 

10 

6 

3 
3 

4 


o 
18 
10 

30 
o 

38 

12 

O 

30 


7  45 


18 

46 

o 

o 

25 

50 

30 
o  ■ 

8 

37 
10 
10 
o 
o 
58 

1  45 
o  14 

4  35 

2  45 

5  59 


I 

3 
10 

II 

7 

3 
8 

3 
9 
3 
5 
9 
9 
5 
4 


43 
o 

25 
7 


Feet. 
9 

II 


4 

4 

9X 
12 

9 

5 
10-12 

5>^ 

13X 
II 

5 
4 


6 
12 

24 

6 
18 

9 
II 

36 

14 

2 

2 
II 

17 

4-7 

IS 

19 

13 
4 
6 

9>^ 
12 
21 

4 
18 


7K 
5 
i4>^  II 


5 

4-5 

5 
7 

2 

8 
18? 

4 

iiK 
12 

IS 
17 

20 


Fee/. 
6/2 


9)i 


3% 


3 


10 


!>2^ 


2? 
2 


4 
14 

l)i 

4 
10 


^3H 


9'A 


7'i 
15 


i<r 


loX 
6 


10 


13? 


10 


TABLE  47.  [Page  481 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Courtmacsherry,  Ireland 

Coverack,  P^ngland 

Cow  Head  Harbor,  Newfoundland. 

Cowes  (West),  England 


Coy  Inlet,  Patagonia,  East  Coast 

Coyhuin  River,  Chile . 

Cozumel,  Bay  of  Honduras  . 

Crane  Island,  River  St.  Lawrence 

Cranford  Bay,  Mulroy  Bay,  Ireland 

Crapaud,  Prince  Edward  Island 

Cr^maill^re  Harbor,  Newfoundland 

Crichton  Harbor,  Korea,  South  Coast 

Crimon  Islands,  Java  Sea 

Crinan,  Scotland 

Croc  Harbor,  Newfoundland 

Croisilles  Harbor,  New  Zealand 

Cromarty,  Scotland 

Cromer,  England 

Crow  Harbor,  Nova  Scotia 

Crowdy  Head,  Australia,  East  Coast 

Crooked  Island,  Bahamas 

Crookhaven,  Ireland 

Cucao  Bay,  Patagonia,  West  Coast 

Cuckolds  Point,  River  Thames,  England 

Culdaff  Bay,  Ireland,  West  Coast 

Culebra,  or  Passage  Island,  Caribbean  Sea 

Culiacan  River,  Mexico,  West  Coast 

Culleh  Harbor,  Fife  So'und,  British  Columbia 

Cumberland  Basin  (Sackville),  Bay  of  Fundy  . 

Cumsingmun  Harbor,  Canton  River,  China 

Cupchi  Point,  China,  East  Coast. 

Cupica  Bay,  New  Granada 

Curieuse,  Seychelles,  Indian  Ocean 

Curtis,  Port,  Australia,  East  Coast. 

Cutwell  Harbor,  Newfoundland 

Cuxhaven,  Germany  . 

Cypress  Harbor,  Sharp  Passage,  British  Columbia. 


Daggs  Sound,  New  Zealand 

Dahouet,  France . 

Dalawan  Bay,  China  Sea,  East  Coast 

Dalcahue,  Patagonia,  West  Coast 

Dalhousie  Harbor,  Gulf  of  St.  Lawrence 

Dalkey  Island,  Ireland 

Dalrymple  Bay,  Madagascar,  West  Coast 

I  )alrymple,  Port,  Tasmania 

Dampier  Strait,  Moluccas. 

Danes  Island,  Spitzbergen 

I^anger  Point,  Australia,  East  Coast  . 

1  )arnley  Island,  Torres  Strait 

Darra  Salaam,  Africa,  South  Coast 

Dartmouth,  England 

Darwin  Harbor,  Choiseul  Sound,  Falkland  Islands 

Darwin,  Port,  Australia,  North  Coast 


I  )auphi!i,  Fort,  Madagascar 

Davy  Point,  Bay  of  Bengal 

De  Roompot,  Onrust,  North  Sea 

I  )eal,  England 

Dealy  Island,  Melville  Island 

Deep  Harbor,  Fife  Sound,  British  Columbia ., 

Deep  Point,  Durian  Strait 

Deer  Harljor,  Newfoundland 

Deer  Sound,  Orkneys 

Delagoa  Bay  (Port  Xlelville),  .\frica.  South  Coast 

Delagoa  Bay  (Portuguese  Factory),  .Vfrica,  South  Coast 


h,  m. 
4  36 

4  35 
10  41 

10  45 

11  45 
9  30 
o  5« 
8  30 

5  24 

8    3 
o 


50 

o 

49 

30 

o 

56 
o 
o 

15 

o 


10 

7 
9 
8 

4 
6 

9 
II 

7 
8 

9 
7 

4  9 
Noon. 

I  45 

5  53 
9    o 

11  30 

12  o 

II  55 

0  6 

8  o 

3  30 
5  10 

9  40 
7    o? 

1  8 
Noon. 

II     -JO 

65 

II      o 

o  26 
3  10 
10  45 
5  o 
o    5 


24 

30 

30 
o 

16 
30 


5  25 

4  30 

8  15 
I     o 

II   15 

I  48 
Noon. 

5 

7  49 
10  30 

4  30 

5  20 


o 


Feet. 
8X 


40 
21 

i;^ 
17 
4 
8 

4K 
6 

6K 

12 

14 


-A 

5 


6 
19? 

8^ 
I 

6? 
16 

45  X 
6^ 

13 

7 

10-12 

2-4? 
10 
16 

8 

32 
5 

9 
13 
15 

10 

II 

■  i% 
6 
12 
12 

W4 

16-24    < 

7 

6 

15 
16 

4 
16 
10 

3^ 
10 

15 
12 


Feet. 

11% 

9Yz 


13 

6 

2% 


5 
5 

8 
II 
II 

4K 
3 

8 

15? 
6 


38 


6 

23K 


II 


AVz 


2—12 

Irreg. 


ir 

I2>^ 
2 


31     B 


Page  482]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Fed. 


Delagoa  Bay,  Shefeen  Island,  Africa,  South  Coast 

Delfzijl,  Germany 

Delgado,  Cape,  Africa,  East  Coast 

Demerara  River,  Guayana 

Denham  Sound,  Shark  Bay,  Australia,  Northwest  Coast. 

Denial  Bay,  Australia,  Soutii  Coast 

Denison,  Port,  Australia,  Ea5t  Coast 

Deoghur  Harbor  (entrance),  Hindoostan,  West  Coast... 

Depuch  Isle,  Australia,  West  Coast 

Desire,  Port,  Patagonia,  East  Coast 

Devarenne  Strait,  New  Caledonia 

Devonport  Dockyard,  England 

Dhardur  River  (entrance),  Hindoostan,  West  Coast 

Dheli  River,  Sumatra 

Diamond  Island,  Bay  of  Bengal 

Diamond  Point,  Malacca  Strait 

Diego,  San,  Cape,  Tierra  del  Fuego 

Diego  Garcia  Island,  Indian  Ocean 

Diego  Ramirez  Islands,  Tierra  del  Fuego 

Dielette,  France 

Dieppe,  France 

Digby  Gut,  Bay  of  Fundy 

Dilhi,  or  Dielli,  Timor 

Dillon  Bay,  Erromango  Island,  New  Hebrides 

Dingle,  Ireland 

Direction  Hill,  Magellan  Strait 

Discovery,  Port,  America,  Northwest  Coast 

Dislocation  Harbor,  Tierra  del  Fuego 

Diu  Harbor,  Hindoostan,  West  Coast 

Dives,  France ... 

Divy  Point,  Bay  of  Bengal 

Dodandowe  Bay,  Ceylon , 

Dodo  River,  Bight  of  Benin 

Domingo,  San,  Port,  Patagonia,  West  Coast 

Domino  Run,  Labrador 

Donaghadee,  Ireland 

Donegal  Harbor,  Ireland 

Doris  Cove,  Tierra  del  Fuego 

Dornock  Road,  Scotland 

Douany,  Comoro  Islands 

Douglas,  Isle  of  Man , 

Douglas  Road,  Bahamas 

Dover,  England 

Downham  Reach,  Orwell,  l^ngland 

Drayton  Harbor,  St.  J  uan  de  Fuca  Strait 

Drogheda  (Bar),  Ireland 

Duart,  Isle  of  Mull 

Dubba  River,  Hindoostan,  West  Coast 

Dublin  ( Bar),  Ireland 

Duck  Cove,  New  Zealand 

Dumbarton,  Scotland 

Dumrah  River  (Bay  of  Bengal) 

Dunbar,  Scotland 

Dunbeacon,  Ireland , 

Duncansby  Ness,  Scotland 

Dundalk,  Ireland , 

Dundee,  Scotland 

Dungeness,  England 

Dungeness,  Magellan  Strait 

Dunk  Island,  Australia,  East  Coast 

Dunkerque,  France 

Dunkerron,  Ken  mare  River,  Ireland 

Dunmanus  Harbor,  Ireland „ , 

Dunmore,  Ireland 

Durnford,  Port,  Africa,  East  Coast 

Dusky  Bay,  New  Zealand 

1 ) vina  ( Bar),  White  Sea 


h. 

4 
II 

4 
4 
o 
o 

9 
II 


m. 
40 

30 

o 

20 

5 

15 
30 

o 


10  40 
o  10 


5  43 
4  30 

3  o 
10  30 

Noon. 

4  30 


I 

4 

6 

II 

II 

I 

5 

3 
8 

2 

I 

II 

9 


30 
o 

40 

6 

o 

o 

30 
51 

53 

30 

40 

o 

39 


1  50 

4  17 
Noon. 

6  40 

II  13 

5  18 

3  o 
II  47 

4  o 
II 

8 

II  12 

o  27 

2  o 


12 

30 


II       o 

5    o 

10  10 

11  12 
10  50 

o  20 

845 

2  8 

3  51 
10  14 
10  56 

2  32 

10  45 

8  30 

9  28 

"  55 


3  45 

3  57 
5  27 

4  45 
II   15 


Feet, 
12 
8>^ 
16 

9 

I 

6 

9 
14 
18K 

1% 

27 

8 
8 

9>^ 
10 

6 
6 

27 
27 

27K 
6 

4 

10^ 

38 
7 
4 
6 

21 

5 
7 

7 

iX 
iK 
4 
I 
2 
20^ 

4 

8X 
2 
2 

4 
2 


II- 


12- 


6-' 


9 
o 

AVz 
0% 

2,% 

;i^ 

36 
o 

9yz 

2% 
2 

o 


4 


7 
10 


20-22 


20^ 
20>^ 

23 


73/ 
23 


aVz 
16 


4 

9 
8X 


16 


15 


II 

10 


9-1 1 


II 

ii'A 
ii'A 
19 


13K 

8 
7X 


TABLE  47.  [Page  483 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &C.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Dyer  Island,  Africa,  South  Coast 


Easdale  Sound,  Scotland 

Easter  Island,  South  Pacific  _,. 

East  Cape,  New  Zealand 

East  Point,  Prince  Edward  Island 

East  Alligator  River,  Australia,  North  Coast 

East  London,  Africa,  South  Coast 

Eclipse  Harbor,  Labrador 

Ecrehos,  France 

Eddystone  Point,  Australia,  East  Coast 

Eden  Harbor,  Patagonia,  West  Coast 

Edgar,  Port,  Falkland  Islands 

Edge  Passage,  America,  Northwest  Coast 

Edina,  Africa,  West  Coast 

Edmonstone  Island,  Sherbro  River,  Africa 

Kgg  Island,  Gulf  of  St.  Lawrence 

Egniont  Bay,  Prince  Edward  Island 

Egmont,  Port,  Falkland  Islands 

Eider  River  (entrance),  North  Sea. 

Eider  River,  Tonning 

Fides  Fiord,  Freroe  Islands 

l"-igg  Island,  Scotland 

Elbe  (entrance),  Germany , 

Elbe,  Outer  light-vessel,  No.  i 

Elena,  Santa,  Port,  Patagonia,  East  Coast 

Elena  Bay,  Ecuador 

Elizabeth  Bay,  Africa,  Southwest  Coast 

Ellen,  Port,  Islay 

Ellen  woods  Anchorage,  Bay  of  Fundy 

Elliot,  Port,  Australia,  South  Coast 

Emden,  Germany 

Ems  River  (outer  buoy),  Germany 

I^ncounter  Rock,  Yellow  Sea 

Endeavor  River,  Australia,  North  Coast 

Endeavor  Strait,  Australia,  North  Coast 

Endermo  Harbor,  Japan 

English  Bank,  San  Carlos,  Patagonia,  West  Coast 

English  Harbor,  Antigua 

English  River,  Delagoa  Bay,  Africa,  South  Coast. 

Enora  Bay,  Japan 

Fran  Bay  (Palawan),  China  Sea,  East  Coast 

Erebus  Bay,  Barrow  Strait 

Erme  River,  Bigbury  Bay,  England 

Erqui,  France 

Erronan,  or  Futuna,  New  Hebrides 

Escumenac  Point,  Gulf  of  St.  Lawrence 

Esperanza  Inlet,  Vancouver  Island 

Espirito  Bay,  Brazil 

Espiritu,  Santo,  Cape,  Magellan  Strait 

Esquimau,  St.  Juan  de  Fuca  Strait 

Essington,  Port,  Australia,  North  Coast 

Estevan,  San,  Port,  Patagonia,  West  Coast 

Etches,  Port,  America,  Northwest  Coast 

Evangelists,  Patagonia,  West  Coast 

Exmouth,  England . 

Expedition  Bay,  Korea 

Exuma,  Bahamas 

Eyemouth,  Scotland 

Eyre,  Port,  Australia,  South  Coast 


Fair  I  sle,  Shetlands 

Fairy,  Tort,  Australia,  South  Coast 

Falkland  Sound  (North  Entrance),  Falkland  Islands 
Falkland  Sound  (South  Entrance),  Falkland  Islands 

Fall  Harbor,  Labrador 

Falmouth,  England 


h.  m. 

2  50 

5  10 
o  39 
855 
8  3Q 
8  15 

3  45 


32 

39 


o  15 


15 
30 

50 


2  o 

3  o 

7  30 
Noon. 

I  55 

II      o 

6  15 
Noon. 

0  15 

4  o 

1  18 


5    o 
9  54 


0  34 
10  o 
10  44 

8     o 

1  o 

4  35 
o    4 


7  30 


10 
o 

5 
5 
7 
4 


ID 

6 

40 

59 
24 
10 


Noon. 

3    o 

8  30 

Irregular. 

3  24 


15 

15 
o 

21 

30 

20 

2  15 
10  30 


o 
I 
I 
6 

2 
7 


II      o 

o  31 


45 
o 

40 

57 


Feet. 
5 

10-12 


7 
15 


31 

7 
6 

6 

17-22 
4 


II 

4 
II 

10 

9'A 
14 
II 

9/2 
17 
8 

5-6 
5 

13 
5-6 

9 

8-10 

II 

5-10 

9% 
5 

2 

5 

4 

6% 

8 

16X 
■  1/ 


74 

4 

4 

12 

4 
36-42 

7-10 
13 

5 
9% 

5 
12X 

15? 
6 

5 
3 


16 


Feet. 


22%, 


14-17 

8 
6 
2 


7K 

ID 


11/2 
24>^ 


5-8 

8K 
II? 


12 


Page  484]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


False  Point,  Bay  of  Bengal,  West  Coast 

Famine,  Port,  Magellan  Strait 

Fanning's  Island,  South  Pacific 

Fanny  Hole,  Mulroy  Bay,  Ireland 

Fansiak  Channel,  Canton  River,  China,  East  Coast 

Fareham  (close  to  the  Upper  Quay),  England 

Fareham  Bridge,  England 

Farewell  Cape,  New  Zealand 

Fatsizio,  Japan 

Fayal,  Azores,  Atlantic  Ocean 

Fecamp,  France  . 

Fen^rine,  Madagascar 

Fenit,  Tralee  Bay,  Ireland 

Feolin  Ferry,  Jura .. 

Fernando,  Noronha  Island,  South  Atlantic 

Fernando  Po,  Bight  of  Biafra 

Ferolle  Cove,  New,  Newfoundland 

Ferolle  Harbor,  Old,  Newfoundland 

Ferribly  Sluice,  River  Humber 

Ferro,  Canary  Islands .. 

Ferrol,  Spain 

Ferry  Side,  South  Wales 

Filey  Bay,  England 

Finisterre,  Cape,  Spain 

Fish  Head,  Gulf  of  Manan,  Bay  of  Fundy 

Fishguard,  Wales 

Fitz-Roy  Island,  Australia,  East  Coast 

Fitzroy  Port,  Falkland  Islands 

Flamand  Bay,  St.  Domingo  . 

Flamborough  I  lead,  England 

Flamenco,  Port,  Chile 

Flatholm  Islands,  Bristol  Channel 

Fleetwood,  Port,  England 

Fleetwood,  Wyre  Light 

Flesh  Bay,  or  Bay  St.  Bras,  Africa,  South  Coast 

Fleur  de  Lis  Harbor,  Newfoundland 

Flinders  Group,  Australia,  East  Coast 

Flushing,  Belgium 

Fog  Islands,  Hang-chu  Bay,  China,  East  Coast 

Fogo  Island,  Newfoundland 

Folkestone,  England 

Folly  Point,  Petitcoudiac  River,  Bay  of  Fundy 

Fongwhang  Group  (Bullock  Harbor),  China,  West  Coast 

For9ados  River,  Bight  of  Benin 

Fore  Carreah  River,  Africa,  West  Coast 

Formby  Point,  England 

Formoza,  Mt.,  Malacca  Strait 

Fort  Dauphin,  St.  Domingo 

Fortune  Bay,  Patagonia,  West  Coast 

Forward  Harbor,  British  Columbia ,  .. 

Foulness,  Crouch  River,  England 

Fowey,  England 

Fowler's  Bay,  Australia,  South  Coast 

Fox  Bay,  Falkland  Islands 

Foyle  Lough  (Warrenpoint),  Ireland 

Foynes  Island,  Ireland 

France,  Port  de,  or  Noumea  Bay,  New  Caledonia 

Francis,  St.,  Bay,  Tierra  del  Fuego 

Francis,  St. ,  Cape,  Africa,  South  Coast 

Eraser  River  (entrance),  British  Columbia 

Fraserburg,  Scotland .. 

Frechette  Island,  River  St.  Lawrence 

Frederick  Reef,  Australia,  East  Coast 

Frederickshaab,  Greenland 

Fredriken  Siel,  (iermany 

Freycinet  Estuary 

Freycinet  Reach,  Shark  Bay,  AustraHa,  Northwest  Coast  . 


High  Water,  Full 
and  Change. 


//.  m. 

8  15 

Noon. 


6 

I 

II 

II 


17 
o 

48 

51 

20 

o 

II  45 
10  44 


9 
6 


3 

41 

o 

o 


5 
4 

3 

II 

6 


I 


10  50 
9  28 
6  41 
o  30? 

3  o 
49 
20 

o 
16 
56 
9  15 

4  45 
rregular. 

4  30 
10 

54 
12 
II 

30? 

15 

15 


9 

6 

II 

II 

3 

7 
9 


o  54 
II  45 


7 
II 
II 

8 

4 
7 


20 

7 
49 
30 
22 
40 


10  35 

o 


o 


8 

7 
o  50 

3  o 
o  5 
14 


5 
10  30 


o 
20 

35 


8  25 
4    o 


I 


34 

30 
o  40 

8    o 


8 
6 
II 
4 
3 


o 

3 

15 

15 
o 


Rise. 


Springs. 


Feet. 
8 
6 
4 


:^ 
V/a 
\x)i 

1% 
14 

5 

4 
23K 

12;^ 
6^ 
6? 

7 

5? 
4K-6>^ 
20-4: 

9? 
15 
23 
16 


II>^ 

7-12 
6 
2-3? 
16 

5 
37? 
26X 

27J^ 

6? 

2-4 
8-12 

15 

17 

4 

20 

45 
17 

5 
II 
28 
II 

S% 

7 
16 

wA 
15 

6 
6 
6^ 

15,'^ 
4 

5 

7-10 

II 

14 
6 

12^ 

4 

3X 


Neaps. 


Feet. 


8 

5 

8K 
4^ 
10 


18 
9X 


16^ 
12;^ 

18^ 


12 

28? 

20>^ 


I       II 


16;^ 
38 


8K 

yA 

113/ 


5 
12 


9 


TABLE  47.  [Page  485 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps 


Frio,  Porto,  Brazil 

Fugloe  Fiord,  Faroe  Islands 

Funchal  Bay,  Madeira 

Funk  Island,  Newfoundland 

Fury  Cove,  Patagonia,  West  Coast 

Fury  Harbor,  Tierra  del  Fuego 

Fury  Island,  Tierra  del  Fuego 

Fury  and  Hecla  Strait,  Arctic  Regions. 


Gaalong  Bay,  Hainan  Island,  China  Sea 

Gabo  Island,  Australia,  South  Coast 

Gaboon  River,  Africa,  West  Coast 

Gallant,  Port,  Magellan  Strait 

Galle,  Pointe  de,  Ceylon,  South  Coast 

Gallegos,  Port,  Patagonia,  East  Coast 

Gallinas  River,  Africa,  West  Coast 

Galloway,  Mull  of 

Galway,  Ireland 

Gambia  River,  Africa,  West  Coast 

Gambier  Islands,  Australia,  South  Coast 

Ciambier  Islands,  South  Pacific , 

Garliestown,  Scotland,  West  Coast 

Garroch  Head 

Gaspe  Basin,  Gulf  of  St.  Lawrence 

Geby,  Fohou  Island,  Gilolo  Passage,  Moluccas 

Geelong  Harbor,  Australia,  South  Coast 

George,  Cape,  Nova  Scotia 

George  d'Elmina,  St.,  Africa,  West  Coast 

George,  Port,  Bay  of  Fundy 

George,  St.,  Basin,  Australia,  Northwest  Coast 

George,  St.,  Harbor,  Newfoundland 

George's  Bay,  Tasmania 

George's,  St.,  Sound,  Gulf  of  Mexico,  Middle  Entrance. 

George's,  St.,  Sound,  Gulf  of  Mexico,  West  Entrance 

Geriah,  or  Viziadroog,  Hindoostan,  West  Coast 

Germain,  St. ,  France 

Ghubbet,  Ghazirah .. 

Ghubbet,  Ne,  Sokotra,  Indian  Ocean , 

Ghubbet,  Gollonsir,  Sokotra,  Indian  Ocean 

Ghubbet,  Hashish,  Arabia,  Southeast  Coast 

Gibraltar  (new  Mole),  Spain 

Gigha  Sound,  Scotland 

Gijon  Bay,  Spain,  North  Coast 

Gilmorris  Island,  Africa,  West  Coast 

Gipp's  Land  Lakes  (entrance  to),  Australia,  South  Coast 

Gizri  River,  Hindoostan,  West  Coast 

Glasgow,  Scotland 

Glasgow,  Port,  Scotland 

Glenan  lies,  France 

Glennie  Isles,  Australia,  South  Coast 

Gloucester,  England 

Gloucester,  Cape,  Tierra  del  Fuego 

Gluckstadt,  Germany 

Goa  Bay,  Hindoostan,  West  Coast 

Goapnath  Point,  Hindoostan,  West  Coast 

Goeree  Gat,  North  .Sea 

Gogah,  Hindoostan,  West  Coast 

Gold  Stream  Harbor,  America,  Northwest  Coast 

Golovnin  Bay,  America,  Northwest  Coast 

Gomera,  Canary  Islands 

Gometra,  Loch  Tuadh,  Isle  of  Mull 

Gonai ves  Bay,  St.  Domingo 

Good  Bay,  Newfoundland 

Goods  Bay,  Patagonia,  West  Coast 

Good  News,  British  America,  Northwest  Coast 

Good  Success  Bay,  Tierra  del  Fuego 

Goodbout  River,  Gulf  of  St.  Lawrence 


2  40 
II   15 

o  48 
7    o? 

I  15 

2    30 
2    30 

7     o 


5 
o 

2 

8 

6 

II 

4 
8 
2 
I 


SO 
30 

34 
o 

50 

45 

15 

35 
10 

o 
50 


1  49 

2  40 


2  30 

9  15 

4  30 
II   17 

0  20 

10  3 
9  42 

1  31 
Irregular. 

11  o 

6  20 

9  30 

7  o(irr.) 

7  20 

10  o 

1  47 

2  22 

3  o 
6    o 

8  30 

9  45 
I  25 

0  18 
3  12 

11  44 

9  45? 

1  30 

3    9 

10  30 

2  25 

2  o 

3  50 
I  o 
6  23 
o  45? 

5  29 
8    o 

ID   40 

0  30 

6  15 

4  3 

1  52 


Feet. 

7 
2-3? 

4 
4 
8 

4-5 
6 

7 

8 

2 
46 

4 

15? 
14^ 
6-9 

5 

17 
10 

5 

5 

VA 

4 

6 

32 

24-37 
6U 

3 

^U 

2^-4 

9 

34 

10 

7 

8 
10 

4 

4 
14 
II 

3 
10 

9 

9 
13 

9 
4-7 

5 
n>^ 

7 
18 

7X 
27-30 

15 


9" 

11^ 

)Vz 
7 

13K 
6-8 

II 


FeeL 


12? 
II 


12 


2Vo 


28 

2 


7 
25 


2^ 
II 


7>^ 
10 


SA 

21 
12 


8 


Page  486]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full, 
and  Change. 


Rise. 


Springs. 


Goold  Island,  Australia,  East  Coast 

Goole,  River  Humber,  England 

Gooria  Creek  (entrance),  Hindoostan,  West  Coast 

Goose  Cove,  Newfoundland 

Gorda  Sound,  Virgin  Islands 

Gore,  Port,  New  Zealand 

Gor^e,  Africa,  West  Coast 

Goree  Road,  Tierra  del  Fuego 

Goulburn  Islands,  Australia,  North  Coast 

Goury,  France 

Gowlland  Harbor,  Discovery  Passage,  Vancouver  Island 

Gracia  Point,  Strait  of  Magellan 

Gracias,  Cape,  Harbor,  Bay  of  Honduras   

Grand  Cestos,  Africa,  West  Coast 

Grand  Harbor,  Grand  Manan,  Bay  of  Fundy 

Grand  Lahou,  Africa,  West  Coast 

Grand  Passage,  Bay  of  Fundy 

Grand,  Port,  Alauritius 

Grand  Rustico,  Prince  Edward  Island 

Grande-digue,  Madame  I.,  Cape  Breton  Island 

Grande  Point,  Chile 

Granton  Pier,  Scotland 

Granville,  France 

Gravelines,  France 

Graves,  Port,  Howe  Sound,  Gulf  of  Georgia,  British  Columbia 

Gravesend,  England 

Great  Barrier  Island  (Nagle  Cove),  New  Zealand 

Great  Barrier  Reef,  Australia,  East  Coast 

Great  Pish  Bay,  Africa,  West  Coast 

Great  St.  Lawrence  Harbor,  Newfoundland 

Great  Sandy  Strait,  Inskip  Point,  Australia,  East  Coast 

Greatman  Bay,  Ireland 

Green  Island,  River  St.  Lawrence 

Greencastle  Point,  Ireland 

Greenock,  Scotland 

Greenwich,  England 

Green's  Harbor,  Newfoundland 

Gregory  Bay,  Magellan  Strait 

Gregory,  Port,  Australia,  West  Coast 

Grenada  (St.  George  Harbor),  Caribbee  Islands 

Grenadines,  Caribbee  Islands 

Grey,  Port,  Swan  River,  Australia,  West  Coast 

Grey  River,  New  Zealand 

Greytown,  Mosquito  Coast 

Gribanika  Pt. ,  White  Sea 

Griffin  Bay,  Haro  Archipelago 

Griffith  Island,  Barrow  Strait 

Griguet  Bays,  Newfoundland 

Grimsby,  England 

Grindstone  Island,  Bay  of  Fundy 

Grisnez,  Cape,  France 

Grondine,  River  St.  Lawrence 

Gruinard  Island,  Scotland,  West  Coast 

Ciuadaloupe  ( Point  a  Pitre) 

Guayaguayare  Bay,  Trinidad 

Guambacho  Bay,  Peru 

Guardafui,  Cape,  Africa,  East  Coast 

Guarmey  Bay,  Peru 

Guatulco,  Mexico,  West  Coast 

Guayaquil,  Ecuador 

Guay mas,  Mexico,  West  Coast 

Guernsey  (St.  Peter  Port),  Enghsh  Channel .'...'... 

Guia  Narrows,  Patagonia,  West  Coast 

Guinchos  Kay,  Bahamas 

Guichen  Bay,  .Australia,  South  Coast 

(iun  Cay,  Bahamas 

C.undavi  River  (entrance),  Hindoostan,  West  Coast 


h. 

m. 

6 

45 

7 

26 

II 

0 

7 

0? 

8 

30 

9 

0 

7  45 

4 

0 

6 

0 

7 

6 

5 

30 

10 

17 

10 

30 

5 

20 

II 

7 

4 

20 

10 

43 

I 

0 

6 

40 

7  55 

9  45 

2 

20 

6 

13 

Noon. 

Noon. 

I 

10 

6 

25 

8 

48 

2 

30 

8 

30 

8 

30 

4  39 

2 

45 

II 

2 

0 

8 

I 

43 

6 

44 

9 

30 

II 

30 

2 

40 

3 

0 

9 

0 

10 

15 

9 

0 

4  50 

"regular 

0 

15 

7 

0.-" 

5 

36 

II 

47 

II 

27 

9 

0 

6 

37 

10 

0 

4  25 

6 

0 

6 

15 

6 

0 

I 

30 

7 

0 

8 

0 

6 

37 

2 

10 

7  40 

0 

37 

8 

30 

2 

0 

Feet. 
6 

13 

2-3? 

8 

22 
II 

8 
2 

4 
21 

4 
20X 
^Yz 
4 
b% 

5 
16 

37 

19 

12 

^lYz 

ID 

7 
5-6? 

7 
6 

i5>^ 
16 

14 

9I4: 

19 

3X 
21 

3 

i^ 

iK 

i-i^ 


3 
12 


2-3? 

19X 
41 

21K 

9 

14^ 

iX 

7 
2 
6 
2 

5 
II 

4 

26 

8 

3 

4 

3 

19 


TABLE  47.  [Page  487 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Gunfleet  Sand,  England 

Giitzlaff  Island,  China,  East  Coast. 

Guysborough,  Nova  Scotia 

Gweedore  (Bunbeg),  Ireland 


Haarlem,  Netherlands 

Habitable  Island,  Lapland 

Habitants  Harbor,  Cape  Breton  Island 

Hachken  River,  Japan 

Haimun  Bay,  China  Sea 

Haiti,  Cape,  St.  Domingo 

Haiyun-tau  (Thornton  Haven),  Yellow  Sea.    

Hajamri  River,  Hindoostan,  West  Coast 

Hakluyt  Head,  Nova  Zembla 

Hakodadi  Harbor,  Yezo  Island,  Japan 

Halifax,  Nova  Scotia 

Halt  Bay  and  Gray  Harbor,  Patagonia,  West  Coast 

Hamburg,  Germany 

Hamilton,  Port  (Korea),  Yellow  Sea. 

Hammelin  Pool,  Shark  Bay,  Australia,  Northwest  Coast 

Hammerfest,  Norway 

Hammond  Knoll,  England,  East  Coast 

Han-kau,  China,  West  Coast 

Hangata,  Japan 

Hang-chu  Bay  (Seshan  Islands),  China,  East  Coast 

Hang-chu  Bay  (Fog  Islands),  China,  East  Coast 

Hang-chu  Bay  (Chapoo  Road),  China,  East  Coast 

Hang-chu  Bay  (off  Can  pu),  China,  East  Coast , 

Hanover  Bay,  Australia,  Northwest  Coast 

Hanover  Sound,  Bahamas , 

Hanstul  (mouth).  Gulf  of  Kutch,  Hindoostan - 

Hants  Harbor,  Newfoundland 

Harbor  of  Mercy,  Magellan  Strait 

Harbor  Grace,  Newfoundland 

Harbor  Island,  Nova  Scotia 

Hardy,  Port,  New  Zealand , 

Haro  .Strait  (Channels  leading  to,  from  St.  Juan  de  Fuca  Strait) 

Harrington,  Port,  England 

Hartlepool,  England 

Harvey,  Port  (Call  Creek),  Vancouver  Island 

Harwich,  England 

Hastings,  England 

Hastings  Harbor ,  Bay  of  Bengal,  East  Coast 

Hatiling  Bay,  Moluccas 

Haute  Isle,  Bay  of  Fundy 

Havana,  Cuba 

Havannah  Harbor,  Sandwich  Islands,  New  Hebrides 

Haverfordwest,  Wales 

Havre,  France 

Hawke  Bay,  New  Zealand 

Hawke  Bay,  Newfoundland 

Heart's  Content,  Newfoundland 

H^aux  Lights,  France 

Heawandou  Pholo  Atoll,  Maldives 

Heda  Bay,  Japan 

Helena,  .St.,  Bay,  Africa,  West  Coast 

Helena,  St.,  Island,  South  Atlantic 

Helford,  England 

Helgoland,  German  Ocean 

Helier,  St.,  Jersey,  English  Channel 

Hellevoetsluis,  Netherlands 

Henry,  Port,  Patagonia,  V\  est  Coast 

Heppens,  Germany 

Hernando  Island,  Strait  of  Georgia,  British  Columbia 

Hermite  Isle,  Australia,  West  Coast 

Heron  Islet,  Capricorn  Group,  Australia,  East  Coast 

Herradura,  Port,  Chile 


High  Water,  Full 
and  Change. 


li.  m. 
II  40 
II   30 

8  20 

5  32 

9  o 

7  9 

8  20 

6  4 

9  o 
6    o 


30 

40 

30 
o 

49 

15 

29 

30 

o 

10 

40 


Rise. 


Springs. 


10  36 

11  45 
II  45 

Noon. 


II 

8 
2 

7 
I 

7 
7 
9 


30 

15 
o 

13 

22 

25 
40 

55 


Irregular. 

II    15 

3  28 
o  30 
o    6 

10  53 

ID   40 

6     o 

11  21 

8  14 


7 
6 

9 

7 

II 

7 
5 
9 


15 

42 

51 

50 

o 

30 
45 
30 


2 

3 

4 

II 

6 

2 


30 
II 

43 
33 
36 
30 


Noon, 
o  30 
6    o 

10    o 

9    o 
9    8 


Feet. 
12 
15 

II 


9 

6-7 

3 

12 

8 

4 

4 
6 

6 

VA 
II 

9 

33-38 
ii'A 
14 
17 
25 

24-38 
4 

4 
4 


6K 
8 
10-12 

23 

15 
10 

11^ 
24 

3-4 

33 

3 

4 

VA 

22 

3 

6 

4 
31 

\y. 

6 
3 

15;^ 

9X 

31K 

SA 

5  , 
12X 
12-14 

14 
10 

5 


Neaps. 


Feet. 
8 


4K 
8 


3 

^'A 

6 

18 

11^ 

9^ 
I7j4 


28;^ 


2% 
18 

4 

^A 
^iA 


iiA 
23 


Page  488]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Herradura,  Nicoya  Gulf 

Hervey  Bay,  Australia,  East  Coast 

Hesquiat  Harbor,  Vancouver  Island 

Hewett  Bay,  Tierra  del  Fuego - 

Heybridge,  Blackwater  River,  England 

Heynish,  Tiree  Island,  Scotland 

Hicks  Bay,  New  Zealand 

Hie-chechin  Bay,  China,  East  Coast  . i. 

Hi-ide,  Japan 

Hjerting,  Jutland 

Highfield,  America,  Northwest  Coas» 

Hillsborough  River,  Charlottetown,  Prince  Edward  Island 

Hillsborough  (Head  of  River),  Prince  Edward  Island 

Hillsborough  Island  (New  Port),  Bonin  Islands 

Hillswick  Firth,  Shetland 

Hiogo  and  Kob^  Bay,  Japan 

Hirtshals,  Jutland 

Hoaksiel,  Germany , 

Hobarton,  Tasmania , 

Hoe-e-tow  Bay,  China,  East  Coast , 

Hokianga  River  (entrance),  New  Zealand 

Hokianga  River  (Kokohu),  New  Zealand 

Hokitika  (Bar),  N  w  Zealand , 

Hollesley,  England 

Holmes  Bay,  America,  Northwest  Coast , 

Holsteinborg,  Greenland , 

Holy  Island,  England ! 

Holyhead,  Wales 

Hon-cohe  Bay,  China  Sea,  West  Coast 

Hondeklip  Bay,  Africa,  Southwest  Coast ■ 

Honfleur,  France 

Honghai  Bay,  China,  East  Coast 

Honolulu,  Sandwich  Islands , 

Hongkong,  China,  East  Coast 

Hoogly  River  (Eastern  Channel  light- vessel).  Bay  of  Bengal,  West 

Coast 

Hoogly  River,  Diamond  Harbor,  Bay  of  Bengal,  West  Coast 

Hooper  Island,  Korea,  South  Coast 

Hope  Harbor,  Falkland  Islands 

Hope  Sound  (Mia-u-tau  Group),  Yellow  Sea 

Hope  Weg  Light,  Germany 

Hopedale,  Labrador 

Horn,  Cape,  Tierra  del  Fuego 

Horn  or  Blaavand  Point,  Jutland 

Horn  Reefs,  North  Sea ., 

Horton  Bluff,  Bay  of  Fundy 

Hougue,  La,  France 

Hourdel,  France 

Hout  Bay,  Africa,  West  Coast 

Houtman  Rocks,  Australia,  West  Coast 

Howden,  River  Tyne,  England 

Howe,  West  Cajse,  Australia,  South  Coast 

Howth  Harbor,  Ireland 

H  uacho  Bay,  Peru 

Huafo  Islands,  Patagonia,  West  Coast 

Huapilinao  Head,  Patagonia,  West  Coast 

Huasco,  Port,  Chile 

Iluelva,  Port,  Spain 

I  lui-ling-san,  China,  South  Coast 

Huildad  Inlet,  Patagonia,  West  Coast 

Hu-i-tan  Bay,  China,  East  Coast 

Hull,  England 

Hull  Bridge,  Crouch  River,  England 

Hulu  Shan  Bay,  Yellow  Sea 

I I  ungry  Point,  Australia,  South  Coast 

Hunter  Island,  Bass  Strait 

Hunter,  Port,  Australia,  East  Coast 


//.  m. 

3    9 
9  14 

Noon, 
o  30 
o  20 
5  30 
9  o 
7    o 

II  25 
2  45 


10  45 

11  o 
II  32 

9  45 

7  15 
4  28 

Noon. 

8  15 


15 

45 


10  15 

9  39 

11  30 

1  o 
6  30 

2  30 

10  II 

11  30 
2  30 
9  29 

10    o 

4  o 
10  15 

9    o 

Noon. 

9  10 

8    ID 

10  24 

0  35 

5  38 
4  40 

1  44 

Noon, 
o  30 
8  42 

11  26 

2  20 
II  30 


9    o 

11  9 

4  45 

Noon. 

I   25 

8  30 

1  54 

8  30 

o  48 

12  15 

6  29 

12  25 

2  30 
4  18 

10  30 

9  45 


Feet. 
10 
10 
12 

61^ 
12 
12 

7 

2-4 


16 

954 

ID 

I 
II 

\% 
16 
10 
10 

8K-9 
8? 

13 
10 

15 
16 


/A 

2 

4X 

10^ 
12-15-18 

11^ 
7 
6X 

loK 
7 
9 
5 

48 

18^ 

5 

2K 
12 

6 

13 

7 

15K 
6 

14 

7K 
16-20 

16 

203/|.' 
16 

8 

7 
8 

6-7 


Feet. 


8 
6 


8 

7 


3X 


6? 
10 

"J4 

I2>^ 


18 


40 

I4K 
21 


10 


I6X 
II 
6 
4-6 


TABLE  47.  [Page  489 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Hurst  (Camber),  England 
Husum,  Denmark 


Icacos  Point,  Trinidad. 

Ichabo  Island,  Africa,  West  Coast 

lengen,  New  Caledonia — 

Ilfracombe,  England 

Iki,  Japan 

Ilha  Grande  Bay,  Paratio,  Brazil 

Ilheo,  Port  d',  Africa,  West  Coast 

Ilo-Ilo,  Port,  Filipinas 

Inagua,  Bahamas 

Indefatigable  Island,  Galapagos 

Independencia  Bay,  Peru 

Indian  Tickle,  Labrador 

Indio  Point,  South  America,  East  Coast 

Indus  (Gizree  Bunder),  Hindoostan,  West  Coast  . 

Inhambane  River,  Africa,  East  Coast 

Inishbofin,  Ireland 

Inishkeel,  Ireland 

Inishturk,  Ireland 

Inkanskie,  White  Sea 

Inman,  Cape,  Tierra  del  Fuego 

Intsi  Point,  White  Sea 

Inverary,  Scotland 

Inverness,  Scotland 

Investigator  Road,  Australia,  North  Coast 

lona  Sound,  Scotland 

Ipswich,  England   

Iquiqui  Road,  Peru 

Ireland  Island,  Bermuda 

Isidro,  St.,  Cape,  Magellan  Strait 

Island  Harbor,  Choiseul  Sound,  Falkland  Islands 

I sland  Country  Harbor,  Nova  Scotia 

Islay,  Peru 

Isle-aux-Coudres,  River  St.  Lawrence 

Isles  de  Los,  Africa,  West  Coast 

Isthmus  Bay,  Smyth  Channel — 

I  ves,  St.,  England 


Jacinto,  San,  Port  Ticao  Island,  Filipinas 

Jackson,  Port  (North  Head),  Australia 

Jacmel,  St.  Domingo -. 

Jafrabad,  Hindoostan,  West  Coast 

Jago,  St.,  Bay,  Magellan  Strait 

James  Island  (Adam  Cove),  Galapagos  Islands. 
James  Island  (North  side),  Galapagos  Islands  . 
James  Island  (West  end),  Galapagos  Islands... 

Jashk  .Shoal,  Persian  Gulf 

Jask,  Cape,  Persian  Ciulf 

Jebogue,  Bay  of  Fundy 

Jedore,  Nova  Scotia 

Jekatarina  Islands,  Lapland 

Jerba,  Mediterranean 


lencoacoara,  Brazil 


Jersey  (St.  Ilelier),  English  Channel 

Jersey  (Rosel) 

Jervis  Bay,  Australia,  East  Coast 

Jezirat  Arabi,  Persian  Gulf 

Jezirat  Hamar-al-nafur,  Arabia,  Southeast  Coast. 

Jezirat  Jun,  Persian  Gulf 

Jezirat  Kabr,  Persian  Gulf 

Jezirat  Kais,  Persian  Gulf- 

Jezirat  Kharg  or  Kareg,  Persian  Gulf 

fezirat  Larek,  Persian  Gulf 

I  ezirat  Tumb,  Persian  Gulf 


High  Water,  Full 
and  Change. 


//.  w. 
10     o  and 
12     o 
2  20 


14 
o 

15 

42 


I  45 

3    o 

Noon. 

8     o 

56 

50 

37 

45 

50 

15 

34 
10 

36 

15 
o 

55 


I 

4 

6 

II 

9 
4 
4 

5 

4 

9 
2 

II 


N  oon . 
o  18 
8 


o 
II 

35 
45 
4 
o 
20 
40 

53 
25 
35 
30 
44 


Rise. 


6  30 

8  15 
Irregular. 

II  35 
27 

14 

34 
10 


9 

2 
2 

3 
9 
6 

10 

7 
6 


30 

o 

4 

45 
2: 


'J 

3  10 

II  30 

6  29 


15 
20 
30? 

30 


II  30 


o  45 

8    o 

10  15 


Springs. 
Feet. 

9 
7 

6 

4X 

27X 
8 

8-10 

6 

4 
6 

4 

7 

10 

12^4: 
II 

12X 
14 
4 
16 

ID 

12 

9 

I3K 

5 

4 

8 

6 

6>^ 

7 

17 
13 

5 
21 

6 

6 

2-3? 

9 
20 

5 
5 
5 
8 
6 

15 
(^'< 
10 

7 
12 

30' 

5 

10 
10 

8>^ 
1% 


Neaps. 

Feet. 
6 


4 
4 

21'/ 


2;^ 


9'< 
8 

9yz 

9'^ 


10 

15 


7 
15 


11^ 

aH 

5 

9 

23 


iitimmitmtmtmtmgamtmmiimiiam 


Page  490]  TABLE  47- 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Jiddah,  Red  Sea 

Jijginsk  Island,  White  Sea 

Joao,  San,  Brazil 

Johanna  Island  (anchorage) 

Johanna,  Pomony  Harbor,  Comoro  Islands  . . 

John,  Port,  America,  Northwest  Coast 

John,  St. ,  Bay  of  Fundy 

John,  St.,  Newfoundland,  East  Coast 

John,  St.,  Newfoundland,  North  Coast 

John,  St.,  River,  Africa,  South  Coast 

Jones'  Harbor,  Newfoundland 

Jonquiere  Bay,  Gulf  of  Tartary 

Joombas  River,  Africa,  West  Coast 

Josef,  San,  Port,  Patagonia,  East  Coast 

Jourimain  Island,  New  Brunswick 

Juan  de  Nova,  Madagascar 

Juan  P'ernandez  Island,  Chile 

Juan,  San,  Porto  Rico 

Juan,  San,  Port,  Peru 

Juby,  Cape,  Africa 

Juggee,  Seer  River,  Hindoostan,  West  Coast 

Juisl,  Germany 

Jukan  Islands,  Lapland 

Julian,  San,  Port,  Patagonia,  East  Coast 

Julianshaab,  Greenland 


Julien,  St.,  Harbor,  Newfoundland 

Junk  Fleet  Entrance,  Canton  River,  China 

Junk  River,  Africa,  West  Coast 

Junkseylon  Island  (East  side),  Malacca  Strait 

Jura  Island  (Small  Isles),  Scotland 

Jura,  Feolin  Ferry,  Scotland 

Juria,  Hindoostan,  West  Coast 


Kaikora,  Penin,  New  Zealand 

Kaipara  Harbor  (entrance).  New  Zealand 

Kalang  Bayang  Harbor,  Java 

Kalgalakska,  White  Sea 

Kalian  Point,  Banka  Strait 

Kandalaksha,  White  Sea , 

Kanushin,  Cape,  White  Sea 

Kapiti  Island,  New  Zealand 

Karachi,  Manora  Point,  Hindoostan,  West  Coast . . 

Karakoa  Bay,  Hawaii 

Kata  Channel,  Japan 

Katwyk,  Netherlands 

Kawau  Island,  New  Zealand .. 

Kawhia  Harbor,  New  Zealand 

Keats,  Port,  Australia,  North  Coast 

Kediwari  River,  Hindoostan 

Keelacarry,  Ceylon 

Kedgeree,  Bay  of  Bengal 

Keehng  Islands  (Port  Refuge),  Indian  Ocean 

Kegashka  Bay,  Gulf  of  St.  Lawrence 

Kelung  Harbor  (Formosa),  China  Sea,  East  Coast 

Kenmare  River  (West  Cove),  Ireland 

Kenn  Reef,  Australia,  East  Coast 

Kent  Group,  Bass  Strait 

Kentish  Knock,  England 

Keppel  Buy,  Australia,  East  Coast 

Keret,  White  Sea 

Keret  Point,  White  Sea 

Kerguelen  Island,  Indian  Ocean 

Kesm,  Persian  Gulf 

Khor  Jerameh,  Arabia,  Southeast  Coast 

Khor  as  Shem,  Persian  Gulf 

Khor  Rabbagy,  Arabia,  Southeast  Coast 


High  Water,  Full 
and  Change. 


A.  m. 


5 
6 

3 

4 

I 

II 

7 

ID 

4 

7 

ID 

8 

ID 

9 


15 

24 

40 

o 

o 

21 

30 
40 

8 

49 
o 

ID 

O 

30 


30 

2 

10 


I 

10 

9 
10 

5 

7 

6 

II 

5 
10 

5 
4 
2 


30 

28 

o 

45 
6 

21  a.  m. 

30  p.  m. 

50 

45 

o 

3 

41 

o 


5  30 
10  55 


6  50 

8  o 
3  25 

II  54 

9  o 
10  30 

49 

4 


6 


30 

30 

30 
o 

57 


9 

II      o 

10  30 

5  50 

10  45 

10  30 

3  52 
8    o 

11  10 
II  47 


9 
3 
4 
2 
II 
9 


o 

8 

30 
o 
o 

30 


10  40 
10  10 


Rise. 


Springs. 


Feet. 
3 


4 
14 
II 
II 

13 

27 
6 

r/z 

s% 

i^ 

6 

30 
6 

5 
4 
^Vz 

3 

8 
6 

13 
30 

7 

(>% 

5 
ilVz 

y/2 

16 
8 

ID 
2 

7 
12 

7 

15 
6 

7X 

5 

10 
12 
22 

7 

18 

5 

5 

3 

10 

5K 


9-14 
6 

2 
12 
ID 

8K 
9K 


Neaps. 
Feet. 
10 14 


23 
4 
5K 


25 
3 


i      5 

;  3 


4X 
13 

6 

8 


SH 

7 


TABLE  47.  ,  [Page  491 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Kijouk  Phyou  Harbor,  Bay  of  Bengal 

Kilbaha,  Ireland 

Kilda,  St.,  Hebrides 

Kildin  Island,  Lapland 

Kilkieran  Cove,  Ireland 

Killala  Bay,  Ireland 

Killeany  Bay,  Arran  Islands,  Ireland    

Killingholme  ( Humber  River),  England 

Killybegs,  Ireland 

Killyleagh,  Ireland 

Kilmichael  Point,  Ireland 

Kilrush,  Ireland 

Kincardine,  Firth  of  Forth,  Scotland 

King  Island,  Bass  Strait,  Franklin  Road 

King  Island,  Bass  Strait,  Sea- Elephant  Bay 

King,  Port,  Falkland  Islands 

King  Sound,  Australia,  West  Coast 

King  George  Sound,  Australia,  South  Coast 

King's  Cove,  Xewfoundland 

Kingsbridge,  England  ....    

Kingston,  Australia,  South  Coast 

Kingstown,  Ireland 

Kinsale,  Ireland 

Kinsiang  Point,  China,  East  Coast 

Kircubbin,  Ireland 

Kirindi,  Ceylon 

Kirkcudbright,  Scotland 

Kirkwall,  Orkneys 

Kirpon  Harbor,  Newfoundland 

Kishm.     {ScY  Kesm.) 

Kiswara  Harbor,  Africa,  East  Coast 

Kitnapatnam,  Bay  of  Bengal,  West  Coast 

Kiu-kiang,  China,  West  Coast 

Klaskino  Inlet 

Klaskish  Inlet,  Vancouver  Island 

Klemtoo  Passage,  America,  Northwest  Coast 

Klewnugget  Inlet,  America,  Northwest  Coast 

Knox  Bay,  Vancouver  Island 

Knysna  Harbor,  Africa,  South  Coast 

Koehvatte  Bay,  Moluccas 

Koepang,  Timor 

Kokohu,  New  Zealand 

Ko-kun-to  Group,  Korea 

Kok-si  kon,  Port,  Formosa 

Koombanah  Bay,  Australia,  West  Coast 

Kori  or  Lukput  River,  Kotasir,  Hindoostan,  West  Coast. 

Kouloi  River 

Kou  Zomen,  WTiite  Sea 

Kovda  Bay,  White  Sea  .    

Koweyt,  Persian  Gulf 

Kowie  River,  Africa,  South  Coast 

Krakatoa,  Strait  of  Sunda 

Kiidi  River,  Hindoostan,  West  Coast 

Kuper  Harbor,  Korea,  South  Coast 

Kuper,  Port,  America,  Northwest  Coast 

Kuriyan  Muriyan  Bay  and  Islands,  Arabia 

Kurrachee.     (.SV'<' Karachi.) 

Kutch,  Gulf  of  (mouth),  Hindoostan 

Kweshan  Islands,  China,  East  Coast 

Kyau-chau  Bay,  Yellow  Sea 

Kyem  River,  White  Sea 

Kykduin,  Netherlands 

Kyle  Akin,  Loch  Alsh,  Scotland 

Kyle  Rhea,  Scotland 

Kynumpt  Harbor,  America,  Northwest  Coast 

Ky uquot  Sound,  Vancouver  Island , 


High  Water,  KuJ' 
and  Change. 


//.  m. 
10     o 

4  16 

5  30 

6  45 

4  34 

5  22 

4  28 

6  2 

5  16 
o  40 
8  30 
4  42 
2 
I 


53 
o 

30 
^o 


9 

7 

O    ID 
II    56 

7 

5 
o 

II   10 

4  43 
7  o 
o  42 

3  30 
II   10 


15 

46 

6 


10 
7 

4 
II 


9 
5 

30 
o 


Noon. 
Noon. 

Noon. 

o  30 
Noon. 

3  45 


II 

0 

10 

15 

2 

25 

II 

30 

9 

0 

II 

15 

I 

15 

3 

30 

3 

25 

0 

15 

4 

0 

7 

0 

50 

28 

40 


8  20 

II  30 

9  30 
5  o 
5  23 

7 
6 
6 


o 

16 

o 


Rise. 


Springs. 


Feet, 

9 
13 

12 

15X 
loX 
13X 

nX 
II 

45^ 
14 

17  K 

7 
12 

5 

33 

1-4 


10 

5 

II 
ii'/i 

iiy, 


o  30 

Noon. 


Neaps. 


Feei. 
6 

914 


II 

8 
10 

9% 

3 

loK 
15 


2X 


9 
9K 


23 

10 

7l'2 

5 

iX 

12 

IX 

24 

12 

12 

13 

8 

17 

16 

5 
7 
9 

6/^ 

ID 

7 

18 

10 

3 

4-3 

loX 

20 

6 

6 

9 

4-5 

4 

ID 

iiX 

8X 

13 

10^2 

6/4 

14 

12 

9 

4 

12 

15  s' 

II 

15 

II 

14 

II 

12 

Page  492]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


La  Poile  Bay,  Newfoundland 

Labuan  Island,  Victoria  Harbor,  Borneo 

Labyrinth  Islands,  Magellan  Strait 

Lacul  Harbor,  St.  Domingo 

Lady  Bay,  Australia,  South  Coast 

Lady  Elhot  Islet,  Australia,  East  Coast 

Lagos,  Portugal 

Lagos  River  (Bar),  Bight  of  Benin 

Lagos  River  (Consulate  Wharf)    

Lagos  River  (Palaver  Islands) , 

Laguimanoc,  Port,  Luzon 

Laguna  de  Terminos,  Gulf  of  Mexico 

Lakadivh  Group,  Hindoostan,  West  Coast 

Lamalin,  Newfoundland 

Lambayeque  Road,  Peru 

Lamlash,  Scotland 

Lamo  Harbor,  Africa,  East  Coast 

Lancaster,  England 

Landshipping,  Cleddau  River,  Wales 

Langeoog,  Germany 

Langshan  Crossing,  Yang-tse-Kiang 

Lankeet  Island,  Canton  River,  China , 

Lansew  Bay,  China,  East  Coast 

Lanzarotte,  Canary  Islands 

Laredo  Bay,  Magellan  Strait , 

Largs,  Scotland 

Lark  Harbor,  Newfoundland   

Latham  Island,  Africa,  East  Coast 

Latitude  Bay,  Tierra  del  Fuego 

Lau-mu-ho,  Yellow  Sea 

Laun,  Great  and  Little,  Newfoundland 

Laura  Harbor,  Tierra  del  Fuego 

Laurenny,  Wales 

Lavata  Bay,  Chile 

Lawrence,  Great  St.,  Harbor,  Newfoundland 

Le  Have,  Cape,  Nova  Scotia 

Le  Have,  Nova  Scotia,  Crooked  Channel 

Le  Have,  Mother's  Island 

Le  Have,  Getson's  Cove 

Le  Have,  Bridgewater  (McKean's  Wharf) 

Le  Have,  Lunenburg  (Spidler's  Cove) 

Le  Maire  Strait,  Tierra  del  Fuego 

Leervig  Fiord,  Fserce  Islands 

Leith,  Scotland 

Leman  Shoal,  England,  East  Coast 

Lennox  Cove,  Tierra  del  Fuego 

Leopold,  Port,  Barrow  Strait .. 

Lepreau,  Bay  of  Fundy 

Lerwick,  Shetland 

L'Etang  Harbor,  Bay  of  Fundy 

Leubu  River,  Chile , 

Leven,  Port,  Madagascar 

Levrier  Bay,  Africa,  West  Coast 

Lewis,  St.,  Sound,  Labrador 

Liant,  Cape,  Gulf  of  Siam,  China  Sea,  West  Coast 

Liau  Ho  (Bar),  Yellow  Sea 

Liau  Ho  (entrance) 

Liau-tung,  Chingho,  Yellow  Sea 

Liau-tung  Gulf  (Sand  Point),  Yellow  Sea 

Liau-tung,  Northwest  Head  of  Gulf 

Lief kenshock 

Limb^  Strait,  Moluccas 

Limerick,  Ireland 

Linmouth,  England 

Lindy  River  (entrance),  Africa,  East  Coast 

Lingeh,  Persian  Gulf 

Lintin  Island,  Canton  River,  China,  East  Coast  .  .. 


High  Water,  Full 
and  Change. 


h.  III. 


o 

45 
30 
o? 

37 
o 

7 
o 


I  30 
Noon. 
10  30 


9 

4 

II 

4 
II 

6 
II 

I 
II 
10 

I 
II 
II 
10 

4 
2 
I 
8 
I 
6 

9 
8 

7 
7 
7 
7 
8 

7 
4 
o 

2 
6 

4 
o 
II 
10 
II 
10 


15 
o 

49 

6 

16 

27 

25 
40 
20 

o 

o? 

30 

50 

37 
o 

5 
30 
15 

o 

23 

20 

30 
48 

51 

51 

55 
6 

54 
o 

30 

17 

o 

40 

6 

18 
o 


J' 

19 

30 

3  30 
Noon 
6  40 


7 
o 
o 

20 
50 
30 
25 


6  16 
6    2 

4  15 

Noon? 
Noon. 


Rise. 


Springs. 


Neaps. 


Feet 
6 
6 

5K 
3? 
3 
7-8 
13 

3 

2 

I 

5K 

6 

3 
10 
II 

20 

8 
12 

(^Vz 
13 

9? 

9 
10 

5^? 
10 

4 
5 
7 
6 
20 
5 
7 
7 

7X 
7 

I^ 

7X 
7 

8 
6 

24K 
6 

23>2 

6-7 

yA 

12 

6>^ 

7 
10 

30X 
12 

V/z 


TABLE  47.  [Page  493 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  P^uU 
and  Change. 


Rise. 


Springs. 


Neaps. 


Lisbon  (Belem),  Portugal 

Liscanor  Bay,  Ireland 

Liscomb  Harbor,  Nova  Scotia 

Lishan  Bay,  China,  East  Coast 

Lissa,  Adriatic 

Listerdeep,  Fairway  Buoy,  Denmark 

Lister  Roads 

Litau  Bay,  Yellow  Sea 

Litke  Ridge,  White  Sea 

Little  Fish  Bay,  Africa,  West  Coast 

Littlehampton,  England 

Little  Metis,  Gulf  of  St.  Lawrence 

Little  Milford  Quay,  River  Cleddau,  Wales  . 
Little  Natashquan,  Gulf  of  St.  Lawrence  .  . . 

Little,  Port,  Newfoundland 

Little  Tancock  Island,  Nova  Scotia 

Liverpool,  England 

Liverpool  Bay,  Nova  Scotia 

Liverpool  River,  Australia 

Liza  Bay,  Lapland 

Lizard  Island,  Australia,  P2ast  Coast 

Lizard  Point  (Perran  Vose  Cove),  England  . 

Llanelly  (Bar),  Wales 

Lloyd,  Port,  Bonin  Islands 

Loanda,  San  Paul  de,  Africa,  West  Coast  . . . 

Loango  Bay,  Africa,  West  Coast 

Lobah  Point,  Banka  Strait 

Lobito  Bay,  Africa,  Southwest  Coast 

Lobo  Point,  Peru 

Lobos  Cay,  Bahamas 

Lobos  Head,  Patagonia,  West  Coast 

Loch  Aline,  Scotland 

Loch  Alsh,  Scotland 

Loch  Boisdale,  Scotland 

Loch  Broom,  Scotland 

Loch  Carron,  Scotland 

Loch  Cuan,  Scotland 

Loch  Duich,  Scotland 

Loch  Dunvegan,  Scotland 

Loch  Eil  (Head  of  Loch),  Scotland 

Loch  Eport,  Scotland 

Loch  Eriboll,  Scotland 

Loch  Erisort,  Scotland 

Loch  Etive,  Stonefield,  Scotland 

Loch  Etive,  Bunawe,  Scotland 

Loch  Ewe,  Scotland 

Loch  Fleet,  Scotland 

Loch  Goil,  Scotland 

Loch  Harport,  Scotland 

Loch  Hourn,  Scotland 

Loch  Inver,  Scotland 

Loch  Laxford,  Scotland 

Loch  Leven  (Head  of  Loch),  Scotland 

Loch  Linnhe,  Scotland 

Loch  Long,  Scotland 

Loch  Maddy,  Scotland 

Loch  Moidart,  Scotland 

Loch  Nevis,  Scotland 

Loch  Roag,  Scotland 

Loch  Ryan  (Head  of  Loch),  Scotland 

Loch  Skiport,  Scotland , 

Loch  Strivan,  Scotland 

Loch  Sunart,  Scotland 

Loch  Tarbert,  West,  Harris  Island,  Scotland 
Loch  Tarbert,  East,  Harris  Island,  Scotland 
Loch  Tarbert,  West,  Argyleshire,  Scotland  . 
Loch  Tarbert,  East,  Argyleshire,  Scotland  .. 


h.  m. 


4  2.:; 

8 

0 

10 

15 

4 

10 

0 

30 

2 

0 

3 

0 

II 

45 

2 

30 

II 

3(' 

2 

10 

6 

31 

II 

0 

10 

42 

7  43 

II 

23 

7  50 

6 

30 

5 

5^^ 

9 

15 

5 

0 

6 

16 

6 

8 

4  30 

4 

30 

II 

0 

4 

15 

8 

0 

7  40 

0 

29 

5 

:■>?, 

6 

16 

5  47 

6 

40 

6 

29 

5  36 

6 

0 

6 

7 

6 

27 

6 

6 

7  43 

6 

43 

7 

3 

7  54 

6 

39 

0 

22 

0 

6 

5 

54 

5  45 

6 

40 

6 

44 

6 

28 

S 

26 

0 

6 

6 

6 

5 

44 

5  47 

6 

II 

II 

12 

5 

52 

II 

55 

5 

40 

6 

4 

6 

10 

2 

^0 

"  53 


Feet. 
12 

13X 

16 

2K 

6 
15 

16 

13 

19 

5 

7X 
26 

8 

12 

9 
7-10 

14^ 
25 

3 

5 

^Yz 
10 

5-6 


SYz 
aYz 

6K 

h 

5X 


aYz 

o 


4 
5 

2% 
2 

2Yz 

zYz 

\Yz 

I 

I 

2.Y2. 

6 

lYz 

3Y2 

4 

9 


Feet. 

9 
10 

AYz 


8 

nYz 
3 

6 
20'/ 


iU/2 
18X 


II 

9Yz 
10  K 

9Yz 
II 
II 


II 

11;^ 


6 
10 

10J4: 
II 

iiX 

^Yz 


8 


^Yz 
10 


Page  494]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Loch  Tongue,  Scotland 

Loch  Torridon,  Scotland 

Loch  Tuadh,  Scotland 

Lofoten  Islands,  Norway 

Loheyyah,  Red  Sea 

Loire  River  (St.  Nazaire),  France 

Lomas  Point,  Peru 

Lombock  (Ampanam  Bay),  Java  Sea 

London  Bridge,  England 

London  Docks,  England 

Londonderry,  Ireland 

Looe  (East),  England 

Lopez,  Cape,  Africa 

L'Orient  ( Port  Louis ),  France 

Lord  Howe  Island,  South  Pacific 

Lorenzo,  St.,  Channel,  Mexico,  West  Coast . . . 

Lo-shan-kau,  Yellow  Sea 

Lough  Larne,  Ireland 

Lough  Rossmore,  Ireland . 

Louis,  Port,  France 

Louis,  Port,  Mauritius 

Louis,  St.,  Bay,  St.  Domingo 

Louisburg  Harbor,  Cape  Breton  Island 

Low  Bay,  Falkland  Islands 

Low  Inlet,  America,  Northwest  Coast 

Low,  Port,  Patagonia,  West  Coast 

Lowestoft,  England 

Laubo  River  (entrance),  Africa,  East  Coast 

Lucipara  Pass,  Banka  Strait 

Lukput,  Kori  River,  Hindoostan,  West  Coast. 

Lunaire  Bay,  St.,  Newfoundland 

Lundy  Island,  England 

Lung-mun  Harbor,  Yellow  Sea 

Lyme  Regis,  England 

Lymington,  England 

Lynn  Deep,  England 

Lynn  Harbor,  England 

Lynn  Road,  England 

Ly ttelton,  Port,  New  Zealand 


k.  m. 

7  S3 
6  20 

5  29 

Noon. 

I  30 

3  40 

"  19 
o 

58 

53 
I 


4 
3 


8 
I 
I 

8 
5  26 

30 

II 
8  30 
8  30 

4  30 
10  48 

5  20 

3  " 

o  30 

Irregular. 

8  o 
5  o 
o  30 
o  40 

9  57 


Irregular. 

o  15 
7     6 

5  15? 
10     o 

6  21 
10  25 

o  15 
6    o 


3  50 


Mabou  River,  Cape  Breton  Island 

Macah6,  Brazil 

Macao,  China,  East  Coast .. 

Macassar,  Celebes 

McDougall  Harbor,  Africa,  Southwest  Coast  .. 
McLaughlin  Bay,  Northwest  Coast  of  America 

Maceio,  Brazil 

Machias,  Seal  Island,  Bay  of  Fundy 

Macowa,  Red  Sea 

Macquarie  Harbor,  Tasmania 

Macquarie,  Port,  Australia,  East  Coast 

Macquereau  Point,  Gulf  of  St.  Lawrence , 

Madame  Island,  Madagascar 

Madoc,  Port,  Wales 

Madras  Road,  Coromandel  Coast 

Magadoxa,  Africa,  East  Coast 

Magdalen  Islands,  Gulf  of  St.  Lawrence 

Magdalen  River,  River  St.  Lawrence 

Magdalena,  Santa,  Island,  Magellan  Strait  .... 

Magdalene  Bay,  California 

Mahato  Island,  Africa,  East  Coast 

Mahneah  River,  Africa,  West  Coast 

Mahone  Bay,  Nova  Scotia 

Mahone  Bay,  Heckman's  Anchorage 

Mahone  Bay,  Prince's  Inlet 

Mahone  Bay,  Ham  Island 


9  0 

2  30 

ID   0 

4  40 

2  30 

I  0 

4  30 

II  5 

0  30 

7  30 

8  56 

2  0 

4  0 

7  30 

7  34 

4  30 
8  20 

I  15 

Noon 

7  35 

4  30 

7  40 

8  0 

7  45 

7  42 

7  47 

Feet. 
15 

15  , 
11^ 

9 

3 

15X 

5 
6 

20J< 
2014: 

16 
4-6? 

13 

6 

6 
II 


II 

13 

J-3? 

5 

5>^ 
17 

7 

i>% 
22 
10 
12 

5 
27 

7 
11^ 

8 
23 


23;* 

lYz 

4 

9X 
6% 

5K 
5^ 
14 

18 
2 

4-5 

5 

5 

17 

Z% 
8 

6-i 

10 

7 
II 

7 


1% 


TABLE  47.  [Page  495 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Mahone  Bay,  Martin's  River 

Mahone  Bay,  Chester 

Mai  Island,  New  Hebrides 

Maiden  Rocks,  Ireland,  Northeast  Coast 

Maiko,  Fort,  Japan 

Majambo  Bay,  Madagascar 

Makatein,  Arabia,  Southeast  Coast 

Makelleh,  Arabia,  Southeast  Coast 

Makongai  Island,  Fiji  Islands 

Makumba  River,  Madagascar 

Makung  Harbor,  Pescadres,  China  Sea 

Malabrigo,  Port,  Peru 

Malacca  Strait  (light-vessel,  One  Fathom  Bank) 

Malacca  Strait  (off  Mount  Formosa) 

Malacca  Road,  Malacca  Strait 

Malaga,  Spain 

Malahide  Inlet,  Ireland 

Malcolm  Atoll,  Maldives 

Maklon,  Chelmer  River,  England 

Male,  Maldives 

Malludu  Bay,  Borneo 

Malo,  St. ,  France 

Malpelo  Point,  Peru ..• 

Man  of-^^'ar  Cay,  Bahamas 

Mana  Island,  New  Zealand 

Manama,  Persian  Gulf 

Manawatu  River,  New  Zealand 

Manceniila  Bay,  St.  Domingo 

Mandwa  Creek,  Hindoostan,  West  Coast 

Mangalore,  Hindoostan,  West  Coast 

Manganitoe  Bay,  Moluccas 

Mangarol  Bunder,  Hindoostan,  West  Coast 

Manicouagon  River,  River  St.  Lawrence 

Manila  (Luzon  Island),  China  Sea,  East  Coast 

Manning  River,  Australia,  East  Coast 

Manorah  River,  Hindoostan,  West  Coast 

Manta,  Port,  Ecuador 

Manau,  Navigators  Islands 

Manukau  Harbor  (entrance).  New  Zealand 

Manybranch  Harbor,  Falkland  Islands 

Maple  Bay,  Vancouver  Island 

Maplin  Light  (Thames),  England 

Maquereau  Point,  Gulf  of  St.  Lawrence 

Maracas  Bay,  Trinidad,  Caribbee  Island 

Maranham,  Brazil  

March  Harbor,  Tierra  del  Fuego 

Marcouf,  St.,  France 

Mare  Harbor,  Falkland  Islands 

Margarets,  St.,  Bay  (Shut-in  Island),  Nova  Scotia 

Margarets,  Newfoundland 

Margate,  England 

Maria,  Cape,  Saghalin  Island,  Sea  of  Okhotsk 

Maria,  Santa,  Island,  Chile 

Maria  Van  Diemen,  Cape,  New  Zealand 

Marion  Bay,  Australia,  South  Coast 

Maristow,  River  Tavy,  England 

Marjoribanks  Harbor,  Korea,  West  Coast 

Mark,  St.,  Bay  of,  St.  Domingo 

Marka,  or  Muerka,  .\frica.  East  Coast 

Maroni  Bay,  Comoro  Islands 

Maroni  River,  Guayana 

Martaban,  Bay  of  Bengal 

Martin,  St.,  Cove,  Tierra  del  Fuego 

Martin,  St.,  Cove,  Cape  Horn  Islands,  Tierra  del  Fuego 

Martin,  St.,  de  la  Arena,  Spain,  North  Coast 

i\Lartin  Vas  Rocks,  South  Atlantic 

Martinique,  Robert  Harbor,  Caribbean  Sea 


High  Water,  Full 
and  Change. 


h.  m. 
7  43 

7  44 
6  30 

10  43 
6  27 

4  30 
9  o 
830 
6    o 

4  45 

10  30 

5  o 

6  o 

8  o 

7  30 
Noon. 

11  15 

10  30 

o  32 
o 

10 

6 


30 

30 

5 

4  o 
8  10 
o 
20 
o 
o 


7 

5 
10 

7 

10  45 

11  o 

5    o 
10  30 

2  15 

10  40 

9  15 
I  30 

3  4 


9  30 
7  40 


5 
o 

30 
o 

10 

55 
o 


47 
28 


o 
2 

3 

7 

3 

9 
6 

7 

9 

II  40 

2  o 

10  20 

8  o 

2  6 

5  47 

3  30 
8    o? 

30 
53 
30 
20 

30 
3  50 
3  30 
3  45 


Rise. 


Springs. 


Feet. 

VA 

7 

5 

6X 

Z% 
16 

6 

7 

4 
17 

2 

15 
II 

II 

3 
10 

3 
10 

3 
6-8 

35 
10 

4 
8 

7 
8 

4-5 
7 

7 

7 
12 

3>^-6 

4 

16 

6 

6 

13 

12 

W/z 

5 

5 
16K 

6 
20 

6 

VA 

4K-6K 

15K 

5 
6 

7 

4 

^Yz 
29 

I? 

8 
10 

8 
21 

8 
15 

4-5 


Neaps. 


Feet. 


6X 
I 


3 

7 

12 

^Yz 
8 

6 

26 

6 
6 

5 

SY 

5 
7 


ID 


loK 

3 

4 
1034: 


6 
13 

^Yz 


Page  496]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Mary,  Cape,  St.,  Newfoundland 

Mary,  St.,  Harbor,  Madagascar,  East  Coast 

Mary,  St.,  Harbor,  Newfoundland 

Mary,  Port,  St.,  Isle  of  Man 

Mary,  St.,  Scilly  Islands 

Maryport,  England 

Mascat,  Persian  Gulf 

Mason  Bay,  New  Zealand 

Massacre  Bay  (Tasman  corner).  New  Zealand... 
Massacre  Bay,  Motu  Pipi  River,  New  Zealand  .. 

Massowah,  Red  Sea . . 

Matan  River,  Gulf  of  St.  Lawrence 

Matoya  Harbor,  Japan 

Matuku,  Plji  Islands  . ., 

Maule  River,  Chile 

Maullin  River,  Chile 

Maulmain,  Bay  of  Bengal 

Mauritius  (Port  Louis) 

Mauritius  ( Grand  Port) 

Mayday  Bay,  Palawan 

Mayhe  Island,  Indian  Ocean .. 

Mayne  Harbor,  Smyth  Channel 

Mayotta  Island,  Mozambique 

Mayumba,  Africa,  Southwest  Coast 

Mazambo,  Port,  Madagascar 

Mazatlan,  Mexico,  West  Coast 

Mbau  Roads,  Fiji  Islands 

Mboli  Harbor,  Florida  Island,  Solomon  Islands  . 

Meichen  Sound,  China,  East  Coast 

Melbourne,  Australia,  South  Coast 

Melinda,  Port,  Africa,  East  Coast 

Mellacoree  River,  Africa,  West  Coast 

Mellish  Reef  (Sand  Cay),  Australia,  East  Coast  . 

Mellon,  Ireland 

Melo,  Port,  Patagonia,  East  Coast ., 

Memory  Rock,  Bahamas 

Menadou  Bay,  Cape  Breton  Island 

Menam  River  (Paknani),  China  Sea,  West  Coast 

Mensular  Island  (Southeast  end),  Sumatra 

Merbat,  Arabia,  Southeast  Coast 

Mercy  Bay,  Banks  Land 

Mercury  I>ay,  New  Zealand 

Mergui,  Bay  of  Bengal,  East  Coast 

Merigomish,  Nova  Scotia '. .. 

Merville,  France 

Metalanim,  Port,  Caroline  Islands 

Metlahcatlah,  America,  Northwest  Coast 

Metway,  Port,  Nova  Seotia 

Mevagizey,  England 

Mexillones,  Port,  Bolivia ., 

Mezen,  White  Sea 

M'hul  Dwarka,  Hindoostan,  West  Coast 

Miau-tau  (Depot  Bay),  Yellow  Sea , 

Miaveness,  Fa?roe  Islands , 

Michael,  St.,  Azores , 

Michael  Seymour,  Port,  Gulf  of  Tartary 

Middle  Cove,  Tierra  del  Fuego , 

Middle  Island,  Patagonia,  West  Coast 

Middlesborough,  River  Tees,  England 

Middleton  River,  Bight  of  Benin 

Middleton  Reef,  South  Pacific , 

Midway  Island,  North  Pacific 

Miguelon  Road , 

Mikuni  Roads,  Japan 

Milford  Haven  (St.  Ann  Light-house),  Wales 

Milford  Sound,  New  Zealand,  Middle  Island 

Millman  Island,  Palawan,  West  Coast 


4 

7 

II 

4 
II 
II 
II 

8 

9 
I 
2 
6 
6 

ID 
O 
2 
O 
I 

9 
4 
I 

4 
4 
4 
9 
5 
5 
o 
2 
4 
7 
7 
6 

3 

7 
8 

5 
6 


,  m. 

30 
o 

40 

10 

18 

3 
15 
10 

45 

50 

o 

15 

50 

18 

o 

30 

o 

30 

o 

55 
o 

40 

10 

35 
30 
40 
46 
30 

30 

48 

15 

40 

55 
I 

40 

50 

15 

7 

o 

o 


7 
10 

ID 

9 
4 


21 
3<i 

20 


Noon. 


7 

5 
10 

I 

10 
10 

3 
12 

5 
3 


50 

4 

32 

48 

30 

35 
12 

30 

30 

.  30 
?^oon. 

3  55 

4  15 
8 


30 
13 


5 
9 

10 


56 

15 

27 


Feet. 


7 
5 

20 

15X 
18 

6 


14 

o 
II 

6 
5 

5 
8 

22 
3 

6 
11^ 

7 
15 

7 

6 

About  6 

17 

II 
II 

5-6 
18X 
15 
3 

9yz 
4 

2 

7 
18 

534: 
21 

3-4>^ 

21 

8 

15K 
3 
15-22 

7 
6 

6K 
6 

3 


5 
6 

1-4 

2 
24 

8 

2H 


Feet. 
5 

5 
16 

1134: 

13 

6 

9 
10 


^7  , 

2% 


13M 


3X 


5 
12 


4K 


18 
6 


TABLE  47. 
TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c 


[Page  497 


-Continued. 


Place. 


Millport,  Cumbrae  Island,  Scotland 

Min  River  (Temple  Point),  China,  East  Coast 

Min  River  (Losinof  Island),  China,  East  Coast 

Mindanao,  South  Point,  Filipinas , 

Minehead,  England 

-Mingan  1 1  arbor,  Gulf  of  St.  Lawrence 

Mingan  Island,  Gulf  of  St.  Lawrence 

Minimet^ash,  Prince  Edward  Island 

Minow  Islands,  Madagascar,  West  Coast 

Mint juiers  Rocks,  France 

Miramichi  (Bar),  Gulf  of  St.  Lawrence 

Mirapor-vos,  Bahamas , 

Mirs  Bay  (Tide  Cove),  China,  East  Coast , 

Miscou,  Gulf  of  St.  Lawrence 

Mistanoi jue,  Labrador 

Mistley  Quay,  Stour  River,  England , 

Miwara,  Japan , 

Moala,  Fiji  Islands 

Mocha  Island,  Chile  . , 

Mocha  Road,  Red  Sea,  East  Coast 

Moerdijk 

Mogador,  Africa,  West  Coast 

Molyneux  Bay,  New  Zealand 

Mombaza,  Port,  Africa,  East  Coast 

Monach  Islands,  Scotland,  West  Coast 

Monckton  ( Railway),  Bay  of  Fundy , 

Mondego  (Bar),  Portugal 

Monganui  Harbor,  New  Zealand , 

Monrovia,  Africa,  West  Coast , 

Montagu,  South  Australia,  East  Coast 

Monte  Video,  South  America,  East  Coast 

Montgomery  Isles,  Australia,  West  Coast 

Montrose,  Scotland 

Monts,  Point  de.  Gulf  of  St.  Lawrence 

Montt,  Port,  Reloncavi  Sound,  Chile 

Morecaml)e,  England 

Moreno  ( Constitucion  Road ),  Peru 

Moreton  Bay,  Australia,  East  Coast 

Morewellham,  River  Tamar,  England 

Morjovets  Island,  White  Sea 

Morlaix  Road,  France , 

Morro  (Sandy  Point),  Ecuador 

Mossel  Bay,  Africa,  South  Coast 

Moudiuga  Island,  White  Sea , 

Mount  Louis  Bay,  River  St.  Lawrence 

Mourondava,  Madagascar,  West  Coast 

Mouton,  Port,  Nova  Scotia , 

Moville,  I  reland 

Mowah  lUmder,  Hindoostan,  West  Coast 

Mozambique  Harbor,  Africa,  East  Coast 

Mucaras  Keef,  Bahamas , 

Muerka.     {See  Marka.) 

Mugeres  Harbor,  Bay  of  Honduras , 

Mull  of  Cantyre,  Scotland 

Mulroy  Bay  (Bar),  Ireland , 

Mumbles  Light-house,  Wales 

Mungalaum  Island,  China  Sea,  East  Coast 

Mongullo  or  Mongallo  River,  Africa,  East  Coast 

Murray  Islands,  Torres  Strait , 

Musa,  Port,  Babuyan  Islands , 

Mutlah  River  (entrance  to  Biddah  River),  Bay  of  Bengal,  West  Coast 

Mutlah  (Muda  Kali),  Bay  of  Bengal,  West  Coast 

Mutton  Island,  Ireland,  West  Coast , 

Myggenses  Fiord,  Foeroe  Islands 


Na  Vatu  Reef,  South  Pacific 

Naafe  River,  Bay  of  Bengal,  East  Coast . 


High  Water,  Full 
and  Change. 


//.  »l. 

II    50 

10  27 

Noon. 

7     o 

6  24 

1   16 


30 
o 


I 

3  3 

5  o 

6  6 
5  30 
9  30 

10    o 

2  30 
10  30 

0  48 

10  37 

5  50 
10  30 

Noon. 

4  o 

1  18 

3  o 

4  o 

5  44 

o  15 

2  30 

8  IS 

6  o 
830 


Noon. 

•  25 
Noon. 

o  48 
1 1  26 
10 


o 
30 


b   12 
II   20 

53 
o 

30 


4 

5 

3 

5  50 
2    o 

4  45 
7  54 
7  6 
I      o 

4  15 
7  40 

9  30 

10  35 

5  40 

6  I 

11  o 
4  45 
9  30 


10  o 

11  45 
4  20 

9  o 

6  8 

10  o 


Rise. 


Springs.  Neaps. 


Fecf. 
10 
18 

17 
6 


6 

6 

5 

15 
35 

5 

5 
6 

11^ 

II 

5 


9 

10-12 

8 

II 

47 
7 
9 
6 

5-7 
4-6 

36 

13 

12 

18-20 

27 

4 

4-7 

io>^ 

17 
24 
II 

6 

6-8 

12 

VA 

VA 

12 

12 

3 

1% 
4 
1134" 

5 
12 

10 

5 

14 
15  ^ 

13^ 


9% 


Feet. 
6 

13 

14,5^ 

24K 
4 
4 


26 
3 


74 


10 

6 

14-15 
21 


6;^ 


5'^ 

9%. 


'/\ 


9!^ 


\Z    B 


Page  498 j  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Feet. 


Naalsoe  Fiord,  Fseroe  Islands 

Nafa-Kiang,  Loo  Choo  Islands 

Nagasaki  Bay,  Japan 

Nagore,  Bay  of  Bengal,  West  Coast 

Nairai  Island,  Fiji  Islands 

Namki  Islands,  China,  East  Coast 

Namoa  Harbor,  China  Sea,  West  Coast 

Namoa  Island  (Clipper  Road),  China,  East  Coast 

Namquan  Harbor,  China,  East  Coast 

Namu  Harbor,  America,  Xorthwest  Coast 

Nanaimo  Harbor,  Gulf  of  Georgia,  Vancouver  Island 

Nancowry  Harbor,  Nicobar  Islands   

Nandi  Passage  and  Bay,  South  Pacific 

Nangamessie  Harbor,  Sumba 

Nangka  Island,  Banka  Strait 

Nanoose  Harbor,  Vancouver  Island 

Napoleon  Road,  Gulf  of  Tartary 

Narrinda  Bay,  Madagascar,  West  Coast 

Narrows  (First),  Magellan  Strait 

Narrows  (Second),  Magellan  Strait 

Naruto  ( Fukura),  Japan 

Nash  Point,  Bristol  Channel 

Nasparte  Inlet,  Vancouver  Island 

Nass  Bay,  America,  Northwest  Coast 

Nassau,  New  Providence,  Bahamas , . 

Nassau  Bay,  Tierra  del  Fuego 

Natal,  Port,  Africa,  South  Coast ' 

Naturaliste  Channel,  Shark's  Bay,  Australia,  Northwest  Coast 

Navallo,  Port,  France 

Nazaire.  St.,  France ■. 

Naze,  The,  England 

Neath,  England 

Needle's  Point,  England 

Negapatam,  Bay  of  Bengal 

Negro  Harbor,  N  ova  Scotia 

Negro  River,  Patagonia 

Nelson,  New  Zealand 

Nelson,  Port,  Australia,  Northwest  Coast 

Nemoro  Anchorage,  Japan 

Nempkish  River,  Vancouver  Island 

Nerbudda  River  (Broach  Point),  Hindoostan,  West  Coast 

Neuf,  Port,  Gulf  of  St.  Lawrence 

Neuf,  Port,  River  St.  Lawrence 

Neuharlinger  Siel,  Germany 

Neuzen  or  Terneuse,  North  Sea 

Neville,  Port,  Vancouver  Island 

New  Perlican  Harbor,  Newfoundland , 

New  Providence,  Southwest  Bay,  Bahamas 

New  River,  Xew  Zealand 

New  Ross,  Ireland 

New  Year  Sound,  Tierra  del  Fuego 

Newcastle,  Australia,  East  Coast 

Newcastle,  England 

Newcastle,  Ireland 

Newhaven,  England 

Newport,  Wales,  South  Coast 

Newport,  Wales,  West  Coast 

New  Quay,  Wales 

Newton  Stewart,  Carty  Quay,  Scotland,  West  Coast 

Ngaloa,  Fiji  Islands 

Nhatrang  Bay,  China,  West  Coast 

Nicholas,  St,  Harbor,  Gulf  of  St.  Lawrence 

Nicholas,  St. ,  Port,  Pern 

Nicholson,  Port  ( Lambton  Harbor),  New  Zealand ...'!.'."!!!.'. 

Nicobar  Island  (Nancowry  Harbor),  Indian  Ocean  ...•: 

Nicolas,  St.,  Bay,  Magellan  Strait 

Nicoya  Gulf  (Port  Herradura),  Central  America 


h.  m. 

4  o 

6  28 

7  15 

8  15 

5  53 
«  30 

10    o 

"   15 

10    o 


5  o 
9  15 

6  35 
II  ^o 


5 

2 

4 

9 

10 

6 

6 


o 
30 

30 
o 
o 

14 
25 


Noon. 


5 

30 

o 

30 


II  45 
3  42 


40 

6 

16 

46 

o 

8  12 
II       O 

9  50 
Noon. 

o 


30 
40 
10 
30 
45 
35 
30 
30 

30 
10 


5 
o 

3 
2 
8 
II 
I 
o 
7 
7 
o 

6  4 
830 
9  o 
4  23 

II     4 

II  51 

7  10 

7  o 
7  30 
Noon. 
6  o 
830 
I 
5 
4 
9 
o 

3 


55 
15 
30 
15 
50 
9 


Feet. 
6K 
7 
9 

3^-4>^ 
17 

7% 

7 

17 
15 
14 

8>^ 

A'A 
17 
12 

15 

2^ 

15 

36-42 

23 

6X 
33 
12 

23 
4 
6 
6 
6 

13 

15X 
12K 
13K 

7K 

3 

7 

14 
14 
27 

4 
14 
25 
13 
14 

sU 

15 

17 

4 

4 

8 


y/z-s 

lOX 

14^ 
20 

38 
12 

15 
12 

5 

6 
10 

3 

5 

8X 
6 

10 


12% 


13K 


2 
25 


II 

10 


10 


8 
9 

II 


2^ 

6 
10 


12 

15 

29 

9 


7 
3 


TABLE  47.  [Page  499 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  \c.— (  ontinucl. 


Nieuport,  Belgium 

Nieuwediep,  N etherlands . 

Niger  River  (Nun  entrance),  Africa,  West  Coast . 

Nikolslioi  Channel,  White  Sea 

Nikolskoi  lower,  White  Sea 

Ximroi  I  Sound,  China,  East  Coast 

Ninepin  Group,  China,  East  Coast 

Xing-hai,  Yellow  Sea 

Xin-po-fu,  Yung  River,  China,  East  Coast 

Nisqually,  America,  Northwest  Coast 

Xoamh  Island,  Scotland 

Xoarlunga,  Port,  Australia,  South  Coast 

Noel  Bay,  Bay  of  Fundy 

Noir  Island,  Tierra  del  Fuego 

N^oirmoutier,  France 

Nolloth,  Port,  Africa,  Southwest  Coast 

Nootka  Sound,  Vancouver  Island 

Norderney,  (jermany 

Nore,  England 

Norfolk  Island,  South  Pacific 

X^orth  Balabac  Strait,  China,  East  Coast 

North  Cape,  Cape  Breton  Island 

X'orth  Harbor,  Newfoundland 

X'orth  Sands,  Malacca  Strait 

X'^osari  Khari  (Bar),  Hindoostan,  West  Coast 

Xoss  Island,  Madagascar 

Notske  Bay,  Japan 

Noumea  Bay,  New  Caledonia 

X'^ova  Zembla  Harbor,  Lapland 

Novogorod  Bay,  Korea 

Nowanugga,  Hindoostan,  West  Coast 

Nuchatlitz  Inlet,  Vancouver  Island 

Nuevo  Gulf,  Patagonia,  East  Coast 

Nuevo,  Port,  Central  America 

Xukulau,  Port,  Fiji  Islands 

X'^uma-choa,  Comoro  Islands 

X'^unez  River,  Africa 

Nyminde  Gab,  Jutland 

Nysna  or  Knysna  Harbor,  Africa,  South  Coast.. 


Oazy  Harbor,  Magellan  Strait 

Oban,  Scotland 

Obb  of  Harris,  Isle  of  Harris,  Scotland 

Observatory  Inlet,  America,  Northwest  Coast. 

Observatory  Island,  China  Sea,  East  Coast 

Octavia  Bay,  New  Granada 

Oelar,  Cape,  Banka  Strait 

Ogden  Channel,  America,  Northwest  Coast 

Oho  Sima,  Loo  Choo  Islands 

Oibo  Harbor,  Africa,  East  Coast 

Okarito  Lagoon,  New  Zealand 

Old  Providence,  Bay  of  Honduras 

Olenji  Islands,  Lapland 

Oleron,  Isle  d',  France 

Olga  Bay,  Gulf  of  Tartary 

Omaider  Island,  Gulf  of  Akabah,  Red  Sea  . . . . 

Omersari  River,  Hindoostan,  West  Coast 

Omonville,  France 

'Om-rasas-Masirah,  Arabia,  Southeast  Coast  .. 

One-Fathom-Bank  Light,  Malacca  Strait 

Onega  River,  White  Sea 

C)no  Islands,  South  Pacific   

Ooloogan  Bay,  China  Sea,  East  Coast 

Oonting,  Port,  Loo-Choo  Islands 

( )osaka  River  (entrance),  Japan 

( )dsaka  City,  Japan 

Oosima,  Japan 


High  Water,  Full 
and  Change. 


o 

7 
4 
5 


18 

27 
8 

25 
o 

^o 


6 
10 

10  o 
Noon. 

1  o 

6  o 
5  2 
4  30 
o  41 

2  30 

3  2 
2  35 

Noon. 

11  15 

o  30 

7  45 
10  50 

8  o 


o 

;o 
o 
o 

50 


8  25 

6  36 
2  30 
I  45 

Noon. 

7  o 
10 

47 
o 
o 

45 
30 


3 
6 

3 

10 

2 
3 


10 

5 
6 

I 

II 

3 
6 
I 
7 
4 
II 


18 
22 
16 

5 
o 

30 

30 

o 

30 

15 

40 


Irregular. 


7  30 
3  50 

5  30 

6  o 

45 

29 

o 

o 

17 
o 

30 

35 

7  30 

8  17 

6  50 


I 

7 

10 
6 

9 
6 

9 

6 


Rise. 


Springs. 


Feet. 
16 

4 
6 

3 
2 

20 

5 
6 

9 
18 

6 

50^2 

5 
16 

SX 
12 

7^ 
i5>^ 
7 
5 
4 
7K 

15 
18 

15 

4)^ 
4 
10 

2^ 
18 
12 
10 
12 

3>2-5 
14 
15 

6-7 

7 
12 

23 

5X 
13 
12 
20 

6 

9 

I 
12 
19 

3 

4 
18 

15^ 

ID 
15 

6-7 

4 

5>^ 
8 

5 


Neaps. 


Feet. 
13 


15 

7 

43;^ 


13 


5 
12 


^Yz 


14 


\iYz 


6 

9Yz 
SY2 
12 


12K 
12 


\y4 

Y2 


Page  500]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Oosuka,  Japan 

Oparo  or  Rapa  Island,  Ahurei  Bay,  South  Pacific. 

Oporto,  Portugal 

Orange  Bay,  Tierra  del  Fuego 

Orange,  Cape,  Magellan  Strait 

Orete,     (.S'lV  New  River.) 

Orford  Haven  ( Bar),  England 

Orford  Quay,  England 

Orfordness,  England 

Orinoco  River  (entrance),  Guayana 

Orleans  Island,  River  St.  Lawrence. 

Ormond,  Kenmare  River,  Ireland 

Ornsay,  Isle  of  Skye 

Orlov  Letni,  Cape,  White  Sea 

Os  Ilheos,  Brazil 

Osaki,  Japan 

Oscuro  Cove,  Patagonia,  West  Coast 

Osprey  Reef,  Australia,  East  Coast 

Ostend,  Belgium 

Otago  Harbor,  New  Zealand 

Otaheite,  South  Pacific 

Otterswick,  Orkneys 

Otway,  Port,  Patagonia,  West  Coast 

Ou-ou  Kinsh  Inlet,  Vancouver  Island 

Ounalashka  Island,  America,  Northwest  Coast  ... 

Ouro  River,  Africa,  West  Coast 

Ovalau,  Fij  i  Islands 

Owasi,  Japan 

Ower  Shoal,  England,  East  Coast 

Oxbaasheia,  Svee  Fiord,  Norway 

Oystreham,  France 


Packsaddle  Bay,  Tierra  del  Fuego 

Padstow,  England 

Pagham  (entrance),  England 

Pago  Pago,  Navigator's  Islands,  South  Pacific 

Paimpol,  France   

Palais,  Port  le,  Belle  Isle,  France 

Palliser,  Cape,  Ne  w  Zealand 

Palm  Isles,  Australia,  East  Coast 

Palma,  Canary  Islands 

Palmas,  Cape,  Africa,  West  Coast 

Palmedo  Road,  Sumba  Island 

Palmeira  Point,  Ceylon 

Paluan  Bay,  Mindoro 

Pamarung  Islands,  Borneo,  East  Coast 

Pampang  Bay,  Java 

Panama  Road,  Central  America 

Panbula  River,  Australia,  East  Coast 

Pancol,  China  Sea,  East  Coast 


Pansand  Hole,  England 

Paposo,  Chile 

Paquique,  Cape,  Bolivia 

Para,  Brazil,  North  Coast 

Parahiba,  Brazil 

Paranagua,  Brazil 

Parenga-renga  Harbor,  New  Zealand 

Parida  Island,  New  Granada 

Parsboro,  Bay  of  Fundy 

Pasado,  Cape,  Ecuador 

Pasages,  Port,  Spain 

Passage  or  Culebra,  Port,  Caribbean  Sea  . 

Passage  Island,  Banda  Sea 

Passandava  Bay,  Madagascar,  West  Coast . 

I'aterson's  Inlet,  New  Zealand 

Patterson,  Port,  Australia,  North  Coast  . . . 
Patrick,  Port,  Scotland 


h.  i/i. 
9  16 
Noon. 

2  30 

3  30 

-> 


o 


II  30 
o  30 

II  15 

6    o 


5 

■■> 

5 
5 
4 
5 


40 

43 
50 
18 

30 

55 

o  55 

8  36 
o  25 
2  50 

Noon. 

9  13 
II  37 

Noon. 

7  30 
Noon. 

6  o 

7  o 
6  30 

Noon. 
9  38 


30 
13 


II  30 
7  II 


6 


o  30? 
4  30 


9  30 


3 

23 

9 

0 

9 

40 

Noon. 

9 

40 

9  45 

Noon. 

5 

0 

3 

0.'> 

7  54 

3 

15 

0 

17 

3  30 

3 

0 

9 

0 

Noon. 

5 

0 

I 

ID 

4 

0 

II 

ID 

Feet 

1-2 

ID 

5 


17 
10 

4 
20 

6 
19 

7 

iX 
II 

6 
12 

7X 
8-9 

3-5 
5 

8 
21 

6 

20;^ 
i6>^ 
3K 
31 

hX 

6 
8-10 

9? 
4 
15 
7-1 1 

5 
8-10 

7-8 

ii;-22 

\-6 

6 

iS'A 
5 

II 
9-12 

6X 
7 

43 
10 
12 

I 

6 
15 

5 
13-20 

15 


Feet. 

iK? 


13 

loX 


15 
5 


16 


10;^ 

I2>^ 

23^ 

loX 


10-16 

13 


37K 


6 

6-12 

12 


TABLE  47.  [Page  601 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Patta  Bay,  Africa,  East  Coast 

Patteson,  Port,  Vanu  Lava  Island,  Banks  Islands 

Paty tan  Bay,  Java 

Paul  de  Loanda,  San,  Africa,  Southwest  Coast 

Paul,  St.,  Island,  Indian  ( kean   

Paul,  St.,  Island,  Ciulfof  St.  Lawrence 

Paumben  Pass,  Bay  of  Bengal,  West  Coast 

Payta,  Port,  Peru 

Pearce  Point,  Australia,  North  Coast 

Pecket  Harbor,  Magellan  Strait 

Pedro  Gonzales,  Trapichi  Island,  New  Granada 

Pedro,  San,  Pass,  Patagonia,  West  Coast 

Peejow.     {See  Pidioe.) 

Peel,  Isle  of  Man 

Pegasus,  Port,  New  Zealand 

Peh-tang-ho,  Yellow  Sea 

Pei-ho  or  Peking  River  (entrance),  Yellow  Sea 

Pei-hcLor  Peking  River  (Tien-tsin) 

Pelew  Islands,  North  Pacific 

Pelican  Lagoon,  Kangaroo  Island,  Australia 

Pelorus  Sound,  New  Zealand 

Pellworm,  Denmark 

Pemba  Channel,  Mozambique 

Pemba  Island,  Mozambique . 

Pembroke  Dockyard,  Wales 

Penang,  Malacca  Strait 

Peiias,  Cape,  Tierra  del  Fuego 

Pender  Harbor,  Strait  of  Georgia,  British  Columbia 

Peniche,  Portugal 

Penmarch  Rocks,  France 

Pennington  River,  Bight  of  Benin 

Pentillie,  River  Tamar,  England 

Pentland  Firth,  Stroma,  South  side 

Pentland  Firth,  Swona,  Last  side 

Pentland  Firth,  Swona,  West  side 

Pentland  Firth,  Great  Skerry,  East  side 

Pentland  Firth,  Great  Skerry,  West  side 

Penzance,  England 

Percy  Isles,  Middle  or  No.  I  Island,  Australia,  East  Coast 

Percy  Isles,  South  or  No.  2  Islet,  Australia,  East  Coast 

Perim  Island,  Gulf  of  Aden 

Pernambuco,  Brazil 

Peros  Banhos,  Indian  Ocean 

Perouse,  La,  Strait,  Japan 

Perron,  Cape  Shark's  Bay,  Australia,  Northwest  Coast 

Perth,  Scotland 

Perula  Bay,  Mexico,  West  Coast 

Pescadore  Islands  (Makung  Harbor),  China  Sea 

Peter,  St. ,  Bay,  Cape  Breton  Island 

Peter,  St.,  Harbor,  Prince  Edward  Island 

Peterhead,  Scotland 

Petit  Passage,  Bay  of  Fundy 

Petit,  Port,  Bay  of  Islands,  Newfoundland 

Petrel  Bay,  St.  Francis  Isle,  Australia,  South  Coast 

Petucura  Rock,  Patagonia,  West  Coast 

Pheasant  Point,  Wusung  River,  China,  East  Coast 

Philip  Bay,  East  side,  Magellan  Strait 

Philip,  Port,  Lonsdale  Point,  Australia,  South  Coast 

Philip,  Port,  Queen's  Cliff,  Australia,  South  Coast 

Philip,  Port,  Nepean  Point,  Australia,  South  Coast 

Philip,  Port,  Dromana,  Australia,  South  Coast 

Philip,  Port,  Schnapper  Point,  Australia,  South  Coast 

Philip,  Port,  Bellarine  Jetty,  Australia,  South  Coast 

Phihp,  Port,  Harvey  Point,  Australia,  South  Coast 

Philip,  Port,  Geelong,  Australia,  South  Coast 

Philip,  Port,  Williamstown,  Australia,  South  Coast 

Philip,  Port,  Melbourne,  Australia,  South  Coast 


High  Water,  Full 
and  Change. 


/i.  m. 


4 
6 

3 

4 

ir 

8 


30 

40 

o 

30 
o 

o 

I  30 

3  20 
6  55 
9  30 
3  50 
o  30 


II 
II 


50 


3  40 
7    o 


5  o 
9  35 
I  50 
4    o 

4  15 

6  12 
Noon. 

6  2 
6     o 


54 
16 

15 

55 
47 

10  24 

9  35 

11  4 

10  53 
4  30 
10  30 
10  30 
Noon. 

4  45 
I  30 

10  30 

o  45 

J  j5 


10  30 

7  30 

8  30 

o  34 
10  41 
10  42 
Noon. 

o  50 


35 
30 
42 


ID    50 

10  53 
19 
14 
21 

39 
30 

31 

48 


Rise. 


Springs. 


Feet. 

ID 

5 
7 
5 
3 

5 
2 

20-26 


7 
16 

9 

I 

8 

ID 
ID 

ArVz 

6 

6 

II 

ID 
II 
12 
21 

9 
12 

13 


5 
13K 


Neaps. 


Feet. 


10-18 
6 


13 

6 


7 


9K 
6 


(y'A 


x(>% 

I2>^ 

16 

13 

14 

7 

s^ 

8-6 

5 

6 

5^ 

9K 

7 

^Yz 

7 

6 

4 

4 

2 'A 

loX 

,    ^H 

22 

18 

,SK 

6 

16 

13 

8 

24 

7 

S'A 

3 

2 

2K 

^A 

3   ^ 

2^ 

2U 

2 

2/2 

2 

3 

2K2 

S'A 

2% 

2H 

2 

Page  502]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Hi^h  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 

Feet. 
4 


21 
4>^ 


Pichidanque  Bay,  Chile 

Pictou  Harbor,  Nova  Scotia 

Pidioe  or  Peejow  P>ay,  Lombock 

Piedras  Cay,  Cuba 

Piel  Harbor,  England 

Pierre  Strait,  Newfoundland 

Pierre  Island,  China  Sea,  East  Coast 

Pigeon  Bay,  Yellow  Sea 

Pihkishan  Islands,  China,  East  Coast 

Pillar,  Cape,  Magellan  Strait 

Pillar,  C'ape,  Tasmania 

Pillars,  River  .St.  Lawrence   

Pimlea  Harbor,  Africa,  East  Coast 

Pinas  Bay,  New  Granada 

Ping  Yang  River,  Korea 

Pinmill,  Orwell  River,  England 

Pio  Quinto,  Port,  Bal)uyan  Islands 

Pirie,  Port,  Spencer  Gulf,  Australia,  South  Coast 

Pisco  Bay,  Peru 

Piti  Palena,  Patagonia,  West  Coast 

Piti  River,  Hindoostan,  West  Coast 

Placentia,  Newfoundland 

Plank  Point,  Spencer  Gulf,  Australia,  South  Coast 

Playa  de  Incia,  Cuba 

Playa  Parda  Cove,  Magellan  Strait 

Pleasant,  Port,  Falkland  Islands 

Plettenberg  Bay,  Africa,  South  Coast 

Ploughrescan,  France 

Ploumanach,  France 

Plumper  Cove,  Howe  Sound,  Gulf  of  Georgia,  British  Columbia. 

Plumper  Sound  (Fane  Island),  Vancouver  Island 

Plymouth  Breakwater,  Elngland 

Plymouth  (Sutton  Pool),  England 

Plymouth,  New,  New  Zealand 

Pomba  Bay,  Africa,  East  Coast 

Pomeroy  Inlet,  Labrador 

Pomquet,  Nova  Scotia 

Ponapi  Island,  Caroline  Islands,  North  Pacific 

Ponga  River,  Africa,  West  Coast 

Poolbeg  Light-house,  Ireland 

Poole,  England 


Poolewe,  Loch  Ewe,  Scotland   

Pools  Harbor,  Newfoundland 

Pootoo  Island,  China,  East  Coast 

Poqueldon  Harbor,  Patagonia,  West  Coast 

Portaferry,  Ireland 

Port-au-Choix,  Newfoundland 

Port-au-Prince,  St.  Domingo 

Port-en-Bessin,  F'rance 

Port  Macdonnel,  Australia,  South  Coast 

Port  Pela  (Adriatic) 

PorfRhin,  Mulgrave  Islands,  Marshall  Islands 

Port  Royal,  Jamaica 

Port  Spain,  Trinidad,  Caribb^e  Islands 

Portchester,  England 

Porlendik,  Africa,  West  Coast 

Porthcawl,  Wales 

Porth-dyn-lleyn,  Wales 

Portishead,  England 

Portland  Bay,  Australia,  South  Coast 

Portland  Breakwater,  England 

Porto  Frio,  Brazil 

Porto  Praya,  St.  Jago,  Cape  Verde  Islands 

Porto  Santo  Bay 

Portree,  Isle  of  Skye 

Portrieux,  France 


//.   771. 

9  20 
10     o 


8 
II 

S 


o 

5 
1>1 


6  39 


8  30 


Feet. 

5 
6 

10-12 

28 

4 
8 

17 

6 

17 
12 

14 

21 

12 

6 

9-11 

4 
10 

9 

8 

6-8 

6J4 
6 

25K 
24X 
12 

12 

12 

15 

7 

4 

6 

12 

12-14 

6K 

W/z 

4 

12 

18 

18-21 

5 
I? 

20 

4 

3^ 

I 

4 

13^ 
6 

28'^ 

16 

40 

3  iiT- 

ty^ 

4K 

5 

7 
15 
31 


10 


14 


1814: 
18K 


11^^ 

9 
II 

4 

2ji 

9-1 1 
4X 


12-16 


15K 


10;^ 
21;^ 
31 


I03^ 
23K 


TABLE  47.  [Page  503 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Portsbridge  (Portsmouth),  England 

Portsmouth  Dockyard,  England 

Possession  Bay,  Magellan  Strait   , 

Possession,  Cape,  Torres  Strait , 

Possession  Island,  Torres  Strait 

Post-Office  Island  (Charles  Island),  Gallapagos  Islands 

Post-Office  Island,  Torres  Strait 

Poulamente  Bay,  Madame  Island,  Cape  Breton  Island , 

Poulton-le-Sands,  England 

Poverty  Bay,  New  Zealand , 

Pratas  Shoal,  China  Sea 

Preservation  Inlet,  New  Zealand 

Preston,  England 

Prince  Frederick  Harbor,  Australia,  Northwest  Coast 

Prince  Regent  River  (St.  George  Basin),  Australia,  Northwest  Coast. 

Prince  of  Wales  Strait,  Banks  Land 

Prince's  Island,  Bight  of  Biafra 

Princess  Royal  Harbor,  Australia,  South  Coast 

Prospect  River,  Nova  Scotia 

Pubnico  ( Beach  Point),  Bay  of  Fundy 

Puerto  Bueno,  Patagonia,  West  Coast 

Puerto  de  Baitiqueri,  Cuba 

Puerto  de  la  Luz,  Gran  Canaria,  Africa,  West  Coast 

Puerto  de  Maravi,  Cuba , 

Puerto  de  Mata,  Cuba 

Puerto  de  la  Plata,  St.  Domingo 

Puerto  de  Taco,  Cuba 

Puget  Sound  (Nisqually),  America,  Northwest  Coast 

Pugwash  Harbor,  Nova  Scotia 

Pulicat  Shoals,  Coromandel  Coast 

Pulo  Aor,  Sumatra,  Northeast  Coast 

Pulo  Condore,  China  Sea,  West  Coast 

Pulo  Leat,  Caspar  Strait 

Pulo  Mendanao,  Caspar  Strait 

Pulo  Panjang,  Gulf  of  Siam 

Puluqui  Island,  Patagonia,  West  Coast 

Puna  Island,  Ecuador 

PwlheH  (Bar),  Wales 


Qlawdzeet  Anchorage,  America,  Northwest  Coast 

Quaco,  Bay  of  Fundy 

Quan-chow-wan,  Gulf  of  Tongking 

Quatsino  Sound,  Vancouver  Island 

Quebec,  River  St.  Lawrence , 

Queda,  Malacca  Strait 

Queen  Charlotte  Sound  (entrance),  New  Zealand. 

Queensferry,  Firth  of  Forth,  Scotland 

Queenstown,  Ireland 

Quelan  Cove,  Patagonia,  West  Coast , 

Quentin,  San,  Port,  California , 

Queullin  Island,  Chile 

Quicavi  Bluff,  Patagonia,  West  Coast 

Quilca  River,  Peru 

Quilimane  River  (entrance),  Africa,  East  Coast  .. 

Quilleboeuf,  France 

Quiloa,  Africa,  East  Coast 

Quoile  Quay,  Strangford,  Ireland 


Rabat,  Africa,  West  Coast 

Race,  Cape,  Newfoundland 

Rachada,  Cape,  Malacca  Strait 

Radama,  Port,  Madagascar,  West  Coast. 
Ragged  Island,  Sumbawa,  Java  Sea 


Ragged  Point,  Borneo,  East  Coast. 


Raine  Island,  Torres  Strait 

Rajang  River,  Borneo 

Rajapur  River  (entrance),  Hindoostan,  West  Coast. 


h.  m. 
II  48 
II  41 

835 


9 
I 
2 
I 

7 

u 

6 

4 


o 
o 

ID 
O 

26 

5 
o 


II  20 
II  49 

Noon. 
o  20 


3  45 
II  56 


43 
25 
24 

7 
o  52 

7  56 

6  49 

7  30 
849 
6    o 

10  30 
9  25 


30 

30 

30 
o 

5 
o 

46 


I  30 
II  35 


II      o 

6  38 
Noon. 

8  50 
2  37 

5     I 
o  28 

9  5 


o  57 
8    o 

4  15 

ID      6 

4  45 

0  45 

1  46 

7  o 

5  30 
4  40 

8  10 


8  10 

4  45 

II      o 


Feet, 


36- 


12^ 

-42 
6 

9K 
6 

9% 
6 

27X 
6 

5 
8 

10 

28 

24-37 

3 

4K 
1-4 
7 

12 
8 

2^ 
10 


234: 

3? 
2^ 
18 

7 
2% 

5 

4 
4 
2 

II 

1314: 

17-22 

30 
9-10 

II 

18 

s% 

8 
18 

11^ 

9 
20 
20 

6 
16 

9% 
12 
II 

9-12 

13 

13 

3 

7 
10 

13 

9 


Feet. 
4 

ID 


4 

21^ 


4 


6 
10 


15 

4 


9% 


14-17 
25 


13 


6 

14 

9 


1% 
9X 


9 

7 


Page  504]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.- Continued. 


Place. 


Rajapur  River  (town),  Hindoostan,  West  Coast 

Rajpuri  River  (entrance),  Hindoostan,  West  Coast 

Ramos  River,  Bight  of  Benin 

Ramree  Road,  Bay  of  Bengal,  East  Coast 

Ramsay  Sound,  Wales 

Ramsey,  Isle  of  Man 

Ramsgate,  England , 

Ramso  Fiord,  Norway 

Random  Head  Harbor,  Newfoundland 

Rangoon,  Bay  of  Bengal,  East  Coast 

Rangoon  River  (entrance),  Bay  of  Bengal,  East  Coast 

Raoul  or  Sunday  Island,  South  Pacific 

Ras  Hafiin,  Africa,  East  Coast , 

Ras  Jerdaffoon.     {St'c  Guardafui  Cape.) 

Ras  Madraka,  Arabia,  Southeast  Coast 

Ras  Sharmah,  Arabia,  Southeast  Coast , 

Ras-el-Khaimeh,  Persian  Gulf 

Ras-al-Asidah,  Arabia,  Southeast  Coast 

Ras  Shebali,  Arabia,  Southeast  Coast 

Ras-al-Hed,  Arabia,  Southeast  Coast 

Rathmullan,  Ireland 

Ratna-ghiri,  Hindoostan,  West  Coast 

Realejo,  Central  America , 

Red  Bay,  Ceylon,  South  Coast , 

Red  Bay  (Pier),  Ireland 

Red  Bay,  Labrador 

Red  Island,  Durian  Strait , 


Redbrldge,  England 

Refuge  Cove,  Bass  Strait 

Rdgneville,  France 

Reikiavik,  Iceland 

Reloncavi  Inlet,  Patagonia,  West  Coast 

Rendezvous  Island,  Borneo,  Southwest  Coast 

Rendezvous,  Strait  of  Georgia 

Renfrew,  River  Clyde,  Scotland 

Resolution  Bay,  Marquesas ... 

Resolution,  Port,  Tanna  Island 

Reunion  Island  (St.  Pierre),  Indian  Ocean .'.... 

Reunion  Island  (St.  Denis),  Indian  Ocean 

Reunion  Island  (St.  Gilles),  Indian  Ocean 

Reunion  Island  ( St.  Paul),  Indian  Ocean 

Rewa  Road,  Fiji  Islands.     {Scy  Nukulau  Port.) 

Rhio,  Rhio  Strait 

Ribble  Light-house,  England 

Richibucto  River,  Gulf  of  St.  Lawrence 

Richmond  Harbor,  Prince  Edward  Island 

Richmond  River,  Australia,  East  Coast 

Rio  de  la  Plata,  Cape  Castillos    

Rio  de  la  Plata,  Buenos  Ayres 

Rio  de  la  Plata,  Barragan  Bay 

Rio  Grande  do  Sul,  Brazi  1 

Rio  Janeiro,  Brazil 

Rio  Negro,  Patagonia,  East  Coast 

Rio  Nunez,  Africa,  West  Coast 

Ristegouche  River,  Campbelltown,  Gulf  of  St.  Lawrence. 

Rivadeo,  Spain,  North  Coast , 

Ri voH  Bay,  Australia,  South  Coast 

Rocas,  Atlantic 

Roche,  Cape,  River  St.  Lawrence 

Roche  Harbor,  I  laro  Strait 

Rochefort,  France 

Rochelle,  France 

Rockall,  North  Atlantic !!'.."!.".'.!!!!!.' 

Rocky  Island,  Gulf  of  Siam 

Rodney  Bay,  O wasi,  Japan 

Rodrigue  Island,  Indian  Ocean 


High  Water,  Full 
and  Change. 


k.  m. 

O  20 

10  40 

4  20 

10  O 

6  o 

11  12 
II  44 
10  45 

7  8 

5  30 

3  15 

6  o 
6  15 


9 

9 

II 

8 

10 

9 

5 
10 

3 

2 


o 
o 

45 

30 
o 

30 
42 

30 
6 
20 
10  31 

7  45 

5  o 

10  42  and 
o  57 
o     5 

6  20 
5  o 
o  44 


7  o 

1  15 

2  30 

5  35 
Noon. 

0  22 

1  o 
I  7 

9  50 

10  51 

3  30 

6  o 

9  20 

8  30 
Noon. 

7  o 


II 

10 

4 

3 
o 

5 
9 


o 
o 
o 
o 
o 

33 
15 


Irregular. 
4     6 
3  31 

3  30 

4  o 
7  o 
I  45 


Rise. 


Springs. 


Feet. 

7 
II 

5 
12 

17 

19X 
15 

7 

21 

21 

5 
4 

10 

8 
7 

10 
9 

8 
II 

2X 

4 

3K 
io}4 


8 
35 
17K 
14 

8 

14 
9 
4 
3 

3/2 

4 

7 
24 

4 
3 

2 
3-5 
5-9 

4 
14 

15 

10 

15 

4 
10 

6 
12 
17 
17 
12 

4 


TABLE  47.  [Page  505 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Roebuck  Bay,  Australia,  West  Coast 

Roji,  Hindoostan,  West  Coast  ..   

Romania  Point  (Malay  Peninsula),  China  Sea,  West  Coast 

Romdals  Islands,  Norway 

Rona  (South)  Light,  Scotland 

Roodewall  Bay,  Africa,  Southwest  Coast 

Roque,  St. ,  Cape,  Brazil 

Roscoff,  France 

Rosel,  Jersey,  English  Channel 

Roshnoff,  Cape,  America,  Northwest  Coast 

Rosslari  Point,  Ireland 

Rota,  Spain 

Rotterdam,  Netherlands 

Rottnest  Island,  Australia,  West  Coast 

Rottum,  Netherlands 

Rouen,  .France 

Rouge  Harbor,  Newfoundland 

Roundstone    Ireland 

Rovama  River,  Africa,  East  Coast 

Royal  Harbor,  Ruatan,  Bay  of  Honduras 

Royal  Island,  Bahamas 

Royal  Road,  Strait  of  Magellan 

Royalist,  Port,  Palawan,  East  Coast 

Royan,  France 

Ruapuke  Island  (Foveaux  Strait),  New  Zealand 

Rugged  Island,  Bahamas 

Rugged  Island,  Nova  Scotia 

Ruggles  Bay,  Falkland  Islands 

Rupon,  Hindoostan,  West  Coast 

Rush,  Port,  Ireland 

Rutland  Island,  Ireland,  West  Coast 

Ryde,  England 

Rye  Bay,  England 


Sable,  Cape  (Clam  Point),  Bay  of  Fundy 

Sable,  Cape  (Clarke's  Harbor),  Bay  of  Fundy 

Sable  Island  (North  side),  Nova  Scotia 

Sable  Island  (South  side).  Nova  Scotia 

Sables  d'Olonne,  Les,  France 

Sabon  Island,  1  )urian  Strait 

Sacred  Bay,  Newfoundland 

Sacrificios,  Port,  Mexico,  ^^"est  Coast 

Saddle  Island,  East,  China,  East  Coast 

Sado  ( Yebisu),  Japan 

Safety  Cove,  America,  Northwest  Coast 

Sagitsu-no-ura,  Japan 

Saguenay,  Chicoutimi,  Gulf  of  St.  Lawrence... 

Saguenay,  Tadousac,  Gulf  of  St.  Lawrence 

Saigon,  Cape  St    James 

Saigon  (Saigon  City),  Cochin  China 

Saintes,  Caribbean  Sea 

Saipan  Island,  Ladrone  Islands 

Sal,  Cape  Verde  Islands 

Salango  Island,  Ecuador 

Salcombe,  England 

Saldanha  Bay,  Africa,  West  Coast 

Salee  River,  Boisee  Island,  Korea 

Salm  River,  Africa,  West  Coast 

Salmedina  Rocks,  Spain 

Salomon  Islands,  South  Pacific 

Saltash,  River  Tamar,  England 

Salt  Cay  Anchorage,  Bahamas 

Saltees,  St.  George's  Channel 

Salut  Isles,  Brazil 

Salvador,  San,  Port,  Falkland  Islands 

Samana  Bay,  Hayti 

Samanco  Bay,  Peru 


High  Water,  Full 
and  Change. 


h.  III. 

0  30 

1  40 

ID    30 
10   45 

6  20 

2  ^o 


49 
15 
30 
30 
24 

45 
50 

o 
28 

o? 

28 

o 
45 
45 
47 

o? 

38 
I  o 
8  o 
7  59 

7  30 
ID  30 

6  8 

5  22 
II  20 
II  20 

8  27 
8  58 

7  30 

6  30 

3  26 


4 
6 

7 
6 

I 

3 

7 

10 

2 

7 
4 
4 
7 
7 
9 
II 

3 


7 

3 
II 

5 
I 
8 

4 
2 
2 

4 
6 
6 

7 
o 

5 
2 

5 
8 

I 

6 

5 
8 

5 
4 
8 

9 
6 


23 

15 
o 

o 

o 

o 
II 
45 
30 
30 
45 
45 
45 
41 
41 
30 
20 
10 
27 

45 
45 
15 
40 

26 
10 
30? 

30 


Rise. 


Springs. 


Feet. 

30 

18 

12 

6 

14K 
6X 
10 


15 
5 

I2>^ 

7 
1% 


i->3/ 
16 
3/2 

13X 
8 

3 

VA 

5 
10 

S% 
II 

13;^ 
22 

8M 
II 

4 

4 
14 
10 

f' 

14 
2 

14 

9 
12 

17 

12^ 
12 

5 
12 

15 

5 


6 

12K 

2 

15 

4 

6-10 
8 

3? 


Neaps. 


Feet. 

18 

14 

9 


8 
17 


r- 


4 

loX 


10 

6 
6 

7 

yA 

8 
17X 

9 
10 


II 

8 
10 


1 1/2 

3X 
16-27 

8 


II 
3 


m» 


Page  506]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


//.  m. 


Sambilangs,  Malacca  Strait 

San  Bento  River,  Africa,  West  Coast 

San  Bias,  Patagonia 

San  Bias,  Mexico,  West  Coast 

San  Fernando,  Trinidad    

San  Juan  del  Sur,  Central  America    

San  Juan  River,  New  Granada 

San  Lucar,  Spain 

San  Miguel,  California    

Sanboronbon  Bay,  South  America,  East  Coast 

Sandalwood  Bay,  Fiji  Islands 

Sand  Point,  Gulf  of  Liautung,  Yellow  Sea 

Sandwich,  Port,  Malicollo  Island,  New  Hebrides 

Sandy,  Cape,  Australia,  East  Coast 

Sandy  Cove,  East,  Bay  of  Fundy 

Sandy  Cove,  West,  Bay  of  Fundy 

Sandy  Island,  Madagascar,  West  Coast 

Sandy  Islet,  Australia,  West  Coast 

Sandy  Point  Road,  Magellan  Strait 

Sang-tau  Bay,  Yellow  Sea 

Sanguianga  (entrance),  Ecuador 

Sanguir  Island,  Moluccas 

Sangwin  River,  Africa,  West  Coast 

Sanmoon  Bay,  St.  George  Island,  China,  East  Coast 

Sannana  Bay,  Moluccas 

San-Shui,  Si  Kiang,  China,  East  Coast 

Santa  Catalina  Island,  California 

Santa  Cruz  River,  Patagonia,  East  Coast 

Santa  Cruz,  or  Agadir,  Africa 

Santa  Cruz  Islands,  South  Pacific 

Santa  Cruz  Island,  California 

Santa  Cruz,  Teneriffe,  Canary  Islands 

Santa  Maria  Island   Chile 

Santander,  Spain 

Santiago  de  Cuba,  Cuba 

Santona,  Spain 

Saparooa  Island,  Moluccas 

Sapetiba  Bay,  Brazil 

Sapie  Bay,  Sumbawa 

Sarawak  River  (Moratabas  entrance),  Borneo,  West  Coast 

Sarawak  River  (Santubong  entrance),  Borneo,  West  Coast 

Sarawak  River,  Sarawak  Junction,  Borneo,  West  Coast 

Sarawak  River,  Sarawak  City,  Borneo,  West  Coast 

Sarmiento  Bank,  Magellan  Strait 

Sarn  Badrig,  or  the  Causeway,  Wales 

Sarn-y-Bwch  Reef,  Wales 

Sau-o  Bay,  Formoza* 

Saugor  Island,  Bay  of  Bengal 

Saumarez  Reef,  Australia,  East  Coast 

Scales  Point,  Blackwater  River,  England 

Scalloway,  Shetland 

Scapa,  Orkneys 

Scarborough,  England 

Scarborough  Shoal,  Filipinas 

Scarries  Rivers,  Africa,  West  Coast 

Scarnish,  Tiree  Island,  Scotland 

Schiermonnikoog,  Netherlands 

Schooner  Retreat,  Northwest  Coast  of  America 

Scilly  Islands  (St.  Agnes  Lsland),  England 

Scilly  Islands  (St.  Mary  Island),  England 

Scilly  Islands  (Trescow),  England 

Sea  Bear  Bay,  Patagonia,  East  Coast   . .  .■ 

Seaforth,  Loch,  Athhne,  Scotland 

Seaham,  England 

Seal  Cove,  (irand  Manan,  Bay  of  Fundy , 

Seal  Island,  Cape  Sable,  Bay  of  Fundy 

Seamount  Bay,  Mulroy  Bay,  Ireland 


4  30 
I   30 

9  41 
4  36 

3  8? 
6     o 

I  53 

9  25 

10  45 

6    o 

4  50 

5  30 
8  50 

10  47 

5  o 
10  35 
Noon. 

o  55 
4  10 


5  15 
10  20 


9 

9 

o 

4 
9 
I 
10  20 

3  30 

8  30 

3  30 


35? 

30 

45 

50 

35? 

30 


o 
o 
o 
o 
o 

20 


8  10 

7  30 

7  40 

5  50 
10    o 

8  o 
Noon. 

9  30 

5 
II 

o 

lo 

31 
40 

30 
30 
18 

22 


9 

4 
II 

7 
5 
9 
o 

4 
4 
4 
o 
6 
3 


45 
16 

24 


10  54 

9  49 
6  44 


Feet. 
12 

5 
12 

5 

10? 
12 
12K 

5 
6 

6? 
7 
4 
6-8 

21K 
23 
15 
18 

5 
7 
9 
6 

4 

15 

9 

5-6 

5? 
40 

9 
4-5 
5? 
8 
6 

15 
2 

121^ 

6 

10 

9 

10 

15-18 

15-18 

36-42 

13 

14 

6 
12 

6 

14X 


7A- 

10 

5 
10 

12 

sX 
14 
16 

15X 
16X 
20 

15 

wA 

20 

123/ 


Feet. 

10 
3 

8 
4 


173^ 
19 


4 
AYz 


29 
4? 
12 


6 
9 
9 


4X 
6-9 

10 

4/2 

7'- 

12/2 


II 

12 

11J4: 
12X 

10 

TO  !< 

15  ' 

10-^ 


TABLE  47.  [Page  507 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &C.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Sebastian,  San,  Brazil , 

Sebastian,  San,  Tierra  del  Fuego 

Sebastian,  San,  Spain,  North  Coast 

Sebastian,  San,  Bay,  Africa,  South  Coast , 

Sedashigar  Bay,  Hindoostan,  West  Coast 

.Seer  River,  Hindoostan,  West  Coast 

Seer  River,  J  uggee , 

Segoro  Wedie  Bay,  Java 

Sein,  Chausee  de,  France 

Seldom-come-by,  Newfoundland 

Seleney  Bay,  Lapland 

Selsea  Bill,  England    

Semiahmoo  Bay,  Gulf  of  Georgia,  America,  Northwest  Coast  , 

Senegal  ( Bar),  Africa,  West  Coast 

Senegal  (Guet  N'dar),  Africa,  West  Coast 

Senegal  (St.  Louis),  Africa,  West  Coast -,... 

Seoul  River  (Po-teu-mai),  Korea 

Seoul  River  (Seoul),  Korea 

Serraia,  Hindoostan,  West  Coast 

Serrana  B.ank,  Mosquito  Coast 

Serranilla  Bank,  Mosquito  Coast 

Sesham  Islands,  Hang-chu  Bay,  China,  East  Coast 

Setubal,  Portugal 

Seudre  River  (entrance),  France 

Seurin,  St.,  France 

Seychelle  Archipelago  (Mayhe  Island),  Indian  Ocean 

Seymour  Narrows,  British  Columbia 

Seypan  Island.     {SW  Saipan.) 

Seven  Islands,  Lapland 

Seven  Islands  Bay,  Gulf  of  St.  Lawrence 

Sha-lui  tien  Banks  (West  part),  Yellow  Sea 

Shab  Kadtin,  Arabia,  Southeast  Ccast 

.Shdb'bu-saifeh,  Arabia,  Southeast  Coast 

Shalbet  Island,  Hindoostan,  West  Coast 

Shallow  Plarbor,  Falkland  Islands 

Shanghai,  Yang-tse-Kiang,  China,  East  Coast 

.Shao-king,  Si  Kiang,  Cliina,  East  Coast 

Sharja,  Persian  Gulf 

Sharks  Bay,  Xaturaliste  Channel,  Australia,  Northwest  Coast. 

.Sharks  Bay,  Denham  Sound,  Northwest  Coast 

Sharks  Bay,  Freycinet  Reach,  Australia,  Northwest  Coast 

Sharks  Bay,  T'reycinet  Estuary,  Australia,  Northwest  Coast  . . 

Sharks  Bay,  Cape  Perron,  Australia,  Northwest  Coast 

.Sharks  Bay,  Hamelin  Pool,  Australia,  Northwest  Coast 

Sharpness,  England 

Shediac  Harbor,  New  Brunswick 


2 

7 

3 

3 
10 

ID 
I 

9 
3 
7 
7 
II 
2 


o 
o 
o 
8 
o 

30 
30 

o 

21 
13 

9 

45 
o 


8  42 

8  42 

ID      O 

7  20 

9  30 
I      o 


Irregular. 
II  45 


30 

31 
II 

o 
o 


Sheephaven,  Ireland 

Sheerness,  England 

Sheet  Harbor,  Nova  Scotia , 

Shefeen  Island,  Africa,  South  Coast 

Slielburne,  Nova  Scotia 

Sheldrake  Island,  Gulf  of  St.  Lawrence 

Sherbro  River,  Africa,  West  Coast 

Shields,  North,  England 

Shihtau  Bay,  Yellow  Sea , 

Ship  Harbor,  Nova  Scotia 

Ship  Harbor  (New  Island),  Falkland  Islands. 

Shippigan,  Gulf  of  .St.  Lawrence 

Shoal  Bay,  Australia,  North  Coast 

Shoal  Bay,  East  Coast 

Shoal  Water  Bay,  Australia,  East  Coast , 

Shoalhaven  River,  Australia,  East  Coast 

ShoU  Bay,  Smyth  Channel 

Shoreham,  England 

Shushartie  Bay,  Yancouver  Island 

Si  Kiang,  or  West  River  (San-shui),  China,  East  Coast 


8  20 

1  40 

2  50 

9  20 

9  45 
Noon. 

9  30 
o  40 


II 

45 

0 

5 

3 

0 

4 

15 

0 

45 

S 

0 

7 

5«? 

I 

0  and 

8 

0 

5 

32 

0 

37 

8 

6 

4 

40 

8 

4 

6 

0 

7  50 

3 

23 

I 

30 

7  54 

ID 

30 

3 

42 

6 

0 

8 

30 

ID 

30 

8 

30 

II 

45 

II 

34 

Feet. 
4 

12 
6 

II 

6 

8-10 

9 

16X 
12 

6 

6 

6 
16K? 

16 

2 

2 
14 

15 


/4- 

II 
12 

9 
10 
10 
10 

9 

6 

10 

3 
6 
6 
5 
5 


5/2 
S'A 
28? 

4 

16 

12 
7 

5 
6 

13X 
9 

18-25 

12-18     . 

6-9 

6 

18 

12 


Feet. 

9 

5 


12 
3 

12K 


13 

7 
II 

5 
8 

7 

7 


15? 
2 

^% 

13X 
^Yz 

SVz 
3 
5 
10 

7 


3 
10-15 


13X 
5-6 


Page  508J  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Si  Kiang,  or  West  River  (Shao-king),  China,  East  Coast 

Si  Kiang,  or  West  River  (Wuchan),  China,  East  Coast 

Siak  River,  Malacca  Strait 

Siak  River  (off  the  town) 

Sidili  River,  China  Sea,  West  Coast 

Sidmouth,  Cape,  Australia,  East  Coast , 

Sierra  Leone,  Africa,  West  Coast 

Sillabar  River  (Bar),  Sumatra 

Simidsu,  Japan , 

Simoda,  J  apan 

Simonoseki,  Japan 

Simons  Bay,  Africa 

Simpson,  Port,  Northwest  Coast  of  America 

Singapore,  New  Harbor,  Malacca  Strait 

Singoteer  Mata,  Hindoostan,  West  Coast 

Sinou,  Africa,  West  Coast 

Sir  C.  Hardy  Islands,  Torres  Strait,  East  Coast 

Sir  E.  Pellew  Islands,  Australia,  North  Coast . . . : 

Sisal,  Gulf  of  Mexico 

Sitka,  America,  Northwest  Coast 

Siyako  Island,  Japan 

Skaapen  Fiord  (between  Stormo  and  Sando),  Faroe  Islands 
Skaapen  Fiord  (between  Hesto  and  Sando),  Faroe  Islands  . 

Skagen,  or  the  Skaw,  Jutland 

Skerry,  Great  (East  side),  Pentland  Firth 

Skerry,  Great  (West  side),  Pentland  Firth 

Skerries,  Ireland,  North  Coast 

Skerries,  Ireland,  East  Coast 

Skidegate  Inlet,  Queen  Charlotte  Islands 

Skip  Ness,  Scotland 

Skull,  Ireland 

Slaughden,  Orford,  England 

Slievebane  Bay,  Ireland,  West  Coast 

Sligo  Bay  (Mullaghmore),  Ireland 

Sligo  Harbor,  Ireland 

Sluissche-gat,  North  Sea 

Slyne  Head,  Ireland,  West  Coast 

Smalls  Light-house,  St.  George's  Channel 

Smer wick,  I  reland 

Smith  Sound,  Newfoundland 

Smoky  Bay,  Australia,  South  Coast 

Smyth  Harbor,  Tierra  del  Fuego ., 

Snape  Bridge,  Orford,  England 

Snapper  Point,  Australia,  South  Coast 

Socoa,  France 

Society  Bay  ( Sullivan  Bay),  Yellow  Sea 

Socotra  Island,  Indian  Ocean 

Sofala  River,  Africa,  East  Coast    

Solitary  Islands,  Australia,  East  Coast 

Solomon  Islands,  Indian  Ocean 

Solovet  Road,  White  Sea 

Sonderho,  Fano,  Denmark 

Sooke  Harbor,  Vancouver  Island 

Soonmianee  Harbor,  Persian  Gulf 

Sosnovaia  Bay,  White  Sea 

Sosnovets,  W  hite  Sea 

Souma,  White  Sea 

Sourabaya  Strait,  Java 

Sourabaya  Strait  ( Jansen  Channel),  Java 

South  Rock,  Ireland _ 


High  Water,  Full 
and  Change. 


■m. 


9     o 


9  44 

9  15 

7  55 
6    o 


30 
o 

P 


s 
44 
I  30 

9  45 
5  20 
5  o 
9  15 
7  30 


Southampton,  England 

Southwest  Bay,  New  Providence 
Southwest  Cape,  New  Zealand  . . . 

Southerness,  Scotland 

Southwold,  England 

Spain,  Port,  Trinidad 


o  34 
o  16 


5 

5 

5 
II 


o 

30 

56 

4 


10  53 
6  15 


II 
I 


o 
o 


49 
18 


II  50 

4  2 
I     o 

5 
5 

5  23 
o  50 

4  30 

6  o 

3  50 

7  8 

o  15 
Noon. 

3     o 


4 
3 


40 
19 

o  15 

7  20 

o 


15 

30 

o 

22 
O 

O 
40 


II    44 

6  30 
Irregular. 
Irregular. 

10  58 

10  30  and  ( 

o  45  ^ 

7  30 
Noon. 

11  20 
10  20 

4  30 


Rise. 


Springs. 


Feet. 


12 
II 

7 

10 
8 

4X 
7 

sX 

17-22 

10 

24 

4 

10 

4-7 
2 
12 
9% 
9% 

9% 
I 


5 

13 
17 

9 


loX 


I3X 
21 

V/z 
6 

6 

,.x 

8 
19 
5 
5 
4 

9? 

6 
18 

SYz 
4-6 

8X 

13 

13 

4 

7 

28 


Neaps. 


Feet. 
3  , 


6y\ 
14-17 

lYz 


4 
lYz 

V/z 

(^Yz 

3 
10 

14 

lYz 


^Yz 
^Yz 

ID 
10 


2V. 


s-i 


loX 

9^ 


aYz 

3 


TABLE  47.  [Page  509 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Spaniards  Bay,  Newfoundland 

Spencer  Bay,  Africa,  West  Coast 

Spencer  Gulf  (Thorny  Passage),  Australia,  South  Coast. 

Spencer  Gulf  (Point  Lowly),  Australia,  South  Coast 

.Spencer  Gulf  (Port  Augusta),  Australia,  South  Coast 

Spencer  Gulf  (Point  Riley),  Australia,  South  Coast 

Spencer  Gulf  (Wallaroo),  .\ustralia,  South  Coast 

Spenser's  Anchorage,  Bay  of  Fundy 

Sphax  Roads,  Mediterranean 

Spicers  Cove,  Bay  of  Fundy 

Spider  Island,  China,  East  Coast 

Spiekeroog,  (Germany 

Spitzbergen  (Bell  .Sound) 

Spitzbergen  ( I )anes  Sound) 

Spurn  Point  (Humber  River),  England 

Staten  Island,  Tierra  del  Fuego 

Staunton  Island,  Yellow  Sea . 

Stephens,  Port,  Australia,  East  Coast 

Stephens,  Port,  Falkland  Islands 

Stewart  Harbor,  Tierra  del  Fuego 

Stirling  (  Firth  of  Forth),  Scotland 

Stirrup  Cays,  Bahamas 

Stockton  (Tees),  England 

Stonefield  (Loch  Etive),  Scotland 

Stonehaven,  Scotland 

Stornoway  (Lewis  Island),  Scotland 

Strangford  ( Killard  Point),  Ireland 

Strangford  (Quay),  Ireland 

Strangford,  Head  of  Lough  (Turley  Rocks),  Ireland 

Streaky  Bay  (Blancheport),  Australia,  South  Coast 

Stroma  (South  side),  Pentland  Firth 

Stromness,  Orkneys 

Stuart  Channel  (Oyster  Harbor) 

Stuart  Channel,  Cowitchin  Harbor,  Vancouver  Island 

Stuart  Island,  Strait  of  Georgia 

Suadiva  Atoll,  Maldives 

Sual,  Port,  Luzon 

Sudero  Fiord,  Faroe  Islands 

Suez  Bay  (head  of  Gulf),  Red  Sea 

Sughra,  Arabia,  Southeast  Coast 

Sumburgh  Head,  Shetland 

Sunday,  or  Raoul  Island,  South  Pacific 


Sunderland,  England . 

Sunderland,  North,  England 

Supe  Bay,  Peru 

Surat  (entrance),  Hindoostan,  West  Coast 

Surat  (town),  Hindoostan,  West  Coast 

Surge  Narrows,  Strait  of  Georgia   

Surinam,  Guayana 

Sussex,  Port,  Falkland  Islands 

Sutton  Pool,  England 

Sviatoi  Nos,  Lapland 

Svind  Fiord,  Faroe  Islands    

.Swain  Reefs,  .Vustralia,  East  Coast .. 

Swallow  Bay,  Strait  of  Magellan 

Swan  Island,  Tasmania 

Swan  Point,  Australia,  West  Coast 

Swan  River,  Gage  Road,  .\ustralia,  West  Coast. 
Swan  River,  Port  Grey,  Australia,  West  Coast  .. 

Swansea  (Mumbles  Light-house),  Wales 

Swatau,  China,  East  Coast 

Swift  Bay,  Australia,  North  Coast 

.Swona  ( East  side),  Pentland  Firth 

Swona  (West  side),  Pentland  Firth 

Sydney,  Australia,  East  Coast 

Sydney  Harbor,  Cape  Breton 


7  45 

10  50 

Noon. 

7  o 

8  30 

5  45 
5  45 

11  42 

4  30 
"  35 

10  o 

11  30 
8  56 

0  24 

5  26 

4  30 

1  30 

8  30 

7  45 

2  50 

3  52 
7    o 

4  40 

7  3 
I   10 

6  46 

10  53 
o  31 

0  44 

1  o 

9  47 
9  o 
6    o 


6    o 
I     o 


6 

II 

8 

9 
6 

3 

2 

4 
2 

4 
6 
6 
8 

5 
9 

Noon. 

10  25 

I    17 

9  35 
o  10 

8  50 

9  o 
6     I 

3     o 
Noon. 
10  24 

9  35 

8  38 

9  o 


o 
o 
o 

45 

o 

22 

30 
50 

45 
o 

o 

o 

15 
32 
15 


Feet. 


5-6 

6-8 

6-8 

9-12 


4-5 

39 

5 

37 

17 


/A 

8 
8 
6 

4 

VA 

4 
II 

14 
13 
14 

5 


10 

10 

10-12 

12-14 

4 
6 


7 
6 

5 

14K 
15 

3 

19 

19 

12 

9-10 

6 

14 

6K 
10 

5 

6 

26 

1-1%. 

9 
18 
10 
10 


5 


Feet. 
3 


33 
3 
30K 


15 

5M 
4 


^y^ 


II 

ii'A 

9% 


VA 


VA 
4 


II 


15 


5-6 

^y^ 


20X 


VA 
7 
4 
4 


Page  510]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Ta-tsing  ho,  Yellow  Sea 

Table  Bay,  Africa,  West  Coast 

Taboga,  New  Granada 

Tabou  River,  Africa,  West  Coast 

Tabuai  Island,  South  Pacific 

Tadeo,  San,  River,  Patagonia",  West  Coast 

Tahiti,  South  Pacific 

Tahri,  Persian  Gulf 

Tai-cho  ho.  Yellow  Sea 

Taichow  Islands,  China,  East  Coast 

Tai-Tai  Bay,  China  Sea,  East  Coast 

Takush  Harbor,  British  Columbia 

Talcahuano,  Chile 

Talcan  Island,  Patagonia,  West  Coast 

Tailung  Channel,  Canton  River,  China 

Ta-lien-whan  Bay,  Yellow  Sea 

Tama  no  Ura  Harbor,  Goto  Island,  Japan 

Tam-Sui  Harbor,  China  Sea,  East  Coast 

Tamar  River  (Georgetown),  Tasmania 

Tamar  River  ( Launceston),  Tasmania 

Tamar,  Port,  Magellan  Strait 

Tamatave,  Madagascar,  East  Coast 

Tanab^,  Ki  Channel,  Japan 

Tanera,  Summer  Islands,  Scotland 

Tangier,  Africa,  N  orth  Coast 

Tangtang  Harbor,  Madagascar,  East  Coast 

Tanjong  Api,  China  Sea 

Tanjong  Bolus,  Malacca  Strait ., 

Tanna,  New  Plebrides : 

Tappanoely  Harbor,  Sumatra , 

Taranaki,  or  New  Plymouth,  New  Zealand , 

Tarbert,  Ireland , 

Tarifa,  Spain 

Tarn  Point,  Solway,  Scotland 

Task^,  Japan 

Tatamagouche,  Nova  Scotia , 

Tatiyama  Bay,  Japan , 

Ta-tong  River,  Korea 

Tauranga  Harbor,  New  Zealand , 

Tavoy  River  (entrance).  Bay  of  Bengal,  East  Coast  ... 

Tay  River  (Bar),  Scotland . .    

Tay-  bay-00  bay,  China  Sea,  Eas t  Coast 

Teavarua  Harbor,  Raiatea  Islands,  South  Pacific 

Teboncas  Road,  Baly,  North  Coast 

Teelin  Harbor,  Ireland 

Tees  River  ( Bar),  England 

Teignmouth,  England 

Tellicherry,  Hindoostan,  West  Coast 

Tenby,  Wales 

Tenerife,  Cape  Verd  Islands  (Santa  Cruz) 

Terceira,  Azores , 

Teriberka  River,  Lapland , 

Teremakau  River,  New  Zealand 

Terneuse,  or  Neuzen,  North  Sea 

Terschelling  (West),  Netherlands 

Tetrina,  White  Sea , 

Tetuan,  Africa,  North  Coast 

Texel  (Outside  Shoals),  Netherlands 

Thirsty  Sound,  Australia,  East  Coast , 

Thomas,  St.,  Island,  Africa 

Thompson  Sound,  New  Zealand 

Thorny  Passage,  Spencer  Gulf,  Australia,  South  Coast 

Thorsminde,  J  utland 

ThreeTIummock  Island  (East  side),  Bass  Strait 

Three  Kings  Islands,  New  Zealand , 

Three  Points,  Cape,  Africa,  West  Coast 

Three  Rivers,  River  St.  Lawrence 


High  Water,  Full 
and  Change. 


h.ni. 
4  10 
2  40 
4  o 
4  45 


II  45 

Noon. 


o? 

15 
o 

30 


5 
o 

9 
9 
I     o 

10  14 

I     3 
I  30 

10  47 
8  40 

11  45 

0  5 

1  o 

I  40 

4 
6 


18 
o 

37 
42 


4  30 


35 
10 

30 
57 


I  46 
II  22 


9 
10 

5 
6 

7 


Ir 


44 
o 

50 
30 
10 
10  30 

2  6 

10  15 
rregular. 

5    o 

5  16 

3  45 

6  o 

11  40 
5  42 


o  32 
7  20 
9  55 
\  35 


h  40 

3  17 

2  23 
6  30 

10  45 

3  25- 

11  30 

12  o 

3  34 
II  30 

8    o 

4  o 
II  30 


Rise. 


Springs. 


Feet. 

5 
14 

3-4 

3 
6 

i^i^ 

6 

14 

sK 

H 
5 

i5>^ 


loH 
6-8 
7-10 

10 


Neaps. 


Feet, 
8 


II 


8 
4-6 


6 

8 

6 

5^ 

14 

loX 

Z% 

5 

6 

7 

io>^ 

Vz 

3 

6 

12 

9 

W/z 

io>^ 

6 

y/2 

23 

18 

^% 

1/2.' 

8 

5 

5 

13 

6 

4^2 

20 

16 

14 

6 

I 

6;i 

11^ 

8/. 

15 

12}{ 

13 

9/2 

5 

4 

27 

20 

^Yz 

6 

AVz 

12 

9 

15 

II 

6 

7 

2;^ 

I'A 

4 

3>2 

2-18 

4X 

8 

6 

6-8 

2 

10 

7 

4 

I 

7K 


TABLE  47.  [Page  511 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Thurso,  Scotland , 

Ticao  Island  (Port  San  Jacinto),  Filipinas 

Tictoc  Bay,  Patagonia    

Tien  pak  Harbor,  China,  East  Coast 

I'illy  Bay,  Strait  of  Magellan 

Tinghae,  Chusan,  China,  East  Coast - 

Tobago,  Caribbean  Sea 

Tobermory,  Isle  of  Mull : 

Toboe  Ali  Point,  Banka  Strait 


Toboolchi  Bay,  Saghalin  Island 

Tomo  ( Inland  Sea),  Japan 

Tongatabu,  South  Pacific 

Tongsang  I  larbor,  China,  East  Coast 

Tonning,  Germany 

Toona,  Gulf  of  Kutch,  Hindoostan 

Tooniang  Island  (Bias  Bay),  China,  East  Coast  '. 

Toorbut  Point,  Australia,  East  Coast 

Topaze  Harbor,  British  Columbia 

Torbay,  England 

Toro  Point,  Chile , 

Torta  Bay,  Africa,  West  Coast , 

Tortola,  Virgin  Islands 

Touron  Bay,  Cochin  China 

Tova,  or  Na  Vatu  Reef,  South  Pacific 

Towan  Island,  China,  East  Coast 

Townshend  Harbor,  Tierra  del  Fuego 

Tracadie,  prince  Edward  Island 

Tracey  Harbor,  British  Columbia 

Tracy  Island,  Korea,  South  Coast 

Tree  Islands,  Norway 

Trawbreaga,  Lough,  Ireland 

Trdguier,  France 

Trek  Island,  White  Sea 

Trepassey,  Newfoundland 

Tr6port,  France 

Tres  Cruces,  Point,  Patagonia,  West  Coast 

Triangles,  Gulf  of  Mexico 

Trieste,  Adriatic 

Trincomalie  Harbor,  Ceylon,  South  Coast 

Tringano  River,  Gulf  of  Siani,  China  Sea,  West  Coast 

Trinidad  (Port  Spain),  Caribliee  Islands 

Trinity  Bay  (Bull  Island),  Newfoundland 

Trinity  Harbor,  Newfoundland 

Trinity  Opening,  Great  Barrier  Reefs 

Tripoli  (Syria),  Mediterranean 

Tristan  da  Cunha,  South  Atlantic 

Triton  Bay,  New  Guinea  ..: 

Triton  Harbor,  Newfoundland 

Triton  Bank,  Magellan  Strait 

Tromso,  Norway 

Troon,  Scotland 

Troubridge  Shoals,  Australia,  South  Coast 

Truro  (Quay),  England 

Tsang-chow  Island  (Bias  Bay),  China,  East  Coast 

Tsau-lianghai  or  Chosan  Harbor,  Korea 

Tsu-sima  Sound,  Korea 

Tsugar  Strait,  Japan 

Tsuruga,  Japan 

Tudri  River  (Bar),  Hindoostan,  West  Coast 

Tudwall,  St.,  Road,  Wales 

Tuesday  Bay 

Tumaco  Road,  Ecuador 

Tunis,  Mediterranean 

Turks  Islands,  Bahamas 

Turna  Bay,  White  Sea 

Turner,  Cape,  Prince  Edward  Island 


High  Water,  Full 
and  Change. 


//.  til. 
8  28 
6  30 

I  45 
Noon. 

1  30 
II      o 

3    o 

5  36 

8  30  and 
10     o 
16 
o? 
50 
30 
55 
50 
o 

45 
o 
o 

45 
-  30 

8  30 
3    o 

6  8 

9  20 

2  30 

7  o 
Noon. 

8  58 

"  45 

6  10 

5  32 

10  48 

7  o 

11  9 

I   15 


4 
II 
6 
II 
I 
I 
8 
9 
3 
6 

9 
3 


Rise. 


Springs. 


9  35 
8   18 

8  o 

4  30 
7  22 
7  10 

9  15 
10  20 


8 

o? 

o 


I  45 
II   50 


4 

5 
8 


18 

5 
30 

7  45 

8  30 
5  o 
I  30 

ID      O 

7  45 

1  o 

2  y:, 


9  54 
6  10 


Feet, 

13X 
6 

II 

6 
12 

4 
13 

10-12 


»/2 
2 


4 

z% 

7-12 

2 

8 

7 
2-4? 

15 

8 
10 

7 
10 


5 
2 

14 

6 

12 

3 

3 

II 

4 


Neaps. 


Feci. 
9% 


9 
2 

9K 


6 

12 

11^ 

16 

13 

6 

8 

16 

ii>^ 

nA 

10 

3 

1^2 

4 

4 

13 

5 

3/2 

2 

16 

ii>< 

11;^ 

8X 

7 

llVz 

8^ 

25 

1^% 

20 

(>% 

5 

27 

21 

16 

3 
2 
2 


VA 
4-6 

6 


S% 


k 


Page  512]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Turtle  Island  (North),  Australia,  West  Coast 

Turtle  Island,  South  Pacific 

Tuticorin  Harbor,  Gulf  of  Manar,  Bay  of  Bengal,  West  Coast. 

Tutukaka  Harbor,  New  Zealand 

Tweed  River  (Danger  Point),  Australia,  East  Coast 

Twofold  Bay,  Australia,  P2ast  Coast 

Tylatiap  Harbor,  Java,  South  Coast 

Tynemouth  (Bar),  England 

Tyssen  Island,  Falkland  Islands 

Ty tando  Inlet,  Java 

Typa  Anchorage,  China,  East  Coast 


Ubatuba,  Brazil -• 

Ubian  Island,  Sulu  Sea 

Uinne,  New  Caledonia 

Uist,  North  (Kalhn),  Scotland,  West  Coast 

Uist,  North  (Vallay),  Scotland,  West  Coast 

Uist,  South  (Loch  Boisdale),  Scotland,  West  Coast. 

Ulladulla  Harbor,  Australia,  East  Coast 

Ullapool,  Loch  Broom,  Scotland 

Ummen  Nakheilah,  Persian  Gulf 

Underwood,  Port,  New  Zealand 

Ungava,  Hudson  Bay 

Union  Bay,  La  Plata 

Union,  Portia,  Gulf  of  Fonseca,  Central  America... 

Unsang,  Borneo 

Upernavik,  Greenland 

Upstart  Bay,  Australia,  East  Coast 

Uraga,  Japan 

Urakami,  Japan 

Urie  Firth,  Shetlands 

Ursula  Island,  Palawan,  China  Sea,  East  Coast 

Usborne,  Port,  Australia,  West  Coast 

Ushant,  France 

Ushruffi  Islands,  Red  Sea 

Utria,  New  Granada 


Vfero,  Norway ■ 

Valdivia,  Port,  Chile 

Valentia  Harbor,  Ireland 

Valery,  St.,  en-Caux,  France 

Valery,  St.,  sur-Somme,  France 

Vallay,  North  Uist,  Scotland,  West  Coast   

Vallenar  River,  Patagonia,  West  Coast 

Valparaiso,  Chile 

Vanderlin  Island,  Australia,  North  Coast 

Vansittart  Bay,  Australia,  Northwest  Coast 

Vansittart's  Saddle,  Yellow  Sea 

Vao,  Port.     {Sei.'  Alcmene,  New  Caledonia) 

Vatoa  or  Turtle  Island,  South  Pacific 

Vavau,  South  Pacific 

Veere- gat,  Netherlands . 

Ventry,  Ireland , 

Venus  Bay,  Australia,  South  Coast 

Venus  Harbor,  Australia,  South  Coast .. 

Vera  Cruz,  Gulf  of  Mexico 

Vernon  Channel  (Chusan  Arch),  China,  East  Coast 

Versovah,  Hindoostan,  West  Coast 

Verte  Bay,  Nova  Scotia 

Victoria,  Port,  Brazil 

Victoria,  Port,  Australia,  South  Coast 

Victoria,  Strait,  Juan  de  Fuca  Strait 

Victoria  River,  Holdfast  Reach,  Australia,  Northwest  Coast 
Victoria  River  (Mosquito  Flat),  Australia,  Northwest  Coast 
Victoria  River  (Sandy  Island),  Australia,  Northwest  Coast.. 
Victoria  River  (Turtle  Point),  Australia,  Northwest  Coast  .. 
Victory  Pass,  Smyth  Channel,  South  America,  West  Coast  . 


High  Water,  Full 
and  Change. 


k. 

II 
6 
I 

7 
9 

8 
8 

3 

8 

6 

10 


m. 

o 

II 

15 
o 

30 

15 

45 
20 

o 

30 
o 


t>  IS 

6  48 

5  59 

6  10 

5  47 
8  30 

6  40 

7  30? 
6  10 


3 
3 

8 

II 

9 
5 
7 
9 
II 


ID 

15 

O 

o 
o 

55 
30 

45 
o 

45 

32 

14 

o 


Noon. 

10  35 

3  42 

10  46 

11  46 
6 
o 
9 
9 
9 
4 
8 
6 
6 
I 


II 


10 
18 
32 
30 
15 
20. 

6 
II 

20 
o 

44 
56 
15 


9  40 
Noon. 
10     o 

3    o 

2  40 
rregular. 

9     o 

0  19 

1  17 

7  15 

I  25 


Rise. 


Springs. 


Fed. 
18 

4 
2^ 

9 
6 

5-7 
3J^ 
143. 


6 

5 

7 

4X 
5 
4 
13X 

12^ 
6 

I4>^ 

8? 

8 
67 
12 


4K 
6 

lYz 

34 

19X 
2-6 
12 

9 

5 
II 

27 

27 

\\% 

5 

5 

7 

6 
10 

4 

4 

5 

15 
loK 

7 

6 

2 

14 
16 

9 

4 

5 
7-10 

16 

15-24 
3-10 

7-13 

6 


Neaps. 


Feet. 


Wa 


7 

4K 

5 


II 


3K 


9^ 
9% 


K-i 
4 
5 


^iU 


VA 

8 

21;-^ 
2114 

8>i 


4 
II 

1H 


5-8 
10 


TABLE  47-  [Page  513 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


High  Water,  Full 
and  Change. 


Rise. 


Springs. 


Neaps. 


Vigo,  Spain 

Vila  Harbor,  Sandwich  Lslands,  New  Hebrides 

Vin  Harbor,  Gulf  of  St.  Lawrence 

Vincent,  St.,  Cape,  Madagascar,  West  Coast 

Vincent,  St. ,  Caribbean  Sea 

Vincent,  St. ,  Port,  New  Caledonia 

Vingorla,  Hindoostan,  West  Coast... 

Virgin,  Cape,  Magellan  Strait 

Viti  Levu,  Fiji  Islands 

Vivero,  Spain,  North  Coast .  .. 

Viziadroog.     (.fo' Geriah.) 

Vladimir,  St.,  Bay,  Gulf  of  Tartary 

Volcano  Islands,  China,  East  Coast 

Voronov,  Cape,  White  Sea 

Vulavu,  Isabel  Island,  Solomon  Islands 


h. 
3 
5 
5  45 


o 
o 


4 

3 

5 

II 


45 
o 

SO 
o 
8  30 
6  47 
%    o 


Irregular. 
II  30 
II  20 
About  4    o 


Waagoe  Fiord,  Faroe  Islands 

Waddington  Harbor,  Bute  Inlet,  British  Columbia... 

Wahaay  Harbor  (Ceram),  Moluccas,  North  Coast 

Waikato  River,  New  Zealand 

Waikawa  Harbor,  New  Zealand 

Wairoa  River,  New  Zealand 

Wakaya  Islands,  Fiji  Islands 

Wakefield,  Port,  Australia,  South  Coast 

Walker  Cheek,  Choiseul  Island,  Falkland  Islands 

Walker,  River  Tyne,  England 

Wallace  Harbor,  Nova  Scotia 

Wallis  Island,  Torres  Strait 

Walton  Bay,  England 

Walvisch  Bay,  Africa,  West  Coast 

Wanchu  River  (entrance),  China,  East  Coast 

Wanchu  River  (City),  China,  East  Coast 

Wang-kia  Bay,  Yellow  Sea 

Wang-kia-lia  Bay,  Yellow  Sea ,  , 

Wanganui  River,  New  Zealand 

Wanganui  Inlet,  New  Zealand 

Wangari  Harbor,  New  Zealand 

Wangaroa  Harbor,  New  Zealand 

Wangaruru  Harbor,  New  Zealand 

Wangeroog,  Germany 

Wapitagun  Harbor,  Gulf  of  St.  Lawrence 

Waratah  Bay,  Australia,  South  Coast 

Waree  River,  Hindoostan,  West  Coast 

Warleigh  Quay  ( River  Tavy),  England 

Warnboro'  Sound,  Australia,  West  Coast 

Warrenpoint  (Carlingford),  Ireland 

Warrenpoint  (Lough  Foyle),  Ireland 

Warsheek  Roads,  Africa,  East  Coast 

Waterford  T Bridge),  Ireland 

Waterford  ( Duncannon  Fort),  Ireland 

Waterloo  Bay,  Africa,  South  Coast 

Webeck 

Webling  Point,  Spencer  Gulf,  Australia,  South  Coast 

Week  Islands,  Tierra  del  Fuego 

Wei-hai  or  Kyau-chau  Bay,  Yellow  Sea 

Wei-hai-wei  Harbor,  Yellow  Sea 

Weir  Head,  River  Tamar,  England 

Welcome  Bay,  Patagonia,  West  Coast 

Wellesley  Islands,  Australia,  North  Coast 

Wells,  England 

Wells  Bar,  England 

Wenman  Isles,  Galapagos  Islands , 

We>er  (entrance),  (iermany 

Weser  (light- vessel),  (iermany 

West  Cove,  Kenmare  River,  Ireland 

West  Gat,  Netherlands 

West  Hill,  Australia,  East  Coast 


o 
o 
o 

30 
30 

45 

o 

40 

20 


10  30 

Irregular. 

7     3 


54 
o 

30 

30 

o 


10  15 

11  20 

7  o 

8  15 

7  10 

II  35 
10  30 

Noon. 

9  40 
5  47 


II 

6 

4 
6 

5 
4 
6 
6 
2 

5 
9 
6 


10 
20 

30 
6 

20 
o 

21 

10 
o 
o 

30 
17 


o  50 


30 

o 
20 

ID 


II    30 

0  20 
3  52 

1  45 
10  20 


Feet. 
12-13 

5 

5 

12 

8 
36-42 

SU 

15 

2 

15 

17 

4-5 

9>^ 
13 
3-4 
12 

9 

7 

4 

i: 

s'A 

io>^ 
8 

7 


6 

15K 

9 
12 

8 
7 
9 
7 
9 
10 

5 
8 

8 

H'A 
3-4 
14^ 

6j4 

8 
13K 

12X 
6 

7 

6-9 

5 
12 

9 

5X 

8-12 
12 
18 

14 
10 
10 

7 
24 


Feet. 

3 
I 


VA 


9 

7 
4 
3 


22'^ 


7 

9 
6 

6 
7 


12 

5 

10^ 

ID 


Zl  ^ 


Page  514]  TABLE  47. 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


West-kappelle,  North  Sea 

West  Quoddy,  Bay  of  Fundy 

West  River,  China,  East  Coast.     {See  Si  Kiang.) 

Western  Port  ( Muscle  Rock),  Austraha 

Western  Port  (Bourchier  Channel),  Australia 

Western  Port  (French  Island  Spit).  Australia 

Westmanshaven,  Faroe  Islands 

Westness,  Orkneys 

Weston-  super-mare,  England .. 

Westport,  Ireland 

Wexford,  Ireland 

Whaingaroa  Harbor,  New  Zealand 

Sin  March , 
In  April 
In  May  and  June 

Whitby,  England 

White  Dog  Islands,  China,  East  Coast , 

Whitehaven,  England 

Whitehaven,  Nova  Scotia 

Wick,  Scotland 

Wicklow,  Ireland 

Wide  Bay,  Australia,  East  Coast 

Widewall,  Orkneys 

Wigton,  Scotland 

Wilberforce,  Cape,  Australia,  North  Coast . . 

Wild  Wave  Bay,  Loo  Choo  Islands 

Wilham,  Port,  Falkland  Islands 

William,  Port,  New  Zealand 

William  Port,  Scotland,  West  Coast • , 

Willemstad,  North  Sea , 

Willis  Islets,  Australia,  East  Coast 

Willoughby,  Cape,  Kangaroo  Island,  Australia 

Willunga,  Port,  Austraha,  South  Coast 

Winter  Harbor,  Melville  Island 

Winterton  Ness,  England 

AVisbeach,  England 

Wisbeach  Eye,  England 

Wivenhoe,  Colne  River,  England 

Wolstenholm  Sound,  Arctic  Regions ^ 

Woodbridge  or  Bawdsey  Haven  TEar),  England. , , 

WoodVjridge  (Kingston  Quay),  England 

Woodbridge  ( Wilford  Bridg* ;,  England , 

Woodlark  Island,  Louisiade  Archipelago  ....    , 

Wood's  Bay,  Strait  of  Magellan ^ 

Woody  Island,  Great  Sandy  Strait,  Australiu,  East  Coast 

Woolwich,  England 

Workington,  England 

Wotje  or  Romanzoff  Islands,  Marshall  Islands 

Wrabness,  Stour  River,  England 

Wrange'r  Oog,  Germany 

Wrath,  Cape,  Scotland 

Wreck  Bay,  Loyalty  Islands 

Wreck  Reef  ( Bird  Islet),  .\ustralia.  East  Coast 

Wuchu,  Si  K  iang,  China,  East  Coast , 

Wusung  River  (entrance),  Yang-tse- Kiang,  China,  East  Coast 

Wusung  River  (Fort  A  ),  China,  East  Coast 

Wusung  River  (Pheasant  Point),  China,  East  Coast 

Wyk,  I'ohr  Island,  Denmark 

Wynkoop's  Bay,  Java 


Yafa,  Mediterranean 

Yama  Gawa  Harbor,  Japan 

Yang-ho,  Yellow  Sea 

Yang-tse- Kiang  (light- ship  at  entrance),  China,  East  Coast 

Yamada  Harbor,  Japan   

Yarmouth  Haven  ( Brush),  England 

Yaamouth,  Bay  of  Fundy 


High  Water,  Full 
and  Change. 


/i.  m. 

o  40 

II  12 

O    12 


I 
I 

8 

9 
6 

4 
7 
9 
I 

I 

o 

3 

9 

II 


13 
o 
o 

II 

54 
57 
21 

50 
40 

15 

30 

45 
o 

14 
8    o 

II  22 

10  29 

8  30 

9  3 

11  30 

6  10 

8  o 

5  15 

0  45 
II  10 

3  30 
8    o 

4  10 
4    o 

1  30 

8  25 

7  30 


o  10 
II     8 

II  45 
o  35 
o  55 
7  15 

0  34 
9  14 

1  37 
II    4 

2  30 
o  29 

Noon. 

7  30 
6  30 

8  3 


o  30 
o  30 

0  35 

1  50 
5    o 

10  o 
7  15 
o  15 

Noon. 

4  30 


ID 


Rise. 


Springs. 


Feet. 


hU 


21 


8K 
loX 
10 


72 
10 

37 

12^ 

5 
12 

7-8 

15 
18 

23  K 

10 

9 

6 

10 

10 
8 

7 

8 
18 
10 

6 

6 

6 


15 

20 

15 
7K 
12 

ID 

7 

4 

8 

10 

18X 
20 

7 
12 

9? 
i5>^ 
5-6 
6 

i-i>^ 

IS 

15 

13 

8 

4>^ 

8K 
6 

»5 


16 


TABLE  47.  [Page  615 

TIME  OF  HIGH  WATER  ON  FULL  AND  CHANGE  DAYS,  &c.— Continued. 


Place. 


Yarmoutli  Bridge,  England 
Yarmoutli  Road,  England  . 


Yarmouth,  Isle  of  Wight,  England 

Yealni  River,  Bigbury  Bay,  England 

Vedo  Bay  (Yokohama),  Japan , 

Yellaboi,  Africa,  West  Coast 

Yeu,  He  d',  France 

Ylo  Road,  Peru 

Yobuko,  Japan  

Yokohama,  Yedo  Bay,  Japan 

York,  Cape,  Australia,  East  Coast 

York  Factory,  Hudson  Bay 

York  Road,  Magellan  Strait 

York  Harbor,  Newfoundland 

Youghal,  Ireland .. 

Yugi  Sima,  Japan 

Yu-lin-kan  Bay,  China  Sea 

Yung  River,  Chinhae,  China,  East  Coast 

Yung  River,  Ning-po-fu,  China,  East  Coast . 

Yung-hing  Bay,  Korea 

Yura  Harbor,  Japan 

Yuranouchi,  Japan 


Zambezi  River  (Pearl  Island),  Africa,  East  Coast 

Zand  Bay,  Java 

Zanzibar,  Africa,  East  Coast 

Zanzibar  (Channel),  Africa,  East  Coast 

Zaudzi,  IVIayotta,  Comoro  Islands 

Zebu,  Port,  Filipinas 

Zeyla,  Africa,  East  Coast 

Zierikzee,  Netherlands 

ZooUa,  Red  Sea 


High  Water,  Full 
and  Change. 


;;/. 


9  15 

10    o  and 
noon. 


5 
6 

7 
3 
8 

9 

6 

II 

II 

2 


Z7 
o 

10 

6 

15 
16 

o 
15 

15 

o 


10  37 

5  H 
II 


9 

II 

I 

5 
6 

6 


25 

5 

20 

o 

20 

5 
o 


4  30 

5  o 
4  20 

4  15 
4  10 
Noon. 

7  15 
2     o 


Rise. 


Springs. 


Feet. 

S 
6 

7 
16X 

10 

H% 
6 

9 

6% 
10 
10-14 

9 

12X 

9 

■2.%. 

12-15 

434' 

II 
II 

12 

7 
4-5 


Neap' 


Feet. 
4 
\% 

4^ 


10 

4X 

7 


10 


8X 


9 
3 


[Page  516 


STANDARD    FIXED    STARS. 


TABLE  48. 

[From  the  Nautical  Almanac] 
[Stars  marked  (*)  are  Circumpolar  Stars.] 


Mean  places  for  1880.0.     (Jan.  0^.258  Washington.) 


Star's  name. 


Magni- 
tude. 


Risrht  ascension. 


An.  variation. 


Declination. 


An.  variation. 


a  Andromedse  

y  Pegasi  {Algenib) 

^  Hydri 

a  Cassiopese 

fi  Ceti 

21  Cassiopeae 

£  Piscium 

a  Ursse  Minoris  {Polans) 

01  Ceti 

38  Cassiopeae 

Tj  Piscium 

a  Eridani  {Achernar)  .  ... 

0  Piscium 

/?  Arietis 

50  Cassiopeae , 

a  Arietis 

f'  Ceti 

1  Cassiopere  . 

y  Ceti 

a  Ceti 

48  Cephei(H.) 

f  Arietis 

a  Persei , 

(5  Persei , 

T]  Tauri 

f  Persei 

y'  Eridani 

y  Tauri 

e  Tauri , 

a  Tauri  I^Aldebaraii) 

9  Camelopardalis 

I  AurigK . 

1 1  Orionis 

a  Auriga;  (  Capella) , 

/3  Orionis  {Rigel) 

(3  Tauri 

Groombridge  966 

r5  Orionis 

c  Leporis 

e  Orionis 

a  Columbae 

a  Orionis 

22  Camelopardalis  (H.)  .. 

H  Geminorum 

a  Argus  {Cunoptts) 

y  Geminorum 

a  Canis  Majoris  {Sirhis) 

51  Cephei  (H.) 

e  Canis  Majoris 

6  Canis  Majoris 


2 
3-2 

3 

var. 
2 

6 

4 
2 

3 
6 

4-3 
I 

4 

3-2 

4 

2 

4-5 
4 

3-4 
2-3 

6 

4-5 
2 

3 
3 

3 

3 
4 

4-3 
I 

4 
3 
5 
I 
I 

2 

6.7 
2 

3 
2 

2 
var. 

5-4 

3 
I 

2.3 
I 

5 
2.  I 

2 


h.  m.     s. 
o    2  1 1 .  1 78 

o  7  3-449 
o  19  25.  129 

o  33  42.  344 

o  37  33-873 

o  37  44-717 

0  56  42.  970 

1  14  46.424 
I  18  1.522 
I  22  19.215 


I  25 

I 

I 


3.722 

33  4-366 

39  3-533 
I  48  o.  746 

1  53  12.814 

2  o  24. 638 
2  6  38. 360 

2  19  II. 587 

2  37  5-013 

2  56   O.  428 


3  5  8.787 
3  8  0.333 
3  15  45-621 
3  34  22.  980 
3  40  21. 138 

3  46  35-  441 

3  52  25.847 

4  12  57.909 
4  21  36. 613 
4  29  2.  153 

4  42  7-  596 
4  49  10.  790 

4  57  42.825 

5  7  49-  559 
5  8  46. 265 

5  18  42.  393 
5  23  41-581 
5  25  52.615 
5  27  26.  346 
5  30  7-475 

5  35  18.302 

5  48  40.  538 

6  5  37-025 
615  42. 090 
6  21  17.383 

6  30  46.  804 
6  39  51-580 
6  43  45-  342 

6  53  54-671 

7  3  30-  791 


+ 


+  3 

3 

21 

2 

4 


+ 


+ 


+  7 
3 
4 
4 
3 


+ 


+  5 
3 
3 
4 
2 

+  3 

7' 

3 
2 

3 

+  2 

3 
6 

3 
I 

+  3 

2 

30 
2 

+  2 


089 
084 

243 
369 
013 

842 
109 
642 
998 
364 

200 

233 
163 
302 

993 

370 
170 
850 
103 
130 

374 

438 
252 

243 

555 

758 
797 
408 

496 
437 

919 
898 
426 

424 

881 

788 

995 
064 
647 
042 

172 

247 
618 

633 
330 

469 

645 
124 

359 
440 


-{-  28  25  41.20 
+  14  30  59-  78 

—  77  55  51-98 
+  55  52  44-  04 

—  18  38  43.43 

+  74  19  52.39 
+  7  14  37.82 
+  88  40  8.  92 

—  8  48  9. 40 
+  69  38  46.  39 


+ 

+ 
-f 


14  43  37-  36 

57  50  47-  39 

8  33  11-65 

20  13  15.91 


+  71  50  21.  10 

-|-  22  53  40.  10 
+  8  16  59.07 
-f  66  51  40.49 
+  2  43  45.  61 
+  3  37  4-  65 

+  77  17  27.28 
+  20  35  56.  32 
+  49  25  56.  65 
+  47  24  7-33 
+  23  43  58.  14 

+  31  31  32.91 

—  13  51  2.  08 
-\-   15  20  12.30 

+  18  54  47-  45 
-f  16  16  0.94 

+  66  8  10.86 
-f  32  58  28.  59 
4-  15  14  8.69 
+  45  52  26.35 

—  8  20  29.  24 

+  28  30  15.93 

+  74  57  37-54 

—  o  23  21.  77 

—  17  54  32-78 

—  I  16  47.37 

—  34  8  19.48 
+  7  23  o.  04 
+  69  21  32.  70 
+  22  34  25.46 

—  52  37 '50-56 

+  16  30  1.57 

—  16  33  8.98 

+  87  13  45-  72 

—  28  48  34.  96 

—  26  12  11.44 


+  19-90 
20.  04 
20.  24 
[9.80 
9.82 


+ 


+ 


+ 


+ 


+ 


+ 


+ 


+ 


9.72 

9-47 
9.  01 
8.  71 
8.70 


71 
41 

25 
77 
66 


7.  22 
7.06 

6.45 
5.39 
4-34 


80 
62 
13 
85 
1-43 


1.  00 
0.51 
9.03 
8.34 
7-59 

6.69 
6.  09 

5-37 
4.  10 

4-45 

3-42 
3.  16 

2.  96 
2.87 
2.  61 

2.  14 
1. 01 
o.  60 
1.48 
1.86 

2.  71 
4.68. 

3-84 
4-67 

5-45 


TABLE  48. 
Mean  places  for  1880.0.     (Jan.  of^.asS  Washington.) 


[Page  517 


Star's  name. 


6  Geminorum 

Piazzi  vii,  67  . 

a  Geminorum  ( Castor) 

a  Canis  Minoris  {Procvon).  .. 
(S  Geminorum  {Po!/nx) 

0  Geminorum 

3  Ursaa  Majoris  (H.) 

15  Argus  (0 

E  Hydrae 

1  Ursas  Majoris 

(T^  UrsEe  Majoris 

K  Cancri . 

I  Argus 

I  Draconis(H.) 

a  Hydrte 

d  Urs£e  Majoris 

6  Ursae  Majoris 

e  Leonis 

jj,  Leonis 

a  Leonis  {Regiibis) 

32  UrsEe  Majoris 

y'  Leonis „ 

9  Draconis  (H.) 

p  Leonis .. 

Tl  Argus 

/  Leonis 

a  Ursae  Majoris 

(5  Leonis 

(5  Crateris 

r  Leonis 

\  Draconis  

V  Leonis  .. 

/3  Leonis 

\  Ursae  INIajoris 

o  Virginis 

4  Draconis  (H) 

/?  Chamaeleontis 

ri  Virginis 

ai  Crucis 

j8  Corvi  

K  Draconis  

32  Camelopardalis  (H.)  {foil.) 
12  Canum  Venaticorum 

6  Virginis 

a  Virginis  {Spica)  .. . .. 

C  Virginis 

T]  Ursae  Majoris 

7j  Bootis 

/?  Centauri 

a  Draconis 

a  Bootis  {Arcttiri(s) 

6  Bootis 

5  Ursae  Minoris 

a^  Centauri 

e  Bootis 

a"  Librae 

/3  Ursae  Minoris 

/3  Bootis 

P  Librae 

fi^  Bootis 


Magni- 
tude. 


3-4 
6 

2.  I 
I 
I.  2 

5 
6 

3 
3-4 

-> 

5 

5 
2 

4-5 
2 

5-4 
3 
3 
4 
I.  2 

6 
2 

5-4 
4 
var. 

5 
2 

2.3 
3-4 
5 

3-4 

5.4 

3 

2-3 

4 

5-4 
5 

3-4 
I 

2.3 

3-4 

5-4 

3 

4-5 

I 

■  3-4 
2 

3 
I 

3-4 

I 

4-3 
5-4 
I 

2.3 

2.3 
2 

3 

4-3 

2 


Right  ascension. 


//.  /«,  J 
7  12  57 
7  18  22 
7  26  56 
7  y:,  ' 
7  37 


5^^ 


7  46  9 

8  o  51 
8  2  26, 
8  40  25 

8  50  59 

8  5948 

9  I  14 
9  13  52 
9  19  51 
9  21  41 

9  23  50 

9  24  49 
9  39  2 

9  45  56^ 
10  I  58 

o  9  18 
o  13  21 
o  24  51 
o  26  29 

o  40  24 

o  42  56 

0  56  18 

1  7  43 
I  13  20 
I  21  45 

I  24  15 
I  30  48 
I  42  56 
I  47  30 

1  59  5 

2  6  33 
2  II  19 
2  13  46 

2  19  55 

5 


2  28 


28  21 

48  15 
50  24 

3  44 
18  52 


3  28  34 
3  42  48 
3  48  58 

3  55  21 

4  I  8 

4  10  II 
4  21  6 

4  27  47 
4  31  28 
4  39  44 

4  44  14 

4  51  4 

4  57  25 

5  10  33 
5  19  57 


387 
965 

239 
289 

319 

194 
289 
107 
302 
119 

905 

785 
562 

427 
450 

640 
332 
314 
167 
864 

188 

294 
514 

585 
4^5 

928 
614 

571 
542 
994 

735 
325 
299 
783 
813 

877 
406 

028 

377 
129 

283 
626 
767 
290 
370 

762 

724 
314 
912 

495 

286 
660 

754 
617 
818 


473 
181 

548 
038 
502 


An.  variation. 


+ 


+ 


+ 


+ 


+ 


+ 


+ 


+ 

+ 
+ 


+  5 
3 


+  4 
3 
5 

2 


2 
o, 
2 
3 

+  3 

2 
2 

4 
I 


+  2 

+  2 

—  o 

+  4 

+  2 


590 

307 
838 
146 
681 

683 
060 

556 
184 

137 

368 

255 
601 

073 
949 

417 
047 
418 

423 
202 

431 
316 
290 
166 
3" 

159 
754 
201 
996 
088 

632 
071 
065 

185 
060 

897 

356 
069 
271 
140 

597 
372 
816 

lOI 

154 

053 

373 

859 
170 

623 

735 
043 
201 

039 
622 

308 
240 
260 
221 
268 


Declination. 


-j-  22  12  7.  28 
4-  68  42  27.  84 
+  32  9  0.41 

+  5  31  52.17 
+  28  18  53.29 

+  274  30.  26 
+  68  49  29.  22 


—  23  57 


■47 


+  6  51  30.10 
-|-  48  30  41.  00 

+  67  37  10.  13 

+  11  9  1.65 

—  58  46  16.36 
+  81  51  17.25 

—  88  20.51 

+  70  21  21.  99 

+  52  13  23.42 
+  24  19  34.  27 
+  26  34  17.36 
+  12  2,?,   12.27 

+  65  42  21.  06 
-j-  20  26  53.  91 
+  76  19  48.  15 
+  9  55  25.40 

—  59  3  10. 34 

+  II  10  48.34 
+  62  23  53.81 
+  21  10  52.  21 

—  14  7  44. 93 
+    3  31     i-6i 

+  69  59  33.  70 

—  o  9  40. 06 
+  15  14  35.41 
+  54  21  42.88 
+    9  23  59-11 

+  78  16  57.40 

—  78  3846.37 
-(-    o    o     1.47 

—  62  25  57.47 

—  22  43  56.80 

+  70  26  57.82 

+  84  3  52.85 
+  38  58    0.82 

—  4  53  51-78 

—  10  32     3.  10 

-f-    o     I     6. 69 

+  49  54  45-  48 
+  19    o    0.74 

—  59  47  36-11 
+  64  56  56.  82 

+  19  48  29.  72 
+  52  24  21.81 

+  76  13  44-17 

—  60  20    9.  75 

+  27  34  51-97 

—  15  32  30-42 
+  74  38  43-  59 
+  40  51  52.69 

—  8  56  19.  14 
+  37  47  56.  28 


An.  variation. 


6.  27 
6.80 

7.51 
8.96 
8.36 

8.97 
o.  10 
o.  14 

2.94 
3.88 


26 

23 
94 
35 
41 


5-53 
6.18 

6-39 
6.77 

7-43 

7.79 
8.04 
8.38 
8.41 
8.76 

8-93 
9-37 
9.66 

9 
9 


44 
78 


9.87 

9.84 

20.  09 

20.  02 

20.01 

20.  05 
20.  04 
20.  03 

9-93 
9.94 

9.92 
9-63 
9.51 

9-30 
8.90 

8.51 
8.09 
8.  16 
7.64 

7-35 

8.87 

6-77 
6.05 
5.01 

5-35 

5.18 
7.75 
4.38 
3.52 
2.79 


Page  518] 


TABLE  48. 

Mean  places  for  1880.0.     (Jan.  0^.258  Washington.) 


Star's  name. 


Magni- 
tude. 


Right  ascension. 


An.  variation. 


Declination. 


An.  variation. 


■y"  Ursse  Minoris... 
a  Coronse  Borealis. 

u  Serpentis 

e  Serpentis 

f  Ursae  Minoris 


e 
6 


Coronse  Borealis . . , 

Scorpii 

Scorpii  , 

Groombridge  2320 
Ophiuchi 


7  Herculis . . 

a  Scorpii  ( A  nta res) 

7]  Draconis 

A  Draconis 

^  Ophiuchi .  . 


a  Trianguli  Australis . 

T)  Herculis 

K  Ophiuchi 

d  Herculis 

£  Ursse  Minoris 


a'  Herculis. 

44  Ophiuchi 

/3  Draconis 

a  Ophiuchi 

6j  Draconis 5 


H  Herculis 

i/*'  Draconis  (/r.) . 

y  Draconis 

y^  Sagittarii 

fi^  Sagittarii  


6  Ursre  Minoris 

^  Serpentis 

a  Octantis 

I   Aquilte  (3  H.  .Scuti) 
a  Lyrce  (  Vega) 


(i  Lyrse 

(T  Sagittarii 

50  Draconis 

f    Aquilse  .. 

d  Sagittarii 

6  Draconis 
r  Draconis 

6  Aquilse  . . 
K  Aquilse  .. 

7  Aquilae . . 


\  Ursre  Minoris  . . 
u  AquiltE  {Altair) 

£  Draconis 

(3  Aquilse 

r  Aquilse 


a 


^  Capricorni 

K  Cephei 

a  Pavonis  . . 

K  Capricorni 

s  Delphini. .. 


Groombridge  3241 . 
u  Cygni 


3 

2 

2.3 
3-4 
4-5 

4 

2-3 
2 

6.5 
o 

3-4 
I.  2 

3-2 

5 
3-2 


3 

3-4 

5 

4-5 

var. 

5 

3-2 

2 


3-4 
4-5 
2.3 
3-4 
4 

4-5 

3 
0 

4-5 
I 

var. 

2.3 
6 

3 

5 

3 

5 

3-4 

5 

3 

6.7 

1.  2 
4 

4 
6.5 

3-4 

4-5 
2 

5 
4 

6.7 

2.  I 


fi  Aquarii '       5.4 

■"  <-"ygni 4 

12  Year  Cat.  1879 j       6 


/i.  m.  s. 
5  20  55.  780 
5  29  36.451 
5  38  21.441 
5  44  50-  113 
5  48  22.  545 

5  52  37-  296 
5  53  14358 

5  58  27.  609 

6  5  59.803 
6  8  3.445 

616  7. 904 
6  22  3.  102 
6  22  22.  209 
6  28  13.543 
6  30  II.  112 

6  35  58.418 

6  38  46.  935 
6  51  59.252 
6  57  10.  372 
6  58  19.  064 


9  10.  548 

19  2.533 

27  43-  234 
29  21. 830 

n  39-  345 


7  41  45-  737 
7  44  4-  477 
7  53  49-  339 

7  58  5-987 

8  6  35.  202 

811  2.  174 

8  15  5-943 
8  24  26.417 
8  28  40.  548 
8  32  52. 528 

8  45  38-  955 
8  47  49-  445 
8  50  14.  113 

8  59  53-579 

9  10  36.  771 


i2  31.434 
17  51.165 


9  19  26.  804 
9  30  26. 073 
9  40  33. 261 

9  44  10.  758 

9  44  55-669 
9  48  34.  228 
9  49  25.  085 
9  58  16.  666 


20  1 1  23.  699 
20  12  54.  116 
20  16  9.  113 
20  20  27. 068 
20  27  28.  750 

20  30  30.  830 
20  37  20.456 
20  46  10.  775 
20  52  41.952 
20  53  59- 002 


+ 
+ 

+ 


+ 
+ 
+ 
+ 

+ 


s. 

o.  141 
2.540 
2.951 
2.987 
2.270 

2.485 
3-538 
3-478 
o.  136 

3-138 


1.798 

+  3-  670 

4-  o.  806 

—  o.  139 

+  3-298 


+ 
-t- 
+ 

+ 


+ 
4- 
+ 


+ 


6.  291 
2.055 
2.835 
2.  209 
6.  362 


2-733 
3.  660 

1-351 

2.  782 
0.356 


2-345 

—  1. 081 

+  1-394 
+  3-  853 
+  3-586 

-  19-436 
+  3-  100 
-f-io8.  100 
+  3-  264 
+  2. 032 

+  2.214 

+  3-  723 

-  1.903 

+  2.755 
+  .3-513 

+  o.  032 

—  I.  Ill 

+  3-  024 
3-230 


+ 

+ 


,85; 


—  62.  137 
+  2. 928 

-  0.175 
+  2. 947 
+  2. 933 


+ 

+ 
+ 
+ 


+ 
+ 
+ 


3-332 
1.907 

4790 
3-440 
2.866 

o.  213 
2.044 
3.240 
2.234 
2.519 


+  72  15  40. 15 
+  27  7  II.  10 
4-  6  48  16.  30 
+  4  50  24  87 
+  78  9  46.  43 

+  27  13  36.23 

—  22  16  41.  40 

—  19  28  31.77 

+  68  7  34-  95 

—  3  23  1.30 

+  46  35  59-  Zl> 

—  26  9  50.  28 
+  61  47  10. 00 
+  69  I  39.  76 

—  10  19  19.  88 


+ 
+ 
+ 
+ 


68  48  17.  19 
39  9  6. 20 
9  33  47-63 
33  44  36.  22 
82  13  56.  22 


+  14  31  42.96 

—  24  3  45.  13 
+  52  23  26.  20 
+  12  38  56.06 
+  68  48  45.  66 

+  27  47  32-  04 

+  72  12  26.  56 

+  51  30  12.52 

—  30  25  25.  71 

—  21  5  18.  15 

+  86  36  32.  81 

—  2  55  41.39 

—  89  16  29.41 

—  8  19  3437 
+  38  40  22.  36 

+  33  13  27.49 

—  26  26  37.  48 

+  75  17  28.61 
+  13  41  11.57 

—  19  9  50.06 

+  67  27  0.91 

+  73  7  55-29 
+  2  52  37.45 

—  7  17  32.56 
+  10  19  19.63 

+  88  5635.92 
+  8  33  9. 64 
+  69  57  42.  71 
6  6  ^o.  16 


+ 
+ 


6  56  26.43 


—  12  54  55.31 
+  77  20  56.  12 

—  57  7  1-94 

—  18  36  12.96 

+  10  53  47-  62 

-f  72  7  30.  43 
+  44  51  7-69 

—  9  25  55-  73 
+  40  42  22.47 
4-80  6  4. 00 


12.  80 
12.  31 
11.56 
11.07 
10  90 

10.  61 

10.53 
10.  16 

9-50 

9-54 

8.76 

8.34 
8.22 

7.78 
7.58 

7.27 
7.02 

5-84 
5-40 
5-33 

436 
3.65 
2.82 
2.89 
1.66 


1.65 

0.58 

—  0.39 

+  0.58 


+ 


+ 


+ 


1.  04 
0.65 
2. 13 

2.  19 
3-15 

3-96 
409 
4.42 
5.10 
6.  II 

6.31 

6.78 
6.  91 

7-73 
8.53 

8.81 

9-25 
9.15 
8.74 
9.92 


+  10.89 
10.99 
II.  19 

11.  50 
12.01 

+  12.  22 

12.  71 
13.28 

13-73 
+  13.69 


+ 


TABLE  48. 
Mean  places  for  1880.0.     (Jan.  0^.2^8  Washington.) 


[Page  519 


Star's  name. 


61   Cygni  (/;•.) 

C  Cygni 

a  Cephei 

1  Pegasi  

/3  Acjuarii 


Magni- 
tude. 


(3  Cephei . 

I  Aquarii . 

e  Pegasi , 

1 1  Cephei , 

fi  Capricorni  . 


79  Draconis 
u  Aquarii . . 
a  Gruis  .  . . 
6  Aquarii.. 
TT  Aquarii.. 


71  Aquarii 

226  Cephei  (B.), 

C  Pegasi 

I  Cephei 

2.  Aquarii 


a  Pis.  Aus.  {Fomalhaui) 
a  Pegasi  {Markab)  . 

0  Cephei 

6  Piscium , 

1  Piscium 


y  Cephei 

Groombridge  4163. 
w  Piscium 


5-6 


4-5 
3 

3 

5-4 
2-3 
S 

5 

6.7 

3 
2 

4-5 
5-4 

4-3 
5.6 
3-4 
4-3 
4 

1.2 
2 

6.5 
4-5 
4-5 

3.4 

7 

4 


Right  ascension. 


h.  in.    s. 
21  I  31.  173 

21  7  49-  730 
21  15  42.  8cS8 
21  16  32. 280 
21  25  14.473 

21  27  6.  349 
21  31  21.747 

21  38  17-559 
21  40  9. 606 

21  46  45.  167 
21  51  22. 324 

21  59  37.  198 

22  o  39. 868 
22  10  30.  041 

22  19  8. 896 


22  29  II. 
22  30  9. 


352 
749 


22  35  28.557 
593 
133 


22  45  24. 
22  46  21. 


22  51  1. 017 

22  58  47.  027 

23  13  42.  245 
23  21  52. 826 

23  33   46.  752 

23  34  25. 844 
23  49  o-  599 
23  53  8.988 


An.  variation. 


+ 


+ 


+ 


+ 


+ 


2.'688 

2-551 
1-437 
2-774 
3.164 

0.797 
3.198 
2.948 

0.  904 
3.278 

0.734 
3-083 
3.810 
3-170 
3-065 

3-083 

1.  081 
2.989 

2.  120 
3-131 

3-328 
2.9S5 
2.  440 
3.041 
3-085 


Declination. 


2.  40S 
2.856 
+  3-078 


8  l: 


—   30  15  27.  25 

+  14  33  36-  90 
-f-  67  27  16.  78 

+  5  43  13-42 
+  4  58  34-31 

+  76  57  45-53 
+  73  44  32-  28 
+  6  II  57.05 


An.  variation. 


+  38  9  36-  84 
+  29  44  7-  96 
+  62  4  37. 13 
4-  19  17  32.  22 

—  6    6  52.42 

+  70    2     1 .  20 

—  8  23  28.68 
+.  9  19  32.  75 
+  70  45  31-57 

—  14  6  55.21 

+  73  8  4.05 

—  o  54  7. 29 

—  47  32  27.96  I 

—  8  2  48.  10 
+  o  4  8.81 

—  o  44  7. 29 
+  75  36  28.  50 
+  10  12  20.  51 
+  65  34  9.61 


73 


+ 


+ 


+ 


7-52 
4.  60 
5-12 

5-25 
5-66 

5-72 

5-97 

6-35 
6.51 

6-79 

6.97 

7-35 
7.  22 
7.80 
8.14 

8.45 
8.52 

8.71 
8.86 
9.08 

9.  00 
9-32 
9-63 
9-75 
9-49 


+  20.  08 
20.  00 

+  19-94 


+ 


+ 


Page  520] 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  NORTH  AMERICA. 


e 


•s 
a 

H 


Places. 


Salisbury  Island 

Nottingham  Island 

Digges  Island 

Cape  Wostenholme 

Charles  Island 

Do 

Cape  Weggs 

Prince  of  Wales  Sound 
C.  of  Hope's  Advance  . 

Akpatok  Island 

Green  Island 

Button  Islands 

Cape  Chidleigh 

Resolution  Island 

Do 

Black  Head 

Eclipse  Harbor 

Nachvack  Bay 

Saddle  Island 

Port  Manvers 

Nain 


Hopedale  Harbor  ... 

Aillick  Harbor 

Cape  Harrison 

Indian  Harbor 

Outer  Gannet  Island 

Gready  Harbor 

Cartwright  Harbor.. 

Indian  Tickle 

Round  Hill  Island  . . 
Occasional  Harbor  . . 

Cape  St.  Lewis 

Battle  Islands 


Table  Head 
Belle  Isle  . . 


Cape  Bauld . . . 

Bell  Island  . . . 

Cape  St.  John 

Do 


Funk  Island 

Offer  Wadham 

Toulinguet  Islands 

Seldom-come-by  Harbor 

Cape  Freels 

Greenspond  Island 

Cape  Bonavista 

Catalina  Harbor 

Bonaventure  Head 

Heart's  Content 

Baccalieu  Island  

Harbour  Grace 

Cape  St.  Francis 

St.  John's  Harbor 

Cape  Race  

Cape  Pine 

Trepassy  Harbor 

Cape  St.  Mary 

Little  Placentia  Harbor . 

Burin  Harbor 

Laun 

St.  Pierre 

Brunet  Island 

Burgeo  Islands 


Exact  locations. 


E.  point  ... 

S.  point 

W.  extreme 


E.  point . . 
W.  point. 


E.  point  ... 
N.  E.  point 
do  ... 


S.  point  . 
E.  point . 


E.  side 

Islands  off  entrance 


Entrance 

Obs.  spot  on  N.  side  of 
harbor. 

Obs , 

do  

N.  extreme 

Obs 

Summit 


Caribou  Castle 

Obs 

Summit 

E.  summit  of  Twin  Island 
S.  E.  point 

N.  E.  extreme  of  S.  E. 
island. 


Light-house 


N.  extreme , 

S.  end , 

Gull  Island  summit 

Tilt  Cove,  Union  Copper 
Mine. 

Summit 

Light-house 

E.  side  of  W.  island 

Shiphill 

Gull  Island 


Light-house 

Green  Island  light-house. 


Lat.  N. 


Episcopal  Church 

Light-house 

Light-house  on  beach 

N.  W.  extreme 

Chain  Rock  Battery 

Light-house 

do 

Shingle  Neck 

Light-house 

W.  side  Cooper's  Cove..  . 

Light-house 

Gr.  Laun  R.  C.  Churcli  . . 
U.  S.  Coast-Survey  Station 
Mercer's  Hd.  light-house. 
Summit  Eclipse  Island..  . 


20 

10 

2 


63  27 
63  10 
62  37 
62  30 
62  44 
62  50 
62  30 
62  o 
61 
60 
61 
60  45 

60  25 

61  21 
61  30 
60  o 
59  48 
59  o 
57  45 
57  o 
56  32  51 

55  27  6 
55  9  o 

54  55  50 
54  26  55 
54  o  5 

53  50  o 
53  42  36 
53  34  20 
53  26  10 
52  40  8 
52  21  16 

52  15  36 
52  6  o 

51  53  o 

51  38  48 
50  42  10 

49  59  54 
49  53  o 

49  45 
49  35 
49  39 
49  36 


49 
49 


15 

4 


48  42 
48  30 
48  16 

47  52 

48  8 

47  41 
47  48 
47  34 
46  39 
46  Z1 
46  43 
46  49 

47 
47 
46  56 
46  46 


17 
o 


Long.  W. 


47 
47 


15 

36 


o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 

15 


o  / 

76  40 

78  4 

7835 
77  50 

74  18 

75  o 
74  8 
72  8 
70  10 

67  5 
67  25 

64  53 

65  o 

64  54 
64  30 

64  28 
64  7 
63  36  o 
62  38  o 
62  7  o 
61  40  41 

60  II  40 
59  5  o 
57  56  30 
57  12  40 

56  31  48 
56  23  o 
56  59  40 
56  o  o 

55  36  5 
55  44  19 
55  38  25 
55  32  20 

55  43  o 
55  22  22 

55  25  10 
55  35  30 
55  21  40 
55  2>7   17 


Authorities. 


Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lt.  Comdr.  Murray,  U.  S.  N. 
Lieut.  Raper,  R.  N. 

Do. 
Capt.  Manby,  R,  N. 
Com.  Maxvfell,  R.  N. 


Lieut 

Capt. 
Lieut 
Com. 
Lieut 


Com. 
Adm. 


.  Raper,  R.  N. 

Do. 

Chimmo,  R.  N. 

,  Raper,  R.  N. 

Maxwell,  R.  N. 

,  Raper,  R.  N. 

Do. 

Do. 

Maxwell,  R.  N. 

Do. 

Bayfield,  R.  N. 

Do. 


Lieut.  Raper,  R.  N. 

Capt.  Orlebar,  R.  N. 

Do. 
Lieut.  Raper,  R.  N. 
Com.  Maxwell,  R.  N. 
Lieut.  Raper,  R.  N. 


29 

53  10  56 

Comdr.  Kerr,  R.  N. 

40 

53  45    0 

Lieut.  Raper,  R.  N. 

30 

54  46  12 

Do. 

50 

54  12    0 

Do. 

20 

53  25  12 

Do. 

20 

53  37  45 

Do. 

I 

53    4  42 

Com.  Maxwell,  R.  N. 

10 

53    2  45 

Lieut.  Raper,  R.  N. 

55 

53  23  35 

Do. 

35 

53  22  30 

U.  S.  C.  and  G.  Survey. 

58 

52  47  40 

Com.  Maxwell,  R.  N. 

25 

53  12  30 

Lieut.  Raper,  R.  N. 

30 

52  48    0 

Do. 

2 

52  40  54 

Adm.  Bayfield,  R.  N. 

24 

53    4  28 

Capt.  Orlebar,  R.  N. 

5 

53  31  40 

Lieut.  Raper,  R.  N. 

20 

53  22  10 

Do. 

30 

54  II  30 

Do. 

55 

53  58  43 

Comdr.  Maxwell,  R.  N 

25 

55    8  40 

Lieut.  Raper,  R.  N. 

30 

55  32    0 

Do. 

51 

56  10  36 

U.  S.  C.  and  G.  Survey. 

30 

55  51  40 

Lieut.  Raper,  R.  N. 

12 

57  36  52 

Comdr.  Maxwell,  R.  N 

TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  521 


Places. 


La  Poile  Ray 

Cape  Ray 

Cod  Roy  Island 

(ape  St.  George 

(  ow  Head 

I'ort  Saunders 

Rich  Point 

Ferrolle  Point 


Exact  locations. 


Gr.  Espic  Church 

S.  extreme 

S.  side  Boat  Harbor 

Red  Island,  S.  E.  point  . 

N.  \y.  extreme 

N.  E.  point  of  entry 

W.  extreme 

Cove  Point,  N.  E.  extreme 

Flower  Cove !  Capstan  Point 

Green  Island |   150  fms.  from  N.  E.  end.. 

Cape  Norman Extreme 


Lat.  N. 


Long.  W. 


Chateau  Bay S.  pt.,  Castle  Island  .... 

Amour  Point '  Light  house 

Wood  Island 1  S.  pt 

Greenly  Island '  Light-house 

Hradore  Hills Summit,  1,135  ft 

Old  Fort  Island , , 

Great  Mecatina  Island  . .  I  S.  E.  pt 

-Mecatina  Harbor S.  point  of  Dead  Cove  . . 

Little  Mecatina  Island  . .  |  S.  pt 

St.  Mary  Rocks : do 

South  Maker's  Ledge  . 


47  39  50 
47  37  2 

47  52  30 

48  33   48 

49  55  20 

50  38  30 

5°  41  39 

51  2  10 
51  18  10 
51  24  10 
SI  38  o 

51  58  o 

51  27  35 

51  23 

51  22 

51  34 
51  22 

50  44 
5<^  46  44 
50  31  o 
50  13  o 
50    9    o 


o 

35 
o 

o 

o 


S. edge 


Cape  Whittle 

Natashquan  Point 

C"learwater  Point ,  S.  W.  extreme 

Carousel  Island i  Light-house 

Point  de  Monts do 

QuEBFX  Mann's  Bastion,  Citadel 

Mo.N'TRE.A.L Cathedral 

Father  Point Light-house 

Cape  Chatte Extreme 

Cape  Magdalen ,  Light-house 

Cape  Rosier do 

Cape  Gaspe do 


50 
50 
50 
50 


Anticosti  Island Heath  Point  light 

Southwest  Point I  Light-house 


E.  pt 


Bonaventure  Island 

Leander  Shoal 

-Macquereau  Point | 

Chaleur  Bay Carlisle 

Do I  Dalhousie  Island 

Miscow  Island N.  E.  pt..  Point  Birch 

Mirimichi  Bay j   Portage  Island,  N.  pt. 


11  o 

6     o 

12  27 
5  40 

49  19  35 
46  48  32 

45  30  24 

48  31  25 

49  6  o 
49  15  40 
48  51 
48  45 


37 
15 


49    5  20 
49  23  50 


4 
I 

,    .-    14 
Point  Escumenac Light-  house ^47     4  32       64  46  59 


48  29 

48  25 

48 

48 

48 

48 

47 


12 
I 


o 
o 
o 
o 

24 

o 


North  Point  P.  E.  Island do  

Richmond  Harbor |  Royalty  Point  ... 

East  Point Light-house 

Charlottetown Flag-staff  on  fort. 


47  3  46 
46  34  o 
46  27  9 
46  13  55 


X     Magdalen  Islands I  North  Bird  Rock I  47  50  57 


E.  extreme 47  37  40 


Light-house 


Magdalen  Islands,  East 
Island. 

Magdalen  Islands,  En- 
try Island. 

Magdalen  Islands,  Am- 
herst Harbor. 

Magdalen  Islands, 
Deadman  Rock. 


St.  Paul  Island j  Light-house,  N.  li.  end . 

Do Light-house,  .S.  VV.  end 


N.  side  of  entrance 
W.  pt 


47  14  23 
47  16    3 


47  13  50 
47  II  20 


58  24    ID 

59  18    22 

59  23 
59  13 
57  50 
57  18 
57  24  27 
57  2  40 
56  44  30 
56  33  40 
55  53  12 


55  51 

56  51 


8 
10  50 


12 


60  8  o 

61  44.  o 

63  27  3 

66  22  40 

67  21  55 
71  12  19 

73  33  4 

68  27  18 
66  46  o 
65  19  30 

64  12  o 
64  9  15 


61  41  48 
63  36  o 


64  10 

64  18 

64  48 

65  16 

66  22 

64  31 

65  2 


o 
o 
o 
o 

10 

o 
o 


63  59  19 

63  43  o 
61  58  15 

63  6  53 

61  9  15 
61  24  30 


47  16  30   61  42 


61  49  26 

62  12  25 


60 
60 


8  20 

9  36 


40 

10 

o 

o 


57 
57 
57 

57  47  o 

58  53  o 

58  59  20 

59  21  o 
59  45  o 
59  58  o 


Authorities. 


Lieut.  Raper,  R.  N. 
Adm.  Bayfield,  R.  N. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 
Adm.  Bayfield,  R.  N. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Capt.  Orlebar,  R.  N. 
Lieut.  Raper,  R.  N. 
Adm.  Bayfield,  R.  N. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 
Adm.  Bayfield,  R.  N. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Adm.  Bayfield,  R.  N. 

Do. 

Do. 
Comdr.  Ashe,  R.  N. 

Do. 
Adm.  Bayfield,  R.  N. 
Lieut.  Raper,  R.  N. 
Adm.  Bayfield,  R.  N. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Adm.  Bayfield,  R.  N. 
Lieut.  Raper,  R.  N. 
Adm.  Bayfield,  R.  N. 
Do. 

Do. 
Lieut.  Raper,  R.  N. 

Admiralty,  R.  N. 

Adm.  Bayfield,  R.  N. 

Do. 


Do. 
Do. 


Page  522J 


TABLE  49. 

MARITIME  POSITIONS. 

BAST  COAST  OF  NORTH  AMERICA— Continued. 


H 

e 

ft 


Places. 


e 
w 
X 

e 


V 

B 
S 
fa 


a 


Exact  locations. 


Cape  Breton  Island Cape  North 

St.  Ann's  Harbor '  E.  pt.  entrance 

Sydney  Harbor Light- house  on  flat  pt 

Scatary  Island '  Light-house,  N.  E.  pt''. . . . 

Louisburg I do 

Cape  Hitchinbroke 1 

Madame  Island 

Port  Hood 


Sable  Island. 


S.pt. 

Just-au-corps    Island,    at 

entrance. 
Light-house,  E.  end 


Lat.  N. 


Custom-house 


Lt. -house,  N.W.  entrance 

R.  C.  Church  .steeple 

Light-house 

do 

Green  Island 

Beacon 

Dock-yard  observatory  . . 

Light-house 

Shut-in  Island 


Pictou 

Cape  St.  George  .... 

Gut  of  Canso 

Arichat  Harbor 

Cape  Canso  

White  Head  Island  . 

Country  Harbor  . 

Wedge  Island 

Halifax 

Sambro  Island 

Margaret's  Bay 

Tancook  Island 

Cape  Le  Havre , 

Coffin  Island 

Little  Hope  Island  . . 

Shelburne  Harbor |  Two  lights,  McNutts  I 

Cape  Sable Light  house 

Seal  Island ■ do 

Cape  Fourchu 1 do 

Cape  St.  Mary ' 

Bryer's  Island i  Light-house 

Annapolis  Harbor "^ 

Haute  Island 

Cape  Chignecto 


Black  Rock. 

Light-house 


Cape  Enrag^ Light-house 

Ouaco do 


Prim  Point  light 


St.  John's 

Cape  Lepreau 

Etang  Harbor 

St.  Andrew's 

Campo  Bello  Island  . . 
Grand  Manan  Island  . 

Gannet  Rock [ do 

Machias  Island :  Light-house,  E.  pt 


Reed's  Pt.,  time-ball  sta'n 

Light-house 

S.  pt.  tower 

S.pt.  hght 

Light-house,  N,  pt 

Light-house,  N.  E.  pt 


Astronomical  station 

Cong.  Church 


Light-  house 


Calais 

Eastport 

Quoddy  Head 

Machias 

Petit  Menan  Island  . . . 

Baker's  Island 

Mount  Desert  Rock  . . . 

Bangor  

Belfast 

Rockland 

Matinicus  Rock 

Manhegan  Island 

Seguin  Island 

Bath 

Brunswick 

Augusta Baptist  Church 

Portland Custom-house 

Do Portland  Head  light-house 

Cape  Elizabeth Light-house 

Wood  Island j do 

Boon  Island do 


Town  Hall 

Light-house 

--..do  

....do  

Thomas  Hill 

Methodist  Church. 
Episcopal  Church  . 

Light-house 

....do 

....do  

Winter  St.  Church 
College  spire 


47  3  o 
46  21  o 
46  16  12 
46  2  o 
45  54  34 
45  34    o 

45  28    o 

46  o    o 

43  58  30 

45  40  50 
45  52  o 
45  41  50 
30  48 
19  49 
45  12  o 
45  6  o 
45  o  36 

44  39  38 
44  26  II 

44  34 
44  29 
44  12 
44  3 
43  49 
43  37  30 
43  23  19 
43  24 

43  47 

44  7 
44  16 

44  31  34 

45  15 
45  19 


Long.  W. 


45 
45 


45  36 
45  23 


45 
45 
44 
45 


15  45 
3  42 


4 

4 


o 
20 

44  57  o 
44  45  52 
44  30  38 

44  30  7 

45  II  5 
44  54  15 
44  48  54 

44  43  I 
44  22  2 

44  14  48 

43  58  7 

44  48  23 
44  25  29 
44  6  6 

43  47  o 
43  45  52 
43  42  25 
43  54  55 

43  54  29 

44  18  52 
43  39  28 
43  37  22 
43  33  50 
43  27  23 
43  7  16 


Authorities. 


60  25     o  Lieut.  Raper,  R.  N. 
60  27    o  Do. 

60     7  22  Adm.  Bayfield,  R.  N. 

59  41     o  Lieut.  Raper,  R.  N. 

59  57  15  Adm.  Bayfield,  R.N. 

60  42     o  Lieut.  Raper,  R.  N. 

61  3  o      Do. 
61  36  o      Do. 

59  46  o  Admiralty  Light  List. 


62  42  10 
61  52  o 
61  29  30 
61  I  47 

60  55  29 

61  8  9 
61  32  o 
61  52  39 

63  35  17 
63  33  49 

63  54 

64  6 
64  18 
64  36 

64  45 

65  16 

65  37  II 

65  58  o 

66  10  o 
66  II  o 
66  22  o 
65  47  20 
65  o  o 
64  58  o 


64  29  o 

65  20  o 

66  3  45 
66  27  o 

66  49  o 

67  3 
6655 
66  44 

66  47 

67  6 


o 
o 
I 

13 


67  16  50 

66  59  14 

66  57  I 

67  27  22 

67  51  51 

68  II 
68  7 


56 
42 


68  46  59 

69  o  19 
69  6  52 

68  51  18 

69  18  57 

69  45  31 
69  49  o 

69  57  44 

69  46  37 

70  15  18 
70  12  29 
70  12  10 

70  19  45 
70  28  36 


Do. 
Lieut.  Raper,  R.  N. 

Do. 
Adm.  Bayfield,  R.  N. 
Admiralty  Light  List. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 
Bayfield  and  Shortland. 
Bayfield. 
Lieut.  Raper,  R.  N, 

Do. 

Do. 

Do. 

Do. 

Do. 
Admiralty  Light  List. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 
Admiralty  Light  List. 
Lieut.  Raper,  R.  N. 

Do.  .. 

Do. 

Do. 
Admiralty  Time-Ball  List. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 
Light  List. 

Do. 

Do. 

U.  S.  C.  and  G.  Survey. 

Do. 
Light  List. 
U.  S.  C.  and  G.  Survey. 

Do. 
Light  List. 
U.  S.  C.  and  G.  Survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  523 


CI) 

O 

o 


Places. 


X 

S 
Jt 
w 

CS 

c 

■ 


e 


e 


« 
a 
a 
9 


Exact  locations. 


Lat.  N. 


Whale's  Back Light- liciuse    43     3  30 

Portsmouth ;  Navy-yard  flag-staff . 43     4  56 

Do Fort  Constitution '  43     4  16 

Hampton '.  Baptist  Church !  42  56  15 


Isles  of  Shoals. 


Newburyport 

Do 

Ipswich 

Annisquam  Harbor 
Cape  Ann 


White  Island  light-house. 


Gloucester 
Do.. 


Academy ' 

Plum  Island  light-house.. 

Light-house 

...do ] 

Thatcher's    Island  light-  ' 
house. 

Universahst  Church • 

Ten-Pound  Island  light- 
house. 

Beverly Hospital      Point     light- 
house. 

Salem South  Church 

Do I  Derby's  Wharf  It. -house  .j 

Marblehead Light-house 

C.-^MBRlDGE ]   Harvard  Observatory 

Boston '  Navy-yard  flag-staff 

Do State  House 

Do Little     Brewster    Island 

light-house. 

Do Minot's  Ledge  light-house 

Plymouth ^   Pier-head 

Do Gurnet  light-house I 

Barnstable Light-house 

Cape  Cod !   Highlands  light-house  ... 

Nauset  Beach ;  E.  side  Cape  Cod 

Chatham . .    Light-house 

Monomoy  Point ' do 


42  58 

42  48  30 
42  48  53 
42  4t  5 
42  39  41 
42  38  20 

42  36  46 
42  36    5 


42  32  46 

42  31  10 

42  30  58 
42  30  18 
42  22  48 
42  22  22 
42  21  28 
42  19  39 


Nantucket 
Nantucket  S.  shoals 

Sankaty  Head 

Tarpaulin  Cove 

Vineyard  Haven  .  . . 

Gay  Head 

Cuttyhunk 

New  Bedford 


Seaconnet  Point 
Beaver  Tail  . . . . 
Newport  


South  Church 

Light  ship 

Light-house 

....do  

W.  Chop  light-house 

Light-house 

....do  

Baptist  Church 


37 
10(15) 
33  32 
16  55 
40  56  (o) 

16  59 

28    6 

28  49 
20  52 

24  50 
38  10 


Light-house 4 

Flag-staff,  torpedo  station:  4 

Bristol  Ferry 1   Light-house •  4 

Providence 1   Unitarian  Church 4 

Point  Judith j  Light-house 4 

Block  Island 1  Light-house,  S.  E.  end  ...  i  4 

Watch  Hill  Point Light-house 4 


Montauk  Point   i do 


.Stonington 


Light-house, 

entrance. 
Groton  Monument 


E.  side  of 


New  London , 

Little  Gull  Island Light-house 

Gardner's  Island i  Light-house,  N.  point 

Plum  Island 1  Light-house,  W.  point 


Light-house,  Lynde  Point 
Yale  College  spire  (middle) 

Light-house 

...do 


Saybrook 

New  Haven 

Bridgeport  Harbor 
Norwalk  Island . . . 

Shinnecock  Bay I do 

i^ire  Island I do 

Albany I  Dudley  Observatory 

New  York Navy-yard  flag-staff 

Do i  City  Hall 

Fort  Tompkins Light-house 


16  9 

58  44 
o  10 

43  20 
2  21 

5t 


26  30 
26  56 
29  7 
38  33 
49  26 

21(38) 

9  8 

18  12 


4  13 
19  41 


21  16 

12  21 

8  29 

ID  23 
16  15 
18  28 
9(24) 

2  53 
o 

40  37  55- 
42  39  50 
40  42  2 
40  42 
40  36 


41 
41 
41 

41 
41 
41 
41 
41 
40  51 


44 
4 


Long.  W. 


70  41  48 
70  44  22 
70  42  34 
70  50  12 

70  37  25 

70  52  28 
70  49  10 
70  46  6 
70  40  54 
70  34  30 

70  39  59 
70  39  56 

70  51  22 

70  53  38 
70  53  2 
70  50  2 

7 
3 
3 


71 
71 
71 


70  5- 


43 

5 

50 

25 


70  45  34 
70  39  12 
70  36  3 

70  16(52) 

70  3  39 

69  57  4 
60  57  (o) 
60  59  38 

70  5  57 
69  51(50) 

69  57  55 

70  45  28 
70  36  o 
70  50  7 
70  56  59 
70  55  36 


71 
71 
71 
71 


13  30 

23  59 
19  40 

15  38 
71  24  19 
71  28(54) 
71  33  8 


71  51  27 
71  54  21 


72 
72 
72 


4  47 
6  26 

844 
72  12  43 
72  20  36 

72  55  45 

73  10(48) 
73  25  II 

72  30  16 

73  13  9 
73  44  56 

73  58  51 

74  o  24 
74  3  17 


Authorities. 


U.  S.  C.  and  G.  Survey. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 
U.  S.  C.  and  G.  Survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 


Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  524] 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  NORTH  AMERICA— Continued. 


o 
O 


Places. 


a 


s 

.2 

e 

M). 

b 


9 

Q 
(A 

V 

c 
u 
» 

V 


a 

e 
fa 


fa 
e 


a 

0 

fa 
a 


en 

fa 
e 
« 


fa 

e 


Exact  locations. 


Sandy  Hook Light-house  . . 

Do I  Lightship  ... 

Navesink  Highlands N.  light-house 

Barnegat  Inlet |  Light-house  . . 

Tucker's  Beach do 

Al:)secum  Inlet 

Five-Fathom  Bank  ... 

Cape  May 

Philadelphia,  Pa  . . 

Do 


Wilmington,  Del 
Cape  Henlopen  .... 
Assateague  Island . . 

Hog  Island 

Cape  Charles 

Baltimore 

Annapolis 


Point  Lookout 

Washington,  D.  C 

Do 

Do    

Old  Point  Comfort 

Norfolk  

Do 

Richmond,  Va 

Cape  Henry 


Elizabeth  City  .... 

Edenton 

Currituck  Beach  . . 

Body's  Island 

Cape  Hatteras  .... 

Ocracoke 

New  Berne 

Cape  Lookout  

Beaufort,  N.  C 

Federal  Point 

Frying- Pan  Shoals 

Georgetown,  S.  C  . 

Do 

Cape  Romain 

Charleston 

Do 

Beaufort,  S.  C 

Port  Royal 


Tybee  Island 

Savannah 

Sapelo  Island 

Darien 

St.  Simon's 

Brunswick 

Cumberland  Island. 


Amelia  Island  .. 

Fernandina 

St.  Mary,  Ga... 
St.  John's  River 

Jacksonville 

St.  Augustine 

Do 

Cape  Canaveral . 

Jupiter  Inlet 

Fowey  Rocks 

Carysfort  Reef.. 


do 

Light-ship 

Light-house 

State-house  

Navy- yard  flag-staff, 
League  Island. 

Town-hall - 

Light-house 

....do  

...do 

...do  

Washington  Monument. 

Naval  Academy  observ- 
atory. 

Light-house 

Navy-yard  flag-staff 

Naval  Observatory 

Capitol  dome 

Light- house,  Fort  Monroe 

City-hall 

Navy-yard  flag-staff 

Capitol 

Light-house 


Lat.  N. 


Court-house 

do 

Light-house  . . . 

do 

do  

do 

Episcopal  spire 

Light-house  . . . 

Court-house 

Light-house  . . . 

Light-ship  . ,. . 


40  27  40 
40  26(51) 
40  23  45 
39  45  49 
39  30  19 
39  21  56 
38  48(20) 

38  55  56 

39  56  53 
39  53  14 

39  44  27 

38  46  39 
37  54(37) 
37  23(16) 

37  7  9 

39  17  48 

38  58  53 

38  2  16 

38  52  30 
38  53  39 
38  53  20 
37  o  3 
36  50  47 

36  49  33 

37  32  36 
36  55  29 


Episcopal  Church 

Light-house,  North  Island 

Light-house 

do   

St.  Michael's  Church 

Episcopal  Church 

Martin's   Industry  light- 
ship. 

Light-house    

Exchange  spire 

Light-house 

Winnowing  House 

Light-house 

Academy 

Light-house,  N.  pt 

do 


Long.  W. 


36  17  58 
36  3  24 
36  22  32 

35  49    3 

35  15 
6 


35 

35 
34 
34 


37 

43 

33  57(34) 

33  35   (o) 


14 
28 
21 
16 

5 


22    8 
13(21) 
I   (8) 
41  44 

32  46  34 
;2  26    2 

52    5(31) 


33 
33 
33 
32 


32     I  20 

32  4  52 
31  23(28) 

31  21  54 
31  8  2 
31     8  51 

30  58(34) 


30  40  23 

Astronomical  station 3040  18 

Market-house   3°  43   12 

Light-house  entrance  . . . .  i  30  23  37 

Methodist  Church I  30  19  43 

Presbyterian  Church \  29  53  20 

Light-house 29  53  13 

do   1  28  27  37 

do   :  26  55  (26) 

do   I  25  35  22 

do 25   13   15 


Authorities. 


74  o  9 
73  51(58) 

73  59  II 

74  6  25 
74  17  9 
74  24  53 
74  36(10) 

74  57  40 

75  9  3 
75  10  32 

75  33  3 

75  5  4 
75  21(24) 

75  41(55) 

75  53  33 

76  36  59 

76  29  8 

76  19  22 

76  59  45 

77  3  8 

77  o  36 
76  18  26 
76  17  22 

76  17  46 

77  26  4 
76  o  32 

76  13  23 

76  36  31 

75  49  53 
75  33  50 
75  31  17 

75  59  12 

77  2  24 

76  31  28 

76  39  48 

77  55(11) 
77  50  (o) 


79  16  49 
79  II  (o) 

79  22(23) 
79  52  58 

79  55  49 

80  40  27 

80  35(13) 
80  50  43 


81 
81 


5  26 

17  (7) 
81  25  39 
81  23  35 
81  29  26 
81  24  45 


81 

26  31 

81 

27  47 

81 

32  53 

81 

25  32 

81 

39  14 

81 

18  41 

81 

17  8 

80 

31  36 

80 

5  (5) 

80 

5  50 

80 

12  42 

U.  S.  C.  and  G.  Survey. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do, 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  525 


o 


Places. 


'Z 

0 


9 


a 

z 
z 

z 

t 


B5 
8 

« 

e 
.a 
a 


e 
'5 


Exact  locations. 


Alligator  Reef Light-house 

Sombrero  Key do 

Sand  Key : do 

Key  West do 

Do Soldiers'  Monument 

Tortugas Light-house,  Loggerhead 

Key. 

Tampa  Bay Egmont  Key  light ... 

Cedar  Keys Ast.  station,  D^pot  Key . . 

Do Seahorse  Key  light 

St.  Mark's Fort  St.  Mark's 

.\palachi:ola   Flag-staff 

Cape  St.  George Light-house 

Cape  San  Bias do   

Pensacol.\ do 

Do Navy-yard  chimney 

Do    Flag-stafit",  public  square.. 

Sand  Island ;   Light-house 

Mobile  Point do   

Mobile   Episcopal  Church 

Horn  Island Light-house 

Fast  Pascagoula  Coast-Survey  station 

Mississippi  City do 

Ship  Island Light-house 

Cat  Island do 

Pass  Christian do  

Chandeleur do   

Mouth  Mississippi  River    Pass  a  I'Outre  light 

Do S.  Pass  light  ( Fadsport)  . 

Do S.W.  Pass  light 

New  Orlea.xs United  States  Mint 

Barrataria  Bay Light-house 

Timbalier  Island do   

Ship  Shoal do  

Southwest  Reef do  

Calcasieu  Pass do  

Sabine  Pass do  


Lat.  N. 


24  51    (2) 
24  37  36 

24  27  10 

24  32  58 
24  33  26  j 
24  38    4 


27  36 

29 

29 


4 
7  29 
5  49 


29  43 
29  35 


32 
..   IS 

29  39  46 

30  20  47 
30  20  49 
30  24  33 

30  11(19) 

30  13(45) 
30  41  26 
30  13  24 
30  20  42 
30  22  54 
30  12(54) 
30  13(57) 
30  18  54 
30    3     8 

29  II  32 
29     I     o 

28  58  24 

29  57  46  ' 
29  16  33 

29     I (30) 

28  54  58 

29  23(30) 
29  46  (o) 
29  43(55) 


Galveston Cathedral,  N.  spire 

Do Light-house,  Bolivar  Pt  . . 

Matagorda Coast-  Survey  station 

Do Light-house 

Indianola Coast-Survey  station   

Lavaca do   J 

Aransas  Pass Light-house ' 

Brazos  Santiago Light,  S.  end  Padre  Island 

Point  Isabel Light-house 

Rio  Grande  del  Norte  . .  Obs.  N.  side  of  entrance. . 

San  Fernando  River Entrance 

Santander  River do    

Mount  Mecate Summit 

Tampico Light-house 

Cape  Roxo 

Lobos  Cay Middle 

Tuspan  Reefs Middle  islet 

Mexico National  Observatory 

Bernal  Chico Middle  of  islet , 

Zempoala  Point Extreme 

Vera  Cruz San  Juan  d'  Ulloa  light . . 

Sacrificios  Island ' 

Orizaba  Mountain i  7,400  feet 19 

Cofre  de  Perote  Mt 14,000  feet 19 

Alvarado E.  side  of  entrance 18 

Roca  Partida Summit 

Tuxlta,  volcano do . .    

Montepio Landing  place 


17 

29 
18 


29   18 

29  22 

28  41 

28  20 

28  32  28 

28  37  36 

27  51  51 
26  4  38 
26   438 

25  57  22 


25 
23 
22 
22 
21 
21 
21 

19 
19 
19 
19 

19 


23  40 
46  20 


40 

50 
o 

o 

o 

I 

39  50 
27  26 
12  29 


J" 
15 
35 
28 

3 
26 


10 
4 


10 
o 


18 

44 

18 

29 

18 

40 

29  30 

49  o 


o 
o 
o 


Long.  W. 


1^      r       >  > 

80  37  (8) 

81  6  40 
81  52  40 
81  48  4 

81  48  25 

82  55  43 

82  45  40 

83  I  57 

83  3  58 

84  12  42 

84  59  12 

85  2 
85  21 
87  18 
87  16 


40 


87  12  53 


88 


88 
88 
88 
89 


2(53) 
1(27) 

2  28 
3058 
32  45 

I  57 
57(56) 

89  9(41) 
89  15  o 

88  52  36 

89  2  29 
89  10  2 

89  23  31 

90  3  28 

89  56  51 

90  18(17) 

91  4  39 

91  30(13) 
93  17(30^ 

93  50(19) 

94  47  26 

94  46  I 

95  57  26 

96  25  28 
96  31  I 

96  37  21 

97  ^3  25 
97  8  45 
97  II 

97  7 


37 
56 


97  20  30 

97  46  o 

98  4  o 

97  49  o 
97  22  o 

13  3 


12  40 
6  39 


97 
97 
99 
96  23  44 

19  27 

7 

5 
15 


Authorities. 


57 

30 
o 


96 
96 
96 

97 

97 

95  45  42 

95  12  8 
8  o 
6    6 


/  j"- 


95 

95 


U.  S.  C.  and  G.  Survey. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do, 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Capt.  Baker,  U.S.N. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 
Capt.  Baker,  U.  S.  N. 

Do. 
Mexican  Gov't  Survey. 
Capt.  Baker,  U.  S.  N. 

Do. 
Lieut.  Comdr.  Davis. 
Lieut.  Raper,  R.  N. 
Capt.  Baker.  U.  S.  N. 

Do. 
Lt.  Comdr.  Green,  U.  S.N. 

Do. 

Do. 

Do. 


Page  526] 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OP  NORTH  AMERICA— Continued. 


O 


Places. 


(3 

A 

w 
s 


a 
C9 
h 
3 
■B 

M 
■I 

e 
B 


Zapotitlan  Point 

San  Juan  Point 

Coatzacoalcos 

Santa  Ana  Lagoon.  _, 

Tupilco  River 

Tabasco  River 

Carmen  Island 

Laguna  de  Terminos . 


Paypoton  Mount. . 

Lerma 

Campeche 

Do 

Point  Palmas 

Sisal 

Madagascar  Reef . 

Progreso 

Silan 

Lagartos 

Cape  Catoche 

Areas  Cays 

Obispo  Shoal 

New  Bank 

Triangles,  E.  reef. 
Triangles,  W.  reef 
Baxo  Nuevo  Reef 

Arenas  Cays 

Alacran  Reef 

Contoy  Island 

Mugeres  Island 

Cancun  Island 

Cozumel  Island  __ 

Do 

Ascension  Bay 

Chinchorro  Bank  ., 


Half- Moon  Cay 

Mauger  Cay 

Glover  Reef 

English  Cay 

St.  George's  Cay 

Sand-Fly  Cays 

South  Water  Cay 

Belize 

North  Standing  Creek . 

Sittee  Point 

Cockscomb  Mt 

Placentia  Point 

Icacos  Point  

Sarstoon  River 

Dulce  River 

Duke  Gulf 

Do 

Hospital  Bight 

Cape  Three  Points 

Seal  Cays 

Omoa 

Cape  Triunfo 

Congrehay  Peak  

Truxillo 

Utilla  Island __'_'_'_ 

Hog  Isles 

Ruatan 

Ruatan,  Port  Royal  ... 

Bonacca  Island 

Misteriosa  Bank 

Swan  Islands  .  _ 


Exact  locations. 


Extreme 

do 

Light-house 

Entrance 

do 


do 

N.  E.  point 

Vigia  tower,  W.   end 
Carmen  Island. 

.Summit 

Church 

Cathedral 

Fort  San  Jos6 . 


of 


Fort... 

Centre 

Custom-house 

Village 

do 

N.  E.  extreme..  . 

W.  Cay 

i6-feet  spot 

Centre 

Beacon  

Cay  at  S.  W.  end 
Centre  . . 

N.W.Cay 

Perez  Cay 

N.  extreme 

Look-out  tower  . 

Nisuc  Point 

N.  point 

S.  point 

Allen  Point 

Dry  sand  bore  .  . 


Light-house  . 
N. W.  end    .. 

S.  W.  Cay 

Flagstaff 

Centre 

Hut,  S.  end 

Centre 

Fort  George 

Entrance 

Cay 

Summit,  4,000  feet 

Huts  on  point 

S.  extreme 

Entrance 

Entrance,  W.  side 

Fort  St.  Philip '_'_'_ 

Isabel 

Hut,  N.  point  of  entrance. 
N.  W.  extreme 

S.Cay ""; 

Sandy  pit,  at  entrance 

Bluff  pt 1_. 

Summit,  8,040  feet 

Fort 

S.  Cay 

Highest  hill  on  W.  islet.. 

Centre  of  Coxen  Cay 

N.  W.  pt.  of  George  Cay., 

Summit,  1,200  feet 

S.  point 

N.  W.  pt.  of  W.  island"  ^"^! 


Lat.  N. 


18  34  O 
18  19  45 
18  8  15 
18  18  49 
18  26  44 
18  37  28 
18  47  8 

18  38  44 

19  38  o 
19  48  24 

19  50  45 

19  51  36 

21   2   O 

21  10  6 

21  26  30 
21  17  O 
21  23  O 
21  36  30 
21  36   O 

20  12  35 

20  29  O 
20  32  O 

20  54  54 

20  58  O 

21  50   O 

22  7  10 
22  23  36 
21  32  30 
21  12  O 
21  3  O 
20  35  30 

20  16  O 

9  46  55 
8  23  20 


Long.  W. 


7  12  12 

7  36  IS 

6  42  20 

7  19  30 
7  33  15 
6  57  50 

6  48  50 

7  29  20 
57  40 

47  45 

48  10 

30  54 
14  15 
54  o 

49  45 
38  o 
24  20 

5  52  20 

5  57  45 
680 


5  47  II 

5  48  45 
5  38  o 

5  55  45 

6  3  40 
58  o 
18  o 
24  20 
28  o 

44  o 
24  30 


94  54  21 
94  38  57 
94  24  28 

93  51  53 
93  25  25 
92  41  27 
91  30  50 
91  50  17 

90  43  27 
90  36  12 

90  33  51 
90  30  51 
90  22 
2 

18  27 
89  39  6 
88  54  27 

10  27 

4 


90 
90 


o 

37 


92 
92 
91 


53 

5 

27 


57 
27 


87 

91  59 

92  13 

91  52  27 

92  12  48 

i; 

4 

24  21 
89  41  46 

86  48  50 
86  43  6 
86  46  45 
86  44  15 

86  59  50 

87  28  27 
87  23     7 


Authorities. 


87 

32 

30 

87  46 

30 

87 

50  51  1 

88 

3 

21 

88 

4  45  1 

88 

6 

5 

88 

5  36  1 

88 

II 

40 

88 

13 

48 

88 

15 

15 

88 

37  40  1 

88 

22 

13 

88 

35 

51 

88 

56 

20 

88 

46 

23 

89 

I 

36 

89 

9  44  1 

88 

33 

23 

88 

.38  51  1 

88 

20 

15 

88 

4 

31 

87 

27 

47 

86 

55 

0 

85 

59 

18 

86 

59 

16 

86 

S2 

10 

86 

34 

27 

86 

18 

41 

85 

55 

0 

84 

2 

0 

83  56 

28 

Lt.  Comdr.  Green,  U.  S.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Capt.  Barnett,  R.  N. 

Do. 
Lieut.  Fleuriais,  Fr.  N. 
Capt.  Barnett,  R.  N. 
Lieut.  Raper,  R.  N. 
Capt.  Barnett,  R.  N. 

Do. 
Lt.  Comdr.  Green,  U.  S.  N. 
Capt.  Barnett,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.    ■ 

Do. 

Do. 

Do. 

Do. 
Capt.  Owen,  R.  N. 

Do. 

Do.** 

Do, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 

Do. 

Do. 

Do, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 

Do. 
Capt.  Owen,  R.  N. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OP  NORTH  AMERICA— Continued. 


[Page  527 


ci 
o 
O 


9 

t 

e 


Places. 


Great  Rock  Head  . . . 

Cape  Camaion 

Brewer's  Lagoon. 

Patook  River 

Carataska  Lagoon 

Cape  Gracias-a-Dios . 

Caxones  Reef 

Gorda  Bank 

Farrall  Rock  ......  . 

Half- Moon  Cay 

Alargate  Reef 


Exact  locationt,. 


Mosquito  Cays 

Rosalind  Bank 

Serranilla  Bank 

Serrana  Bank 

Quito  Sueno  Bank  . 

Do 

Roncador  Cay 

Old  Providence , 

St.  Andrew's  Island 

Courtown  Cays 

Albuquerque  Bank  

Brangman's  Bluff 

Pearl  Cays    

Pearl  Cays  Lagoon 

Cookra  Hill 

Blewfield 

Little  Corn  Island 

Great  Corn  Island 


Bluff  extreme . 


E.  side  of  entrance 

do...: 

do  

Extreme 

Great  Hobby  Islet 

Gorda  Cay 

Centre 

do 

E.  point 


San  Juan  de  Nicaragua. . 

Mount  Cartago 

Blanco  Point 

Carreta  Point 

Tirby  Point 

Columbus  Island 

Blanco  Peak 

Shepherd  Island 

Cobbler  Rock 

Valiente  Peak 

Escudo  de  Veragua 


S. end  

N.  W.  extreme 

Beacon  Cay  

Little  Cay 

S.  extreme  of  reef 

Spi.t  at  N.  W.  end 

S.  point 

Isabel  House 

S.W.  cove,  Entrance  Island 

Middle  Cay 

Smith  Cay 

Extreme 

Columbilla  Cay 

Mosquito  Point 

Summit 

Schooner  Point 

Gun  Point 

Wells  N.  of  Quin  Bluff. . . 


Church 

Peak,  11,100  feet  . . 

Grape  Cay 

Extreme 

do 

Lime  Point 

Summit,  11,740  feet 

Hut  on  summit . 

Centre 

Summit,  722  feet  .. . 
W.  pt.  of  island . , 


Lat.  N. 


5  53  o 
600 

5  SI  50 
5  48  50 
5  23  40" 
4  59 


5  52 
5  51 
5  8 
5     7 


o 

30 
o 
o 

50 

o 


21     12 

54    o 
47  45 


21 


30 
o 
o 

3  34  30 
22  54 
I  40 
o 
o 


?o 


24 

10 


3     o 
22  35 

20  39 

15  3" 
59  o 
2  17  30 
2    9  17 


o  55  14 
o     I  30 

000 
9  38  30 


25  45 
24  47 
16  30 

14  22 

14  30 

10  30 

6  30 


Long.  W. 


85  27  10 
85  3  o 
84  38  33 
84  17  II 
83  42  36 
83  10  27 
83  8  21 
82  23  27 
82  18  7 
82  42  9 
82  20    o 


82  45  57 
80  51  27 

79  50  54 

80  14  57 
8  21 

7 
5 


81 

81 
80 


21 


81  21 

81  43 


5 

26 
6 

27  53 


81 

81  49  54 
83  21  27 
83  23  II 
83  37  13 
83  45  57 
83  41  57 
•  58  36 
3  36 


8 
S3 


83  42    5 

47  27 
2     o 


83 

S3 

82  39     7 

82  21  47 

82  20  31 

83  3  27 
82  20  33 
82  7  51 
81  55  2 
81  33  57 


Authorities. 


Capt.  Owen,  R.  N. 
Lieut.  Raper,  R.  N. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 

Capt.  Owen,  R.  N. 

Do. 

Do. 
Capt.  Barnett,  R.  N. 
Capt.  Owen,  R.N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Barnet,  R.  N. 

Do. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 

Comdr.  Lull,  U.  S.  N. 
Capt.  Barnett,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


TVEST  COAST  OF  NORTH  AMERICA. 


c: 
d 


Point  Barrow !  Highest  lat.  of  U.  S 71 

Icy  Cape !  Extreme 70 

Cape  Lisburne 849  feet 68 

Cape  Krusenstern [  Extreme '  67 

Chamisso  Island j  Summit I  66 

Cape  Spanberg I  Extreme ;  66 

Diomede  Island Fairway  Rock \  65 

Cape  Prince  of  Wales ...  W .  point 65 

Port  Clarence Point  Spencer |  65 

King  Island N.  point   '  65 

Cape  Nome -. Extreme 64 

Michaelovski Fort ^1  63 

Stuart  Island ,  W.  point 63 

Cape  Romanzoff Extreme 61 

St.  Lawrence  Island !  E.  point 63 

St.  Lawrence  Island N.  W.  point 63 

St.  Matthew  Island S.  E.  point 60 

Pinnacle  Islet   ,  Summit,  930  feet 60 

Aunivak  Island Cape  Etolin 60 

Hagermeister  Island 58 


27  o 
20  o 
56  o 
9  o 
13  II 
42  o 
3842 

33  30 
16  40 


156  15  o 
161  40     o 

166  8  o 
164  37  o 
161  46  o 
163  34  o 
168  43  42 

167  59  12 
166  47  50 


0 

0 

168   I  30 

23 

0 

165   5   0 

28 

0 

161  51  54 

35 

30 

162  32  36 

S2 

0 

166  17   0 

17 

0 

168  35  0 

51 

12 

171  29  0 

18 

0 

172  4  0 

I^ 

0 

172  34  30 

25 

22 

166  8  30 

48 

31 

160  50  0 

Capt.  Beechey,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Tebenkoff. 
Capt.  Kellet,  R.  N. 
Tebenkoff. 
Etalin. 
Pavloff. 

Capt.  Beechey,  R.  N. 
Adm.  Liitke. 

Do. 
U.  S.  C.  &  G.  Survey. 

Do. 


Page  528 


TABLE  49, 

MARITIME  POSITIONS. 

WEST  COAST  OP  NORTH  AMERICA— Continued. 


o 
O 


R 


Si 


© 

"S 

a 

M 

a 
s 


"0 

a 

8 

« 
N 

fa 
V 

a 
e 
« 
a 
a 


Places. 


Cape  Mentschikoff. 

Port  Moller 

St.  George  Island.. 


Attu  Island 

St.  Paul  Island  (Pribiloff 
Island). 

Kyska  Island 

Amchitka  Island 

Adakh  Island 

Atka  Island _. . 

Unalaska  Island 

Sannakh  Reefs 

Sannakh  Island 

Unga  Island 

Humboldt  Harbor,  Pop- 
off  Island. 
Nagai  Island,  Sanborn 

Harbor. 
Koniushi  Island,  N.  W. 

harbor. 
Koniushi  Island,  N.  E. 

harbor. 
Simeonoff  Island,  Sim- 
eonoff  Harbor. 

Cape  Strogonoff 

Chignik  Bay 

Anowik  Island 

Chiachi  Islands 

Light- House  Rocks 

Chirikoff  Island 

St.  Paul  Harbor,  Kodiak 
Island. 

Port  Etches 

Middleton  Island 

Mount  St.  Elias 

Port  Mulgrave 

Lituya  Bay 

Sitka 


Exact  locations. 


Extreme 


S.  side 


Chichagoff  Harbor. 
Village 


Constantine  Harbor 

Bay  of  Islands 

Nazan  Bay  (church) 

C.    .S.    station,    opposite 
wharf  at  Ilinlink. 

S. edge  

N.  E.end 

Shumagin  Islands 
do 


North  Island 

Cape  Knox 

Port  Kaper 

Forsyth  Point 

St.  James  Cape 

Cunisleewas  Harbor 

Skidegate  Bay 

Rose  Spit  Point 

Massett  Harbor . 

Cape  Edensaw  __ 


do 

do 

do 

do 


Extreme  ._ 
Anchorage 
S. end  


(Approx.) 

Cove  N.  W.  of  village 


Summit 


Middle  of  parade  ground . 


Hecate  Bay 

Stamp  Harbor 

Island  Harbor 

Cape  Beale 

Refuge  Cove 

Hesquiat  Harbor .. 

Estevan  Point 

Nootka  Sound 
Port  Langford 

Esperanza  Inlet 

Kyuquot  Sound 

Nasparti  Inlet 

Cook  Cape  

North  Harbor.  __ 


N.  point 

Extreme 

Sausomu  Island 

Extreme  ._ 

do I. 

N.  side  of  entrance. 

Rock  on  bar 

Extreme 

Bar .'. 

Extreme 


Observatory  Islet  _ 

do 

do 

Light-house 

Village  on  W.  side. 

Boat  Cove 

S.  extreme 

Friendly  Cove 

Colwood  Islet 

Observatory  Rock 

Shingle  Point 

Head  Beach 

.-(Oianaer  island 

Observatory  Rock 


Lat.  N. 


57  30  24 

55  54  59 

56  34  23 

52  56     I 

57  7  19 

51  59    4 
51  23  39 

51  49  18 

52  10  36 

53  52  54 

54  13  30 

54  26  12 

55  20  45 
55  19  17 

55     7  36 

55    3  17 

54  58  25 

54  55  30 


Long.  W. 


56  48 


56 
56 


19  20 

5  13 
58 


55  51 
55  45  24 
55  48  22 

57  47  57 

60  20  43 

59  27  22 

60  20  45 

59  33  42 

58  36  57 
57     2  52 


54  20    o 

54  15    o 

52  56  31 

52 

51 

53 


9 

57 

I 

53  22 

54  13 
54    2 


7 

(o) 
o 

o 

o 

o 


34 
49 

4 
15 

0 
22 

49 

13 

46 

48 

54  41  1 

48 

47 

23 

49 

20 

50 

49 

27 

31 

49 

22 

7 

49  35 

31 

49  47 

20 

49  52 

45 

49  59  55  1 

50 

II 

21 

50 

6 

31 

50 

29 

25 

157  58  30 

160  34  54 

169  39  50 

186  47  36 

170  17  52 

182  30  o 
180  47  54 
176  52    o 

174  15  18 

166  31  44 


162  38  o 
162  18  o 
160  38  39 
160  31  14 


159  56  6 

159  23  5 

159  22  18 

159  15  3 


158  46  o 
158  24  24 
156  39 
5 


159 


19 
24 

157  27  4 
155  42  51 
152  21  21 

146  37  38 
146  18  45 
141  o  12 
139  46  16 
137  40  6 

135  19  31 

i33  o  o 

^33  3    o 

132  9  40 

131  9  o 

131  4 
131  22 

131  39 

131  22 

132  o 
132  14 


125 
125 


125  55  43 
124  50  7 

16  54 
13  14 

126  16  6 
126  24  53 
126  31  58 
126  36  58 
126  56  31 

126  59  21 

127  8  56 
127  37  24 

127  56  36 

128  3  5 


Authorities. 


Staninkovich. 
U.  S.  C.  and  G.  Survey. 
Do. 

Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 


Khondobine. 

U.  S.  C.  and  G.  Survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

English. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Capt. 


Richards 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


R.N. 


TABLE  49. 

MARITIME  POSITIONS. 

"WEST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  529 


Places. 


'2 


9 


9 

9 


Koprino  Harbor 

Hecate  Cove. ... 

Triangle  Island 

Cape  Scott ._  _. 

Bull  Harbor,  Hope  Island 

Port  Alexander. 

Beaver  Harbor 


Cormorant  Island 

Baynes  Sound 

Nanoose  Harbor 

Atkinson  Point 

Nanaimo 

Do 

Victoria 

Do 

Esquimault ^ 

Do 

Race  Island 

Sooke  Inlet 

Port  San  Juan 

Port  Harvey 

Port  Neville 

Knox  Bay,  Thurlow  Isl 

Valdes  Island 

Howe  Sound 

Burrard  Inlet 


Fraser  River 

New  Westminster. 

Point  Roberts 

Semiahmoo  Bay . . 


Admiralty  Head 

Steilacoom 

Seattle 

Port  Townsend 

Smith  Island 

New  Dungeness 

Port  Angelos 

Cape  Flattery 

Shoal  Water  Bay 

Cape  Disappointment. 
Kalama 


Exact  locations. 


Observatory  Rock 

Kitten  Islet 

W.  side 

Summit 

N.  point  Indian  Island 

Islet  in  centre 

Shell  Islet 


Lat.  N. 


Long.  W. 


Yellow  Bluft" in  Alert  Bay. 

Beak  Point 

Entrance  Rock. 

Light-house 

do 

Benson's  House 

Laurel  Point 

Light-house 

Duntze  Head 

Light-house 

do 

Secretary  Island 

Pinnacle  Rock . 

Tide  Pole  Islet 

Robber's  Nob .    

Stream  at  head  of  bay 

S.  point 

Plumper  Cove 

Government        Reserve, 
English  Bay. 

Garry  Point 

Military  Ijarracks 

Parallel  station. 

do 


50  30  o 
50  32  26 

50  51 

50  46 

50  54  47 
50  50  49 


53 
41 


5°  42 


49 
49 
49 


5*^  35  2 
49  36  29 

15  43 
19  40 

12  50 

49  10  15 

48  25  22 
48  25  26 
48  25  49 
48  25  40 
48  17  53 
48  19  35 

48  33  30 

50  33  58 
50  31  9 
50  24  15 
50    2  42 

49  24  39 
49  16  18 

49     7     4 

49  13  I 
49     o    o 

49    o    o 


Light-house 

Methodist  Church 
C.  S.  ast.  station  ._ 

do 

Light-house 

do 


Astoria 

Point  Adams 

Yaquina  Head 

Cape  jVrago,  or  Gregory. 
Cape  Blanco 


Crescent  City  _  ._ 
Trinidad  Head.. 

Eureka 

Humboldt 

Cape  Mendocino. 

Point  Arena 

Point  Reyes 

San  Fk.\ncisco  . 
Do 

M.\RE  Isi..\ND   ._ 

Benicia 

Farallon  Islet 

Santa  Clara 

Mount  Hamilton 
San  lose 


do 

do 

do 

do 

Methodist  Church 


Flag-staff 

Light-house 

do  ... 

do  ... 

do  ... 


do     

do 

Methodist  Church 

Light-house .. 

do 

do 

do 

Coast  Survey  ast.  station. 

Piesidio  station 

Stone  block,  obs.  station. 

Church 

Light-house 

Catholic  Church 

Obs.  peak 

Spire  . 


48 
47 

47  35 


9  19 
10  20 


48     6 
48  19 


54 
56 
4 
48  10  55 
48  8  21 
48  23   18 

46  43  4 
46  16  33 
46    o  26 


II 
II 


19 
^,6 


Pireon  i'uint j  Light- house 


46 
46 

44  43  30 
43  20  38 
42  50  7 

41  44  34 
41  3  4 
40  48  II 
40  46  4 
40  26  21 
38  57  10 
37  59  36 
37  47  55 

37  47  30 

38  5  53 
38  3  5 
37  41  49 
37  20  49 
37  21  3 
37  19  58 
37  10  46 


27  51  42 

27  35  44 
29  5  58 

28  26  II 

27  55  29 
27  39  23 
27  24  33 

26  56  56 
24  50  44 
24  7  32 
23  16  o 
23  48  II 
23  56  2 
23  22  28 
23  23  28 
23  26  II 
23  26  46 

23  31  48 

23  42  40 

24  27  37 
26  16  6 
26  3  47 

25  38  26 

25  14  4 
23  28  46 
23  II  26 

23  "  27 

22  53  52 

23  4  52 
22  44  56 

22  40  34 

22  35  51 
22  19  59 

22  44  58 

22  50  36 

23  6  31 


Authorities. 


23  24 

24  44 
24  4 
24  3 


7 

24 
28 

14 


22  50  39 

23  49  42 
23  58  40 


24  5 
24  22 

24  33 


o 

II 

o 


12  23 

8  56 

9  41 
i^  6 


24 

24 

24 

24  'J 

24  24  14 

23  44  42 
23  I  21 
22  24  32 
22  27  49 
16  16 

9 
o 


22 
22 

23 
21 
21 


23 

4 


22  2  5 


56  26 
36  40 

S3  39 
3<3 


Capt.  Richards,  R.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do, 

Do. 
Do. 

Do. 
Achiiiralty  Light  List. 

Do. 
Capt.  Richards,  R.  N. 

Do. 
Admiralty  Light  List. 
Capt.  Richards,  R.  N. 
Admiralty  Light  List. 

Do. 
Capt.  Richards,  R.  N. 

Do. 

Do. 

Do. 
Vancouver  Island  Pilot. 
Capt.  Richards,  R.  N. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 

U.  S.  C.  and  G.  Survey. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  530] 


TABLE  49- 

MARITIME  POSITIONS. 

WEST  COAST  OP  NORTH  AMERICA— Continued. 


Places. 


Exact  locations. 


Lat.  N. 


Long.  W. 


Authorities. 


B 
fa 

•H 


B 
u 

a 


Santa  Cruz 

Monterey 

Point  Pinos 

Piedras  Blancas 

Point  Conception 

vSanta  Barbara 

San  Buenaventura 

Point  Firmino,  San  Pe- 
dro Bay. 

Los  Angeles 

Point  Loma 

San  Diego 

Mexican  Boundary 

San  Miguel  Island 

Santa  Rosa  Island 

Do 

Santa  Cruz  Island 

Do 

Anacapa  Island 

Santa  Barbara  Island.. 

San  Nicolas  Island 

Santa  Catalina  Island  . . 

Ensenada  Harbor 

San  Tomas-.. 

Colnett  Bay 

San  Martin  Island 

Port  San  Quentin 

San  Geronimo  Island  . . 

Canoas  Point 

Guadeloupe 

Playa  Maria  Bay 

Lagoon  Head 

Cerros  Island , 

San  Benito  Island , 

San  Bartolome 

Ascencion  Island . 

San  Ignacio  Point 

Abreojos  Point 

San  Domingo  Point 

San  Juanico  Point 

Alijos  Rocks 

Cape  San  Lazaro . 

Magdalena  Bay 

Cape  Tosco 

El  Conejo  Point 

Todos  Santos 


San  Lucas 


San  Jose  del  Cabo  . . 

Arena  Point 

Arena  de  la  Ventana. 
Pichilinque  Bay 


La  Paz 

Lupona  Point 

San  Evaristo 

San  Marcial  Point. 

Salinas  Bay 

Loreto 

Pulpito  Point 

Muleje  

San  Marcos  Island 
Santa  Maria  Cove  . 
San  Carlos  Point.. 
Santa  Teresa  Bay  . 


Warehouse  flag-staff 36  57  31 

C.  S.  azimuth  station 3^  35  21 

Light-house 36  37  52 

do 35  39  46 

do 34  26  50 

N.  tower,  Mission  Church'  34  26  10 


C.  S.  ast.  station 
Light- house 


34  15  46 

33  42(19) 

Court-housfc 34     3  5 

Light-house 32  40  14 

C.  S.  ast.  station 32  43  6 

Obelisk i  32  31  58 

34  4  19 
33  56  30 

33  53  50 

34  3  12 
34  4  18 
34  o  25 
33  28  16 
33  14  55 


Seal  Point . 
E.  point  — 

S.  point 

N.  E.  point . 
N.  W.  point 

E.  point 

Summit 

do  ... 


Catalina  Peak 33  23     9 


Head  of  bay,  close  to  beach 

N.  W.  shore  of  cove 

Head  of  bay 

Hassler  Cove 

Sextant  Point 

Bight,  at  E.  end 

High  bluff 

North  point 

Mound  on  W.  side 

Hiirhest  point  of  crater  .. 

S.  E.  extremity 

Summit  of  W.  island 

N.  side  of  entrance 

N.  end  of  island 

Extreme 

Extreme  of  rocky  ledge  . . 

Edge  of  cliff 

Knoll 

South  Rock 

Extreme 

Man-of-war  Cove 

Extreme 

do 

Foot  of  hill  forming  Lo- 

bos  Point. 
Steep  sand  beach  in  N.  W. 

part  of  bay. 

N.  E.  side  of  entrance 

Extreme 

do  

S.  E.  part  of  San  Juan, 

Nepomezeino  Island, 
Peninsula  of  El  Mogote . . 

Extreme 

3  m.  S.  of  S.  Evaristo  Hd. 

Extreme 

Beach,  N.  E.  part  of  bay. . 

Catliedral 

Summit 

Equipalito  Point 

S.  sand  spit 

Beach  on  N.  W.  shore  . . . 

Extreme 

Beach  on  N.  side 


31  51  10 

31  33  4 
30  57  39 
30  28  57 
30  22  15 

29  47  II 
29  25  29 
29  10  50 
28  54  51 
28  14  33 
28  I  49 
28  18  8 
27  39  35 
27  5  58 
26  45  45 
26  42  28 
26  18  56 
26  3  18 
24  58  o 

24  47  35 
24  38  22 
24  18  II 
24  20  17 
23  24  41 

22  53  21 

23  3  35 

23  32  47 

24  3  52 
24  15  31 

24  10  TO 

24  24  10 

24  52  3 

25  30  17 

25  59  37 

26  o  41 
26  30  44 

26  53  37 

27  10  21 

27  26  6 

28  o  7 
28  25  3 


122  I  29 

121  52  59 

121  55  59 

121  15    56 

120  28  6 

119  42  42 

119  15  56 

118  17(37) 


118 
117 
117 
117 


14  32 
14  38 


40 

32 
120  21  55 

119  58  29 

120  7  7 

119  33  51 
119  55  2 
119  23 
2 


119 
119  31 
118  24 


4 
29 

19 

5 


116  38  5 
116  40  51 
116  17 
116  6 
115  59 


28 
36 

7 


115  47  45 
115  12  14 

118  18  30 

114  31  46 

114  6  24 

115  II  3 
115  36  10 
114  54  27 

114  18  21 
113  16  25 

113  34  54 
112  41  44 

112  17  52 

115  51  54 
112  18  30 
112  8  50 
III  42  54 
III  30  21 
no  13  57 

109  54  41 

109  40  43 
109  28  57 
109  50  29 
no  20  34 


U.  S.  C.  and  G.  Survey. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Comdr.  Dewey,  U.  S.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Tessan. 
Comdr.  Dewey,  U.  S.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Dixon,  R.  N. 
Comdr.  Dewey,  U.  S.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

U.  S.  C.  and  G.  Survey. 
Comdr.  Dewey,  U.  S.  N. 

Do. 
Comdr.  Philip,  U.  S.  N. 


TABLE  49. 

MARITIME  POSITIONS. 

WEST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  531 


O 
O 


Places. 


a 


9 


Tas  Animas 

Raza  Island 

Angeles  Bay 

Remedies  Bay 

Mejia  Island 

San  Luis  Island 

San  Firmin 

San  Felipe  Point  .. 
Philips  Point 


George's  Island 

Cape  Tepoca 

Libertad  Anchorage. 

Patos  Island 

Tiburon  Island 

Kino  Point -_. 

San  Pedro 

Guaymas 

Ciaris  Island 

Santa  Barbara 

Agiabampo 

Topolobampo 


Navachista 

Play  a  Colorado 

Altata 

Mazatlan 

Palenita  Village 

San  Bias  

Maria Madre  Island.. 

Mita  Point 

Penas  Anchorage 

Cape  Corrientes 

Perula  Bay . 

San  Benedicto  Island 

Socorro  Island 

Roca  Partida 

Clarion  Island 

Clipperton  Island 

Na vidad  Bay 

Manzanilla  Bay 

Sacatula 

Isla  Grande 

Sijuantenejo  Point 

Morro  Petatlan 


Tequepa  Harbor 

Acapulco 

Maldonado  . 

Port  Angeles 

Sacrificios  Point . 

Port  Guatulco 

Morro  Ayuca 

Salina  Cruz 


Champerico 

San  Jose  de  Guatemala. 

Acajutla ,. 

Libertad  . 

La  Union  

Chicarene  Point 

Realejo  (Corinto) 

Salinas  Bay 

Port  Culebra 

Parida  Anchorage 

Port  Nuevo 

Pallia  I  !iinda  . .  __ 

Ci  iLa  (  ^liibo)  Island  _ 


Exact  locations. 


Low  pt 

Landing  place,  S.  side. 
Bight  on  N.  W.  shore... 
Beach  on  W.  shore  ... 
S.  side 

S.  E.  side 

Beach, N.  of  bight 

Peak,  1,000  feet 

Beacon 


N.  E.  shore  __ 
Hill,  300  feet 

Beach  

S.  E.end 

do 


Mound 

N.  side  of  bay 

Signal  station 

N.  W. part 

N.  W.  side  of  bay 

S.  E.  side  of  entrance 

S.  E.  end  of  Santa  Maria 
Island. 

W.  side  of  creek 

N.  side  of  entrance 

do 

Signal  station 


Custom  house 

S.  E.  extreme 

Extreme 

Mouth  of  Rio  Real  . 

Extreme 

Smooth  Rock 

S.  extreme 

S.  E.  part 

Summit 

S. end  

Summit 

W.  end  of  sandy  beach.  _ 
Flag-staff,  U.  S.  consulate 

Beach,  W.  side  of  bay 

Tripod  on  N.  W.  summit. 

Tree  on  beach 

Junction    of    stony    and 
sandy  beaches. 

Lime-kiln 

N.  W.  angle  of  fort 

El  Recordo  Point 

Summit  of  Pt.  Angeles 

Highest  point  of  cape  .  _ 

Cross 

Summit  of  N.  edge  of  cape 
Extreme  of  point 


Inshore  end  of  iron  wharf. 

Near  head  of  pier 

Custom-house 

Inshore  end  of  iron  wharf. 

U.  S.  consulate . 

Extreme  

Light-house 

Salinas  Islet 

Extremity  of  Mala  Point. 
S.  point  of  Deer  Island  .. 

Entrada  Point 

W.  end  of  Sentinela  Islanc 
Observation  ]ioint_ 


Lat.  N. 


28  47  40 
28  49   II 

28  56  39 

29  13  51 
29  33     8 

29  57 

30  25 

31  2 

31  46 


27 
16 

57 
10 


9 


31  o  54 
30  16  5 
29  54  12 
29  16  12 

28  45  55 
28  45  28 
28  3  22 

27  55  53 
26  58  59 
26  41 
26  16 
25  33  56 

25  23  6 
25  II  42 

24  38  52 

23  II  17 

22  30  26 

21  32  30 

21  30  45 

20  45  50 

20  36  26 

20  25  o 

9  34  48 

9  17  15 

8  42  57 

8  59  41 
"  20  55 
o  17  o 

9  13  25 
9  3  15 
7  58  21 
7  40  15 
7  37  50 
7  31  28 

7  16  13 
6  50  56 
6  19  37 
6  39  10 

5  40  41 
5  44  58 

5  52  17 

6  9  55 


4  17  44 
3  55  19 
3  34  17 
28  49 
20  6 
17  9 

27  54 
3  10 
o  36  46 
8  10  13 
8  4  30 

7  43  3- 
7  24  20 


Long.  W. 


05 
06 


12  47 

o  5 


35 
o 


34 
40 

35  19 
25  49 
39  47 
52  10 

43  31 


26 


16 

53 

45  4 
28  51 
21  46 

58  50 
16  o 

o  55  13 

09  57  16 
09  40  48 

09  17  30 

09  10  23 

08  49  o 

08  23  37 

07  59  37 
06  26  39 

05  44  25 
18  40 

3?,  14 
05  ii  37 
05  16  o 

05  39  21 
05  8  54 

10  49  22 

10  56  53 
12  4  7 
14  44  17 

09  13  o 
04  43  26 
04  19  50 
02  7  6 
01  40  25 

01  33   23 

01  27  14 


loi  4 

99  55 

98  35 

96  30 

96  15 


28 

5 

30 

4 


96  8  10 
95  46  43 
95  12  39 

91  55  36 
90  49  53 
89  50  21 
89  19  22 
87  51  o 
87  47  6 
87  12*  31 
85  43  38 
85  42  46 
82  14  32 

81  43  30 
Si  31  58 
81  41  51 


Authorities. 


Comdr.  Dewey,  U.  S.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do 

Do. 

Do. 

Do. 

Do. 
Capt.  Richards,  R.  N. 
U.  S.  S.  Ranger,  1883. 
Comdr.  Dewey,  U.  S.  N. 

Do. 

Do. 

Do. 
Sir  E.  Belcher,  R.  N. 
U.  S.  S.  Ranger,  1883. 

Do. 
Comdr.  Philip,  U.  S.  N. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 
Lieut.  Chas.  Laird,  U.  S.  N. 

Do. 

Do. 
U.  S.  S.  Ranger. 

Do. 

Do. 
Capt.  Kellet,  R.  N. 

Do. 
Sir  E.  Belcher,  R.  N. 
Lieut.  Wood,  R.N. 


Page  532]  TABLE  49. 

MARITIME  POSITIONS. 
WEST  COAST  OF  NORTH  AMERICA— Continued. 


C4 

O 

U 


s 


Places. 


Cocos  Island... 

Panam.\ 

Do 

Taboga  Island 

Cape  Mala 

Malpelo  Island 


Exact  locations. 


Head  of  Chatham  Bay.. 

S.  tower  of  Cathedral 

N.  E.  bastion,  ast.  station 

Church 

Extreme 

Summit 


Lat.  N. 


Long.  W. 


5  32  57 
8  57  6 
8  57  12. 
8  47  45 
7  27  40 
430 


86  59  17 

79  32  12 
79  32 
79  33 

79  59  25 

81  36  o 


5 
16 


Authorities. 


Sir  E.  Belcher,  R.  N. 
Lt.  Comdr.  Green,  U.  S. 

Do. 
Capt.  Kellet,  R.  N. 

Do. 
Comdr.  Aldham,  R.  N. 


N. 


WEST  INDIA  ISLANDS. 


m 
•8 

a 


m 

a 
cs 

e 


a 


Memory  Rock Centre 


Bahama  Island 

Abaco  Island 

Little  Guano  Cay . 

Walker's  Cay 

Great  Isaac  Cay  . . 
Gun  Cay  


Ginger  Cay 

Cay  Lobos  

St.  Domingo  Cay 

Cay  Verde 

Ragged  Island 

Nairn  Cay 

Nurse  Channel  Cay  . 

Long  Island 

Great  Emma  Island. 

Clarence  Harbor 

Eleuthera  Island 

Do 

Royal  Island 

Nassau 


Andros  Island 

Do 

Great  Stirrup  Cay 

Little  Stirrup  Cay 

San  Salvador 

Concepcion  Island .. 

Watlings  Island 

Rum  Cay 

Castle  Island 

Fortune  Island 

Crooked  Island „. 

Bird  Island 

Samana  Cay 

Plana  Cay  

Mariguana  Island 

Hogsty  Reef 

Inagua  Island.   _   _   _ 

Do 

Little  Inagua  Island 

W.  Caicos  Cay 

French  Cay 

Fort  George  Cay 

Caicos  Island 

Turks  Island 

Square  Handkerchief 
Bank. 

Silver  Bank 

Navidad  Bank 


Cape  Maysi 

Port  Baracoa 
Port  Cayo  Moa . 


W.  point 

Light-house.. 

do  ._... 

Highest  part . 
Light  house  . 
do  .... 


Centre 

Light-house 

Centre 

Hill  at  S.  end 

Gun  Point 

E.  point 

Beacon  

S.  point 

Beacon  

Lochaber  flag-staff. 

Pigeon  Cay 

Cow  and  Bull 

Eastern  Pass 

Light-house  


High  Cay 

N.  extreme 

Flag-staff _.    . 

W.end 

N.  W.  point.     __   __ 

W.bay 

Hunchinbroke  Rock  _. 

Harbor  Point 

Light-house 

S. end  

Moss  flag-staff 

Light-house 

W.  point 

N.  W,  point.. 

S.  E.  point 

N. W.  Cay 

Light-house 

N.  W.  point 

do . 

Hill,S.  E.  end 

W.  point 

Old  magazine .. 

Parsons  Point,  S.  islet  . 

Light-house 

N.  E.  breaker 


26  56  53 

26  41   18 

25  51  30 

26  31   10 

27  15  42 
26     2    o 

25  34  30 


22 
22 
21 
22 
22 
22 
22 
22 
23 
23 
25 
25 
25 
25 

24 
25 
25 
25 
24 
23 
23 
23 
22 
22 
22 
22 

23 
22 
22 
21 
20 
21 
21 
21 
21 
21 
21 
21 
21 


44  50 
22  30 
42    o 

I  15 
14     2 

20  44 

31  15 
51     o 

32  15 

5  45 
II  15 
26  15 

31  20 

5  37 

39  30 
10  40 

49  45 

49  12 
41   10 

50  50 
56  40 

37  45 

6  40 

32  40 

47  30 

51  o 

5  30 
34  38 
16  30 

40  30 
56    o 

7  10 
30  40 

37  30 
30 
54 
29 

31 
6 


o 
o 

33 
o 


E.  extreme 20  35     o 

Centre  of  E.  side ..    20     2     o 


Light-house 

do 

Carenero  Point., 


20  15  10 
20  21  40 
20  41  41 


79 

6 

54 

79 

0 

38 

77 

10 

45 

7658 

0 

78 

23 

48 

79 

5 

56 

79 

iS 

14 

78 

5 

56 

77 

34 

6 

75 

44 

39 

75 

10 

34 

75  45 

17 

75 

28 

20 

75 

51 

41 

74 

51 

54 

75 

46 

24 

74 

58  56  1 

76 

15 

17 

76 

37 

8 

76 

51 

48 

77 

21 

58 

77  42 

30 

78 

I 

36 

77 

54  46  1 

77 

57 

6 

75  46 

24 

75 

7 

27 

74 

28 

16 

74  50 

8 

74 

20 

37 

74 

22 

54 

74 

20 

21 

74 

21 

56 

73  49 

15 

73 

38 

-> 

72 

47 

3 

73 

50 

29 

73 

40 

II 

73 

40 

21 

73  42 

33 

72 

28 

15 

72 

12 

51 

72 

7 

14 

71 

31 

12 

71 

7 

26 

70  29 

54 

69 

21 

24 

68 

47 

24 

74 

9  42 

74  29  34 

74  S3   44 

Capts.  Owen  and  Barnett, 
R.N. 

Do. 

Do. 

Do. 

Do. 
Admiralty  Light  List. 
Capts.  Owen  and  Barnett, 
R.N. 

Do. 

Do. 
Caot.  Owen,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Barnett,  R.  N. 

Do. 
Capt.  Owen,  R.  N. 

Do. 

Do. 
Capts.  Owen  and  Barnett, 
R.N. 

Do. 

Do. 

Do. 

Do. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Admiralty  Light  List. 
Lieut.  Lawrance,  R.  N. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 
Lieut.  Lawrance,  R.  N. 
Admiralty  Light  List. 
Capt.  Owen,  R.  N. 

Do. 
k  Do. 

Spanish. 

Lieut.  Aragon,  Sp.  N. 

Comdr.  Hamilton,  R.  N. 


TABLE  4g. 

MARITIME  POSITIONS. 

WEST  INDIA  ISLANDS— Continued. 


[Page  533 


Places. 


Exact  locations. 


Lat.  N. 


Port  Nipe 

Lucrecia  Point 

Port  Sama 

Peak  of  Sama 

Port  Naranjo 

Port  Padre 

Port  Nue vitas 

Maternillos  Point 

Cay  Verde 

Cay  Confites 

Paredon  Grande  Cay 

Cay  Sal 


Bahia  de  Cadiz  Cay. 

Cay  de  Piedras 

Peak  of  Matanzas 

Havana 

Do 

Colorado  Reefs 

Cape  San  Antonio  . . 

San  Felipe  Cays 

Isle  of  Pines 

Piedras  Cay 

Cienfuegos 

Pickle  Bank 

Cape  Cruz 

Santiago  de  Cuba... 
Port  Guantanamo... 


Cayman  Brae  .  . . 
Little  Cayman  . 
Grand  Cayman  . 

Morant  Point  .  _ 

Port  Antonio 

Port  Maria 

St.  Ann's  Bay  __ 

Falmouth 

Montego  Bay  .. 

St.  Lucia 

Savanna-la-Mer 

Kingston 

Port  Royal  _  _ 

Morant  Cays 

Pedro  Bank 

Baxo  Nuevo 


Roma  Point 

Light-house  

E.  side  of  entrance. 
Summit,  885  feet  . . 
E.  side  of  entrance. 

Guinchos  Point 

Light-house 

do 

N.W.  end 

S.  point 

Light-house 

do 


do 

do  ._. 

Summit 

Morro  light-house  

Transit  pier,  arsenal  yard. 

W.  end 

Light-house 

S.W.  point  ..  ..   

Point  Frances 

Light  house 

do 

Contre 

light-house 

ilanca  Battery 

E.  point  of  entrance 


o 

20  47 

21  4 


Cape  Engano  

Samana  Town 

Cape  Cabron 

Port  Plata 

Grange  Point 

Manzanilla  Point 

Cape  Haytien  Harbor.. 

Port  Paix 

Nicolas  Mole 

Gonalves 

Gonave  Island 

Arcadius  Islands . 

Port  au  Prince  .. 

Petite  Riviere  Village.. 

Jeremie 

Navassa  Island 

Formigas  Bank 

Vache  Island 


Jacmel 

Beata  Island. 


E.  point 

W.  point ... 

Fort  George,  W.  end 

Light-house 

Fort  flag-staff 

N.W.  wharf 

Long  wharf 

Fort... 

do 

do 

do 

Lord  Rodney's  statute 

Fort  Charles,  flag-staff 

N.E.Cay 

Portland  Rock,  E.  end  . . 
Sandy  Cay  

Extreme 

Fort 

Extreme 

Fort... 

W.  end  . 

Extreme 

Town  fountain 

Wharf 

Fort  George 

Verreur  Point 

W.  point 

Light-house 

Fort  Islet 

Sand  beach  in  front  of  huts 

Fort 

N.  extreme 

Shoal  spot.  . 

Sand  beach,  near  N.  W 
point. 

Wharf 

N.  W.  point 


14 

24 

9  o 

7  o 

7  30 
18  30 

37  30 

21  40  2 

22  8  45 
22  II  14 

22  29  10 

23  56  30 

23  12  34 
23  14  10 

23  I  54 
23  9  21 
23  8  3 
22  9  o 
21  51  30 
21  55  o 
21  37  15 

21  58  o 

22  I  o 
20  23  20 

19  50  o 

20  o  16 
19  55  o 

19  45  15 
19  39  10 

19  17  45 


Long.  W. 


17  55 

18  II 


5 

15 

18  23  o 
18  26  24 
18  30  34 
18  29  25 
18  27  45 
18  12  20 
17  57  41 

17  55  5(> 
26  30 
8  o 


17 
17 


15  53 


18  35  51 

19  12  30 
19  21  17 

19  48  34 
19  54  45 
19  45  34 
19  46  40 

19  57  40 
19  49  30 
19  25  42 
18  55  26 
18  47  50 
18  33  54 
18  37 
18  38 
18  25 

18  33 
18  6 


15 

15 

10 

o 

o 


18  13  30 
17  36  45 


18 

30 
17 

18 

38 
18 

52 
18 


75  33  18 
75  36  59 
75  47  18 
75  47  40 

75  52  18 

76  35  34 

77  4  34 
77  8  3 
77  37  33 

77  39  23 

78  9  II 
80  27  51 

80  29  26 

81  7  20 

81  43 

82  21 

82  21 

84  47 
84  57 

83  31 
83  II 
81  2 
80  29  18 
80  29  50 
77  43  48 
75  50  30 

75  15  18 

79  46  07 

80  7  17 

81  23  12 

76  II  8 
76  26  51 

76  54  22 

77  12  52 
77  39  52 

77  56  16 

78  10  52 
78  8  54 
76  47  40 

76  50  38 
75  58  20 

77  27  o 

78  39  4 


Authorities. 


68 

19 

58 

69 

19 

23 

69 

16 

0 

70  42 

6 

71 

39 

3 

71 

57 

20 

72 

II 

42 

72 

49  45 

73 

23 

25 

72 

42 

52 

73 

18 

34 

72 

38 

15 

72 

22 

I 

74 

23 

55 

74 

5 

54 

75 

2 

3 

75 

44 

24 

73  43 

40 

72  34  30 
71  33  44 


Rear  Adml.  Milne,  R.  N. 
Spanish. 

Do. 
Comdr.  Parsons,  R.  N. 
Spanish. 

Do. 
Comdr.  Hamilton,  R.  N. 
Spanish. 

Do. 

Do. 

Do. 
Capts.  Owen  and  Barnett, 

R.N. 
Spanish. 

Do. 
Lieut.  Raper,  R.  N. 
Lt.  Comdr.  Green,  U.  S.  N. 

Do. 
Lieut.  Raper,  R.  N. 
Lieut.  Tanner,  U.  S.  N. 
Capt.  Owen,  R.  N. 

Do. 

Do. 
Spanish. 

Comdr.  Howison,  U.  S.  N. 
Capt.  Owen,  R.  N. 
Lt.  Comdr.  Green,  U.  S.  N. 
Spanish. 

French 

Capt.  Owen  R.  N. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lt.  Comdr.  Green,  U.  S.  N. 

Do. 
Capt.  Napier,  R.  N. 
Lieut.  Raper,  R.  N. 
Capt.  Owen,  R.  N. 

Juan  Romero. 
Capt.  Barnett,  R.  N. 
Lieut.  Raper,  R.  N. 
Capt.  Owen,  R.  N. 

Do. 
Capt.  Mayo,  U.  S.  N. 
Capt.  Owen,  R.  N. 

Do. 

Do. 
French  charts. 
Capt.  Owen,  R.  N. 
Light-house  List. 
M.  Hanusse. 

Lt.  Comdr.  Green,  U.  S.  N. 
Staff  Comdr.  Kiddle,  R.  N. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 
Do. 


Page  534] 


TABLE  49. 

MARITIME  POSITIONS. 
WEST  INDIA  ISLANDS-  Continued. 


o 
O 


a 


fa 
e 


Places. 


Frayle  Rock .___. 

Alta  Vela 

Avarena  Point  

Salinas  Point  (Caldera). 

St.  Domingo  City 

Saona  Island 

Point  Espada 

Mona  Island 

Mayaguez 

Aguadilla  Bay 

San  Juan  de  Porto  Rico. 

San  Juan  Head 

Cape  Mala  Pascua 

Guanica 

Culebra  Island 

Vieques  Island 

St.  Thomas 

St.  John  Island 

Tortola 

Virgin  Gorda 

Anegada _ 

Do 

Christiansted,  Santa  Cruz 
Do 

Sombrero 

Dog  Island 

Anguilla 

St.  Martin 

St.  Bartholomew 

Saba 

St.  Eustatius 

St.  Christopher 

Booby  Island 

Nevis „ 

Barbuda 

Antigua,  English  Harbor 
Antigua,  Man  -  of  -  War 

Point. 
Antigua,  Sand  Island  _. 

Antigua,  St.  John 

Redonda  Islet 

Montserrat 

Guadeloupe,  l^asseterre  _ 
Guadeloupe,  Kahouane 

Island. 
Guadeloupe,  Port  Louis_ 
Guadeloupe,Grand  Tene 
Cniadeloupe,  Le  Moule  . 
Guadeloupe,  Gosier  Islet 
Guadeloupe, Cochon  Islet 
Guadeloupe,    Manroux 

Island. 
Guadeloupe,     Point     a 

Pitre. 

Desirade  . 

Petite  Terra 

Marie  Galante 

Saintes  Islands 

Dominica,    Prince   Ru- 

]iert's  Bay. 

Dominica,  Roseau 

Aves  Island 

Martinique,  Fort  Royal. 
Martinique,  St.  Pierre.. 


Exact  locations. 


Centre 

Summit 

Extreme 

do 

British  consulate 

S.  E.  point 

Extreme ._ 

W.  point 


Mouth  of  Mayaguez  R 

Village 

Morro  light-house 

Summit 

Extreme 

Meseta  Point 


Lat.  N, 


Soldier  Point 

E.  point 

Fort    Christian,    S.    W 
bastion. 

Ram  Head 

Fort  Burt 

Vixen  Point 

W.  point 

E.  extreme  of  reefs 

S.  W.  bastion  of  fort 

Lang's  Observatory 

Light-house  . 

Centre 

Custom-house 

Fort  Marigot 

Fort  Oscar 

Diamond  Rock 

Fort  flag-staff 

Basseterre  Church 

Centre 

Fort  Charles 

Flag  staff,  Martello  Tower 

Flag-staff,  dock-yard 

Extreme _ 


Light-house 

Cathedral,  N.  tower 

Centre 

Plymouth  Wharf 

Flag-staff 

Summit 


Tower 

North  point. 
Signal  staff . 
Light-house 

Flag-staff 

Light-house 

Jarry  Mill  .  _ 


E.  point 

Light-liouse 

Tower  at  Grand  Bourg  . . 
Tower  on  Chameau  HilP 
Sand  beach  W.  of  church. 

Flag-staff,  Fort  Young. .. 

Centre 

Fort  St.  Louis 

Up]ier  light,  Ste.  Marthe 
Battery. 


Long.  W. 


17  37  0 

17  28  50 

18  7  0 

18  12  0 

18  28  12 

18  6  42 

18  19  43 

18  4  0 

18  II  56 

18  25  9 

18  28  56 

18  23  0 

17  59  0 

17  57  44 

18  16  46 

18  8  15 

18  20  23 

18  18  8 

18  25  4 

18  30  39 

18  45  " 

18  36  30 

17  45  9 

17  44  43 

18  35  37 

18  16  42  J 

18  13  6 

18  4  7 

17  53  58 

17  39  10 

17  29  10 

17  18  12 

17  13  38 

17  7  52 

17  35  50 

1700 

17  3  22 

17  6  50 

17  6  13 

16  55  18 

16  42  12 

15  59  50 

16  22  4 

16  25  7 

16  31  3 

16  19  59 

16  II  57 

16  12  54 

16  13  14 

16  13  56 

16  19  56 

16  10  17 

15  53  3 

15  51  32 

15  34  34 

15  17  27 

15  42  0 

14  35  58 

14  43  54 

71  41  o 
71  39  II 
70  59  18 
70  35  iS 
69  52  o 
68  34  40 
68  27  34 
67  56  35 


67 
67 
66 


4 

8 

28 


9 
16 

7 
65  36  33 

65  49  33 

66  53  46 


39 
45 


9 
14 


65  17  19 
65  16  18 
64  55  52 

64  42  3 
64  36  47 
64  21  48 
64  24  58 
64  10  46 
64  42  16 
64  41  17 
63  28  13 
63  16  o 
63  4 

63  5 

62  51  30 

63  15  16 
62  59 
62  43 
62  35  25 
62  37  29 
61  49  54 
61  46  7 
61  39  38 

61  55  29 

61  50  28 

62  19  10 
62  13  17 
61  44  9 
61  46  59 

61  32  II 

61  28  9 

61  20  48 

61  29  40 

61  32  21 

61  32  5 

61  33   15 


61 
61 


o  44 

6  45 


61  19  7 

61 

61 


35  55 
27  39 


61  23  52 

63  37  46 
61  4  28 
61  II  12 


Authorities. 


Lieut.  Raper,  R.  N. 
Capt.  Owen,  R.  N. 
Juan  Romero. 

Do. 

Do. 

Do. 

Do. 
Spanish  Survey. 

Lieut.  Sharrer,  U.  S.  N. 

Spanish. 

Lt.  Comdr.  Green,  U.  S.  N. 

Lieut.  Raper,  R.  N. 

Do. 
Spanish. 

Lieut.  Lawrance,  R.  N. 

Do. 
Lt.  Comdr.  Green,  U.  S.  N. 

Lieut.  Lawrance,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Lt.  Comdr.  Green,  U.  S.  N. 

Do. 
Capt.  Barnett,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Lawrance,  R.  N. 

Do. 
Capt.  Barnett,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Admiralty  Light  List.     , 
Lt.  Comdr.  Green,  U.  S.  N. 
Capt.  Barnett,  R.  N. 

Do. 
MM.  Ploix  and  Hatt. 

Do. 

Do. 

Do. 

Do. 

Do. 
MM.  Hanusse  and  Monnier 
MM.  Ploix  and  Hatt. 

MM.  Ploix  and  Caspari. 

MM.  Ploix  and  Hatt. 

Do. 

Do. 

Do. 
Staff  Comdr.  Stanley,  R.  N. 

Do 
Lieut.  Lawrance,  R.  N. 
M.  M.  Monnier  and  Hanusse. 
Lt.  Comdr.  Green,  U.  S.  N. 


TABLE  49. 

MARITIME  POSITIONS. 

WEST  INDIA  ISLANDS— Continued. 


[Page  535 


a 
o 

U 


e 
s 


s 

N 

ii 

s 


Places. 


Exact  locations. 


Martinique,      Caravelle     Summit . 

Rock. 
Martinique,  Cabrit  Islet . 
St.  Lucia,  Port  Castries. 
Barbadoes,  Bridgetown  . 


Barbadoes,  S.  Point 

Barbadoes,  Ragged  Point 

St.  Vincent,  Kingstown. 

Becquia  Island,  Admir- 
alty Bay. 

Grenada 

Tobago  

Tobago,  Rocky  Bay 

Testigos  Islets 

Sola  Island 

Pampatar,  Margarita 
Island. 

Tortugas  Island j 


Orchila  Island 

Roques  Islands 

Bonaive  Island , 

Little  Curafoa  Island . 

Cura9oa  Island 

Do , 

Oruba  Island , 


do 

Tapion  Battery 

Flag-staff,  Rickett's  Bat- 
tery. 

Light- house 

.--.  do  

Police  yard    

N.  point 


Saint  George  light  house  . 

N.  point 

Light-house 

Centre  of  Testigo  Grande 

Centre 

San  Carlos  Castle 

S.  end  of  W.  Tortugillo 
Islet. 

S.  side 

Pirate  Cay 

Light-house 

do , 

Time-ball  station 

Light-house 

, do 


Lat.  N. 


O       I       II 

14  48   19 


Long.  W. 


14  2 

14 

13 

13 


3  23 

1  30 

5  42 

2  55 
13  9  40 
13    9    4 


II 
II 
II 
II 


3 
21 

ID 

25 
19 


O       /        // 
60    53     16 

60  52  S3 

61  o  50 

59  37  19 

59  31  SI 
59  26     6 

61   13  15 
61   14    o 


61  45 


Authorities. 


12 

o 
60  42  24 
63    5 


60  31 


63  36 


48 
o 


10  59  43       63  48     o 
10  57  45       65  26  42 


II 
II 
12 
II 
12 
12 
12 


47  57 

55  56 
2    6 

58  o 
6  45 
6  36 

31     5 


66  12  39 
66  39  30 
68  14  10 
68  39  32 
68  56  44 
68  56  36 
70    2  34 


MM.  Monnierand  Hanusse. 

Do. 
Staff  Comdr.  Parsons,  R.  N. 
Lt.  Comdr.  Green,  U.  .S.  N. 

Lieut.  Lawrance,  R.  N. 

Do. 
Staff  Comdr.  Parsons,  R.  N. 
Lieut.  Raper,  R.  N. 

Staff  Comdr.  Parsons,  R.  N. 

Do. 

Do. 
Comdr.  Ryan,  U.  S.  N. 
Spanish  survey. 
Comdr.  Ryan,  U.  S.  N. 

Do. 

Do. 

Do. 
Netherlands  H.  O. 

Do. 

Do. 
M.  Hanusse. 

Do. 


NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA. 


ASPINWALL 

Porto  Bello 

Caledonia  Harbor 

Carreto  Port 

Caribana  Point. .. 

Fuerte  Island 

Cispata  Port 

Cartagena 

Savanilla 

Magdalena  River 
Santa  Marta 


Rio  de  la  Hacha 
Cape  La  Vela . . . 
Bahia  Honda  . . . 


Espada  Point 

Maracaybo 

Estanques  Point 

Cape  San  Roman 

Marjes  Islets 

Vela  de  Coro 

Tucacos  Island 

St.  Juan  Bay 

Puerto  Cabello 

La  Guayra 

Caracas,  La  Villa  de 

Cape  Codera  

Corsarios  Bay 

Centinella  Islet 

Barcelona 

Cumana 

Escarseo  Point 

Chacopata 

Esmeralda  Islet 

Carupano 


Light-house 

Fort  St.  Jeronymo 

Scorpion  Cay 

Peak 

Extreme 

N.  extreme 

Zapote  Point 

Fort  Pastelillo 

Light-house 

N.  \V.  pt.  of  Gomez  Island 
Ruined  l)attery  North  of 
Cathedral.  j 

Light  on  church j 

Sand  beach  inside  cape  .. 
E.  point,  S.  side j 

Extreme ' 

Zapara  Island  light 

Extreme  . 

do 

N.  islet    

Custom-house 

Ore-house 

Cay 

Observation  bastion 

Bastion  of  San  Fernando. 

Summit,  8,500  feet 

Morro 

W.  point 

Centre 

Morro 

Fort  Boca 

Extreme 

Morro 

Centre 

Light-house 


9  22     9 
9  32  30 

8  54  52 
8  47     o 

8  37  50 

9  24 
9  24 

0  25 

1  o 

0  7 

1  15 


1  33    o 

2  12  34 
2  23    9 

240 

0  58     o 

1  48  54 

2  II      o 

2  29  15 
I  27  56 

0  47    o 

1  10    o 

O   29   22 


o  35 
o  34 
o  49 
o  13 
o  28 
o  40 
o  42 
o  40 


49 

30 

o 

6 

30 

30 
o 

o 

o 
o 


o  40  15 


79  54  ^."t  • 
79  39(40) 
77  42  25 
77  38    o 
76  52  55 
10  45 


76 

75  48 
75 

74  57  55 
74  49  51 
74  13  36 


o 

25 


Ll  Com.  Green,  U.  S.  N. 
Lieut.  Raper,  R.  N. 
Comdr.  Parsons,  R.  N. 
Spanish  survey. 

Do. 

Do. 

Do. 
Comdr.  Ryan,  U.  S.  N. 
Hanusse,  Fr.  N. 
Van  der  Goltz. 
Comdr.  Ryan,  U.  S.  N. 


72  59     o  ,  Light- House  List, 

72     9  42  !  Comdr.  Ryan,  U.  S.  N. 

71  45  42  i  Do. 


71     7 


71  40 
70  17 
70    4 

70  57 


55 
o 

o 

55 
o 

69  34  50 

68  19  55 

68  22  54 

68    o  58 

66  56  43 

50  55 
6  15 

4 
9 


66 
66 
66 
66 


64  .iA 

64  II 

64 

63 

63 

6:1 


13 

25 
o 

38 

17  55 

50  25 

31  55 

iS    o 


Spanish  survey. 
Light- House  List. 
Comdr   Ryan,  U.  S.  N. 
Spanish  survey. 

Do. 
Comdr.  Ryan,  U.  S.  N. 
Spanish  survey. 
Comdr.  Ashman,  Ger.  N. 
Comdr.  Ryan,  U.  S.  N. 

Do. 
Spanish  survey. 

Do. 
Comdr.  Ryan,  U,  S,  N. 
Spanish  survey. 

Do. 
Comdr.  Ryan,  U.  S.  N. 
Spanish  survey. 

Do. 

Do. 
Light- House  List. 


Page  536]  TABLE  49. 

MARITIME  POSITIONS. 
NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued. 


o 
O 


Places. 


Exact  locations. 


s 

V 

e 


8 

»m 

a 


d 


Carupano 

Puerto  Santo  Islet. 
Puerto  Santo  Bay. 
Tres  Puntas  Cape. 
Unare  Bay 


Pena  Point 

Pato  Island 

Trinidad    Island,    Port 

Spain. 
Trinidad  Island,  Chaca- 

chacare  Island. 
Trinidad  Island,  Chute 

d'Eau  Island. 
Trinidad  Island,  Mount 

Maracas. 
Trinidad  Island ,  Galera  Pt 
TrinidadIsland,Icacos  Pt 
Trinidad  Island,  San  Fer- 
nando. 
Macomoco  Point 


Demerara 

Nickerie  River 

Paramaribo. 

Maroni  River 

Salut  Islands 

Enfant  Perdu  Islet. 

Cayenne  

Connetable  Islet 

Carimare  Mt 


Orange  Cape 

Maye  Mountain 
North  Cape 


Cape  Magoari 

Para 

Atalaya  Point 

Itacolomi  Point 

Maranham  Island 

Santa  Anna  Island 

Tuto'ia 

Paranahyba  River 

Ceara 

Jaguarybe  River 

Caigara 

Cape  St.  Roque 

Rio  Grande  do  Norte 

Natal 

Parahyba  River .. 

Parahyba 

Olinda 

Pernambuco 


Cape  St.  Augustine 

Tamandare 

Maceio 

San  Francisco  River 

Cotinguiba  River 

Vaza  Barris  River 

Real  River 

Conde 

Garcia  d'Avila 

Bahia 

Itaparica 

Morro  Sao  Paolo 


Pt.  Herman  Vasquez 

Centre 

Sand  spit  S.  of  Morro 

Extreme 

Obs.  spot,  200  yards  S.  of 
Morro. 

Extreme  _. 

E.  point 

Flag-staff,  water  battery.. 

Rocks  of  S.  W.  point 

Centre 

Summit 


Lat.  N. 


Long.  W. 


10  42 
10  43 
10  43 
10  45 
10  44 


o 
o 

27 
o 

19 


10  43  48 

10  38  IS 
10  38  39 

10  40     3 

10  46     o 

10  44    o 


Extreme [   lo  50     o 

Light-house |   10     3  29 

Pierhead |   10  16  59 


Extreme 


Georgetown  light-house. 

Battery 

Time-ball  station 

W.  light-house 

Light-house 

do 

Landing  place 

Centre 

Summit 


8  39  25 


Extreme 
Summit  . 
Extreme 


do 

Custom-house 

Light-house 

do 

Landing-place 

Light-house 

Entrance 

Amargao  Village 

Landing  place 

Pilot-station  ._ 

Village 

Extreme 

Light-house 

Cathedral 

Light-house  at  entrance. 

Cathedral 

Steeple 

Picao  light-house 


Extreme 

Village 

Light-house 

Light-house  at  entrance.. 

do 

Semaphore  at  entrance  _ . 

do 

Village 

Tower 

Santo  Antonio  light-house 

Fort  on  N.  point 

Light-house 1    i 


49  20 
58  5 
49  30 
44  48 
16  50 
2  40 
56  20 

49  30 
23  20 


4  20  45 
2  46  30 
I  40  17 

Lat.  S. 
O  17  o 
26  59 

35  3 
10  II 

31  48 
16  22 


41  55 
53  20 

42  50 

25  35 
3  15 


29 
45 


15 

5 


46  41 

56  30 

6  35 

o  35 

i   22 


8  20  45 
8  43  40 

39  35 

29  o 

o 

45 
o 

5 


9 
10 

10  58 

11  9 
II 
12 


27 
12 


12  33   40 

13  o  37 
12  52  48 


o  /  // 

63  14  o 

63  10  55 

63  9  43 

62  41  55 
62  44  29 

61  50  50 
61  51  18 
61  30  38 

61  45  54 
61  30  45 
61  24  41 

60  54  12 

61  55  41 
61  28  12 

60  10  15 

58  II  3^ 
57  5  o 
55  12  54 
54  o  3 

52  34  53 
52  21  II 
52  20  25 
51  55  36 
51  50  36 

51  27  46 
50  54  46 
49  56  46 

48  23  30 
48  30  I 
47  20  54 
44  25  56 
44  18  45 
43  3f>  26 
42  18  02 

41  40  35 
38  31  25 

37  44  55 
36  2  52 

35  15 
35  II 
35  12 
34  49 
34  53 
34  51 
34  51 


52 

55 
22 


4 
17 

57 


34  56  16 

35  5  6 

35  44  54 

36  21  51 

37  4  45 
37  12  36 
37  22  46 

37  45  46 

38  2  16 
38  32  6 
38  41  28 
38  54  39 


Authorities. 


Spanish  survey. 

Do. 
Comdr.  Ryan,  U.  S.  N. 
Spanish  survey. 
Comdr.  Ryan,  U.  S.  N. 

Lieut.  Lawrance,  R.  N. 

Do. 
Lt.  Cwmdr.  Green,  U.  S.  N. 

Lieut.  Lawrance,  R.  N. 

Do. 

Do. 

Do. 
Light-House  List. 
Capt.  Chimmo,  R.  N, 

Murray. 

Capt.  Owen,  R.  N. 
H.  N.  M.  S.  Soestdijk. 
Netherlands  H.  O. 

Do. 
Adm.  Mouchez,  Fr.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 

Do. 
Lt.  Comdr.  Davis,  U.  S.  N. 
Adm.  Mouchez,  Fr.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 
Light-House  List. 
Adm.  Mouchez,  Fr.  N. 

Do. 
Lt.  Comdrs.  Green  and  Da- 
vis, U.  S.  N. 
Admr.  Mouchez,  Fr.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Lt.  Comdr.  Davis,  U.  S.  N. 
Adm.  Mouchez,  Fr.  N. 
Do. 


TABLE  49. 

MARITIME  POSITIONS. 

NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued. 


[Page  537 


Places. 


Camamu 

Contas 

Ilheos 

01iven9a 

Una 

Comandatuba 

Santa  Cruz 

Porto  Seguro 

Prado  

Alcobaga 

Caravellas 

Abrolhos  Island  . . . 

Porto  Alegre 

Espiritu  Santo  Bay. 

Guarapiri  Islets 

Benevente 

Itapemirim 

Sao  Joao  da  Barra.. 
Cape  St.  Thome. .  . . 

Macahe 

Santa  Anna  Island  . 

Barra  Sao  Joao 

Busios 

Cape  Frio 


Do 

Port  Frio 

Maricas  Islands . . 
Rio  DE  Janeiro 

Do 


Do 

Do 

Do 

Do 

Petropolis 

Cape  Guaratiba 

Marambaya  Island 

Mangaratiba 

Palmas  Bay 

Angra  dos  Reis 

Ilha  Grande 

Parati 

Parati  Peak 

Ubatuba 

Porcos  Grande  Islet 

Busios  Islets 

Saint  Sebastian  Island  .. 

Do 

Villa  Nova  da  Princessa. 
Santos  

Do 

Alcatrasses  Island 

Concei9ao 

Quemada Grande  Island. 

Iguape  

Bom  Abrigo  Islet 

Ilha  do  Mel 

['aranagua 

Antonina 

Coral  Islet 

Itacolomi   Islet 

Sao  Francisco   

Itapacaroya 

Cambria 

Arvoredo  Island 


Exact  locations. 


Village  

Church 

do   

Centre  of  village 

do  

do  

Church 

Matriz  Church 

River  entrance 

Centre  of  village 

do 

Light-house 

Centre  of  village 

Victoria  Quay 

E.  islet 

Village 

Moscas  Islet 

Point 

Extreme 

Fort  at  entrance 

Summit 

Village 

Church 

Old  light-house  on  sum- 
mit, 1,285  feet. 

Light-house 

Village     

S.  islet   

Fort  Villegagnontlag  staff 

Imperial  Observatory, 
centre  of  dome  (time- 
ball). 

Sugarloaf,  1,270  feet 

CorcovadoPeak,  2,272  feet 

Gavia  Mt.,  2,575  feet 

Raza  Island  light 

Centre  of  town 

Summit 

.Summit  of  S.  W.  end  . . . 

Village 

Beach  at  head  of  bay  . . . 

Landing-place 

Summit 

Fort 

Summit,  4, 134  feet 

Cathedral 

Sand-beach  in  bay 

Summit 

S.  E.  point 

S.  W.  summit,  4,265  feet 

Centre 

Moela  Island  light-house 

Quay 

Summit,  880  feet 

Church 1 

Summit,  623  feet 

Quay 

Summit,  426  feet 

Hillock  near  fort,  262  feet 

Quay 

do 

Centre 

do 

Centre  of  town 

Church 

...     do  

Centre,  950  feet 


l.at.  S. 


13 
14 
14 
14 
15 
15 
16 
16 
17 
17 
17 
17 
18 


56  42 
17  40 

47  40 

56  40 
13  27 
2b  45 
17  20 

25  38 
21  40 

31  45 
43  30 

57  31 
6  15 

20  18  50 
20  38  '25 
20  49  o 

20  57  35 

21  37  37 

22  o  o 
22  23  45 
22  26  o 

22  37  O 
22  46   O 

22  59  30 

23  o  42 

22  53  15 

23  I  43 
22  54  46 
22  54  24 


22  56  48 
o 


22  57 

22  59 

23  3 

22  32 

23 
2T. 


35 

40 

o 

40 

20 


23 

23 

23 
2T. 


3 
4 

22  57  20 

23  9  20 
o  30 

834 

12  20 

„  18  7 

23  25  55 
23  32  22 

23  45  15 
23  58  30 
23  53  o 

23  47  20 

24  3  6 

23  56  o 

24  6  30 
24  10  32 
24  28  45 

24  42  35 

25  6  30 

25  30  55 
25  31  20 
25  26  30 
25  44  10 

25  50  15 

26  14  17 

26  46  45 

27  I  35 

27  17  20 


Loiifr.  W. 


39 
39 
39 
39 
39 
39 
39 
39 


7  4 

0  46 

3  26 

1  46 

1  16 
o  46 

2  6 

4  16 

39  13  16 
39  12  I 
39  14  36 

38  41  47 

39  31  16 

40  20  16 
40  23  46 
40  40  46 

40  46  36 

41  2  21 

40  58  46 

41  47  36 
41  43  16 
41  59  46 
41  54  6 

41  59  6 

42  o  I 
42  I  16 

42  54  6 

43  9  29 
43  10  21 


43  9  21 
43  12  36 
43  17  I 
43  8  44 
43  II  I 
43  33  26 

43  59  28 

44  2  31 
44  8  26 
44  19  6 
44  14  II 
44  42  6 

44  46  41 

45  4  6 
45  3  48 
45  o  41 
45  15  46 
45  22  6 

45  21  6 

46  16  o 
46  19  u 

45  40  51 

46  47  46 

46  41  6 

47  32  56 

47  52  16 

48  19  53 


48  31  .. 
48  43  16 
48  23  16 
48  25  53 

48  39  31 
48  36  59 
48  36  44 
48  23  14 


Authorities. 


Adm.  Mouchez,  Fr.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Lt.  Coradr.  Davis,  U.  S.  N. 
Do. 


Adm.  Mouchez,  Fr.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  538]  TABLE  49. 

MARITIME  POSITIONS. 
NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued. 


o 
O 


9 
» 

im 
m 

u 
pi 


Places. 


« 
fa 

m 
9 

m 

V 

s 
BQ 


K 
e 
it, 

a 
*^ 

Si 
0N 


e 
S 

« 

d 

fa 
fa 
« 


Anathomirim 

St.  Catharine  Island 

Do 

Nostra  Senhora  do  De- 
serto. 

Coral  Island 

Cape  St.  Martha 

Torres  Point 

Rio  Grande  do  Sul 


Castillos 

Cape  Santa  Maria. 

Lobos  Island 

Maldonado 

Ilores  Island 

Monte  Video 


Colonia 


Martin  Garcia  Island. . 
Buenos  Ayres 


Indio  Point 

Piedras  Point 

Cape  San  Antonio 

Medanas  Point 

Cape  Corrientes  .  . 

Port  Belgrano 

Argentina 

Labyrinth  Head  .  _ 

Union  Bay 

San  Bias  Harbor  _ 

San  Bias  Bay 

Rio  Negro , 

Vermeja  Head 


Port  San  Antonio 

San  Antonio  Sierra 

Port  San  Jose  . 

Delgado  Point 

Cracker  Bay  

Port  Madryn 

Chupat  River 

Port  St.  Elena. 

Leones  Island 

Melo  Port 

Port  Malaspina 

Cape  Three  Points 

Port  Desire 

Sea  Bear  Bay 

Port  San  Julian 

Port  Santa  Cruz 

Do 

Cay  Inlet 

Port  Gallegos 

Gallegos  River 

Cape  Virgins 


Cape  St.  Diego 

Cape  St.   John,   Staten 

Land. 
Port  Cork,  Staten  Land. 
Cape  St.  Bartholomew, 

Staten  Land. 

Good  Success  Bay 

Lennox  Cove 

Goree  Road 

Wallaston  Island  ___ 


Exact  locations. 


Fort 

Rapa  Point 

Naufragados  light-house  . 
Quay  .  .. . . 


27  25  32 

27  22  55 
27  50  27 
27  36    o 

27  56  40 

28  3S    o 

29  20  20 
Light-house 32  6  40 


Summit,  230  feet . 

Extreme 

do  


Lat.  S. 


Buena  Vista  Hill,  184  feet. 

Light-house 

Centre 

Light-house 

do „__ 

Cathedral,  S«  E.  tower 

Light-house ,_. 


Centre 

Cupola  of  custom-house. 

E.xtreme 

do 

N.  extreme 

S.  E.  summit 

E.  summit 

Anchor-Stock  Hill., 
Fort 

Summit 

Indian  Head 

S.  W.  end  of  Hog  Islet  . 
Summit  of  Rubia  Point  _ 

Main  Point 

E.  summit 


Point  Villarino 

Summit 

San  Quiroga  Point 

S.E.  cliff 

Anchorage     

Anchorage  off  cave  bluff. 

Entrance 

St.  Elena  peninsula 

S.  E.  summit 

W.  point 

S.  point 

N.E.  pitch  _. l'_~_l 

Largest  ruin 

Well's  Point ". 

ShoU  Point 

Mount  at  entrance 

Keel  Point 

Height  S.  side  of  entrance 
Mound  back  of  wells 

Observation  mound 

S.  E.  extreme 


Extreme  .. 
E.  extreme 


Observation  mark,  summit 
Middle  point 


S.  end  of  beach 

Bluff,  N.  end  of  beach 

Guanaco  Point 

Middle  cove 


34  21  19 

34  40  30 

35  I 
34  58 
34  56  55 
34  54  33 


39 
15 


34  28  20 

34  II  10 

34  36  30 

35  15  45 

35  26  50 

36  18  30 
36  59 
38  5 
38  57 
3843 


5 

30 

o 

50 

39  26  30 
39  57  30 
3 


40 

40  36 

41  2 
41  II 


52 

10 

o 

o 


o 
10 


40  49 

41  41 

42  14  15 
42  46  15 
42  57  o 

42  45  40 

43  20  45 

44  30  40 

45  4  o 
45  3  o 
45  10  10 
47  6  20 
47  45  o 
47  57  15 

49  15  20 

50  8  30 
50  6  45 

50  58  27 

51  33  20 

51  33   21 

52  18  35 

54  40  35 
54  42  50 

54  45  16 
54  53  45 

54  48  6 

55  17  o 
55  19  o 
55  35  30 


Long.  W. 


48  34  39 
48  26  9 

48  3S  •'^7 
48  34  H 

48  33  44 

48  50  4 

49  43  39 

52  7  44 

53  46  48 

54  9  26 
54  53  16 

54  57  10 

55  54  36 

56  12  IS 

57  52  27 

58  15  IS 

58  22  14 


57 

57  5 
56  46  37 

56  41  29 

57  30 
61  59 

55 
3 
7 
9 
9 


62 
62 
62 
62 
62 


10  55 
28 


i 

15 
27 
22 
46 

30 
26 


36 
22  ID 

35  15 


62  45  56 

63  8  16 

64  S4  41 

65  12  29 
64  27  56 

63  37  16 

64  28  20 

64  59  o 

65  3 
65 

65 

65  52  30 

66  32  36 
65  51  46 

65  54  45 
65  4S  40 

67  42  30 

68  23  o 

68  24  o 

69  9  47 

68  59  39 

69  o  31 
68  22  12 

65  5  53 
63  43  25 


64  3 
64  45 


45 


65 

13 

48 

66 

49 

0 

67 

ID 

0 

67 

19 

0 

Authorities. 


Adm.  Mouchez,  Fr.  N. 
Do. 
Do. 
Do. 

Do. 

Do. 
Do, 
Do. 

Do. 

Light- House  List. 
Adm.  Mouchez,  Fr.  N. 
Do. 
Do. 
Lt.  Comdrs.  Green  and  Da- 
vis, U.  S.  N. 
Adm.  Mouchez,  Fr.  N, 

Do. 
Lt.  Comdrs.  Green  and  Da- 
vis, U.  S.  N, 
Adm.  Mouchez,  Fr.  N. 
English  survey. 

Do, 

Do. 

Do. 

Do. 

Do, 

Do. 
H.  M.  S.  Beagle. 

Do. 
English  survey. 
H.  M.  S.  Beagle. 
English  survey. 

H.  M.  S.  Beagle. 
English  survey. 

Do. 

Do. 
H.  M.  S.  Volage. 

Do. 
English  survey. 
Capt.  Fitzroy,  R.  N. 
Capt.  O.  Folger,  R.  N. 
Spanish  survey. 
Englisli  survey. 

Do. 
Com.  Stokes,  R.  N. 

Do. 
H.  M.  S.  Beagle. 
English  survey. 
H.  M.  S.  Beagle. 
English  survey. 
Com.  Stokes,  R.  N. 
English  survey. 

Do. 

Do. 
Do. 

Do. 
Do. 

H.  M.  S.  Beagle. 
Do. 
Do. 
Do. 


TABLE  49. 

MARITIME  POSITIONS. 

NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued. 


[Page  639 


•9 


Places. 


Barneveldt  Islands 

Cape  Horn 

Ilermite  Island 


Exact  locations. 


Centre 

South  summit,  500  feet 
St.  Martin  Cove 


Lat.  S. 


55  48  54 
55  58  41 
55  51  20 


Long.  W. 


66  43  48 

67  16  15 
67  34  o 


Authorities. 


English  survey. 

Do. 
Lieut.  Kendall,  R.  N. 


WEST  COAST  OP  SOUTH  AMERICA. 


e 
if 

a 

a. 


False  Cape  Horn 

Ildefonso  Island 

Diego  Ramirez  Island 
Yojk  Minster  Rock  .. 

Cape  Desolation 

Mount  Skyring 

Cape  Noir  Island 

Landfall  Island 

Cape  Deseado , 

Apostle  Rocks , 

Cape  Pillar 


Dungeness  Point 

Espiritu  Santo  Cape  ... 

Catharine  Point 

Cape  Possession 

Possession  Bay , 

Cape  Orange  

Delgada  Point 

Cape  Gregory 

Cape  San  Vicente  

Elizabeth  Island 

Sandy  Point 

Cape  Valentyn 

Port  Famine   

Cape  San  Isidro 

Cape  Froward 

Mount  Pond 

I   Port  Gallant 

Charles  Island 

Rupert  Island 

Mussel  Bay 

Tilly  Bay 

Borgia  Bay 

Cape  Quad 

Barcelo  Bay 

Swallow  Bay 

Cape  Notch 

Playa  Parda  Cove  

Pollard  Cove 

Port  Augosto 

St.  Anne  Island 

Half  Port  Bay 

Upright  Cape 

Upright  Port 

Port  Tamar 

Cape  Tamar 

Port  Churruca 

Valentine  Harbor 

Cape  Parker , 

Mercy  Harbor 

Mayne  Harbor 

Port  Grappler 

Port  Riofrio , 

I'klen  Harbor 

Halt  Bay , 

Westminster  Hall  Islet. 

Evangelist  Island .. 

Cape  Victory 


S.  extreme 

Highest  summit 

do 

Summit,  800  feet . . 

S.  summit 

Summit,  3,000  feet 

Extreme 

Summit  of  Cape  Inman  .. 

Peaked  summit 

W.  rocks 

N.cliff 

Beacon  

N.E.  cliff 

N.  E.  extreme 

Middle  of  cliff 

Tandy  Point 

N.  extreme 

Extreme 

do 

W.  extreme 

N.E.  bluff 

Light  on  block  house 

Summit,  at  extreme 

Observatory 

Extreme 

Summit  of  bluff 

Summit 

Wigwam  Point 

White  rock,  near  N.W  end 

Summit 

Entrance 

Sarah  Island 

Bluff  on  W.  shore    

Extreme 

Entrance 

Shag  Island 

Extreme 

Summit  of  Shelter  Island. 

Entrance 

Hay  Point 1 

Central  summit 

Point ' 

Extreme  N.  trend 

Entrance 

Mouat  Islet 

S.  extreme 

Summit  of  Blanca  Penin- 
sula. 

Observation  mount 

W.  summit,  over 

Summit  of  Battle  Island. 

Observation  spot 

.....do  , 

Vitalia  Island 

Observation  spot 

Observation  islet 

E.  summit 

Sugar  Loaf 

Extreme 


55  43  15 

55  52  30 

56  28  50 

55  24  50 
54  45  40 
54  24  48 
54  30  o 
53  18  30 
52  55  30 
52  46  15 
52  42  50 


52  23  50 
52  39  o 
52  32  o 
52  17  o 
52  15  10 
52  28  40 
52  26  30 

52  39  o 
52  46  20 

52  49  10 

53  9  39 
53  33  30 
53  38  15 
53  47  o 
53  53  43 
53  51  45 
53  41  45 
53  43  57 
53  42  o 
53  37  10 
53  34  20 
53  31  45 
53  32  10 
53  30  50 
53  30  5 
53  25  o 
53  18  45 
53  15  30 
53  13  40 

6  30 

II  40 

4  3 

6  35 

52  55  46 

52  55  30 

53  I  o 


53 
53 
53 
53 


52  55  o 
52  42  o 
52  44  58 

51  18  29 

49  25  19 
49  12  40 

49  7  30 
48  54  20 

52  37  18 
52  24  18 
52  16  10 


68 
69 
68 
70 


4  40 
17  30 
41  30 


30 

71  36  10 

72  10  20 
72  4  30 
74  18  15 
74  36  30 
74  46  50 
74  42  20 

68  25  40 
68  34  o 
68  45  20 

68  36  30 

69  20  10 
69  24  o 

69  32  10 

70  12  10 
70  25  25 
70  36  15 

70  54  4 

70  31  30 

70  58  31 

70  55  3 

71  17  15 

71  55  30 
7'  59  41 

72  4  45 
10  42 

19  30 
72  27  10 

72  34  15 
72  32  25 
72  38  o 
72  47  30 

72  47  55 

73  o  30 
73  12  5 
73  21  30 
73  15  30 
73  17  45 
73  35  o 
73  16  15 


72 
72 


73   44 
73  47 

20 
10 

73  59 

33 

74  17  45 

74  13  30 

7438 

14 

74  4 

0 

74  17  39  1 

74  23 

27 

74  25 

10 

74  20 

55 

74  23 

10 

75  7 

10 

74  55 

0 

English  survey. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
German  Venus  Exp.,  1874. 
Enghsh  survey. 

Do. 

Do. 

Do. 

•Do. 

Do. 

Do. 

Do. 
Capt.  Mayne,  R.  N. 

Do. 
English  survey. 

Do. 
Capt.  Mayne,  R.N. 

Do. 
English  survey. 

Do. 
Capt.  Mayne,  R.  N. 
English  survey. 

Do. 

Do. 

Do. 
Capt.  Mayne,  R.  N. 

Do. 
English  survey. 
Capt.  Mayne,  R.  N. 

English  survey. 

Do. 

Do. 
Capt.  Mayne,  R.  N. 

Do. 
Chilian  survey. 
Capt.  Mayne,  R.  N. 

Do. 
English  survey. 

Do. 

Do. 


1 


Page  540] 


o 
O 


B 

e 
ed 


TABLE  49, 

MARITIME  POSITIONS. 

"WEST  COAST  OP  SOUTH  AMERICA— Continued. 


Places. 


Cape  Isabel .__. 

Cape  Santiago 

Molyneux  Sound 

Cape  Tres  Puntas 

Port  Henry 

Mount  Corso 

Rock  of  Dundee 

Santa  Barbara  Port 

Guainneco  Islands 


Port  Otway 

Cape  Tres  Montes 

Cape  Raper 

Christmas  Cove 

Hellyer  Rocks 

Cape  Tay tao 


Exact  locations. 


Socorro  Island 

Mayne  Mountain 

Port  Low 

Huafo  Island 

Port  San  Pedro 

Cape  Quillan 

Corcovado  Volcano 

Minchinmaudom  Volcano 

Castro 

Dalcahue 

Oscuro  Head 

Coman  Inlet 

Port  Calbuco 

San  Carlos 

Corona  Point 

Condor  Cove 

Ranu  Cove 

Muilcalpue  Cove  '. 

Milagro  Cove 

Laruehuapi  Cove  . 

Valdivia 

Queule  Bay 

Mocha  Island 

Leiihu  River 

Yanez  Port 

Lota 

Santa  Maria  Island 

Talcahuano   ..    _ 

Do 

Llico 

Port  San  Antonio. 

Aconcagua  Mountain 

Santiago 

Valparaiso  . 

Do l_ 

Quintero  Point 

Pichidanque 

Tablas  Point 

Chuapa  River 

Maitencillo  Cove 

Talinay  Mount 

Lengua  de  Vaca 

Port  Tongoy 

Coquimbo  . 

Do. 


W.  extreme .^ 

Summit 

Romalo  Island 

Summit,  2,000  feet 

Observation 

S.  W.  summit 

Summit 

N.  extreme  obs.  point 

Speedwell    Bay,    hill   at 
N.  E.  point. 

Observation  spot 

Extreme  

Rock  close  to  cape 

S.  E.  extreme 

Middle 

W.  extreme 


Do 

Pajaros  Islets  .. 
Chorros  Islands 
Chaneral  Island 


S.  extreme 

Summit,  2,080  feet 

Observation  islet 

S.  extreme 

Cove  on  S.  shore 

S.  W.  extreme 

Summit,  7,510  feet 

S.  summit,  8,000  feet 

E.  end  of  town 

Chapel 

Observation  point 

Olvidada  Island 

La  Picuta 

Mole,  landing  place 

Light-house 

Landing 

Anchorage 

Landing  place  , 

do 

do 

Niebla  Fort  light 

Choros  Point ,_  .. 

N.  point 

Tucapel  Head 

Anchorage 

Beach,  fronting  village  . . 
Head  of  cove  on  S.  E.  side 

Fort  Galvez 

Light  on  Quinquina  Island 

Village 

do   ._. 

Summit 

Observatory 

Site  of  Fort  San  Antonio. 

Playa  Ancha  Pt.  light 

Summit 

S.  E.  point  of  island 

S.  W.  extreme 

S.  entrance  point .. 

N.head. 

Summit 

Extreme 

Obs.  spot  W.  of  village 

Tortuga  Point  light 

Smelting  works,  north  of 

town. 
N.  islet 

S.  summit 

S.  W.  point  of  largest..  _. 
S.  W.  summit 


Lat.  S. 


SI    SI    SO 

50  42     o 

50  17  20 
50  2  o 
50    o     " 

49  48 
48  6 
48  2 
47  39 


42 
42 
42 


33  I 
33  I 
32  46 

32     7 


18 
o 

IS 
20 

^o 


46  49  31 

46  58  57 
46  49  10 

46  35    o 
46    4    o 

45  S3  20 

44  S5  SO 
44-9  o 
43  48 
43  41 
43  19 
43  17  10 
43  II  20 
42  48  o 
42  27  45 
23     o 

4 

3 


30 
50 
3S 


41  46 
41  52 


o 
o 
8 
o 

41  46  40 
40  46  19 
40  43  18 

40  35  52 
40  21  4 

40  II  47 

39  53  7 
39  23 
38  19 
37  35 
37  22 
S 


o 

35 
20 


15 


37 

37  2  48 

36  42  o 

36  36  45 
36  46  2 

33  34  13 
33  38  30 
33   26  42 


S3 

30 

o 

55 


31  51  45 
31  39  30 
31  17  5 
30  so  45 
30  13  40 

30  15  14 
29  56  IS 
29  56  24 

29  55  10 

29  35  o 

29  IS  45 

29  I  15 


Long.  W. 


75  13  20 
75  27  45 

74  SI  30 

75  22  o 
75  13  20 
75  34  o 
75  40  30 
75  28  20 
75  10  o 

75  18  20 

75  25  30 

75  37  55 

75  31  30 

75  12  o 

75  6  o 


8  45 
45 


35 
o 


o 
o 
o 

15 


75 
74  7 

73  59 

74  42 

73  41  50 

74  22  o 
72  44  40 

72  30  30 

73  45  20 
73  36 
73  25 

72  45 

73  7 
73  48  40 
73  52  55 
73  SI  o 
73  49  50 
73  45  o 
73  45  20 
73  41  50 
73  25  5 
73  14  o 
73  56  50 
73  39  55 
73  40  o 
73  10  40 
73  31  45 
73  7  27 
73  3  25 
72  6  12 

71  38  o 

69  56  30 

70  41  32 

71  38  42 
71  39  22 

71  32  56 

71  33  22 

71  34  SI 

71  35  20 

71  39  21 

71  39  o 

71  38  43 

71  31  9 

71  21  5 

71  20  II 


71  22  21 

71  33   35 

71  34  38 

71  36  12 


Authorities. 


English  survey. 

Do. 
Capt.  Simpson,  Ch.  N. 
English  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Capt.  Fitzroy,  R.  N. 
English  survey. 
H.  M.  S.  Beagle. 
Capt.  Fitzroy,  R.  N. 
H.  M.  S.  Beagle. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 
English  survey. 
Capt.  Fitzroy,  R.  N. 

Do. 
Chilian  survey. 

Do. 
Capt.  Fitzroy,  R.  N. 
Light- House  List. 
Chilian  survey. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 
Chilian  survey. 
H.  M.S.  Beagle. 
Chilian  survey. 

Do. 
Capt.  Mallet,  Fr.  N. 
H.M.S.  Beagle. 
English  survey. 
Light-House  List. 
Chilian  survey. 

Do. 
Capt.  Fitzroy,  R.  N. 
Dr.  A.  B.  Gould. 
Lt.  Comdr.  Davis,  U.  S.  N. 
Light- House  List. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Leeky,  R.  N.  R. 
Light-House  List. 
Capt.  Mayne,  R.  N. 

Capt.  Pltzroy,  R.  N. 
Do. 
Do 
Do. 


o 
O 


S 
fa 


TABLE  49. 

MARITIME  POSITIONS. 

VnSST  COAST  OF  SOUTH  AMERICA— Continued. 


[Page  641 


Places. 


Huasco 

Herradura  de  CarrisaL. 

Port  Carrisal 

Matamoras  Cove 

Salado  Bay 

Copiapo 

Caldera 

Do 

Cabeza  de  Vaca  Point . . 
Flamenco 

Do 

Chaneral  Bay 

St.  Felix  Island 


Pan  de  Azucar  Island  .. 

Lavata 

San  Pedro  Point 

Port  Taltal 

Grande  Point 

Paposo  Road 

Reyes  Head 

Cobre  Bay 

Jara  Head 

Antofagasta 

Chimba  Bay 

Moreno  Mountain 

Constitution  Cove  (Bo)  . 
Mexillones  Mount  (Bo). 

Port  Cobija  (Bo) 

Algodon  Bay  (Bo) 


San  Francisco  Head 

Loa  River 

Lobos  Point 

Pabellon  de  Pica 

Patache  Point 

Iquique 

Mexillon  Bay 

Pisaqua 

Gorda  Point 

Lobos  Point 

Arica 

Schama  Mount 

Coles  Point 

Vlo 

MoUendo 

Islay 

Quilca 

Pescadores  Point 

Atico 

Chala  Point 

Lomas 

San  Juan  Port 

Nasca  Point 

Mesade  Dona  Maria... 

Carreta  Mount 

Sangallan  Island 

Paraca  Bay 

Pisco 

Chincha  Islands 

Frayles  Point 

Asia  Rock 

Chilca  Point 

Morro  Solar 

San  Lorenzo  Island 

Callao  . 

Pescadores  Islands 


Exact  locations. 


Light  on  mole 

Landing-place 

Island 

Outer  point  S.  side 

Summit  of  Cachos  I'oint . 

Landing-place 

Summit  of  island 


Light  on  mole  head 

Extreme 

S.  E.  corner  of  bay 

Patch  Point  summit 

Bryson  Point 

Peterborough    Cathedral 
Rock. 

Summit 

Cove  near  S.  W.  point . .. 

Summit..  ._. 

Taltal  Point 

Outer  summit 

Huanillo  Point 

Extreme  pitch 


Lat.  S. 


28 
28 
28 


27 
27 


Point  W.  of  village 

Summit 

Post-olfice 

E.  point  of  large  island  ._! 
Summit 

Shingle  point  of  island  .. 

Summit 

Landing-place     [ 

Tocopilla  Smelting  Station 

W.  pitch 

Mouth 

Outward  pitch 

Summit 

Extreme 

Mole 

Landing-place 

Pichalo  Point,  extreme  .. 

W.  low  extreme 

Summit .    

Iron  church  

Highest  summit 

Extreme 

Mouth  of  rivulet 

Flag-staff 

Custom-house 

W.  head  of  cove 

S.  W.  extreme 

E. cove  

Extreme 

Flag-staff  on  point 

Needle  Hummock 

Summit 

Central  summit 

Summit 

N.  sunmiit 

N.  extreme  of  W.  point .. 

Cathedral .. 

Boat-slip,  E.  side  N.  island 

Extreme 

Summit _ 

S.W.  pitch 

Summit 

Light-house 

San  Lorenzo  1  ight 

Summit  of  largest 


26  9 

25  39 
25  31 

25  24 
25  7 
25  5 
24  34 
24  15 

23  53 
23  41 
23  33 
23  28 
23  26 
23  6 
22  34 
22  6 

21  55 
21  28 

21  5 
20  57 
20  51 
20  12 

'9  5 
[9  36 
[9  19 
[8  45 
f8  28 

58 
42 

37 
I 

o 

42 

23 


30 
45 
20 


27  54  10 
27  39  20 
27  20 

2 

3 


o 
56 
15 
26  51  5 
26  34  30 
26  34  30 
26  21  25 
26  16  12 


J  y 


7 

7 

7 

7 

7 

6 

6 

6  I 

5  48 

5  33 
5  20 

57 

41 

9 

50 
48 

42 

38 

I 

48 
2  31 
2  II 
2  4 
2  4 
I  47 


P 


Long.  W. 


15 

30 

o 

55 
o 

25 ; 

30  ! 
O 
O 

o 

5 
30; 

42 

30 
o 

5 

50 
o 

30 
40 

5 
42 

I 

30 

o 

40 

43 

35 
o 

o 

o 

o 

20 

50 


o 

15 

56 

o 
o 

50 

o 
o 

42 

20 
o 
o 
o 

30 

3 

3 
10 


71 
71 
71 
71 
71 


15  45 
12  48 


15 
38 
26 


II 

9 

3 

70  58  45 
70  53  07 
70  53  45 

70  51  55 
70  44  25 

70  44  15 
70  42  o 
80  II  43 


70  43  57 
70  44  3 
70  41 


18 


70  35  10 
70  30  16 
70  29  50 
70  36  29 

70  33  o 
70  32  28 
70  25  o 
70  26  55 
70  34  56 
70  37  II 
70  31  39 
70  17  42 
70  13  40 

70  II  17 
70  2  45 
70  12  12 
70  10  26 
70  14  40 
70  10  22 
70  10  30 
70  15  21 


Authorities. 


Light 
Capt. 
Mr.  J 
Capt. 


Light 
Capt. 

H.  M 
Lieut, 
T.  A. 


■House  List. 

Fitzroy,  R.  N. 

,  B.  Pike. 

Fitzroy,  R.  N. 

Do. 

Do. 

Do. 

■House  List. 

Fitzroy,  R.  N. 

Do. 

.  S.  Beagle. 

Lecky,  R.  N.  R. 

Hull,  R.  N. 


70 

17 

50 

70 

21 

50 

70 

20 

0 

70  52 

31 

71 

22 

31 

71 

20 

01 

72 

2 

40 

72 

7 

16 

72 

27 

16 

73 

16 

41 

73   41 

31 

74 

27 

lb 

74 

51 

I 

75 

9 

36 

75 

30 

46 

75 

49 

5^^ 

76 

16 

36 

76 

27 

31 

76 

18 

31 

76 

12 

47 

76 

24 

15 

76 

31 

6 

7638 

II 

76  48  56  1 

77 

2 

31 

77 

15 

44 

77 

15 

44 

77 

16 

6  1 

Capt.  Fitzroy,  R.  N. 

Capt.  Fitzroy,  R.  N. 
Chilian  survey. 
Capt.  Fitzroy,  R.  N. 
Chilian  survey. 
Capt.  Fitzroy,  R.  N. 
Chilian  survey. 
Capt.  Fitzroy,  R.  N. 
H.  M.  S.  Petrel. 
Chilian  survey. 
Capt.  Fitzroy,  R.  N, 

Do. 

Do. 

Do. 
English  survey. 

Capt.  Fitzroy,  R.  N, 
Do. 

Capt.  Fitzroy,  R.  N. 

Do. 
Lieut.  Marquis,  Fr.  N. 
French  survey. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 
Lt.  Comdr.  Davis,  U.  S.  N. 

Capt.  Fitzroy,  R.  N. 

Do. 
Lieut,  le  Pord,  Fr.  N. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut,  le  Clerc,  Fr.  N. 
Mr.  Dathan,  R.  N. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 

Do. 
Lt.  Conidr.  Davis,  U.  S.  N. 

Do. 
Capt.  Fitzroy,  R.  N. 


Page  642]  TABLE  49. 

MARITIME  POSITIONS. 
"WEST  COAST  OP  SOUTH  AMERICA— Continued. 


CO 

o 


Places. 


S 


la 

e 

« 

s 


C8 

*H 

s 

m 

e 

« 


Pelado  Island  ... 

Supe 

Guarmey 

Colina  Redonda 

Samanco  Bay 

Chimbote  

Chao  Islet 

Guanape  Islands  

Huanchaco  Point 

Malabrigo  Bay 

Pacasmayo  Point 

Eten  Head  .  .^ 

Lambayeque 

Lobes  de  Afuera  Island. 
Lobos  de  Tierra  Island. 

Aguja  Point 

Payta,  Saddle 

Payta 

Parinas  Point 

Cape  Blanco 

Tumbez 


Exact  locations. 


Guayaquil  River 

Guayaquil,  Concejo 

Puna 

Point  Santa  Elena  . 

Plata  Isle 

Cape  San  Lorenzo  . 

Manta  Bay 

Caracas  Bay 

Cape  Pasado . 


Point  Galera 

Cape  San  Francisco. 


Esmeralda  River  _. 

Mangles  Point 

Tumaco 

Guascama  Point.  .. 

Gorgona  Island 

Buenaventura 

Chirambiri  Point  .. 

Cape  Corrientes 

Cupica  Bay 

Cape  Marzo .. 

Isla  del  Rey 

Darien  Harbor 

Flamenco  Island  .. 

Chepillo  Island 

Point  Chame 


Summit 

W.  end  of  village 

W.  end  of  sandy  beach  __ 

Summit 

Cross  Point 

Village 

Centre    

Summit  of  highest 

S.  W.  extreme 

Rocks 

N.  W.  extreme 

Summit  over 

Beach  opposite 

Cove  on  E.  side 

Central  summit 

W.  cliff  summit 

S.  summit 

W.  tower  of  Cathedral 

Extreme 

Under  middle  of  high  clift 
Malpelo  Point 


Light  on  Santa  Clara  I  . 

S.  point  of  city .» 

Mandiuga  Point  light  .. 

W.  extreme 

E.  point • 

Marlingspike  Rock 

Light-house 

Punta  Playa ._. 

Extreme 


N.  extreme 

S.  W.  extreme. 


W.  point  of  entrance 

S.  point  of  creek  entrance. 
S.  pt.  of  El  Morro  Island. 

Extreme 

Watering  Bay 

Basan  Point 

N.  extreme 

S.  W.  extreme 

Entrance  to  Cupica  River 

S.  E.  extreme 

Extreme  of  Cocos  Point. . 

Graham  Point 

N.  point 

Centre 

Extreme 


Lat.  S. 


II  27  10 

10  49  45 
10  6  15 

9  38  35 

9  15  30 
9  4  40 
8  46  30 

34  50 
5  40 

42  40 

=5  15 
56  40 
46  o 
46  45 
26  45 

55  30 
12  o 
5  2 
40  50 
16  40 
30  42 


8 
7 
7 
6 
6 
6 
6 

5 
5 
5 
4 
4 
3 


Long.  W, 


10  45 

12  24 

44  30 

11  30 

16  55 

3  30 

56  46 

35  25 
o  21  30 

Lat.  N. 
O  50  10 
o  40  o 


59  52 

36  o 

49  36 

37  10 
58  10 
49  27 


17  6 
28  46 
41  19 

49  45 
8  12  30 
8  28  50 
8  54  30 
8  56  32 
8  39  o 


Authorities. 


77  49  16 

77  43  16 

78  9  16 
78  20  36 
78  29  I 
78  30  14 
78  45  16 

78  55  31 

79  5  16 
79  24  16 

79  33  41 
79  50  6 

79  55  46 

80  40  II 

80  49  6 

81  6  16 
5  36 
7 

17 

12 

80  28  12 

80  24  31 
79  52  20 

79  52  50 

81  o  42 

81  3  55 

80  55  55 
80  43  10 
80  25  24 
80  30  37 


81 
81 
81 
81 


17 
I 
I 


80 
80 


5  40 

7  55 


78 

77 


79  42  9 
79  3  30 
78  45  29 
78  24  24 
II  16 
II  45 
77  29  44 
77  33  28 
77  30  31 

77  40  55 

78  SA   40 

78  5  35 

79  31 
79  7 


15 

55 


79  41  45 


Capt.  Fitzroy,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Comdr.  Miller,  U.  S.  N. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Bager,  R.  N. 
Capt.  Fitzroy,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Lt.  Comdr.  Davis,  U.  S.  N. 
Capt.  Fitzroy,  R.  N. 

Do. 
Light-House  List. 

Do. 
English  survey. 
Light- House  List. 
English  survey. 
Capt.  Kellett,  R.  N. 

Do. 
Light- House  List. 
Capt.  Kellett,  R.  N. 

Do. 

Do. 
Do. 

Do. 

Do. 

Do. 
English  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Kellett,  R.  N. 


ISLANDS  IN  THE  ATLANTIC  OCEAN. 


Fseroe  Is.,  Strom  Islet.. 
Fseroe  Islands,  Halde- 

roig  Islet. 
Freroe  Is.,  Numken  Rock 

Rockall  Islet 

Azores  Is.,  Corvo  Island 
Azores  Is.,  Flores  Island 
Azores    Islands,    Fayal 

Channel. 
Azores  Is.,  Fayal  Island 

Do 

Azores  Is.,  Pico  Island  . 
Azores  Is.,  St.  George  T. 


Thorshaven  Fort  flag-staff 
Halderoig  Church 

Summit,  70  feet 

S.  point 

Santa  Cruz  Fort 

N.  Magdalen  Rock 

Castle  of  Santa  Cruz 

Caldera,  summit  3,351  ft. 

Summit 

Topo  Lslet,  off  S.  E.  pJint. 


62 

2 

26 

62 

18 

20 

61 

23 

0 

57 

35 

52 

39  40 

7 

39 

27 

0 

38 

32 

9 

38 

31 

45 

38 

34 

30 

38 

25 

0 

38 

33 

6 

6  43     8 

7  o  36 

6  45  30 
13  42  21 


31 
31 


8     o 
8  49 


28  34 

28  38  54 
28  44  o 
28  28  12 

27  46  27 


Danish  H.  O. 
Do. 

Do. 

Capt.  Hoskyn,  R.  N. 
English  survey. 
Capt.  Vidal,  R.  N. 
Do. 

Do. 

English  survey. 

Do. 

Do. 


O 

o 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  IN  THE  ATLANTIC  OCEAN— Continued. 


[Page  543 


Places. 


Exact  locations. 


Azores  Is.,  Graciosa  I    . 
Azores  Is.,  Terceira  I  _. 

Azores  Is.,  St.  Michael  I. 

Do 


Azores  Is.,  Santa  Maria  I 
Azores  Is.,  Formigas  I.. 
Madeira  Is., Porto  Santo  I 
Madeira  Is.,  Desertas  .. 
Madeira  Is.,  Madeira 
Islands. 

Do 

Do 


Do 

Salvage  Island 


Canary  Is.,  Alegranza  I. 
Canary  Is.,  Lanzarote  I. 

Do 

Canary  Is.,  Lobos  I 

Canary  Is.,  Fuerta  Ven- 
tura Island. 
Canary  Is.,  G.  Canaria  . 

Do 

Canary  Is.,  Teneriffe  I  _ 

Do 

Do 

Canary  Is.,  Gomera  I 

Canary  Is.,  Ferro  Island. 
Canary  Is.,  Palma  Island 
Cape  Verde  Islands,  San 
Antonio  Island. 

Do 

Cape  Verde  Islands.,  St. 

Vincent  Island. 
Cape  Verde  Islands,  St. 

Lucia  Island. 
Cape  Verde  Is.,  Raza  I. 
Cape  Verde  Islands,  St. 

Nicholas  Island. 
Cape  Verde  Is.,  Sal  I  .. 

Do 

Cape  Verde  Is.,  Bona- 
vista  Island. 

Do 

Do 

Cape  Verde  Is.,  Mayo  I. 
Cape  Verde  Is.,  St.  Jago  I 

Do__ 

Cape  Verde  Is.,  Fogo  I. 
Cape  Verde  Is.,  Brava  I. 
Bermuda  Is.,  Ireland  I . 

Do 

Bermuda  Is.,  Hamilton  I 
Bermuda  Is.,  St. David's  1 
St.  Paul  Rocks 


Rocas  Reef 

Fernando  Noronha ._ 

Ascension  I 

St.  Helena  Island 

Martin  \'as  Rocks 

Trinidad  Island  _. 

Inaccessible  Island 

Tristan  d'Acunha  Islands 


Praya  Fort 

Monte   del    Brazil,  near 

Angra. 
Custom-house,  Ponte  Del- 
gada. 

Point  Arnel  light 

Villa  do  Porto 

Highest  rock 

Fort  Baleira 

Cliao  Island,  Sail  Rock.. 
Funchal,   flag-staff   Fort 

St.  Jago. 
Fora  Island  light-house.. 
Pico  Ruivo,  summit  6,056 
feet. 

Pargo  (W.)  point 

Light-house,   Gran.  Sal- 
vage Island. 

Delgada  Point  light 

Port  Naos  light 


Lat.  N. 


Pechinguera  Point  light. 

Martino  Point  light 

Jandia  Point  light 


Isleta  Point  light 

Palmas  light 

Anga  Point  light  . 

Santa  Cruz,  Br.  consulate. 
Summit  of  peak,  12,180  ft. 

Port  Gomera 

Port  Hierro 

Light,  N.  E.  point 

E.  point 


Summit,  7,400  feet 

Flag-staff  of  telegraph  sta- 
tion, Porto  Grande. 
N.  point 


E.  point . 
S.  point  . 


N.  point 

S.  point 

N.  W.  point. 


N.  E.  point 

New  Town  Church 

English  Road _. 

Porto  Praya,  flag-staff  on 
Quail  Island. 

Porto  Praya,  S.  light 

N.  S.  da  Luz,  village 

Anchorage  on  W.  side... 
Dock-yard  clock-tower  .. 

Bastion  C 

Gibb's  Hill  light 

Light-house 

Summit,  64  feet 


N.  W.  sandy  islet  . 
The  Pyramid  J... 
Fort  Thornton  _ 
Obs.  Ladder  Hill . 

Largest  islet 

S.  E.  point 

Centre 

Herald  Point 


3^  3  5 
38  38  33 

37  44  15 

37  49  20 

36  56  30 

37  16  44 
33  3  30 
32  35  45 
32  3^    4 

32  43  14 
3-  45     o 

32  48  7 
30    7  39 

29  23  48 
28  57  24 
28  50  56 
28  45  25 
28  3  o 

28  II  o 

28  7  6 

28  35  25 
28  28  12 
28  16  35 
28  8  o 

27  46  30 

28  50  6 
17  5  30 

17  4  o 
16  53  20 

16  49  o 

16  38  o 
16  28  30 

16  51  o 
16  34  o 
16  13  20 

16  II   o 

16  7  36 

15  7  30 

14  54  o 

14  53  40 
14  53  o 

14  48  o 

32  19  24 

32  19  37 

32  15  4 

32  21  40 

o  55  28 

Lat.  S. 

3  51  30 

3  50  30 

7  55  20 

15  55  o 
20  27  42 
20  30  32 

37  19  o 

37  2  45 


Long.  W. 


27  58  46 
27  14  10 

25  41  9 


25  8  21 

25  9  45 
24  47  6 

6  18  43 

6  33   30 

6  53  54 

6  39  3 

6  57  30 

7  16  49 
5  51  8 


29  36 
32  58 
52  8 

49  4 
31  26 


5 

25 

16 

5 

24  51 

6 

8 

6 

6 

15 

9 

6 

38 

2 

7 

5 

55 

7 

54 

22 

7 

46  56 

Authorities. 


24  59  43 

25  17  o 

24  59  22 

24  47  8 

24  38  8 
24  18  38 

22  54  12 
22  55  42 
22  55  44 

22  42  o 

22  55  12 

23  12  42 
23  30  7 

23  31  45 

24  30  38 
24  43  12 

64  49  35 
64  49  10 
64  51  36 
64  40  40 
29  22  28 


33   4a  29 

32  25  30 

14  25  30 

5  43  3 

28  46  57 

29  14  56 
12  23  o 
12  18  30 


English  survey. 
Do. 

Capt.  Vidal,  R.  N. 

Light- House  List. 
English  survey. 

Do. 
Capt.  Vidal,  R.  N. 

Do. 
Lt.  Comdrs.  Green  and  Da- 
vis, U.  S.  N. 
Light-House  List. 
English  survey. 

Do. 
Light-House  List. 

Do. 
Do. 
Do. 

Do. 
Do. 

Do. 
Do. 

Do. 
Capt.  Nares,  R.  N. 
English  survey. 

Do. 

Do. 
Light- House  List 
English  survey. 

Do. 
Lt.  Comdrs.  Green  and  Da- 
vis, U.  S.  N. 
English  survey. 

Do. 
Do. 

Do. 
Do. 
Do. 

Do. 

Capt.  Vidal  R.  N. 
Englisli  survey. 
Lieut.  Perrin,  Fr.  N. 

English  survey. 

Do. 

Do. 
H.  M.  S.  Challenger. 

Do. 
Light- House  List. 

Do. 
Capt.  Nares,  R.  N. 


Prof.  Auvers. 
Lieut.  Raper,  R.  N. 
Admiralty  Chart. 
Capt.  Duperry,  Fr.  N. 
M.  Berard. 
A.  G.  Findlay. 
Capt.  Denham,  R.  N. 


Page  544]  TABLE  49. 

MARITIME  POSITIONS. 
ISLANDS  IN  THE  ATLANTIC  OCEAN— Continued. 


O 
O 


Places. 


Cough's  Island 

Falkland  Islands,   Port 

Egmont. 
Falkland  Islands,  Mare 

Harbor, 
Falkland  Is.,  Port  Louis . 
Falkland  Is.,  Port  Stanley 
Falkland  Islands,  Cape 

Pembroke. 

S.  Georgia  Island 

Shag  Rocks  

Sandwich  Islands 

Do 

New  S.  Orkney  Islands  . 
Do 

New  S.Shetland  Islands, 
Deception  Island. 

Bouvet's  Island  (Circum- 
cision). 


Exact  locations. 


Settlement  Cove 


E.  point  of  entrance 


Entrance  to  Careenage. 

Governor's  house 

Light-house 


N.  cape 

Centre 

S.  Thuld  (approx. ) 

Traverse  Island  Volcano 

(approx.). 
E.  point  of  Laurie  Island. 
E.  summit  of  Coronation 

Islanc',  5,397  feet. 
Port  Foster 


Centre . 


Lat.  N. 


40   19  30 
51   21     o 

51  53  52 

51  32  20 

51  41  10 

51  40  42 

54  4  45 

53  48    o 

59  34    o 

55  57    o 

60  54    o 
60  46    o 

62  55  36 

54  16    o 


Long.  W. 


9  46 
60     4 


58  27    8 

58  6  58 
57  51  30 
57  43    o 


38  15  o 

43  25  o 

27  45  o 

26  33  o 


Authorities. 


44  25     o 

45  53    o 

60  35     o 
Long.  E. 
6  14     O 


A.  G.  Findlay. 
Capt.  Sullivan,  R.  N. 

Do. 

English  survey. 
Capt.  Fitzroy,  R.  N. 


Capt.  Cook,  R.  N. 
A.  G.  Findlay. 
Capt.  Cook,  R.  N. 
Do. 

Lieut.  Raper,  R.  N. 
Do. 

Capt.  Foster,  R.  N. 

A.  G.  Findlay. 


ATLANTIC  COAST  OP  EUROPE. 


s 
a 

M 
•M 
i. 


Greenwich. 

Oxford 

Cambridge  .. 


North  Foreland. 
South  Foreland . 

Dungeness 

Beachy  Head  . . . 


South  Sea  Castle 
Portsmouth  .  .  . . , 

Southampton 

Hurst  Castle 

Needles  Rocks. . 

St.  Catharine 

Portland 

Start  Point , 

Plymouth 

Eddystone 

Falmouth , 

Lizard  Point 

Porthcurnow 


Land's  P2nd 

Scilly  Islands  . . 
Trevose  Head . 

Bideford 

I-undy  Island.. 

Bristol 

Cardiff 

Swansea 

Caldy  Island. .. 

St.  Ann's 

Small's  Rocks  . 

Aberystwith 

Bardsey  Island 
South  Stack  . . . 

Holyhead 

Skerries  Rocks 

Bidstone 

Liverpool 

Liverpool  ... 


Observatory 

University  Observatory. 
Observatorv 


Light-house 

do  .... 

do  .... 

do  .... 


do 

Observatory 

Pier  light-house 

W.hght 

Old  lighthouse 

New  light-house 

Notch  Hill  light 

Light-house 

Breakwater  light 

Light-house 

St.  Anthony  Point  light.. 

W.  light-house 

S.  E.  corner  of  telegraph 

company's  station. 
Longship's  light-house. .. 

St.  Agnes  light-house 

Light-house 

do 

do 

Cathedral 

E.  light-house 

Light-house 

do 

Upper  light-house 

Light-house 

do  


Lat.  N. 
51   28  38 

51  45  34 

52  12  52 

51  22  28 
51  8  23 
50  54  47 
50  44  15 

50  46  39 
50  48  3 
50  53  42 
50  42  21 

50  39  40 
50  34  30 
I   18 


50 
50 


18 


do  

do  

do 

do 

do 

Black  Rock  light 
Observatory 


50  20  2 
50  10  49 
50     8     o 

49  57  34 

50  2  44 

50    3  58 

49  53  31 

50  32  55 

51  4  14 
51  10  o 
51  27  24 
51  27  46 

51  36  55 
51  37  52 
51  40  55 
51  43  14 
24  49 
44  59 
18  23 
18  50 
53  25  15 
53  24  2 
53  26  39 
53  24    4 


52 
52 
53 
53 


Long.  W. 
000 

I    15     4 

0  5  40 

Long.  E. 

1  26  48 
I    22   22 

o  58  18 

0  12    58 
Long.  W. 

'    5  IS 

1  5  58 
I  24  23 


33  4 

34  32 
17  47 
27  18 

28 


27 

53 
o 

7 


5  39  18 


44  45 
20  41 

5 
40  20 


2 
12 


5 
6 

5 
4 
4 
2 

3 
3 
4 
5 

5  40 
4    5 


35  55 
9  45 

55  45 

40  59 
10  28 

9 
24 
47  55 

41  54 
37    8 

36  26 

4  23 
2  28 
4  16 


Nautical  Almanac. 
Do. 
Do. 

Ordnance  survey. 
Do. 
Do. 
Do. 

Do. 
English  Nautical  Almanac. 
Ordnance  survey. 

Do. 

Do. 

Do 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Nautical  Almanac. 


'S 

b 

BQ 

s 

b 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  545 


Places. 


Morecambe  Bay 

Calf  of  Man 

Isle  of  Man 

St.  Bees 

White  Haven 

Mull  of  Galloway 

Ayr  (Firth  of  Clyde). 

Troon  

Ardrossan  

Pladda  Island 


Exact  locations. 


Glasgow 


Cantyre 

Ila  Rhins 

Oban 

Skerry vore  Rocks 

Barra  Head 

Isle  of  Glass 

Stornoway 

Butt  of  Lewis 

Cape  Wrath 

Dunnet  Head 

Kirkwall  (Orkneys)  . 
Start  Point  (Orkneys) 

North  Ronaldsha 

Fair  Island 

Sumburgh  Head |   Light-house 

Scalloway  (Shetland  Is.)-:  Castle 

Lerwick  (Shetland  Is.). .  j   Fort 

Ilillswick    Ness    (Shet-      S.  extreme 

land  Islands). 
Balta  I.  (Shetland  Is.)  . 


Fleetwood  new  light 

Upper  light-house 

Ayre  Point  light-house 

Light-house    

Pier-head  light 

Light-house 

do 

do   

Breakwater  light 

Light-house 

Observatory 

Light-house 

do  

do  

do  

do   

do  

Arnish  Point  light 

Light-house 

....  do    

do     

Stone  pier-head  light 

Light-house 

do  

Summit 


Lat.  N. 


Pentland  Skerries 

Tarbert  Ness 

Buchan  Ness 

Aberdeen •. 

Budden  Ness 

Bell  Rock 

Isle  of  May 

Inch  Keith  Rock. 

Edinburgh 

Berwick 

Earn  Island 

Coquet  Island 

Tynemouth 

North  Shields 

Sunderland 

Do 

Hartlepool    

Flamborough 

Spurn  Head 

Ilumber  River... 


Cairn  on  E.  side 

Upper  light-house 

Light-house 

do 

....   do  

Upper  light-house 

Light-house 

do  

do  

Observatory 

Light-house 

N.  W.  light-house 

Light-house 

do  

do   

do  

N,  pier  light 

Light-house 

New  light-house 

Upper  light-house 

Killingholm  upper  light .. 


53  55  35 

54  3  14 
54  24  56 
54  30  4^ 
54  33   10 

54  38  5 

55  28  9 
55  34  37 
55  38  27 
55  25  30 
55  52  43 
55  18  38 

55  40  23 

56  25  10 
56  19  24 

56  47  8 

57  51  26 

58  II  28 
58  30  40 

58  37  33 
58  40  19 

58  59  10 

59  16  42 
59  23  5 
59  33    o 

59  51  17 

60  8  31 
60  9  22 
60  27  10 

60  45  3 
58  41  26 

57  51  55 
57  28  14 
57  8  33 
56  28  8 
56  26  4 
56  II  8 
56  2  I 
55  57  23 
55  45  53 
55  36  59 
55  20  2 
55  I 
55  o 
54  55 
54  55  7 
54  41  47 
54  6  58 
53  34  41 
53  38  49 


5 

31 

I 


Lowestoft . 
Orfordness 
Harwich  . . . 


Ordnance  survey  station . . 
Light-house 

Ordnance  survey  station  . 


Cape  Clear Old  light-house 

Fastnet  Rock Light-house 

Mount  Gabriel 

Crookhaven  

Mizen  Hill 

Bantry  Bay j  Roancarrig  light 

Calf  Rock Light-house 

Skelligs  Rocks ; do 

Valentia do 

Do Port  Magee 

I )ingle  Bay 1  Tower  on  Carhao  I lill 

Blasket  Islands Great  Foze  Rock 


51  26     2 

51  23  19 

51  33  24 

51  28  33 

51  27  41 

51  39  10 

51  34  10 

51  46    6 

51  56    o 

51  53    8 

52  6  55 
52  I  26 


Light-house 52  29  12 

N.  light-house 52     5  36 

Light-house 51  56  38 


Long.  W. 


Authorities. 


3  O  22 

4  49  37 

22  I 

3^    8 

55  50 
51  22 

38  II 

4  41  39 

4  49  28 

5  17  2 

4  17  39 

5  48  8 


6  30  44 


5  31 

0 

7    b 

45 

7  39 

9 

6  38 

27 

6  22 

10 

6  16 

0 

59  52 
22  30 

57  30 
22  30 

22  10 

38  o 

16  23 

16  25 


Ordnance  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
Ordnance  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.  ■ 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 
Ordnance  survey. 
Admiralty  survey. 


I  30  14 

XJ\J, 

Do. 

0  47  17 

Ordnance  survey. 

2  55  23 

Do. 

3  46  31 

Do. 

I  46  22 

Do. 

246 

Do. 

2  44  54 

Do. 

2  23     7 

Do. 

2  33  21 

Do. 

3    8    5 

Do. 

3  10  54 

Nautical  Almanac. 

I  58  57 

Ordnance  survey. 

I  39  21 

Do. 

I  32  17 

Do. 

I  24  52 

Do. 

I  26  10 

Do. 

I  20    0 

Do. 

I  21  30 

Do. 

I  10  27 

Do. 

0    4  51 

Do. 

0     7  II 

Do. 

0  13     2 

Do. 

Long.  E. 

1   45   28 

Do. 

I  35  12 

Do. 

I   17  25 

Do. 

Long.  W. 

9  29    3 

Do. 

9  36     8 

Do. 

9  32  44 

Do. 

9  42  17 

Do. 

9  48  19 

Do. 

9  44  49 

Do. 

10  14  50 

Admiralty  Light  List 

10  32  29 

Ordnance  survey. 

10  19  15 

Do. 

10  23  17 

Do. 

10  16  52 

Do. 

10  41  25 

Do. 

J 


35  '■ 


Page  546] 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


O 

o 


Places. 


8 
d 


Smerwick 

Tralee  Bay 

Beeves  Rocks 

Limerick 

Shannon  River 

Isles  of  Arran , 

Arran  Island , 

Galvv'ay 

Golam  Head 

Slyne  Head 

Clifden  Bay 

Tully  Mountain 

Inishbofin 

Inishturk  Island 

Westport  Bay 

Newport 

Clare  Island 

Blacksod  Bay 

Eagle  Island 

Broadliaven 

Dounpatrick  Head 

Anghris  Head 

Knocknarea 

Sligo  Bay 

Knocklane 

Donegal  Bay 

Rathlin  O'Birne  Islet.. 

Aran  Island 

Bloody  Foreland 

Tory  Island 

Horn  Head 

Melmore  Head 

Fanad  Point 

Glashedy  Island , 

Malin  Head 

Inishtrahull 

Inishovven  Head 

Moville 

Londonderry ... 

Scalp  Mountain 

Benbane  Head 

Rathlin  Island 

Maiden  Rocks 

Larne  Lough 

Belfast  Lough 

Copeland  Islands 

Donaghadee 

South  Rock . . ; . 

Dundrum  Bay 

Carlingford  Lough 

Boyne  River 

Rockabill 

Howth  Peninsula 

Dublin , 

Do 

Poolbeg 

Kingstown 

Killiney  Hill 

Bray  Head , 

Wicklow 

Tara  Hill , 

Black  Stairs  Mountain 

Tory  Hill 

Wexford , 

Forth  Mountain 

Tuscar  Rock 

Great  Saltee 

Waterford 


Exact  locations. 


Signal  tower 

Light-house 

do  

Cathedral 

Loop  Head  light . . 

Esragh  light 

L'ght-house 

Mutton  Island  light 

Tower 

N.  light-house 

Gortrumnagh  Hill 

Ordnance  survey  station  . 

Gun  Rock  Tower 

Tower 

Inishgat  light 

Church 

Light-house 

Bingham  Castle 

W.  light-house 

Ben  wee  Old  Tower 

Ordnance  survey  station  . 

do  

Tumulus 

Black  Rock  light 

Ordnance  survey  station  . 

St.  John's  Point  light 

Light-house 

Rinrawros  light 

Ordnance  survey  station  . 

Light-house 

Ordnance  survey  station  . 

Tower 

Light-house 

Ordnance  survey  station  . 

Tower 

Light-house 

E.  light-house 

New  Pier  .. 

Cathedral 

Ordnance  survey  station  . 

Summit 

Altacarry  light-house 

W.  light-house 

Fanes  Point  light-house.. 
Grey  Point  (extreme)  . .. 

Light-house 

do   

do  

St.  John  Point  light 

Haulbowline  Point  light  . 

Maiden  Tower 

Light-house 

Bailey  light 

Observatory 

N.  wall  light 

Light-house 

E.  pier  light 

Mapas  obelisk 

Ordnance  survey  station  . 

Upper  light 

Summit 

Ordnance  survey  station  . 

do 

College 

Ordnance  survey  station  . 

Light-house 

S.  end 

Hoop  Point  light 


Lat.  N. 


52  13  46 

52  16  14 

52  39  o 
52  4-  4 

52  33  38 

53  «  58 

7 


38 

13 
46 


53 

53  15 
53  13 
53  23  59 
53  29  47 
53  35  o 
53  36  33 
53  42  27 
53  49  35 
53  53  6 

53  49  38 

54  9  5 
54  17  o 
54  19  18 
54  19  36 
54  16  33 
54  15  30 
54  18  27 
54  20  50 
54  34  8 

54  39  47 

55  o  54 
55  8  13 
55  16  20 
55  12  31 
55  15  14 
55  16  33 
55  19  7 
55  22  50 
55  25  57 
55  13  34 
55  10  50 
54  59  40 


23 
3 

5 


55  5 
55  15 
55  18 
54  55  48 
54  51  7 
54  40  35 
54  41  45 
54  38  41 
54  23  56 
54  13  34 
54  I  II 
53  43  20 
53  35  48 
53  21  41 
53  23  13 
53  20  47 
S3  20  31 
18  7 

15  52 
10  39 
52  57  54 
52  41  55 
52  32  55 
52  20  53 
52  20  4 
52  18  57 
52  12  9 
52  6 

52  7 


Long.  W. 


5j 
53 
53 


10  21  40 

9  52  53 
9  I  18 

8  37  23 

9  55  55 

51  30 
42  6 

3  10 
46 


9 
9 
9 
9 


10  14 
10 


10 

ID  13  II 


I 

3  54 
o  15 


10 
9 
9 
9 
10 
10 
9 
9 


6  41 
40  12 
32  56 
5858 

4  59 

5  32 
49  29 
20  41 


8  46  2 

8  34  25 

837  I 
8  40  14 

8  27  33 
8  49  52 
8  33  36 
8  15  38 
8  14  54 
7  57  15 
7  47  12 
7  37  53 


41 
24 


23  51 
22  22 

13  37 
55  35 

3  20 

19  25 
21  51 

28  45 
10  13 

44  17 
47  21 
44  20 
31  21 

31  49 
25  4 
39  30 

4  41 
15  7 

O  II 

3  5 

20  30 

13  33 


I 

31 

37 

55 

5 

I 


13 

48  17 

7  31 

28  15 

33  41 
12  22 

37  15 

55  43 


Authorities. 


Ordnance  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
Ordnance  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  547 


o 

V 


Places. 


s 

■  M 

8 

'Z 

e 

b 


C8 

e 


Waterford 

(ireat  Newton  Head 

Oungarvan 

Knockmealdown  Mount. 

Melvick  Head 

Mine  Head 

Youghal 

Capel  Island 

Ballycottin 

Cork  Harbor 

Queen.stown 

Kinsale  Old  Head  ...  , . . 

Seven  Heads 

Galley  Head 

Stag  Rocks 

Braye  Harbor 

St.  Heliers 


Vardo 

Vadso 

North  Cape  . 

Fru  Islet 

Ilammerfest 

Tromso    

Hekkingen 

Andenas 

Hjertholm 

Lofoten  Island 

Do V 

Gryto 

Slot 

Troenen    

Buholmen 

Villa 

Halten  Island 

Koppem 

Agdences 

Trondheim 

Grip 

Christiansund 

Treikallen . 

Hestskjcer 

.Stemshesten 

Sando  

Svinoen  Islet 

Hjcerringa  Mountain  . 
Ilornelen  Mountain  .. 

ISatalden  Island 

Kian 

Alden 

I  lelleso 

Bergen   

Lorstakkcn  Mountain 

Marstenen  Islet 

Furen  Islet 

Ulsire 

Hvitingso 

Port  Stavanger 

Obristadbrrekke 

Synesvarde  Mountain. 

Kompas  Mountain 

Gunnershang 

Lindisnces 

Ryoingen  Island 

Christiansand 

Okso 

Hamberg 

Arendal  Inlet 


Exact  locations. 


Cathedral 

Metal  Man  Tower 

Ballinacourty  light 

Ordnance  survey  station  . 

, do  

Light-house 

, do 

Tower 

Light-house 

Haulbowline  Coal  Wharf. 

Roche's  Point  light 

Light-house 

Tower 

Ordnance  survey  station  . 

Largest 

Old  pier  light 

Light  on  Victoria  Pier  . . . 

Fortress 

New  Church 

Extreme 

Light-house 

....  do  

Observatory 

Light-house 

do  

do 

Skraaven  Island  light 

Glopen  light 

Light-house 

do  

Soe  Islet  light 

Light-house 

do 

do 


Lat.  N. 


52 
52 

52 

52 
52 
51 
51 


15  33 
8  13 

4  42 
13  39 

3  o 
59  30 
56  23 

51  52  54 
51  49  31 
51  50  33 


Long.  W. 


Light-house 

Mumkholmen  flag-staff . 

Church 

Storvaden  


Light-house 
Beacon  


Summit . 

do 

Store  . . . 
Beacon  . 


Light-house 
Cathedral  ... 

Summit 

Light-house 


Light-house 

do 

do 

do 

Summit 

do 

Light-house 

do 

do 

Oddero  light 

Light-house 

Mill 

Inner  Torungen  light. 


61  33  28 
61  19  16 
60  45  8 
60  23  37 
60  21  ^9 
60  7  45 
59  57  44 
59  18  22 

59  3  41 
58  5»  15 
58  39  18 
58  36  56 
58  25  51 
58  6  23 
57  58  49 

57  58  5 

58  8  ID 

58  4  12 
58  15  2 
58  24  37 


7  6  24 
7  10  15 
7  :>3   10 


54  54 
32  39 
35  13 

50  15 

51  10 

59  3 
8  18  20 


51  47  33 

8  15  15 

51  36  45 

8  32  0 

51  34  14 

8  42  51 

51  31  47 

8  57  7 

51  28  5 

9  13  27 

49  43  20 

2  12  6 

49  10  29 

2  6  45 

Long.  E. 

70  22  0 

31  7  30 

70  4  3 

29  46  50 

71  II  0 

25  40  0 

71  5  47 

23  59  25 

70  40  15 

23  40  0 

69  39  12 

18  57  0 

69  36  4 

17  50  12 

69  19  38 

16  8  0 

68  24  35 

16  2  30 

68  9  20 

14  40  40 

67  53  15 

13  4  30 

67  23  15 

13  52  30 

66  56  35 

13  28  50 

66  25  45 

II  59  50 

65  28  30 

12  13  30 

64  32  55 

10  42  10 

64  10  23 

9  24  51 

63  48  25 

9  44  45 

63  38  45 

9  45  20 

63  27  4 

10  23  30 

63  13  II 

7  36  5 

63  7  I 

7  43  35 

63  3  4 

7  46  4 

63  5  30 

7  29  55 

62  58  49 

7  12  32 

62  49  20 

6  35  21 

62  19  38 

5  16  25 

62  II  12 

5  7  59 

61  51  21 

5  15  II 

61  38  40 

4  47  38 

4  45  58 
4  47  14 

4  43  2 

5  20  15 
5  19 
5  I 
5  3 

4  52 

5  24  45 
5  44  20 

5  33  51 
5  49  8 

5  58  49 
34  22 

3  II 

29  40 


35 
o 

30 
37 


Authorities. 


3  35 

31  36 
8  48     I 


Ordnance  Survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light  List. 

Do. 

Nor.  Hyd.  Office. 

Do. 

Do. 

Do. 
Light- House  List. 
Admiralty  Chart. 
Nor.  Hyd.  Office, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-Hcuse  List. 
Nor.  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 
Nor.  Hyd.  Office. 

Do. 

Do. 
Light  House  List. 
Nor.  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 

Do. 
Nor.  Hyd.  Office. 

Do. 

Do. 


Page  548] 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


o 
O 


Places. 


fa 
9 

is, 


a 

OB 


Exact  locations. 


Jomfruland Light-house  . . . 

Langotangen do 

Langesund Church 

Frederiksvsern Lookout  Tower 

Svenor Light-house  . . . 

Foerder  Islet do 

Fuglebock i do 

Basto do 

Horten 

Holmestrand 

Drobak  

Oscarsberg 

Christiana 

Torganten 

Fredriksten 

Torbjornskjar 

Koster 


Stromstad 

Nord  Koster  Islands . 

Wadero  Island 

Hollo  Island 

Paternoster  Rocks 

Gottenburg 

Nidingen  Islet 

Warberg 

Falkenberg 

Halmstad 

Engelholm 

KuUen  Point 

Helsingberg 

Landskrona  

Malmo 

Falsterbo 

Trelleborg 

Vstad 

Landhammar 

Hand  Island 

Karlshaum 

Karlscrona 

Gland  Island 

Gottland  Island 

Do 

Faro  Island 

Vestervik 

Haradskar  Islet 

Norrkoping 

Landsort 

Stockholm  

Upsala 

Norrtelge 

Soderarm 

Svartklubben 

Osthammar 

Oregrund 

Djursten 

Forsmark 

Orskar  Rock 

Gefle 

Eggrunds  Islet 

Hamrange 

Soderhamm 

EnSnger 

Hudiksvalls 

Gnarp 

Sundsvall 

I.ungo 

Skags  Head 


Church 

do 

do , 

Fort  flag-staff 

Observatory 

Light-house 

Fort  clock-tower  , 

Light-house 

do 


Steeple 

Light-house 

do 

do 

do 

Signal  station 

Light-house 

Castle  Tower 

Church 

Palace 

Church 

Light-  liouse 

Tower 

Light-house 

Church 

Light  house 

do 

do 

do 

do 

Clock  tower 

Stumhohn  Tower 

Light  on  S.  point 

Hoburg  light,  S.  point. 

Ostergarns  light 

Holmadden  light 

Reservoir 

Light-house 

Steeple  Gov't  House  .. 

Light-house 

Observatory 

do 

Inn 

Light-house 

Light-house 

Church 

Clock-tower 

Light-house 

Church 

Light-house 

Church 

Light-house 

Church 

Court-house 

Church 

Court-house 

Church 

do   

Light-house 

do  


Lat.  N. 


58 
58 
59 
58 
58 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
58 
58 

58 
58 
58 
58 
57 
57 
57 
57 
56 
56 

56 
56 
55 
55 
55 
55 
55 
55 
56 
56 
56 
56 
56 
57 
57 
57 
58 
58 
58 
59 
59 
59 
59 
60 
60 
60 
60 
60 
60 
60 
60 
60 
61 
61 
61 
62 
62 
62 

63 


51  51 
59  27 

0  I 

59  34 

58  13 

1  33 
10  29 
23  8 

25  34 
29  23 

39  52 

40  21 

54  44 
9  o 
7  8 

59  44 
54  5 

56  24 
54  12 
32  45 
20  12 

53  45 
40  58 
18  IS 

6  26 

54  8 
40  21 
14  40 
18 


Long.  E. 


2 

52 
-,6 


56 
o 

25 
23  2 

22  30 

25  36 

23  o 
o  54 

10  24 

9  44 

11  50 

55  18 

26  29 

57  24 
45  42 
8  50 
35  28 
44  28 


20 
51 


35 
31 


45  24 
45  J8 

10  34 

15  19 
20  26 
22  16 

22  26 

31  41 
40  29 

43  50 
55  57 
18  22 

32  54 
43  57 

2  51 

23  30 
38  18 

11  48 


9  36  II 

9  45  48 

9  45  14 
o  3  28 

o  9  26 

o  31  57 
o  36  26 
o  32  40 
o  29  52 
o  19  15 
o  38  8 
o  36  55 

o  43  35 

0  50  14 

1  24  9 

0  47  23 

1  o  45 

I  10  28 

I  o  36 

I  2  16 

I  13  24 

I  28  o 

I  53  54 

1  54  16 

2  14  32 
2  29  48 

2  51  38 

2  51  47 

2  27  16 

2  42  I 
2  49  48 


o  20 
49  9 


18 
6 


3  9 

3  50 

4  II  30 
4  51  06 

4  51  54 

5  36  I 

6  24  4 
8  II  6 

8  59  27 

9  22  36 

6  36  45 
6  59  42 

6  II  28 

7  52  9 

8  3  30 

7  37  39 

8  41  34 

9  24  10 

8  49  45 
8  22  36 
826  33 
8  24  20 

8  9  49 
8  22  38 
7  8  29 
7  32  51 

2  57 

4 


18 

I  51 

7  37 
16  22 


Authorities. 


19 
6 


5 
o 

36 


Nor.  Hyd.  Office. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Swedish  Hyd.  Office. 
Light-House  List. 

Do. 

Do. 

Do. 
Swedish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  Lis'. 
Swedish  Hyd.  Office. 
Light- House  List. 

Do. 

Do. 

Do. 

Do. 
Swedish  Hyd.  Office. 

Do. 

Do. 
Light  House  List. 
Swedish  Hyd.  Office. 
Light-House  List. 
Swedish  Hyd.  Office. 
Light-House  List. 
Swedish  Hyd.  Office. 

Do. 

Do. 
Nautical  Almanac. 
Swedish  Hyd.  Office. 
Light-House  List. 
Swedish  Hyd.  Office. 

Do. 

Do. 
Light-House  List. 
Swedish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 
'Do. 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  549 


.Si 

a 
z 


Places. 


Holmo  Gadd 

Umea 

Bjuro  


e 
v 

«  ;  Pitea 

^     Rodkallen  Rock 

I   Maloren 


Exact  locations. 


Light-house 

Church 

Light-house 


Lat.  N. 


Light-house 
do  ... 


Tornea  

Uleaborg  

Ulko  KallaRock. 
Norskaar  Islet... 

Kasko 

Bjorneborg 

Nystad 

Abo 

Aland  Island 

Do 

Do 

Bogskaien 

Uto  Islet 

Hango 

Renskar  

Helsingfbrs 

Seder  Skars 

Kalbaden  Island  . 
Rodskar  Island  . . 
Hogland  Island.. 

Do 

Sommars  Island  . 

Viborg  Bay 

Stirs  Point 

Kronstadt 


jht. 


Do 

St.  Petersburg.. 

PULKOWA 

Peterhof 

Oranienbaum 

Seskar  Islet 

Naroa 

Steenskar  Rock  . . . 

Ekholm  Islet 

Kokskar 

Revel   

Do 

Nargen  Island 

Sourop  

lialtic  Port 

Odensholm  Island. 
Takhkona  Point..  . 

Dago  Island 

Filsand  Island  . . . . 

.Swalfer  Ort 

Kino 

Pernau   

Riga  


Do 

Rund  Island. 
Dome  Ness  . 

Windau 

Libau  


Memel 

Labiau  . .  . 
Schaaken  . 
Powenden 
Laptau  ... 


Light-house  . . 
Karlo  Island  li^ 

I  Light-house 

do 

Skalgrund  Island  light.. 

Sabskar  light 

Enskar  light 

Obs  ervatory 

Skalskiir  light 

Eckero  light 

Lagskar  light 

Beacon  

Light-house 

Hango  Island  light 

Light-house 

Observatory 

Light-house 

do  

do   

Lower  light 

Upper  light 

Light-house 

Neroa  Island  light 

Light-house 

Light   on    Frederikstadt 

bastion. 

Cathedral 

Observatory 

do     

Pier-head  light 

Light-house 

do   

Light  S.  point  of  entrance 

Light-house 

do     

do   

Light  N.  end  of  W.  mole. 

Cathedral 

Light-house 

W.  light 

Light-liuuse 

do    

do  

DagerOrt  light 

Light-house 

.../.do   

do    

Light  at  S.  entrance 

Light  on  Fort  Kametski 

dike. 

Cathedral 

Light-house 

do   

Light  on  S.  jetty 

Light  at  entrance  of  port. 


Light-house  . 
Church  tower. 
Church  spire  . 
Church  tower . 
do 


63  35  48 

63  49  22 

64  29  18 

65  19  10 
65  19  20 
65  31  42 


65  48 
65  2 


64  20 
63  14 


60 
60 
60 


59 
60 


8 
4 

ID 

6 

o 

5 
59  26  28 

59  36  22 
59  27  55 
59  21 


59  28 
59  49 
59  41 
59  42 
59  27 


59 
59 


30 
6 


58  55 
5^23 


25 
2 

2 

57  54  37 
5«  5 
5823 

57  3 


50 
10 

28 


30 
20 

5 
8 

62  20  6 

61  28  29 

60  43  10 

60  26  57 

60  24  45 

60  13  20 

59  50  50 
59  31  " 
59  46 
59  46 

59  56 

60  9 
60  6 
59  58  45 

59  58  8 
o  40 
6  22 

12  31 

60  14  43 
60  1 1  5 
59  58  14 

59  59  44 
59  56  30 
59  46  19 
59  53  26 
55  40 
2 


o 
10 

43 
40 


56  56  36 

57  48  2 
57  48  10 
57  24  o 
56  31  I 

55  43  45 
S4  51  53 
54  53  47 
54  53  34 

54  53  52 


Long.  E. 

0  /  // 

20  46  36 

20  17  28 

21  35  24 

21  30  0 

22  23  10 

23  36  30 

24  12  0 

24  34  0 

23  27  0 

20  37  40 

21  II  24 

21  22  34 

21  I  0 

22  17  3 

19  34  0 

19  31  20 

19  54  5 

20  25  50 

21  22  0 

22  58  8 

24  24  43 

24  57  17 

25  25  51 

25  37  30 

26  41  5 

27  I  40 

26  58  44 

27  33  46 

27  58  36 

29  3  I 

29  47  12 

29  46  7 

30  19  22 

30  19  40 

29  54  54 

29  46  38 

28  23  I 

28  3  31 

26  23  0 

25  48  58 

25  2  37 

24  46  10 

24  44  45 

24  31  57 

24  24  5 

24  4  30 

23  23  15 

22  36  15 

22  II  36 

21  49  56 

22  4  15 

23  59  34 

24  49  25 

24  0  59 

24  8  25 

23  15  0 

22  39  15 

21  32  0 

20  59  40 

21  6  6 

21  6  52 

20  41  31 

20  34  10 

20  30  5 

Authorities. 


Light- House  List. 
Swedish  Hyd.  Office. 
Light- House  List. 
Lieut.  Raper,  R.  N. 
Light- House  List. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
Light- House  List. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
Light-House  List. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 

Do. 

Conn,  des  Temps. 
Nautical  Almanac, 

Do. 
Light-House  List. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Conn,  des  Temps. 
Light-House  List. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Conn,  des  Temps. 
Light-House  List. 

Do. 

Do. 

Do. 

German  Hyd.  Office. 
Do. 
Do. 
Do. 
Do. 


Page  550J 


nl 
O 
O 


s 
« 
a 

m 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


Places. 


Rudau  

lieiligen  Creutz 

Brlistevort 

Pillau 

Do 

Fischausen 

KONIGSBERG  ... 

Do 

Brandenburg  

Brausberg  

Frauenburg  

Tolkemit 

Blocksberg  

Elbing 

Tiegenort 

Tiegenhof 

Steegen 

Schonbaum  

Bohnsack  

Reichenberg 

Danzig 

Do 

Do 


Weichselmiinde 

Putziger  Heisternest 
Oxhoft 

Putzig 


Exact  locations. 


Church  tower 

do   

Light-house 

do  

Landmark   

City-hall  tower , 

Observatory 

Church  tower 

do   

City-hall  tower , 

Cathedral  tower 

Church  tower 

Lookout  tower , 

Church  tower , 

do 

do  

do 

do  

do 

do 

Observatory 

St.  Mary's  Cathedral 

Neufahrwasser    light 
tower. 

Fortress  tower 

Church  tower , 

Light-house 

Ev.  Church  tower 


Lat.  N. 


Hela '  Light-house 

Rixhoft 

Zamowitz 

Leba 

Stopelmiinde 

Dlinnow ,.. .. 

Marsow   

Jershdft j  Light-house  . 

Zizow i  Church  tower 


do 
Church  tower. 

do 

Church 

Church  tower. 
Church  cross  . 


Riigenwalde 

Gollenburg 

Coslin 

Funkenhagen 

Colberg 

Gross-llorst 

Cammin 

Wollin 

Palitz 

Stettin , 

Jasenitz 

Swineniunde 

Streckelsberg 

Usedom 

Auclam 

Lassau  

Wolgast , 

Criefswald 

Griefswalder  Oie 

Granitz 

Bergen  

Arcona  

Schaprode 

Stralsund , 

Barth 

Darsserort 

Wustrow   

Ribnitz 

Wamemunde  . . . 

Rostock. 

Diedrichshagen  . 


St.  Mary's  Church 

Monument 

St.  Mary's  Church 

Light-house 

St.  Mary's  Church 

Light-house 

Cathedral  tower 

Church  tower 

Church 

N.  Castle  tower 

Church  tower 

Light-house 

Survey  station  near  beacon 

Church  tower 

St.  Nicholas's  Church 

Church  tower 

do , 

St.  Nicholas's  Church 

Light  house 


Castle  tower 

Church  tower 

Light-house 

Church  tower 

St.  Mary's  Church 

Church  tower 

Light-house 

Church 

Church  tower 

Church    

St.  Jacob's  Church 
Survey  station 


54  52  25 
54  53  47 
54  57  40 
54  38  25 
54  38  55 
54  43  49 
54  42  51 
54  41  53 
54  36  50 
54  23  o 
54  21  28 
54  19  19 
54  22  38 
54  9  44 
54  16  30 
54  12  41 
54  19  39 
54  17  19 
54  2 :  45 
54  19  37 
54  21  18 
54  21  5 
54  24  18 

54  23  51 
54  12  16 
54  33  9 
54  43  23 
54  36  6 
54  49  55 
54  47  21 
54  45  29 
54  35  16 
54  32  27 
54  30  45 
54  32  28 
54  26  54 
54  25  27 
54  12  31 
54  II  28 
54  14  40 
10  40 

.  -  5  47 
53  58  29 
53  50  41 
53  33  14 
53  25  41 
53  35  38 

53  55  3 

54  3  8 
53  52  17 
53  51  29 

53  56  59 

54  3  18 
54  5  49 
54  15  2 
54  22  56 
54  25  8 
54  40  53 
54  30  55 
54  18  42 
54  22  14 
54  28  28 
54  20  47 
54  14  42 
54  10  42 
54  5  27 
54  6  32 


51 

54 


Long.  W. 


20  27  55 

20   I  25 

19  59  6 
19  53  55 

19  55  40 

20  o  39 
20  29  44 
20  30  26 
20  15  13 

9  49  45 
9  41  II 
9  31  58 
9  24  43 
9  23  58 
9  8  37 

9  7  24 
9  7  46 

858  4 

8  49  53 
8  47  II 

8  39  46 
8  39  27 
8  40  9 


8  41  3 
8  40  35 
8  33  45 
8  24  53 

8  49  4 
8  20  29 

8  5  II 

7  33  38 

6  51  35 
6  49  30 

6  42  16 

6  32  50 

6  26  6 

6  24  52 

6  13  55 
6  II  5 

5  52  39 
5  34  44 
5  4  6 
4  46  36 
4  37  12 
4  34  47 
4  33  52 
4  32  50 
4  t7  19 
4  I  17 
55  26 
41  47 
51  13 
46  51 
22  53 
55  42 

37  54 
26  II 

26  12 
10  13 

5  30 
43  42 
30  23 
24  2 
26 


Authorities. 


5 
8 

46 


4 
19 

ID 

4 


German  Hyd,  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
German  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
German  Hyd.  Office. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
.  Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


o 
O 


m 
m 

d 

M 
M 

Sk 


Places. 


Eckemforde  . . 

Schleswig . 

Kappeln 

Steinberg  . 

Flensberg .... 
Handewith  . . . 

Diippel 

Schleimunde.  . 

Lysabbel 

Augustenburg 
Hiigeberg.  ... 

Apenrade  . 

Skoorgaarde . . 

Knirsberg. 

Hadersleben   . 
Christiansfield 

Ballum 

List 

Keitum 


Fohr 

Galgenberg 

Husum 

Tonning 

St.  Peter 

Wesselburen 

Biisum 

Helgoland 

Scharhorn 

Neinverke 

Cu.xhaven 

Liidingvvorth    . . 

Ottendorf 

Osterbruck 

Marne 

Oederquart 

Freiburg 

Hammelworden . 

Drochtersen  . 

Assel 

Biitzfloth 

Stade 

Steinkirchen 

Ruxtehude 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


fPage  551 


Basdorf , 

^^'ismar 

SCHWERIN 

Proseken 

Klutz 

Hohenschonberg 

Lubec 

Do 


Gomnitzberg  ... 
Travemlinde . . . . 

Burg 

Marienleuchte  . 

Petersdorf 

Oldenburg  

Lutjenburg 

Hessenstein 

Schonberg  

Schrievenborn  . 

Bulk , 

Elmschenhagen 

Kiel 

Do , 

Reudsburg  

Geltorf 


£xact  locations. 


Survey  station 

St.  Nicholas's  Church 

Observatory 

Church  tower   

Church 

Survey  station 

Observatory 

St.  Mary's  Church,  North 
tower. 

Tower 

Light-house 

Church  tower 

Light-house 

Church  tower 

Church 

do     

Flag-staff  of  lookout  tower 

Church 

Survey  station 

Light-house 

Church 

Observatory 

St.  Nicholas's  Church . . . 

New  Church 

Church  tower 

Church 

Cathedral 

Church 

do 

do 

do 

Survey  station 

Light-house 

Church 

do  

Survey  station 

Church 

Survey  si  ation 

do  

Church 

do  

do  

E.  light-house 

Church 

St.  Nicholas's  Church . . . 

Survey  station 

Church 


Lat.  N. 


do 

do 

......do 

Church 

Light-house  . . . 

Beacon  

Light-house  . . . 

do  

Church 

do 

do 

do 

do 

do 

do 

do 

do 

do 

Church  steeple. 

Church 

do 


54  8  o 

53  53  50 
53  37  38 
53  54  20 
53  58  5 
53  58  54 
53  51  31 

53  52  10 

54  6  44 

53  57  44 

54  26  16 

54  29  43 
54  28  54 
54  17  40 
1738 
19  47 
23  52 
54  21  10 
54  27  25 
54  17  35 
54  20  30 
54  19  28 
54  18  4 
54  24  38 
54  28  25 
54  30  55 
54  39  48 
54  45  24 
54  47  5 
54  45  48 
54  54  28 
54  40  23 
54  54  19 
54  56  48 
54  58  5 
2  46 

3 
8 

15 


54 

54 
54 


55 
55 
55 

55 


55  21 
55  5 
55  3 


52 
12 

5 
27 

31 
4 
13 
51 
21 


54 
54 


54  54 
54  41 
54  41 
54  28  43 
54  19  8 
54  18  26 
12  49 
7  52 
54  10  50 

53  57  15 
53  55  I 
53  52  25 
53  48  3 
53  48  33 
53  46  46 
53  57  17 
53  48  21 
53  49  39 
53  47  40 
53  42  38 
53  41  36 
53  39  21 
53  36  12 
53  33  43 
53  28  43 


Long.  E. 


41  54 

28  9 

25  10 

22  23 
10  10 

5  54 
o  43  53 
o  41  18 

o  44  48 

0  53  o 

1  II  59 
I  14  29 
I  4  18 
o  53  19 
o  35  41 
o  32  59 
o  22  24 
o  12  49 

O  12   4 

10  46 
8  56 
837 
39  59 
5838 
50  23 
34  23 
56  13 
45  47 

26  20 

19  35 

9  45  35 

10  2  24 

o  29 

52  20 

5841 

25  18 

23  35 

26  44 

29  28 
29  4 

8  39  41 
8  26  50 
8  22  3 

8  33  13 
833  58 

9  3  21 

8  56  38 
8  38  29 

8  55  34 
851  53 

7  53  o 

8  24  35 
8  29  58 
8  42  43 
8  45  43 
8  54  8 
8  56  44 

o  54 

14  31 

17  33 
19  41 

23 


10 
9 
9 
9 
9 
9 
9 
9 


19 
26  21 
29  o 
28  48 
36  40 
42  15 


Authorities. 


German  Hyd.  Office. 

Do. 
Nautical  Almanac. 
German  Hyd.  Office. 

Do. 

Do. 
Nautical  Almanac. 
German  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
German  Hyd.  Office. 

Do. 

Do. 

Do. 

Do.  ■ 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


Page  552] 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


o 
O 


Places. 


S 

n 

a 

fa 
« 


fa 

es 


0 


Altona  

Hamburg  

Do 

Berlin 

Potsdam 

Leipzig 

Munich 

GOTHA  

gottingen 

Manheim 

Strasburg  

Bonn 

Harburg , 

Hoheweg 

Langwarden 

Bremerhaven 

Minsener  Old-Oog 

Schillighorn 

Wilhelmshaven . 

Wangeroog 

Spikeroog 

Esens   

Langeoog 

Balstrum 

Nordeney  . 

Juist 

Norden \. 

Emden 

Leer 


Falster 

Do 

Mo^n  Island  

Do 

Proeste 

Kjorge     

Amager  Island. 

Do 

Copenhagen  

Bornholm 

Christianso  Island. 

Kronberg 

Nakkehooed 

Hesselo  Island  ..  . 
Anholt  Island  .  ... 

Spodsbjerg 

Roeskilde 

Nykjobing 

Oddensby  

Seiero  Island 

Do 

Kallundborg 

Omo  Island    

Vordingborg 

Veiro  Island 

Langeland  Island  . 

^ro  Island 

Lyo  Island 

Assens   

Baago  Island 

Kolding 

Bogense  

Nyborg    

Turo  Island 

Soendborg  

Endelave  Island  .. 

Samso  Island 

Horsens 


Exact  locations. 


Observatory 

do 

St.  Nicholas's  Church 

Observatory 

do 


do 

do 

do 

, do 

do 

do 

do 

Ev.  Church 

Light-house 

Church 

New  harbor  light 

Beacon 

Light- house 

Observatory 

Light-house 

Church 

Church  tower . 

Belvedere 

Church 

Light- house 

Church 

Lutheran  Church . 
City  Hall  tower  . 
Ref.  Church 


Giedser  light 

Stubbekjobing  Church  . . . 

Stege  Church  spire 

Mo^n  light 

Church  spire 

Church  tower 

Hollcenderby  Church  spire 

IV  ordse  Rase  light 

New  observatory 

Ronne  light 

Great  tower 

High  spire 

Upper  light 

Light-  house 

do 

do 

Cathedral 

Church  tower 

do  

......do  

Seiero  Point  light 

Church 

do   

Waldemar's  tower 

Light-house 

Fakkebjerg  light 

Church  spire 

Church  tower 

do   

Light-house 

Castle  tower 

Church  spire 

do   

do   

Frue  Church 

Church  tower 

Koldby  Church  tower  ... 

Frelser  Church  spire 


Lat.  N. 


53 
53 
53 
52 
52 

51 

48 

50 
51 
49 
48 

50 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 
53 


32  45 

33  7 
32  57 

30  17 
22  56 
20  6 

845 
56  37 

31  48 
29  II 

35  o 
43  45 
27  51 
42   51 

36  20 

32  54 

46  29 

42  16 

31  52 

47  26 
46  19 

3857 
45  6 

43  46 
42  39 
40  45 
35  49 
22  6 

13  49 


55 
56 
56 
56 


20 
10 


Long.  E. 


54  33  50 
54  53  24 
54  59  3 

54  56  50 

55  7  24 
55  29  44 
55  35  45 
55  38  10 
55  41  14 

55  5  40 
19  19 

2 

7 
II  50 

56  44  15 
55  58  36 
55  38  34 
55  55  30 
55  57  52 
55  52  55 
55  55  9 
55  40  50 
55  9  48 
55  o 
55  2 
54  44  23 

54  51  14 

55  2 
55  16 
55  17  44 
55  29  31 
55  34  3 
55  18  41 
55  3  o 
55  3  37 
55  45  32 
55  48  2 
55  51  44 


26 
19 


34 
9 


56  35 
5825 
59  40 
23  44 


9 

9 

9 

13 

13  4  15 

12  23  30 

II  36  32 
10  42  38 

9  56  34 
8  27  38 
46  10 

5 

59 
8  14 

8  18  J 
8  34  12 

0  54 

1  50 
8  48 


7 
7 
9 


49 
2 

37 
o 


53  58 
41  45 
36  45 
35  41 
22  3 
1348 

59  53 
12  16 
12  25 
27  I 


58  2 

2  52 

17  16 

32  45 

7  36 
38  24 

41  26 

34  47 

42  o 

II  39 
32  2 
20  50 
I  42  49 
I  39  13 
I  51  35 
5  2 
40  29 
24  6 

8  48 

5  7 
5  4 

9  32 
54  59 
22  23 

42  13 
o  24  II 
o  9  16 

9  53  50 
9  48  8 

9  28  40 

10  5  29 

10  47  47 

10  40  2 

10  36  48 

10  16  20 

10  33   37 
9  51  19 


Authorities. 


Nautical  Almanac. 

Do- 
German  Hyd.  Office. 
Nautical  Almanac. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
German  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 
Nautical  Almanac. 
German  Hyd.  Office. 

Do. 

Do. 

Do.. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Light-House  List. 
Danish  Hyd.  Office. 

Do. 
Light- House  List. 
Danish  Hyd.  Office, 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 
Danish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.  ■ 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


;] 


J! 
fa 
« 

s 

m 
m 

A 


e 

X 


it 


u 

m 

e 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OP  EUROPE— Continued. 


[Page  553 


Places. 


Tuno  Island 

Samso  Island , 

Aarhus , 

Mjelm  Islet 

FornEeo 

Randers 

Hals 

Aalborg . 

Cape  Skaw,  or  Skaagen. 

Iliishals 

Haustholm 

Boobjerg 

Ringkjobing 

Loune 

Blaabjerg 

Varde 

Guldager 

Fand  Island 

Ribe 

Mano  Island 


Niewe  Diep  . . 
Amsterdam   .. 

Utrecht 

Leyden  

The  Hague 

Scheveningen. 

Brielle 

Rotterdam 

Hellevoetsluis 

Willemstad 

Goedereede  ... 

Flushing , 

Do 


Brussels 

Antwerp 

Do 

Blankenberghe 

Ostend 

Do 

Nieuport 


Paris 

Dunkerque  .. 
Gravelines  .. 

Calais   

Cape  Grisnez 

Boulogne 

Abbeville 


Cayeux  

Dieppe 

Ailly  Point 

St.  Valery  en  Caux 

Fecamp 

Cape  La  Heve.. .. 

Havre , 

Honfleur 


Caen 

Port  Corseulles  . . 
De  Ver  Point . . . . 
Cape  LaHougue. 

Cape  Barfleur 

Cherbourg  

Cherbourg 

Cape  La  Hague.. 
Casquets  Rocks . . 


Exact  locations. 


Light-house 

Nordby  Church  tower  . . 

Cathedral  spire 

Light-house 

do  , 

Church  spire 

Church  tower 

St.  Rudolph's  Church  .. 

Old  light-house 

Light-house , 

do 

do  

Church  spire 

Church  tower 

Summit,  loo  feet 

Church  spire 

Church 

Nordby  Church 

Cathedral  tower 

Church  spire 


Lat.  N. 


Time-ball  station 

W.  church  tower 

Observatory 

do  

Church  tower 

Light-house    

do 

Time-ball  station 

do  

Light-house 

Light  on  church  tower.. . 

Time-ball  station '. 

Light,  Westhaven  bastion . 


Observatory 

do   

Notre  Dame  Cathedral.. 

Fort  light-house , 

Light-house , 

Church  tower 

Templars  tower 


Observatory 

Tower 

Light  on  N.  breakwater.. 

Light  on  old  fort 

Light-house 

Column 

Tower 

Light-house 

Tower  


55 
55 
56 
56 
56 
56 
56 
57 
57 
57 
57 
56 
56 
55 
55 
55 
55 
55 
55 
55 


56  59 

57  6 
9  26 
8  o 

26  36 

27  36 
59  54 

2  54 

43  46 
35  6 

6  50 
30  48 

5  27 
47  17 

44  50 


37 
31 


13 

52 


26  26 
19  42 
16  II 


52  57  50 
52  22  30 

5  10 
9  20 

4  40 

6  16 
54  29 

51  54  30 

51  49  19 
51  41  48 

51  49  8 
51  26  33 
51  26  24 


52 
52 
52 
52 
51 


50  51 

51  12 
51 
51 
51 
51 
51 


II 

28 

13  17 

1847 

14  13 
13  50 

7  53 


48  50  II 
51  2  9 
51  o  18 

50  57  45 
50  52  10 

50  44  32 

50  7  5 
50  II  42 

49  55  32 

Light-house I  49  55  7 

Light  on  E.  breakwater . .  49  52  26 

Notre  Dame  Church 49  46  4 

49  30  43 
49  29  16 

49  25  32 


Light  on  E.  breakwater. 
Notre  Dame  Church . 
S.  light 

Steeple 

W.  light-house . 


Church  tower. 
E.  jetty  light  . 
Light-house  .. 

do  

do   


49  II  14 
49  20  18 
49  20  28 
49  34  19 
49  41  50 
Light, centre  ofbreakwater   49  40  28 

Naval  Observatory 49  38  54 

Light-house 49  43  22 

Light  on  N.  \V.  rock 49  43  22 


Long.  E. 


10  26  50 
10  ^^  o 
10  12  50 
10  48  32 
10  57  40 
10  2  18 
10  18  53 
9  55  22 
10  36  38 

9  56  44 
8  36  10 

8  7  23 
8  14  52 
8  14  36 

8  14  43 
8  28  57 
8  24  12 
8  24  3 
8  45  52 
832  38 


40  36 
4 
50 


53 
7 

29  3 
18  30 
15  10 
10  45 
28  50 

7  40 
26  26 

5835 
35  48 


Authorities. 


3  34  32 

4  22  18 

4  24  44 

4  24  12 

3  6  54 

2  55  51 

2  55  22 

2  45  34 

2  20  14 

2  22  31 

2  6  34 

I  51  7 

I  35  I 

I  37  5 

I  49  56 

I  30  46 

I  4  42 

0  57  34 

0  42  37 

0  22  17 

047 

0  6  34 

0  13  42 

Long.  W. 

0  21  10 

0  27  34 

0  31  10 

I  16  22 

I  15  57 

I  37  9 

I  38  8 

I  57  16 

2  22  42 

Danish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 
Danish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Ned.  Hyd.  Office. 
Krayenhoff. 
Nautical  Almanac. 

Do. 
Krayenhoff. 
Ned.  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 

An.  de  Brux. 

Do. 

Do. 
Light-House  List. 

Do. 
An.  de  Brux. 

Do. 

Conn,  des  Temps. 

Do. 
French  Light  List. 

Do. 
Conn,  des  Temps. 

Do. 

Do. 

Do. 

Do. 

Do. 
Frencii  Light  List. 
Conn,  des  Temps. 

Do. 

Do. 

Do. 

Conn,  des  Temps, 
French  Light  List. 
Conn,  des  Temps. 
French  Light  List. 
Conn,  des  Temps. 
French  Light  List. 
Frencli  D6p6t  des  C.  and  P. 
Conn,  des  Temps. 
French  Light  List. 


Page  554] 


TABLK  49. 

MARITIME  POSITIONS. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


o 
O 


Places. 


Exact  locations. 


Lat.  N. 


Long.  W. 


Authorities. 


d 
fa 


a 

fa 
e 

S 


ac 


Port  St.  Peter 


Douvres  Rocks 
Cape  Carteret . . 

Coutances , 

Granville 

Chausy  Islands 


St.  Malo 

Cape  Frehel  

Heaux  de  Brehat 

Morlaix 

DeBas  Islet 

Abervrach 

Ushant 

Brest 

De  Sein  Islet 

Bee  du  Raz 

Audieme 

Penmarch  Rocks 

Glenan  Islands 

De  Groix  Island 

L'Orient 

Belle  Isle 

Port  Haliguen 

Hoedic  Island 

Port  Navalo 

Vannes 

Le  Four  Rock 

Croisie 

Guerande 

Port  St.  Nazaire 

Paimbceuf 

Nantes 

Noir  Moutier  Island 

Le  Pilier  Island , 

D'Yeu  Island , 

La  Chaume 

Point  de  Grouin  du  Cou 

Rhe  Island 

Rochelle , 

Aix  Island , 

Rochefort 

Oleron  Island 

Point  de  la  Courbe  . 

Point  Cordovan 

Point  de  Grave , 

Pauillac 

Bordeaux  

Bayonne _ , 

Biarritz 

St.  Jean  de  Luz , 


Fuenterrabia 

Port  Pasages 

San  Sebastian 

Bilbao 

Castro  Urdiales 

Santona. 

Santander 

San  Martin  de  la  Arena 
San  Vincent  de  la  I5ar- 
quera. 

Rivadesella 

Gijon ..   , 

Aviles 

Rivadeo  

Estaca  Point 


Light   on   Castle   Comet 

Breakwater. 

Light-house 

, do   

Cathedral  tower 

Light-house 

Lighten  S.  E.  end  of  large 

island. 

Rochebourne  light 

Light-house 

do  

Tower  St.  Mark's  Church. 

Light-house 

Light  on  Vrach  Islet 

Light-house 

Observatory 

Light-house 

do  

Pier-head  light 

Light-house 

Light,  Penfret  Island 

Light-house 

Church  tower 

Light-house 

Light  on  N.  jetty 

Light-house 

do  

St.  Pierre  Church 

Light-house 

End  of  breakwater 

Steeple 

Spire 

Steeple  

Cathedral 

Light-house 

.do  

do  

do  

do 

Light  N.W,  point 

W.Hght 

Light-house 

Hospital 

Light,  N.W,  point 

Light-house 

do 

do 

Middle  light 

St  Andr^ 

Cathedral 

Light  house 

Light  on  breakwater 

Light  on  Cape  Higuera.. 

Entrance 

Monte  Igueldo  light 

Light  on  Galea  Castle 

Santa  Ana  Castle 

Ruined  castle,  Pasage  Pt. 

La  Darsena   

Light-house 

End  of  new  mole 


49  27  13 


49  6  28 
49  22  27 
49  2 
48  50 
48  52 


54 

7 

13 


48  40  18 
48  41  5 
48  54  33 
48  34  38 
48  44  45 
48  36  57 
48  28  31 
48  23 
48  2 
48  2 
48  o 
47  47  52 
47  43  17 
47  38  53 
47  44  53 
47  18  41 
47  29  10 
47  20  36 
47  32  54 
47  39  30 

17  53 

18  30 

19  44 

16  22 

17  17 
I 


32 

39 
22 

34 


47 

47 

47 

47 

47 

47 

47 

47  2 

46  43  _ 

46  29  40 

46  20  41 

14  40 

9  22 

o  36 


o  41 

36 

5 


46 
46 
46 


45  56  37 
46 


45  41 
45  35 
45  34 
45  II 


Mole  head 

Santa  Catalina  light 
Light-house 

do 

do 


49 
35 
13 

10 

57 

44  50  19 
43  29  29 
43  29  41 
43  23  17 

43  23  50 
43  20  10 

43  19  33 
43  22  36 
43  24  10 
43  26  8 
43  27  52 
43  26  49 
43  23  10 

43  28  28 
43  32  48 
43  38  5 
43  35  o 
43  47  20 


O       I       II 

2  31  31 

2  48  49 
I  48  26 
I  26  39 

I  36  47 
I  49  21 


58  42 
19  II 

5  12 
50  2 

I  39 
34  35 
3  28 
4  29  36 
4  52  4 
4  43  58 
32  28 
22  31 
57  16 
30  36 
21  32 
13  20 
6 


10 

51  54 
55  9 
45  28 
38  6 
31  26 
25  48 


57 
9 


II 
2 

1  32  59 

2  13  17 
2  21  38 
2  22  57 
I  47  46 
I  27  50 

I  33  41 
I  9  6 
I  10  41 

0  57  50 

1  24  38 
I  15  21 

I  ID  25 
I  10  25 

o  44  42 

0  34  42 

1  28  43 

I  33  23 
I  40  II 


I  47  54 
I  56  16 

I  9 

4  10 

16  14 

30  28 

4851 

I  4 

25  24 


5  6  34 
5  40  II 

5  56  8 
7  4  24 

7  44  9 


English  Light  List. 

French  Light  List. 

Do. 

Do. 
Conn,  des  Temps. 
French  Light  List. 

Do. 
Conn,  des  Temps. 

Do. 

Do. 

Do. 
French  Light  List, 
Conn,  des  Temps. 

Do. 

Do. 

Do. 
French  Light  List, 
Conn,  des  Temps. 
French  Light  List. 
Conn,  des  Temps. 

Do. 

Do. 
French  Light  List. 

Do. 

Do. 
Conn,  des  Temps. 
French  Light  List. 

Do. 
Conn,  des  Temps. 

Do. 

Do, 

Do. 
French  Light  List, 
Conn,  des  Temps. 

Do. 

Do. 
French  Light  List. 

Do. 

Do. 

Do. 
Conn,  des  Temps. 
French  Light  List, 

Do. 
Conn,  des  Temps, 
French  Light  List. 

Do. 
Conn,  des  Temps. 

Do. 

Do. 
French  Light  List. 

Spanish  Hyd.  Office. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do, 

Do. 
Do. 
Do. 
Do. 
Light-House  List, 


TABLE  49. 

MARITIME  POSITIONS. 

ATLANTIC  COAST  OP  EUROPE— Continued. 


[Page  555 


Places. 


a 

fa 
9 

it 

■c 
e 
a 


s 

X' 


Port  Cedeiro  ... 

Ferrol 

Do 

Coruna 

Cape  Finisterre  . 

Vigo 

Oporto 

Cape  Mondego  . 
Burlingo  Island. 

Peniche 

Cape  Roca 

Lisbon 


Setuval , 

Cape  St.  Vincent 

Lagos  

Cape  Sta.  Maria 

Agamonte 

Ilaelva 

San  Lucar 

Cadiz ^.. 


Exact  locations. 


Light-house 

Old  naval  observatory 
Priorino  Chico  light  .  . 
Hercules  Tower  light . 

Light-house 

Cr^s  Island  light 

Light,  N.  S.  de  Luz  .  . 

Light-house 

, do 

, do 

do 

Royal  observatory . 


Lat.  N. 


Long.  W. 


42 
41 


Do 

Cape  Trafalgar 

Tarifa 

Algeciras 

Gibraltar 

Do 


Light-house 

, do 

Church 

Light-house 

Castle 

Plaza  at  head  of  mole . . . 

Chipiona  light 

Observatory  of  San  Fer- 
nando. 

San  Sebastian  light 

Light-house 

do  

Light,  Verde  Island .... 
Dock- yard  flag-staff  . ... 
Europa  Point  light 


43  39  o 
43  29  30 
43  27  30 
43  23  10 
42  52  45 
12  30 

9  9 
40  10  59 

39  25  o 
39  21  8 
38  47  5 
38  42  31 

38  31  9 

37  I  15 
37    7  48 

36  58  o 

37  13  15 
37  15  8 
36  43  57 
36  27  40 

36  31  29 
36  10  50 

35  59  55 

36  7  II 

36  7  10 
36  6  30 


8  5  24 
8  13  29 
8  21  8 

8  24  30 

9  15  32 
8  53  54 
838  15 

8  52  I 

9  28  o 
9  24  26 
9  27  13 

9  II  ID 

8  53  o 
8  57  31 
8  39  53 
7  49  36 
7  25  37 
6  57  12 
6  26  34 
6  12  20 


6  ig 
6     2 

5  36 
5  26 
5  21 


7 

17 

35 
2 

17 

o  50 


Authorities. 


Spanish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 
Port.  Geod. 

Do. 
Light-House  List. 

Do. 

Do. 
Lt.  Comdrs.  Green  and  Da- 
vis, U.S.N. 
Light- House  List. 
Port.  Geod. 
Conn,  des  Temps. 

Do. 
Spanish  Hyd.  Office. 

Do. 

Do. 
Nautical  Almanac. 

Spanish  Hyd.  Office. 

Do. 

Do. 

Do. 
Capt.  Nares,  R.  N. 
English  Light  List. 


COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS. 


Malaga 

Almeria 

Cape  de  Gata  . . 

Mazarron 

Cartagena 

Do 

Porman 

Santa  Pola  Bay 

Alicante 

Villajoyose 

Benidonne 

Altea 


Calpe.  ... 
5     Moray  va 

•5     Jarea 

0,     Denia  ... 


Cape  Cullera 

Valencia  ..  .. 

Do 


Columbretes  Islands. 

Oropesa 

Vinaroz 

Port  Alfaques 

Cape  Tortosa 

Tarragona 

Barcelona 

Palamos 

Cadaques  

Cape  Creux 


Light-house 

Monument 

Light-house 

do 

Arsenal  gate 

Escombrera  Islet . .  . . 

Light-house 

do 

Castle  of  La  Barbara 
Light-house 


36  42  39 
36  50  16 

36  43  00 

37  33  24 
37  35  50 
37  33  22 

37  34  32 

38  12  26 
38  20  47 

,  38  30  14 
Tower '  38  30  57 


Light-house 


38  33  41 


J.     Cape  Beam . . . 

b      Port  Vendres  . 


Church  tower 38  38  36 

Tower 38  40  51 

Cape  San  Antonio  light . .  i  38  48  6 

Castle 38  50  30 

Light-house j  39  11     7 

Astronomical  pier 1  39  27  10 

Mole-end  light 39  27     9 

Light-house ,  39  53  57 

do  '  40    4  53 

Mole-headlight '  40  27  48 

Baiia  light 40  ^^  35 

Light-house 40  43  24 

E.  mole  light I  41     6     o 

Old  mole -head  fight I  41  22   10 

Church '  41   51     o 

Clock  tower 42   17     8 

Light-house 42  19  10 


do I  42  30  59 

Fort  I"  anal  light 1  42  31   18 


4  25     7 

Spanish  Hyd.  Office 

2  28  10 

Do. 

2  II  20 

Light- House  List. 

I   15     6 

Spanish  Hyd.  Office 

0  59    9 

Do. 

0  57  58 

Do. 

0  40  21 

Do. 

0  30  38 

Do. 

0  28  34 

Do. 

0  13  31 

Do. 

0  10    6 

Do. 

0     2  43 

Do. 

Long.  E. 

0     2   52 

Do. 

0     9   17 

Do. 

0    12      2 

Do. 

0    6  40 

Do. 

Long.  W. 

0    12   50 

Do. 

0    19    14 

Do. 

0    18   51 

Light- House  List. 

Long.  E. 

0  41    23    ^ 

Spanish  Hyd.  Office. 

0     8  55 

Do. 

0  28  52 

Do. 

0  39  53 

Do. 

0  56  59 

Light- House  List. 

I   15     0 

Do. 

2  10  55 

Do. 

360 

Spanish  plan. 

3  16  25 

French  survey. 

3  18  59 

Light- House  List. 

3     7  29 

Conn,  des  Temps. 

3    6  49  , 

Do. 

Page  556]  TABLE  49. 

MARITIME  POSITIONS. 
COASTS  or  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


B 
ft 


Places. 


e 


Port  Nouvelle  . 

Cette 

Aigues  Mortes. 
Planier  Rock  .. 
Marseilles  .. 

Ciotat  

Toulon  

Hyeres  Islands 

Cannes  

Antibes 

Nice 

Villa  Franche.. 
Do 


Iviza 

Cabrera  Island 

Palma  (Majorca) 

Port  Mahon  (Minorca). 


Cape  Spartivento 

Cape  Sandalo 

Porte  Conte 

Port  Torres 

Cape  Testa 

Razzoli  Island  . .. 

Caprera  Island 

Cape  Figari 

Cape  Tavolara. .. 
Cape  Bellavista  . 
Cape  Carbonera.. 
Cagliari 


Bonifacio  . 

Ajaccio , 

Corti 

Calvi 

Cape  Corso 

Bastia 

Porto  Vecchio 


Cape  Melle. 
Genoa  

Spezzia 

Florence . 
Leghorn  


Capraia  Island 

Elba  I.,  Porto  Longone. 
Pianosa  Island 


Exact  locations. 


W.  jetty  light 

Light,  St.  Louis  mole 

N.  W.  mole-head  light  . . 

Light-house 

New  observatory 

Berouard  mole  light  . 

Arsenal  clock-tower 

Light-house 

, do , 

Garoupe  light 

St.  Francois  tower 

Mole-head  light 

Cape  Ferret  light 


Citadel  flag-staff  .. . 
Port  Cabrera  Castle 

Mole  light 

Light-house 


.do 


Light  on  San  Pietro  Island 

Cape  Caccia  light 

Light-house 

do 

do 

Galera  Point 

Signal  station .    

Light-house 

do  

Cavoli  Island  light 

Cathedral 


Mt.  Pertusato  light  . . 

Cathedral  tower 

Church  tower 

Cathedral  tower 

Giraglia  Island  light. 
Santa  Maria  tower  . . 
Chiape  Point  light.  .. 


Lat.  N. 


43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 
43 


o  51 

23  48 
32  10 

II  57 
18  22 
10  21 


17 
3 


32  50 

33  51 


58 
58 
40  30 


Africa  Rock 

Monte  Christo  Islet 

Giglio  I.,  Port  Giglio.. . 

Civita  Vecchia 

Rome 

Gaeta 

Ponza  Islet 


Light-house 

San  Benigno  light 

Fort  Santa  Maria  light.. . 

Observatory 

Light  on  S.  end  of  Curved 

breakwater. 

Cape  Ferrajone  light 

Fort  Forcado  light 

Light  on  battery,  W.  side 

of  fort. 
Light-house 


38  54  21 

39  7  o 

39  33  39 
39  52  o 

38  52  34 

39  8  43 

40  33  50 

40  50  ID 

41  14  40 

41  18  25 

41  14  15 
40  59  52 

40  55  o 
39  55  45 
39  5  15 
39  13    5 

41  22  10 

41  54  59 

42  18  14 

42  34  36 

43  I  45 

42  41  30 

41  35  45 

43  57  18 

44  24  17 
44  4  o 
43  46  4 
43  32  33 

43     2  56 

42  45  14 
42  35  18 


Long.  E. 


Naples  

Do 

Capri  Island 

Lipari  Island 

Ustica  Island 

Faro  of  Messina 

Milazzo , 

Palermo 

Do 

Trapani 


Summit 

Mole-head  light | 

Light  S.  end  of  breakwater! 

Observatory I 

Orlando  tower ; 

Light  on  end  of  jetty,  in 
battery. 

Observatory 

Light  on  elbow  of  mole 

Carena  Point  light 

St.  Angelo  Chapel 

Fort  Falconara 

Capo  cli  Faro  light 

Mole-head  light 

Observatory 

Light  on  mole  head  ... 
Palumbo  Rock  light  . . . 


3  57 
42    6 

8  20 

13  49 

23  43 

5  36  41 

5  56    5 

6  837 
o  52 
8     I 

16  46 

18  41 

19  40 


3 
3 
4 
5 
5 


7 
7 
7 
T 
7 


1  26  27 

2  57  40 
2  38  II 
4  21     o 

8  51     8 

8  13  57 
8  10  o 
8  24  30 
8  50 
20  30 
29  40 
39  7 
44  20 

43  25 

32  35 

7  33 


Authorities. 


9  II    14 

8  44  19 

9  9     4 

8  45  42 

9  24  9 
9  27  13 
9  21  59 

8  10    9 

8  54  20 

9  50  48 
II  15  22 
10  17  22 

9  50  50 

10  24  33 

10  5  57 


42  21  28 

10  3  49 

42  20  15 

10  18  39 

42  21  35 

10  55  15 

42  5  25 

II  47  6 

41  53  54 

12  28  40 

41  12  25 

13  34  39 

40  53  40 

12  57  34 

40  51  46 

14  14  44 

40  50  15 
40  32  8 
38  29  18 

14  15  32 
14  II  46 

14  56  6 

38  43  17 

38  16  2 

38  13  2 
38  6  44 

13  II  10 
15  38  58 
15  14  48 
13  21  16 

38  7  53 

13  22  4 

38  0  39 

12  29  8 

Conn,  des  Temps. 

Do. 
Light- House  List. 

Do. 
Conn,  des  Temps. 

Do. 

Do. 
Light-House  List. 

Do. 
Conn,  des  Temps. 

Do. 
Light-House  List. 
Conn,  des  Temps. 

Do. 

Spanish  survey. 
Light- House  List. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Italian  Hyd.  Office. 
Light-House  List. 

Do. 

Do. 
French  Survey. 

Conn,  des  Temps. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 

Do. 
Italian  Hyd.  Office. 
Light-House  List. 
Nautical  Almanac. 
Light- House  List. 

Do. 
Do. 

Do. 

Do. 
Conn,  des  Temps. 
Light- House  List. 

Do.. 
Nautical  Almanac. 
French  survey. 
Light- House  List. 

Italian  Hyd.  Office. 
Light- House  List. 

Do. 
French  survey. 
Capt.  Smyth,  R.  N. 
Light-House  List. 
Comdr.  Nares,  R.  N. 
Nautical  Almanac. 
Light- House  List. 

Do. 


TABLE  49.  [Page  557 

MARITIME  POSITIONS. 
COASTS  OF  THE  MEDITERRANEAN,  ARRIATIC,  AND  BLACK  SEAS— Continued. 


C4 

O 

o 


Places. 


Maritime  Island 

IMarsala 

Girgenti 


Gozo  Island 

-Malta  I.,Valetta  Harbor. 

Linosa  Island  

Lampedusa  Island 

Cape  Fassero 

Syracuse  

Augusta  Port 

Catania 

Cape  Taormina 

Messina 

Cape  Peloro 

Cape  Spartivento 

Cape  Colonne 

Cotrone 

Taranto  

Gallipoli 

Cape  Sta.  Maria  de  Leuca 

Cape  Otranto 

Port  Otranto 

Brindisi,  Castello  Island. 

Bari 

Viesti 

Manfredonia 

Tremiti  Islands 

Ancona 

Malamocco 

Venice 


Exact  locations. 


,  point. 


Grado 

Monfalcone 

Trieste 

Do 

Capo  d'Istria , 

Isola  

Pirano 

Salvore  Point 

Citta  Nuova 

Parenzo 

Rovigno 

POLA 

Promontore  Point 

Nera  Point 

Fiume  (time-ball) 

Porto  Re 

Veglia 

Prestenizza  Point 

Cherso 

Galiola  Rock 

Unie  Island 

Lussin  Piccolo 

St.  Pietro  di  Nembo  I  . . 

Gruizza  Rock 

Zengg  

Terstenik  Rock 

Carlopago . 

Zara 

Blanche  Point 
Zara  Vecchia 
Port  Tajer. 
Lucrietta  Rock 
Sebenico 
Rogosnizza  Port 
Zirona  Grande  Island.. 
Trani 


Light  on  S.  \V 

E.  mole  light , 

Port  Empedoche,  extrem- 
ity of  pier. 
Light  on  N.  W.  point..  .. 

Spencer's  Monument 

Landing  Cove 

Carallo  Bianco  light 

Light-house 

Maniace  Castle  light 

Torre  d'Avola  light 

Sciari  Biscari  light 

Semaphore 

San  Ranieri  tower 

Light-house  

, do   

, do 

Mole-head  light 

Cape  St.  Vito  light 

St.  Andrea  light 

Light-house 

do  

Castle 

Fort  a  Mare  light 

St.  Catalolo  light 

Light  on  Sta.  Croce  Rock. 

Light-house 

Caprara  Island  light 

Monte  Cappucini  liglit  ..  . 

Rocchetta  .^lole  light 

Tower  of  St.  Mark 


Lat.  N. 


37  57  13 
Z1  47  10 
37  16  58 

36  4  12 

35  53  o 
35  51  50 

35  29  40 

36  41  10 

37  3  4 
37  12  39 
37  29  35 
37  50  25 

16 


38 

)7  55 


39 
39 


29 
29 
38 


I 

4 

40  24  40 
40  2  48 

39  47  43 

40  6  23 
40  9  6 

40  39  21 

41  8  19 

53 


41 
41 

42 
43 


17 

37  38 

8  JO 


Church  tower 

do  

Observ'y  Naut.  Academy. 

Theresa  Mole  light 

Cathedral  tower 

Church  tower 

Cathedral  tower 

Light-house 

Church  tower . 

Cathedral  tower 

St.  Eufemia  tower 

N.  cupola  of  observatory  . 

Poi  er  Rock  light 

Light-house 

Cathedral  tower . 

Castle 

Mole  head 

Light-house 

Kimen  Point  light 


il  15 
45  20  30 
45  25  58 


Light-house 

Netak  Point  light 

Sta    Maria  Church 

Health  office 

Light-house 

Mole  head 

Light-house ; 

do  

Church  tower ! 

Ligh  -house ' 

Church  tower 

Lestrice  Island  light ' 

Light-house 

Mount  Tartaro 

Mulo  Rock  light 

St.  Cieorge  Church  tower. 
Cathedral  tower 


45  40  37 
45  48  Z2, 
45  38  51 
45  38  59 
45  32  56 
45  32  26 
45  31  48 
45  29  26 

18  29 

13  45 
5  2 
44  51  49 
4.4  45  31 
44  57  25 

19  36 

16  43 
I  30 
7  12 
44  57  36 
44  43  43 
44  37  18 
44  31  56 
44  27  42 
44  24  42 
44  59  30 
44  40  7 
44  31  30 
44  7  5 
44  9  8 

43  56  16 
43  51  18 
43  37  36 
43  45  8 
43  31  o 
43  27  o 
43  31  2 


45 
45 
45 


45 
45 
45 

45 


Long.  E. 


2   2  55 

2  25  59 

3  31  32 


4  13  16 
4  31  o 

52  9 

35  39 

8  57 

17  37 


IT,    20 


5  19 


5  18 


34  19 
3858 

3  31 
12  9 

8  7 
12  23 

56  37 
8  22  17 

8  30  37 
8  28  45 
8  o  27 
50  52 
"  il 
55  34 
31  54 

31  19 
19  9 


20  29 


32  10 
46  o 
45  27 
43  53 
39  35 

34  12 
29  34 

33  37 

35  39 
37  56 
50  46 

53  33 

8  42 

26  41 

34  II 

34  36 
16  30 

23  30 
10  36 

14  6 

28  26 

32,   28 

34  6 

53  34 

34  42 

4  24 


14 

49 


26  21 
12  6 
5  34  24 
58  7 
55  12 
851 
15  9 


Authorities. 


Light- House  List. 
Do. 
Do. 

Do. 
English  survey. 
Capt.  Smyth,  R.  N. 
Light- House  List. 

Do. 

Do. 

Do. 

Do. 
Comdr.  Wharton,  R.  N. 
Italian  Hyd.  Office. 

Do. 
Light- House  List. 

Do. 

Do. 
Italian  Hyd.  Office. 
Light- House  List. 
Italian  Hyd.  Office. 
Light- House  List. 
Capt.  Smyth,  R.  N. 
Light- House  List. 
Italian  Hyd.  Office. 

Do. 

Do. 
Light-House  List. 
Italian  Hyd.  Office. 
Light-House  List. 
Italian  Hyd.  Office. 

Austrian  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 
Austrian  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 


Page  558]  TABLE  49. 

MARITIME  POSITIONS. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


el 

O 


fa 


Places. 


Port  Spalatro 

Solta  I.,  Port  Olivetto  .. 

Spalato  Passage 

Makarska , 

Porno  Rock 

St.  Andrea  Rock 

Lissa  Island 

Pakonjidol  Rock 

Lessina  Island 

Do 

Sabionello  Peninsula 

Sorelle  Rocks 

Curzola  Island 

Curzola    Island,    Porto 
Valle  Grande. 

Lagostini  Island 

Lagosta  Island   

Cazza  Island   

Pelagosa  Rock 

Meleda  Island 

Olipa  Rock 

Pettini  di  Ragusa  Rocks. 

Bobara  Rock 

Molonta  Peninsula 

Ostro  Point 

Cattaro 

Budua  

Katie  Rock 


Antivari 

Dulcigno 

Cape  Rodoni  

Cape  Pali 

Durazzo 

Cape  Laghi 

Skumbi  River 

Semeny  River 

Vojazza  River 

Sassena  Island  

Avlona 

Cape  Linguelta 

Mount  Cica , 

Port  Palermo 

Cape  Kiefali 

Fano  Island 

Port  Pagonia 

Port  Gomenitza 

Port  Parga 


Port  St.  Spiridione 

Corfu 

Paxo  Island 

Prevesa 

Port  Drepano 

Port  Vliko 

Port  Vathi 

Port  Argostoli 

Patras 

Katakolo  Bay 

Zante 

Strovathi,  or  Strivali  Is  . 

Proti  Passage 

Narasin  Bay 

Mothoni 

Koroni  Anchorage 

Petalidi  Bay 

Candia  Island,  Port  Suda 
CandiaI.,MegaloKastron 


Exact  locations. 


Lat.  N. 


43 
43 


Cathedral  tower . . . 
St.  Nicholas  tower 

Cape  Ipeo  light '  43 

Church  tower '. I  43 

Centre .1  43 

Summit '  43 

Hoste  Rock  light ''  43 

Liglit-house 43 

43 
43 


Port  Gelsa  light 

S^.  Giorgio  Point  light. .. 
Cape  Gomera  light |  43 


30  26 

23  55 
19  12 
17  46 

5 
I 

4 

9 

9 

7 
2 


Light-house 

Porto  Bema  mole  head. 

Church  tower 


Glarat  Rock 

St.  George  Chapel 

Light-house , 

do , 

Port  Palazzo  Ruin 

Light-house , 

do   

Summit 

do 

Light-house , 

Health  office 

Mole-head  light 

St.  Domenica  Chapel  . , 

Point  Valovica  summit 

\V.  wind-mill 

Guard-house 

do 

N.  Pyramid 

Ruin 

Pyramid  at  mouth 

do  

do  

Pyramid  summit 

Minaret 

Extreme 

Pyramid 

do   

....  do  

Point  Kastri  light 

Ruin 

Well  Dogana 

Madonna  Island 


42 
42 
42 


28 
43 
34 
25 
50 
30 
48 

57  42 
54  19 

57  37 


42  45  54 
42  45  5 
42  45  6 
42  23  28 
42  47    6 

42  45  30 
42  39  o 
42  35  8 
42  27  4 
42  23  45 
42  25  30 
42  16  42 

42  II  43 


42 
41 


41 
41 

41 


3  56 

55  47 

41  35    8 

41  23  31 

19  54 

844 

2  12 

40  47  3 
40  36  14 
40  29  47 
40  28  6 
40  25  17 
40  12  o 
40  2  57 
39  54  29 
39  51  40 
39  39  27 
39  29  50 
39  16  32 


Convent 39 

Flag- staff  bastion 39 

Madonna  Island  light ...      39 

Fort  Nuovo  minaret    38 

Observation  island 38 

Custom-house '  38 

Lazaretto  light 38 

St.  Theodoro  light '  38 

Castle 38 

Light  in  jetty ;  ;^J 

Mole  light '  37 

Stamphani  Island  light  ..    37 

Marathon  Point !  37 

-      ■         '  -  36 

Round  tower  . 

Mole    , 

Petalidi  Point 
Light-house  . . 
Mole  light 35 


36 

36 
35 


39  54 

37  7 
II  30 

56  30 
47  25 

40  40 
22  4 
II  36 

14  47 
39  10 
47  10 

15  12 
338 

54  32 
4835 
47  50 

57  16 

27  55 
20  ^o 


Long.  E. 


6  26  34 
6  12  16 

6  24  30 

7  I  36 
5  27  30 

5  45  29 

6  12  24 
6  27  19 

6  41  52 

7  12  o 
7  o  24 
7  12  43 
6  51  32 
6  43  7 


855 
51  45 
29  30 
15  43 
22  51 
46  48 

3  o 
8  10  49 

8  25  36 

8  31  23 
8  46  12 

8  50  31 

8  56  25 


9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
20 
20 


12 


41 

29 

27  4 

24  54 

25  41 

26  47 
26  30 
22  II 
19  14 
17  44 
29  42 

17  45 
38  33 
47  53 

54  55 
26  50 

7  12 
17  9 


20  24  55 

19  43  9 

19  56  30 

20  12  20 
20  45  40 
20  44  16 
20  42  44 

20  43  37 

20  29  30 

21  44  47 
21  20  o 

20  55  21 

21  I  12 
21  34  35 
21  41  59 
21  42  36 
21  58  I 

21  56  33 

24    9  30 

25 


Authorities. 


9  35 


Austrian  Hyd.  Office. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 
Mr.  Jarrad,  R.  N, 
Mr.  Christian,  R.  N. 
Lieut.  Dawson,  R.  N. 

Mr.  Gray,  R.  N. 
Comdr.  Mansell,  R.  N. 
Light-House  List. 
Comdr.  Mansell,  R.  N . 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 

Do. 

Do. 
Capt.  Mansell,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 

Do. 


TABLE  49.  [Page  559 

MARITIME  POSITIONS. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


o 


Places. 


fa 


fa 
s 


Kandcliusa  Island 

Stampali  Island,  Malte- 
zana  Port. 

Christiana  Islands 

Milo  Island 

Siphanto  Island 

Naxos  Island,  Xaxia 

Paros  Island,  Port  Trio. 
Paros  I.,  Port  Naussa  .. 

Syra 

Sermo  Island 

Thermia  Island 

Jura  Island 

Port  St.  Nikolo 

St.  Nikalao  Island 

Andros  I.,  Port  Gavrion 

leraka  

Port  Kheli 

Poros  Harbor 

.Egina 

Piraeus 

Athens  

Cape  Colonna 

Port  Raphti 

Petali  Island 

Euripo 

Skiathos  Island 

Salonika 

Port  Baklar 

Lemnos  Island 

Port  Moudros 

Strati  Island 

Mityleni  I.,  Port  Sigri  .. 
Mityleni  I.,  Mityleni  ... 
Mityleni  I.,  Port  lero  .. 

Psara  Island 

Khios  Island,  Port  Scio  . 

Samos  Strait 

Port  Isene 

Kos 

Marniorice  Harbor 

Makry  Harbor 

Rhodes  Port 

Port  Lindo 


Exact  locations. 


Summit , 

Agios  loanes 


N.  point 

Summit,  Mt.  St.  Elias  . . 

Cape  Kondo 

Gate  on  Bacchus  Island  . 

Trio  Point 

St.  Yanni  Church 

Mole  light 

Amyno  Point 

Ruins  of  Cythnus 

North  point 

Light-house 

Port  Mandri 

St.  Nikalaos 

Acropolis 

Custom-house 

Lazaretto 

Temple  of  Venus 

Custom-house 

Observatory 

Extreme 

Statue  Island 

Trago  Island  peak 

Bridge 

Mount  Stavros 

S.  bastion 

Cape  Xeros 

Kastro  Castle . 

Sangrada  Point 

St.  Strati  Church 

Fort 

Light  on  Mityleni  Point 

Sidero  Islet 

Fort  (approx. ) 

Fort 

Chapel  Islet 

Tower 

Landing-place 

Adassi  Point 

Kasil  Island 

Arab's  Tower 

Tower 


Lat.  N. 


36  29  55 

36  34  25 

36  15  20 
36  40  27 
36  54  o 
6 


o 


37 
37 
37    « 
37  26 

37     7 


32 
I 

38 
o 

36 

55 
o 


Dardanelles Hellas  Point  light 

Gallipoli Light-house 

Bosphorus Tofana  Point  light . . . 

Scutari Leander  Tower  light 

Constantinople   Seraglio  Point  light . . 

Do St.  Sophia  Mosque  . . 

Cape  Karabournon Light-house 


37  25 
37  38 
37  39  28 
37  44    o 
37  52 

36  47 

37  19  15 
37  29  16 
37  44  51 
37  56  10 
37  58  20 
37  38  45 
37  52  48 

"  I  28 
27  23 
10  48 
40  37  28 
40  32  40 
39  52  10 
39  50  52 
39  31  58 
12  24 
6 
3 


38 
38 
39 


52 
5 


39 
39 
39 


Yuiada  Road  . 

Burghaz  

Varna 

Kusterjeh  . 

Danube  River 
Fidoni  Island  . 

Odessa 

Dnieper  Bay  . 
Sevastopol  — 
Balaklava  Bay 

Kertch 

Berdiansk 

Saukhoum  

Batoum 


10 
20 
38  32    o 
38  22  40 

37  41  40 
37  16  33 
36  53  36 
36  47  58 
36  39  33 
36  26  36 

36    5  53 


40    2  22 

40  24  18 

41  I  20 
41  I  2 
41  o  30 
41     o  16 

41  19  15 


Fort  Tersana 

Light-liouse 

Erlar  Battery 

Cape  Kusterjeh  light 

Salina  light 

Light-house 

Observatory    . . 

Fort  Nikolaeo 

E.  light-house 

Hospital 

Light-house  

Breakwater  light 

Light-house 

, do 


41 

42 

43 
44 

45 
45 


52 
28 


12  o 
10  20 


9 
16 


46  28 

46  36 

44  36 

44 

45 
46  45 


Long.  E. 


42 
41 


3& 

17 

36 

23 

36  55 

29  50 

21  3 

25 
o 

o 


26  59  25 
26  24  28 

25  13  o 

24  23  15 

24  42  30 

25  23  o 

25  14  21 

25  14  8 
24  58  6 
24.32  23 
24  23  35 
24  44  32 
24  19  40 
24  4  12 
24  44  40 
23 
23 


5  40 

_  9  53 

23  28  27 

23  25  38 
23  38  40 

23  43  55 

24  2  15 


24 

24 
2 


23   27 


16  42 
35  52 


o 
20 


22  58 
26  45 
25  3 
25  14  14 

24  59  13 

25  51  20 

26  34  50 

26  31  39 

25  35 
9 
2 

27  36  55 

27  19  15 

"  18 

6 


26 
27 


o 

15 
27 


28 
29 


5 
13 


28  16  14 

28  8  10 

26  10  50 
26  39  24 

29  I  o 
29  o  45 
29  o  55 
28  58  59 
28  42  o 


58 
39 


27  58  45 
27  35  35 

27  57  16 

28  39  10 

29  40  36 

30  14  23 

30  45 

31  32 
33  36 
33  36  25 
36  28  28 

36  47  5 

40  55  10 

41  36  15 


34 
38 
26 


Authorities. 


English  survey. 
Capt.  Spratt,  R.  N. 

Capt.  Graves,  R.  N. 
Conn,  des  Temps. 
Com.  Brock,  R.  N. 
Capt.  Graves,  R.  N. 

Do. 

Do. 
Light- House  List. 
Com.  Brock,  R.  N. 

Do. 

Do. 
Light- House  List. 
Mr.  Elson,  R.  N. 
Capt.  Graves,  R.  N. 

Do. 
English  survey. 

Do. 
Capt.  Graves,  R.  N. 
English  survey. 
Nautical  Almanac. 
English  survey. 
Capt.  Beaufort,  R.  N. 
Com.  Brock,  R.  N. 
Capt.  Mansell,  R.  N. 
Lieut.  Wilkinson,  R.  N. 
Capt.  Graves,  R.  N. 
Capt.  Spratt,  R.  N. 
Capt.  Copeland,  R.  N. 

Do. 

Do. 
English  survey. 
Light- House  List. 
Capt.  Copeland,  R.  N. 

Do. 
English  survey. 

Do. 
Com.  Graves,  R.  N. 

Do. 
English  survey. 

Do. 

Do. 

Do. 

Light- House  List. 

Do. 

Do. 

Do. 

Do. 
Admiralty. 
Light- House  List. 

Russian  survey. 
Light-House  List. 
Com.  Spratt.  R.  N. 
Light- House  List. 

Do. 

Do. 
Nautical  Almanac. 
Russian  survey. 
Light-House  List. 
Com.  Spratt,  R.  N. 
Light-House  List. 

Do. 

Do. 

Do. 


Page  560]  TABLE  49. 

MARITIME  POSITIONS. 
COASTS  OP  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


O 


a 


a 


Places. 


a 
s 
H 


Trebizond 

Sinope 

Bender  Erekli 

Marmora  Island 

Artaki  Bay 

Tenedos  Island 

Port  Ajano 

Port  Ali-Agha 

Smyrna 

Vourlah 

Sighajik  Harbor 

Budrum   

Adalia 

Alexandretta 

Latakiyah 

Tripoli  Roadstead 

Ruad  Island 

Beirut 

Saida  (ancient  Sidon) . 
Sur  (ancient  Tyre)  . . . 

Acre 

Haifa 


Exact  locations. 


Cyprus  I.,  Famagoosta. 
Cyprus  I.,  Limasol.  ... 
Cyprus  I.,  Lamaka. 


Port  Said 

River  Nile  .. 

Do 

Aboukir  Bay 
Alexandria  . . 


Light-house 

do 

Round  tower 

Light  off  E.  point 

Zeitijn  Adasi  Islet. 

Ponente  point  light 

Nikolo  Rock  .    

W.  point  of  entrance.  . . . 
English  consul's  flag-staff 

Custom-house 

Beacon  on  islet 

Kalessi  Point   

Light-house 

do 

do 

Tower  of  Lions 

Minaret 

Tower,  light-house 

S.  end  of  Jezireh  Island  . . 

N.fort 

Manara 

Minaret 


Lat.  N. 


41  I     o 

42  I  18 
41  18  3 
40  37  40 
40  23  30 

39  50  o 
39  I  21 
38  50  10 
38  25  40 
38  21  48 
38  12  21 

37  I  52 
36  52    o 

36  35  30 
35  30 
34  27 
34  51  42 
33  54  10 
33  34  25 
33  16  45 
32  55  27 
32  49  12 


o 


N. bastion 35     7     5 

Battery j  34  4o     o 

Light-house 34  55     o 


Ben  Ghazi   

Tripoli  Harbor  . 

Sphax  

Alehediah 

Monastir 

Hammamet  Bay 

Kalibia  Road 

Cape  Bon  

Tunis 


Castle 

Lazaretto  Pier 


Mole  battery 

Sidi  Jubber 

Burj  el  Kelb  Battery 

Castle  flag- staff 

Landing-place 

Light-house 

Goletta  light 


Cape  Farina 

Benzert  Road 

Galita  Island 

Bona    

Stora Singe  Island  light 

Cape  Bongaroni Light-house 

Cape  Carbon do  

Algiers i  I>ight-house  near  admiralty 


Extreme 

S.  E.  angle  of  fort 
Monte  Guardia  . . 
Fort  Genois  light 


32    6  51 

32  54  22 


34  43 

35  30 


35 
36 


Cape  Tenez 


Oran , 

Habibas  Island 
Zafarin  Islands . 
Alboran  Island 

Ceuta 

Tangier   

Cape  Spartel . . . 


Light-house 


Light-house  on  N.  mole.. 

Light-house 

S.  point  Isabel  Segunda  I. 

Light-house 

do  

Casbah  tower 

Light-house 


45 
23 

36  49  45 

37  4  45 

36  48  36 

37  10  42 
37  17  3 
37  31  16 
36  57  5 

36  54  29 

37  5  17 
36  46  45 
36  47  23 
3633  8 

35  42  56 
35  43  22 
35  10  50 
35  58  o 
35  53  44 
35  47  10 
35  47  14 


Long.  E. 


Highlight-house 31  1 5  45 

Damietta  Mouth 31  31  30 

Rosetta  Mouth  light 31  29  30 

Nelson  Island  peak [  31  21   23 

Eunostos  Point  light 31  11  43 


52 
24 
24 
20 


39  46  25 

35  13  30 
31  26  34 

27  45  30 
27  47  30 

25  58  45 

26  47  57 

26  57  20 

27  9  10 
26  47    o 

26  47  32 

27  27  35 

30  45  30 

36  10  20 

35  46  30 
35  49  23 
35  51  15 
35  30  35 
35  21  36 
35  II  26 
35 
35 


Authorities. 


4  24 
o     I 


33  58  o 
33  2  36 
33  39    o 

32  18  S3 
31  51  8 
30  19  8 
30  6  o 
29  51  40 

20  2  40 
13  "   15 

10  46  II 

"  5  15 
10  50  42 

10  37  10 

11  62 

II  3  15 
10  18  37 


10 


17  30 

52  55 
56  12 

48  13 

54  29 

29  54 

7  40 

3  30 
21  49 

Long.  W. 

0  37    21 

1  6  33 

2  26  o 
310 
5  16  42 
5  48  40 

5  55  41 


9 

8 

7 
6 
6 
5 
3 
I 


Light- House  List. 

Do. 
Com.  Spratt,  R.N. 
Light- House  List. 
Comdr.  Sutton,  R.  N. 
Light- House  List. 
Capt.  Spratt,  R.  N. 

Do. 
Capt.  Copeland,  R.  N. 
Comdr.  Graves,  R.  N. 
Lieut.  Graves,  R.  N. 
Capt.  Spratt,  R.  N. 
Light-House  List. 

Do. 

Do. 
Capt.  Mansell,  R.  N.    . 
English  survey. 
Light-House  List. 
Capt.  Mansell,  R.  N. 

Do. 

Do. 

Do. 

Com.  Millard,  R.  N. 
Lieut.  Browne,  R.  N. 
Light- House  List. 

Do. 
Do. 
Do. 

Capt.  Mansell,  R,  N. 
Light- House  List. 

Capt.  Spratt,  R.  N. 
Do. 

Com.  Wilkinson,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 

Do. 

Adm.  Mouchez,  Fr.  N. 
Capt.  Nares,  R.  N. 

Do. 
Light- House  List. 

Do. 

Do. 

Do. 
Adm.  Mouchez,  Fr.  N. 
Light-House  I-ist. 

Do. 
Do. 

.Spanish  survey. 
Light-House  List. 

Do. 
French  survey. 
Light- House  List. 


i 


WEST  COAST  OP  APRICA. 


El  Araish 

Sali 

Cape  Dar-el-Beida 


S.  point  of  entrance 

Fort 

Extreme 


35  12  50 
34  4  10 
33  38    o 


6    9  13 

6  48    o 

7  35  39 


Capt.  Arlett,  R.  N. 
German  survey. 
Capt.  Arlett,  R.  N. 


TABLE  49. 
MARITIME  POSITIONS. 
WEST  COAST  OF  AFRICA— Continued. 


[Page  561 


o 
O 


Places. 


e 


e 

X 


Cape  Blanco,  North  .. 

.Mogador  Harbor 

Cape  Chir 

Cape  Noun 

Cape  J uhy 

Cape  Ijoj  ador 

Penha  Grande  

Ouro  River  entrance.. 

Pedra  de  Galha 

Cape  Ulanco,  South  .. 

Portendlk 

St.  Louis 

Ahnadie  Point 

Cape  Verde 

Port  I  )akar 

Cape  Manoel 

Goree  Island 

Bird  Island 

Bathurst 

Carabane 

Nunez  River 


Ponga  River  entrance 


Isles  de  Los 


Matacong  Island  . . 

Scarcies  River 

Sierra  Leone 

Do    

Sherbro  Island . 

Sherliro  River 

Gallinas  River 

Cape  Mount 

Cape  Mesurado  . . . 

Monrovia 

Marshall 

Grand  Bassa 

Cestos 

Singwin  River 

Sinon 

Cape  Palmas 

Tabou  River  

Axim  Bay 

Cape  Three  Points 

Dix  Cove  

Tacorady  Bay 

Chania  15ay 

E\  Mina  Bay 

Cape  Coast  Castle  . 
Accra 


Volla  River  entrance  . 
I  .agos 

Benin  River  entrance  . 

Brass  River 

Calebar  River  (New) . 

Opobo  River 

(^)uaebo  River 

Calebar  River  (Old)  .. 

Fernando  Po  Island  . . 

San  Bento  River 

Prince's  Island 


St.  Thomas  Island 


Exact  locations. 


Extreme 

English  consul's  house.. 

Extreme 

, do   

do  

do  


Lat.  N. 


Dumford  Point 


Extreme 

Village 

Light-house  ., 

do  

do 

do  

do 

Fort 

Flag-staff 

do  

Light-house 

Sand  Island 

Observation  point 

Head  of  bight,  N.  side  of 
Cramford  Island. 

House 

W.  end  of  Yellaboi  Island. 

Light  on  cape 

N.  battery 

N.  island 

Manna  Point 

W.  elbow  of  Kamasoun  I . 

W.  peak  .■ 

Light-house 

Government  house 

Agent's  house    

do 

Factory 

Sangvvin  Point 

Bloobarra  Point 

Light-house 

Tabou  Point   

P'ort  St.  Anthony 

Light-house 

Fort 

Tacorady  Point 

Dutch  Fort 

Fort  St.  George 

N.  E.  bastion 

Light-house 

Dolben's  Point 

English  Church 

N.  point 

Entrance  (approx. ) 

Rough  Corner 

\V.  point  beacon  (approx.) 

Bluff  Point 

T  o  w  n  s  e  n  d    fl'a  g  -  s  t  a  ff 

(Dunketown). 

Light-house 

Joho  Point  (approx.) 

Diamond    Rocks,   centre 

of  largest. 
Fort  San  Sebastian 


33    8    o 

31  30  30 
30  38    o 

28  45     o 

27  57 

7 

7 


Long.  W. 


50 

57 
6 

3 
12  37 


36 


50 
8 


26 
25 

23 
22 

20  46  27 

"   1845 
o 

45 

43  30 
40  30 

3850 

39  55 

39  45 
28    o 

35    o 
o  36 

o    3 


37 
15 


27  24 


9  16 

857 
8  30 


10 

5 
o 


Anno  Bon  Island !  Turtle  Islet   . . 

Cape  Lopez ;  Extreme 

Mayumba  Bay Matooii  Point 

36    H 


7 
7 
7 
6 
6 
6 
6 

5 
5 
5 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 

5 
6 

5 
4 
4 
4 
4 
4 


29  57 
40  36 

22  45 
o    8 

44  30 
19    o 


19 
8 


54  8 
26  25 
12  42 

59  15 

22  10 

24  47 

52  18 

45    o 

47  45 

53 
I 


4 
6 

31 


o 
o 

48 

5 

50 


46  o 
28  21 
46  I 
16  40 

23  7 
27  o 
30  40 
56  24 


Lat.  S. 
I    24   18 
O  36     O 
3   22  42 


835  5 
9  43  30 
9  50    o 

120 


Authorities. 


2  52  30 
4  29     o 

4  50  44 

5  58    o 

6  48  II 

5  40 
2    o 

33  40 
32  6 
31  o 
25  28 
28  31 

24  30 
40  30 

35    o 

44    o 

42    o 

4  30 


48 

26  20 
18  25 


18 

14  30 
4  30 
31  55 
3845 
I  22  51 
o  50    o 

o  48  55 
o  22  45 

4  5 
34  45 

20  16 

2    5 
44  16 

21  30 

14  45 

5  45 


I  56  40 


I 
I 
I 
I 

o 


45  o 
38  o 
20  15 

13  40 
II  30 

Long.  E. 
O  41      o 

3  25  50 

5  3 

6  15 

7  7 
7  40 
7  59 


5 
o 

o 

o 

o 


8  20  46 


3  46   0 

8  47    0 

I  35    0 

9  39    0 

I  40  42 

7  27  56 

o  20  30         6  42  40 


5  38  12 

8  43  40 

10  30  51 


Capt.  Arlett,  R.  N. 

Do. 
English  survey. 
Capt.  Arlett,  R.  N. 

Do. 
Baron  Roussin. 

Do. 
Lieut.  Vidal,  R.  N. 
Baron  Roussin. 
Capt.  Belcher,  R.  N. 
English  survey. 
French  survey. 
Light- House  List. 

Do. 
Lieut.  Perrin,  Fr.  N. 
Light- House  List. 
Lieut.  Leclerc. 
Comdr.  Boteler,  R.  N, 
Capt.  Owen,  R.  N. 
Light-House  List. 
Capt.  Belcher,  R.  N. 

Do. 
Lieut.  Badgeley,  R.  N. 

Comdr.  Boteler,  R.  N. 

Do. 
Light- House  List. 
Lieut.  Bedford,  R.  N. 
Lieut.  Langdon,  R.  N, 

Do. 
Capt.  Vidal,  R.  N. 
Lieut.  Drake,  U.S.N. 
Light-House  List. 
Capt.  Vidal,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
English  survey. 
Light-House  List. 
English  survey. 

Do. 

Do. 
Lieut.  Halloran,  R.  N. 
English  survey. 
Light- House  List. 

Capt.  Glover,  R.  N. 

Do. 
Lieut.  Langdon,  R.  N. 

Do. 

Do. 
Macheachen. 
Downer. 
Lieut.  Langdon,  R.  N. 

Light-House  List. 
Lieut.  Langdon,  R.  N. 
Comdr.  Boteler,  R.  N. 

Do. 

Do. 
Capt.  Owen,  R.  N. 
Mr.  Ray,  R.  N. 


Page  662] 


TABLE  49. 

MARITIME  POSITIONS. 

WEST  COAST  OF  AFRICA— Continued. 


(4 

o 
O 


Places. 


0 


e 


Loango  Bay  

Black  Point  Bay 

Malemba  Bay 

Kabenda  Bay 

Congo  River  entrance.. 

Margate  Head 

St.  Paul  de  Loando 

Lobito  Point 

Benguela   

Elephant  Bay 

St.  Mary  Bay 

Little  Fish  Bay 

Port  Alexander 

Great  Fish  Bay 

Cape  Frio 

Wahvich  Bay 

Ichabo  Island 

Angra  Pequena 

Elizabeth  Bay 

Port  Nolloth 

Hondeklip  Bay 

Roodewal  Bay 

Saldanha  Bay  . 

Table  Bay 

Cape  Town 

Cape  of  Good  Hope 


Exact  locations. 


Indian  Point 

Sandy  Point  . 

Landing  Cove 

Kabenda  Point 

Shark  Point  

Summit 

Flag- staff,  Ft.  San  Miguel 

Extreme .. 

Fort 

Friar  Rocks 

Bay  Island 

Flag-staff 

Bateman  Point 

Tiger  Point 

Extreme . 

Pelican  Point  beacon 


Guano  Island 

S.  point  of  Possession  I. 
S.  beacon 


Constable  Hill 

Robben  Island  liglit. 

Observatory 

Light-house  .. 


Lat.  S. 


4 
4 
5 
5 
6 
6 


38  30 

49    o 

18  30 

33    o 

4  36 

31  50 

8  48  18 

12  20     o 

12  33  30 

13  12  30 
13  26  5 
15  II  50 

15  47  30 

16  30  o 
18  23  o 
22  S3  o 
26  17  o 
26  37  50 
26  58  30 

29  15  50 

30  18  33 
30  33  7 
33  7  51 
33  48  52 

33  56  3 

34  21  12 


Lonar.  E. 


45 

45 

8 

10 

15 

25  25 
13  6 
32  o 

26  10 

48  55 
36  o 

12  55 

52  40 

I  42  o 

I  57  12 
4  26  58 

4  57  20 

4  55  15 

5  12  22 
52  20 
16  20 


27  30 
I  21 

22  33 

28  40 

29  30 


Authorities. 


Mr.  Cunningham,  R.  N^ 
Comdr.  Hay,  R.  N. 

Do. 
Mr.  Ray,  R.  N. 
English  survey. 
Mr.  Luke,  R.  N. 
Capt.  Owen,  R.  H. 
Comdr.  Matson,  R.  N. 
Capt.  Owen,  R.  N. 
Comdr.  Matson,  R.  N. 
French  survey. 
Mr.  Southwick,  R.  N. 
Mr.  J.  Richards,  R.  N. 
Lieut.  Popham,  R.  N. 
English  survey. 
Lieut.  Bower,  R.  N. 
Sir  J.  Marshall,  R.  N. 

Do. 
Capt.  Owen,  R.  N. 
Lieut.  Archdeacon,  R.  N 

Do. 

Do. 

Do. 
Light- House  List. 
David  Gill. 
Light- 1  louse  List. 


EAST  COAST  OF  AFRICA  AND  THE  RED  SEA. 


es 

*m 

6 


e 
e 
e: 


Simon's  Bay 

Cape  Hangklip 

Quoin  Point 

Cape  Agulhas 

Port  Beaufort 

St.  Blaize  

Knysna  Harbor  ... 
Plettenberg  Bay  ... 

St.  Francis 

Cape  Recife 

Port  Elizabeth 

Bird  Islands 

Port  Alfred 

Waterloo  Bay 

Madagascar  Reef.. 

Cove  Rock  

East  London 

Cape  Morgan 

Hole-in-the-Wall.. 

Rame  Head 

Cape  Hermes 

Waterfall  Bluff.... 

Port  Natal 

Dumford  Point 

Cape  St.  Lucia . 

Cape  Vidal 

Delagoa  Bay 

Cape  Corrientes  .  .. 

Inhambane  Bay 

Cape  St.  Sebastian  . 

Bazaruto  Island 

Chuluwan  Island  .. 

Sofala  _    

Zambesi  River  __. 
Quillimane  River.. 

Quillimane 

Mazemba  River  ... 


Time-signal 

Extreme 

do 

Light-house 

Flag-staff 

Light-house 

Fountain  beacon 

Extreme  of  Seal  Point. 
Light-house 

do   

Lady  Donkin's  Monument 

Light-house 

Signal-staff 

Maitland  Signal  Hill... 
Centre 

do 

Light-house 

Extreme 


Extreme 
do 


Light-house 

Extreme 

do 

do     

Reuben  Point  light 

.Small  rock 

Barrow  Hill  light 

Extreme 

N.  point 

Liglit-liouse  . 

Fort  on  N.  side  of  entrance 

Kangoni  Mouth 

Light-house 

Town 

Entrance 


34 

II 

28 

34 

23 

48 

34 

46  45  1 

34  49 

46 

34  23  47  1 

34 

II 

10 

34 

4 

35 

34 

b 

20 

34 

12 

30 

34 

I 

44 

33 

57  43  1 

33 

50 

41 

33 

36 

9 

33 

28 

0 

33 

23 

10 

33 

5 

10 

33 

I 

45 

32 

42 

0 

32 

2 

30 

31 

48 

15 

31 

38 

6 

31 

26 

15 

29  52 

40 

29 

0 

12 

28 

32 

30 

28 

9 

36 

25 

58 

44 

24 

7 

30 

23 

45 

30 

22 

6 

0 

21 

SI 

0 

20 

38 

II 

20 

10 

42 

18 

52 

50 

18 

I 

24 

17 

5' 

50 

17 

15 

0 

18 

31 

40 

18 

50 

20 

19 

38 

17 

20 

0 

37 

20 

48 

40 

22 

9 

2b 

23 

0 
J 

38 

23 

25 

0 

24  50 

20 

25 

42 

12 

25 

37 

24 

26 

17 

21 

26 

54 

10 

27 

3 

0 

27 

20 

48 

27  49 

12 

27 

55 

2 

28 

22 

36 

29 

6 

40 

20 

21 

15 

29 

33 

16 

29 

48 

40 

31 

3 

50 

31 

51 

39 

32 

27 

39 

32 

38 

10 

32 

35 

52 

35 

30  33   1 

35 

10 

35 

32 

0 

35 

0  -> 

9 

34 

53 

35 

31- 

46 

0 

3^ 

II 

47 

30 

57 

24 

37 

I 

9 

38 

4 

0 

Capt.  Dayman,  R.  N. 

Do. 

Do. 
Sir  T.  Maclean 
Mr.  May,  R.  N. 
Capt.  Dayman,  R.  N. 
Mr.  Skead,  R.  N. 

Do. 
Light- House  List. 
Capt.  Dayman,  R.  N. 

Do. 

Do. 
Comdr.  Stanton,  R.  N. 
Lieut.  Archdeacon,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Owen,  R.  N. 

Do. 

Do. 
Mr.  Finlay. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 
Light-House  List. 
Capt.  Owen,  R.N. 
Lieut.  Skead,  R.  N. 
Capt.  Owen,  R.  N. 

Do. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  AFRICA  AND  THE  RED  SEA-ContJinued. 


[Page  563 


o 

o 


Places. 


*M 


es 
e 

■ 


« 

« 


Premeira  Islands  . 
Angoxa  Islands  ._ 
Mafamale  Island  _ 

Port  Mokamba 

Port  Mozambique - 

Do 

Cape  Cab.'ceira 

Port  Conducia 

Lurio  Bay 

Pemba  Bay 

Querimba  Islands. 

Numba  Island 

Cape  Delgado 

Msimbati 

Mikindini  Harbor 

Mgan  Mwania 

Lindi  River  

Mchinga  Bay 

Kiswere  Harbor.. 
Kilwa  Kisiwani ._ 
Monfia  Island. .,  _ 

Dar-Es-Salaam 

Bagamoyo 

Zanzibar 

Tanga  Bay  

Mombaza 

Port  Melinda 

Lamo  Bay 

Manda  Roads 

Port  Dumford 

Kisimayo  Bay 


Exact  locations. 


Brava 

Meurka  Anchorage 

Magadoxa 

Murat  Hill 

Ras  Hafun 

Cape  Guardafui  _.  .. 

Kal  Farun  Islet 

Abd-al-Kuri  Island 

Socotra  Island 

Ras  Antareh 

Meyet  Island 

Port  Berbereh 

Zeyla 

Ras  Sejan 


Hanfelah  Bay 

Disei  Island 

Musawwa'  Harbor. 

Khor  Nowarat 

Suakin 

Makawwa  Island  .. 
St.  John's  Island  _. 

Dffidalus  Shoal 

Kosair  Anchorage  . 

Brothers'  Island 

Safojah  Island 

Ashrafi  Island 

Ras  Gharib 

Zafarana 

Suez .. 

Tor 

Sherm  Yahar  .. 


Centre  of  Casuarina  I  .  _ 
Centre  of  Hurd  Island.. 

Centre 

Mokambo  Point 

St.  George  Island  light  . 

San  Sebastian  light 

Light-house 

Bar  Point 

Pando  Point 

N.  point 

Ibo  Island  light 

E.  point 

Extreme 

Ras  Matunda 

Kinizi 

Madjori  Rock 

Fort  flag-staff 

Observation  spot 

Rustmigi 

Fort 

Moresby  Point 

Flag-staff 

French  Mission 

English  consulate 

E.  side  of  Tanga  Island.. 

Castle 

Vasco  de  Gama's  Pillar.. 

Lamo  Castle 

E.  side  of  Manda  Toto  I. 

Foot  Point 

S.  point  of  Kisimayo  I. .. 

Well 

S.  point  of  town 

Tower 

Peak 

E.  extreme  of  Africa 

E.  point 

Centre 

N.  E.  point 

Tamarida,  mosque 

Extreme  of  rocky  point.. 

Centre . 

Light-house 

Mosque 

Summit 


Lat.  S. 


Sherm  Joobbah 

Sherm  Wejh |  Light-house 

Sherm  Hassejy !  Anchorage  . 

Yeir.bo | do 


Hanfelah  Point 

Village  Bay 

N.  point  of  entrance 

Shatireh  Islet 

Light-house 

S.  point 

Peak 

Light-house 

S.  W.  angle  of  fort 

Light-house 

N.  E.  summit 

Light-house  ..   _     . 

do 

do 

Telegraph  office 

Ruined  fort 

Entrance 

do 


6 
6 
6 

5 
4 

3 

2 

2 
I 
o 


0  /       /' 

17  6  30 
16  33  24 
16  20  30 
15  8  o 
15     2  12 

15  o  45 
14  58  20 

14  53    o 

13  23  40 
12  55  48 
12  20  o 
II  9  18 
10  41  18 
10  19  22 
10  16  31 
10  6  43 

9  59  30 

9  44  22 

9  25  36 

8  57  15 

7  38  10 

49  41 

26  10 

9  43 
4  45 
4  o 

12  48 
15  42 

13  35 
13  o 

22  35 
Lat.  N. 

1  6  48 

1  42  6 

2  I  48 
2  30  o 

10  26  30 

11  50  30 

12  26  o 

12  II  15 
12  39  O 
II  27  30 

II  13  O 

10  25  O 

11  22   O 

12  28  20 

14  44  O 

15  28  10 

15  37   12 

18  15  12 

19  7  o 

20  44  o 

23  36  20 

24  55  30 
26  6  24 
26  18  50 

26  45  45 

27  47  21 

28  20  52 

29  6  29 

29  57  54 
28  13  47 

27  35  45 
27  33  o 
26  13  o 

24  38  35 
24  5  15 


Long,  E. 


39  6  27 

39  49  57 

40  3  57 
40  36  12 
40  48  39 
40  44  51 
40  45  10 
40  40 
40  46 

40  33 
40  40 
40  43  21 

40  41  55 
40  26  34 
40  10  33 
40  2  14 
39  46  41 
39  47  7 
39  39  31 
39  30  42 
39  54  42 
39  17  5 

38  54  27 

39  "  " 
39  6 

39  43 

40  II 
40  56  21 

40  59  40 

41  54  15 

42  33   57 


55 

9 

21 


44  3  27 
44  53  49 
24  39 
7  o 
22  55 
16  45 
9  35 

52  25  35 

53  59  31 
49  35  40 
47  16  35 
44  57  24 
43  29  35 
43  17  35 


45 
46 

51 
51 

52 


40  52  o 

39  45  30 
39  27  23 
19  30 
19  9 


38 
37 
37 
36 
35  51 


15  30 
10  15 

30 

-> 


34  17 

34  50 
33  59  44 
33  42  27 
33  6  30 
32  39  40 

32  33   19 

33  36  56 

35  30  30 

35  32  30 

36  27  o 

17  45 
2  45 


37 
38 


Authorities. 


Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 
Light- House  List. 

Light-House  List. 
Capt.  Owen,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Comdr.  Gray,  R.  N, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Comdr.  Wharton,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Owen,  R.  N. 

Do. 

Do. 
Comdr.  Wharton,  R.  N. 
Capt.  Vidal,  R.  N. 
Comdr.  Wharton,  R.  N. 

Capt.  Owen,  R.  N. 
French  survey. 
Admiralty  Chart. 
Capt.  Owen,  R.  N. 
Lieut.  Carless,  I.  N. 

Do. 
Lieut.  Grieve,  I.  N. 

Do. 
Lieut.  Haines,  I.  N. 
Lieut.  Grieve,  I.  N. 

Do. 
Lieut.  Lartique,  Fr.  N. 
Lieut.  Barker,  I.  N. 
Lieut.  Haines,  I.  N. 

Capt.  Weatherhead,  R.  N. 
English  survey. 
Comdr.  Wharton,  R.  N. 

Do. 
Light-House  List. 
Lieut.  Elwin,  I.  N. 
Capt.  Moresby,  R.  N. 
Light-House  List. 
Sir  G.  S.  Nares,  R.  N. 
Light-House  List. 
Capt.  Nares,  R.  N. 
Comdr.  Mansell,  R.  N. 
Light-House  List. 

Do. 
Eng.  T.  of  V.  Commission. 
English  survey. 

Do. 

Do. 
Light- House  List. 
Sir  G.  S.  Nares,  R.  N. 

Do. 


Page  564]  TABLE  49. 

MARITIME  POSITIONS. 
EAST  COAST  OF  AFRICA  AND  THE  RED  SEA— Continued. 


a 
o 

O 


Places. 


S 


Sherm  Rabigh 

Jiddah 

Lith 

Jelalil 

Kunfidah 

Khor  Nohud 

Farisan  I.  Anchorage 
Gizau 

Loheyya . 

Kamaran  Bay 

Hodeidah  Road 

Jebel  Zukur  Island  ._ 

Mocha 

Perim  Island 


Exact  locations. 


Anchorage 

Jezirah  el  Mifsaka  Island. 

A^ha  Islet 

Anchorage 

Islet 

Entrance 

Jebul  Mandhakh 

Fort 

Hill  Fort 

Harbor 


N.  point 

Pier  end 

Light-house 


Lat.  N. 


22  43  50 
21  28  o 
20    9    o 

19  55  30 
19    7  40 

18  15  50 
16  50  15 
16  53  o 
IS  42  o 
15  20  30 
14  47     o 

14  3  53 
13  19  50 
12  38  59 


Long.  E. 


39     o  30 

39  10  37 

40  12    o 

40  30    o 

41  3  20 
41  27  30 

41  58  15 

42  29    o 

42  38  45 
42  34  o 
42  54    o 

42  45  28 

43  12  58 
43  25     6 


Authorities. 


English  survey. 
Comdr.  Wharton,  R.  N. 
Sir  G.  S.  Nares,  R.  N. 
English  survey. 

Do. 

Do. 
Comdr.  Haines,  I.  N. 
English  survey. 

Do. 
Comdr.  Elwan,  I.  N. 
Lieut.  Whish,  I.  N. 
Comdr.  Wharton,  R.  N. 
Comdr.  Haines,  I.  N. 
Comdr.  Gray,  R.  N. 


ISLANDS  OF  THE  INDIAN  OCEAN. 


- 

a 

d 
w 
w 
Si 


a 

C9 


JS 


P. 


Chitlac  Islet 

Betrapar  Islet    ... 

Kittan  Islet 

Cardamum  Islet . 

Ameni  Islet 

Underut  Islet  ... 

Cabrut  Islet 

Seuheli  Par 

Kalpeni  Islet  ... 
Minikoi  Islet  .. .. 


Heawandu  Island 

Kee  lah  Island 

Mah  Kondro  Island 

Nar  Force  Island 

Hee  tah-doo  Island 

To-du  Island 

Gafor  Island 

Male,  or  King's  Island  . 

Pha-lee-du  Island 

Moloque  Island 

Himmittee  Island 

Kimbeedso  Island 

Esdu  Island 

Wahdu  Island 


Addu  Atoll.. 

Amirante  Islands 


Seychelle  Islands , 
Do.__ 


Do. 


Chagos  Archipelago,  Pe- 
ros  Banhos. 

Chagos  Archipelago,  Di- 
ego Garcia. 

Cargados  Carajos 

Rodriguez  Island,  Ma- 
thurina  Bay. 

Mauritius  I.,  Flat  I 

Mauritius  I.,  Cannonier 

Point. 
Mauritius  I.,  Port  Louis. 
Mauritius  I.,  Grand  Port. 


S.  end 


S. end  ._ 
Centre  ._ 
N.  end.. 
Centre  ._ 
E.end  .. 
N.  islet  . 
S. end  .. 
do 


do  ...  . 

N.  end 

N.  E.  extreme . 


Centre 

do   ,._. 

Flag-staff 

Northern  end 
Centre 


S. end  

N.  E.  point 
E.end 


N.  W.  point. 


He  des  Roches,  centre  of 
N.  beach. 

S.  end  of  Platte  Island 

Port  Victoria,  end  of  Ho- 

doul  Jetty. 
Bird  Island 


Diamond  Islet 

N.  end  of  Middle  Island. 


Establishment  I.,  flag-staff 
Point  Venus 


Light-house 
do  ... 


Martello  tower,  Ft.  George 
Fouquet  Island  light 


40  45 
35     o 


II 
II 

II  27  30 
II   13 
II     6 


10  47 
10  32 
10  6 
10  3 
8  15 


58 
59 
25 

26  „ 
I  30 

25  45 
44  o 
10  20 
41  o 
o 
o 


57 
16 
10  30 
7    o 


6 
6 
6 
5 
5 
4 
4 
4 

3 
2 

3 
2 
2 

o  14  30 
Lat.  S. 
O  35     o 

5  40  56 

5  53    o 

4  37  15 

3  40    o 

5  15    o 
7  13  30 

16  25  12 
19  40  23 

19  52  36 

19  59  45 

20  8  46 
20  24  20 


72  42  54 
72  54  40 
72  59  o 
72  44    o 

72  41  o 

73  40  o 
72  37  40 

72  15 

73  35 
73  o 


10 

54 
o 


72  54  o 

73  12  54 

72  41  54 

73  20  o 
72  53  o 

72  57  24 

73  28  o 
73  30  24 
73  24  54 
73  34  24 

72  48  d 

73  3  o 
73  35  54 
73  13  o 

73  10  o 
53  41  03 

55  27  10 
55  27  59 

55  15  10 

71  43  47 

72  23  so 


59  46  40 
63  2S  37 


57  39  8 
57  32  30 

57  29  26 
57  47  9 


Capt.  Selby,  R.  N. 
Capt.  Moresby,  R.  N. 
Capt.  Selby,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Capt.  Moresby,  R.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 


Com.  Wharton,  R.  N. 
Do. 

Do. 

Capt.  Moresby.  R.  N. 

Do. 


Lieut.  Mudge,  R.  N. 
Lieut.  Neate,  R.  N. 


Lieut.  Clone,  Fr.  N. 
DunEchtT.ofV.  Ex.,  1874. 


o 
O 


ci 

■ 

a 

it. 


'S 

m 
m 

R 

N 

e 

M 

s 


'J'ABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  INDIAN  OCEAN— Continued. 


[Page  565 


Places. 


Exact  locations. 


St.  Denis  light. 
Bel-Air  light 


Reunion  Island 

Do 

Do I  St    Paul  light. 

Do !  St.  Pierre  light 

Tromelin  Island 1  N.  end . 

Agalegas  Island i  N.  W.  point 

Farquhar  Islands  !  Hall's  house . . . 

Alphonse  Island i  N.  point 

Coetivy  Island N.  end 


Cape  St.  Mary 

Leven  Island 

Port  Machikora 

St.  Augustine  Bay. 

Murderers'  Bay 

Cape  St.  Vincent  . . 

Mourondava 

Tsmano 

Kovra  Rythi  Point 

Coffin  Island 

Cape  St.  Andrew  . . . 

Boyanna  Bay  

Cape  Tauzon  

Majunga , 

Makumba  Island  . . , 

Majambo  Bay 

Narinda  Bay 

Port  Radama 

Radama  Islands 

Baratoube  Bay. 


S.  extreme 

Centre 

Barracouta  Island 

Nos  Veh  Island 

Centre  of  Murder  Island 

Extreme 

Village 

do  

Extreme 

Centre 

Extreme 

Barabata  Point 

Extreme 

Village 

E.  pt.  of  Bembetooka  Bay. 

W.  point 

Moormora  Point 

Point  Blair 

N.  point  Nossuvee  Island 
Ambubuk  a  Point 


Europa  Island 

Bassas  da  India 

Geyser  Reef , 

Mayotta  Island 

Johanna  Island 


Nossi  Bi Ilellville  jetty 

Minow  Islands N.  point  Great  Island. 

Cape  San  Sebastian Extreme    

Port  Liverpool N.  point  of  entrance  . . 

Cape  Amber N.  E.  extreme 

Port  Lady  Frances Sunson  Point 

Port  Look(? I  Point  Bathurst 

Port  Leven S.  point  Nossi  How  Island 

Andrava  Bay Berry  Head 

Vohemar Flag-staff. . . 

Cape  East 

Venangue  B^  Bay  

Port  Choiseul 

Cape  Ballones 

St.  Mary's  Island 

Port  Tantang 

Feneri ve  Point 

Tamatave 

Mahanuru   

Matatane   

Santa  Lucia 

Point  Ytapere 

Ytapere  Bay 

Fort  Dauphin 


Ugoncy  Island 

Entrance 

Maran  Seetzy  Village 

Extreme 

Light  on  Madame  Island. 

Flag-staff 

do    , 

Landing-place 

Town 

Village 

N.  end  of  town , 

Extreme 

Village 

Flag-staff 


Centre 

E.  point 

.S.  E.  extreme. 
Light-house  .. 
Landing-place 

Harbor. 
Numa  Choa  Harbor 


Pomoni 


Mohilla  Island 

Glorioso  Islands W.  islet 

Comoro  Island '   Islet  in  Mauroni  Bay 

-Assumption  Island |   Hummock 

Aldabra  Island I  W.  side  of  main  channel 

entrance. 
Cosmoledo  Islands Observation  islet 


Lat.  S. 


20  51  32 
20  53  II 
20  59  45 
19  50 
51 
10  21 
6 
I 
6 


21 
15 


Long.  E. 


10 

7 
7 


37 
30 

45 
o 
o 


55  39  22 

55  19  20 

55  28  39 
54  28  46 

56  32  o 

51  10  24 

52  47  o 
56  22  o 


Authorities. 


25  39  10 

45  6  50 

25  12  30 

44  17  57 

25  3  0 

44  7  20 

23  38  25 

43  38  20 

22  5  18 

43  15  20 

21  54  24 

43  20  21 

20  18  18 

44  19  21 

19  49  30 

44  31  30 

17  53  0 

44  2  20 

17  29  0 

43  46  9 

16  12  10 

44  29  5 

15  56  40 

45  18  30 

15  46  30 

45  43  9 

15  42  54 

46  18  30 

15  42  20 

45  57  33 

15  II  42 

46  59  20 

14  40  18 

47  26  27 

i:  59  0 

47  58  21 

13  55  40 

47  48  5 

13  27  15 

47  59  30 

13  23  38 

48  17  II 

12  49  30 

48  38  57 

12  27  20 

48  45  45 

12  3  18 

49  II  21 

II  57  30 

49  17  26 

12  23  20 

49  35  56 

12  44  12 

49  46  57 

12  49  0 

49  54  0 

12  56  48 

49  56  25 

13  20  0 

50  2  2 

15  15  48 

50  31  21 

15  54  50 

50  16  5 

15  27  18 

49  52  10 

16  14  0 

49  50  59 

17  0  10 

49  50  41 

16  42  30 

49  56  15 

17  23  16 

49  32  4 

18  9  54 

49  28  10 

19  55   0 

48  52  10 

21  58  10 

48  14  50 

24  46  0 

47  13  30 

24  59  42 

47  7  20 

24  58  50 

47  7  30 

25   I  37 

47  2  7 

22  22  30 
21  29  O 
12  26  30 
12  46  43 
12    16    20 


12    25  O 

II    34  48 

40  44 

46  20 


II 

9 
9 


22  35 


40  24  10 
39  40  39 

46  32  35 

45  19  39 
44  24  54 

43  47    o 

47  24    9 
43  19  15 

46  31     ID 

4(^  14  55 


9  41  20  I    47  32  28 


Lieut.  Clou6,  Fr.  N. 

Do. 

Do. 

Do. 
Comdr.  Wharton,  R.  N. 
Capt.  Moresby,  R.  N. 
Lieut.  White,  R.  N. 
Capt.  Moresby,  R.  N. 

Do. 

Capt.  Owen,  R.  N. 

Do. 

Do, 

Do. 

Do. 

Do. 

Do. 
De  Laugle. 
Capt.  Owen,  R.  N. 

Do. 

Capt.  Owen,  R.  N. 
Capt.  Vidal,  R.  N. 

Do. 

Do. 

Capt.  Vidal,  R,  N. 

Do. 

Do. 
Capt.  Jehenne,  Fr.  N. 

Do. 
Capt.  Vidal,  R.  N. 

Do. 
Capt.  Owen,  R.  N. 

Do. 
French  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Owen,  R.  N. 
English  survey. 
Capt.  Owen,  R.  N. 

Do. 

Do. 
Germain. 
Capt.  Ow«n,  R.N. 

Do. 

Do. 
M.  D'Apr^s. 

Do. 

Capt.  Owen,  R.  N. 

Do. 
Capt.  Richards,  R.  N. 
Light- House  List. 
Capt.  De  Horsey,  R.  N. 

Lieut.  Clou6,  Fr.  N. 
Capt.  De  Horsey,  R.  N. 
.'\.dm.  Boss^,  Fr.  N. 
Comdr.  Wharton,  R.  N. 
Do. 

Do. 


Page  566 

TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  or  THTI  INDIAN  OCEAN— Continued. 

Places. 


Prince  Edward's  Islands 

Marion  Island 

Crozet  Is.,  Penguin  Is  _. 
Crozet  Is.,  Possession  I  _ 

Crozet  Is.,  Twelve  Is 

Crozet  Is.,  Navire  Bay.. 
Crozet  Is.,  Hog  Island.. 
Crozet  Is.,  East  Island.. 

Kerguelen  Islands 

Do 

Do 


Kerguelen  Is.,  Molloy, 

Port  Royal  Sound. 
Kerguelen  Islands 

Do 

Heard  Island 

Do 

Do 

St.  Paul's  Island 

Amsterdam 

Keeling  or  Cocos  Islands 
Christmas  Island 


Exact  locations. 


Boot  Rock 

N.  Cape 

Centre  of  S.  W.  islet 

N.  W.  point 

Summit  N.  E.  Island  , 


Summit 

Centre 

Christmas  Harbor 

Bligh's  Cape 

Cape  Bourbon 


U.  S.  Tr.ofV.  Obs.,  1874. 

Cape  Challenger 

Balfour  Rock 

N.  W.  end  Cape  Laurens. 

Sealing-station  . 

Summit  of  McDonald  Islet 

Ninepin  Rock 

Summit,  2,750  feet 

Port  Refuge,  Direction  I. 
Approximate 


Lat.  S. 


46  48 

46  53 
46  36 
46  22 
46  I 
46  28  18 
46  10  40 
46  26  o 
48  40  o 

48  26  45 

49  42  o 


49  21  22 

49  41  o 
49  29  o 
53  2  45 
13  o 
2  50 

38  42  45 

37  51  o 
12  6  22 
10  31  o 


53 
53 


Long, 

E. 

0 

/ 

II 

37  44 

0 

37 

33 

0 

SO 

41 

30 

51 

30 

15 

50 

40 

0 

51 

50 

0 

50 

35 

0 

52 

13 

0 

69 

4 

0 

68 

48 

20 

68 

54 

0 

70 

4 

31 

70 

15 

0 

70  29 

50 

73 

15 

30 

73 

52 

0 

72 

31 

45 

77 

35 

0 

77 

29 

15 

96 

53 

2 

105 

33 

0 

Authorities. 


Sir  G.  S.  Nares,  R.  N. 
Capt.  Crozier,  R.  N. 
Sir  G.  S.  Nares,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Sir  G.  S.  Nares,  R.  N.,  and 

others. 
Comdr.  Ryan,  U.  S.  N. 

Sir  G.  S.  Nares,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Capt.  Denham,  R.  N. 
Capt.  Wickham,  R.  N. 
Capt.  Fitzroy,  R.  N. 

Do. 


SOUTH  COAST  OF  ASIA. 


Aden 

Sughra 

Mokatein 

Howaiyuh 

Ba-L.-Hof 

Banderburum 

Makalleh  Bay 

Shahah  Roads  

Sharmoh 

Kosair 

Sihut 

Ras  Fartak 

Damghot 

Merbat 

Kuria    Maria    Islands, 
Hulla  Niyeh  Island. 

Ras  Sherbedat 

Cape  Isolette 

Masirah  Island 

Do 

Ras-al-Hed 

Maskat 

Deimaniyeh  Islands... 

.Sueik 

Sohar 

Khaur  Fakan  Bay 

Ras  Musendom 

Great  Quoin  Islet 


Shargeh 

Abu-Thabi 

Al  Beda'a  Harbor  .. 

Ras  Rekkin 

Bahrain  Harbor 

Basrah 

Kuweit  Harbor 

Kharig  Islet 

Abu  Shar 

Shaikh  Shu'aib  Islet. 
Kais  Islet 


Telegraph  station  . . 

Sheik's  house 

Black  ruin 

Sheik's  house 

Tower 

S.  E.  house  of  town 

Flag-staff 

Custom-house 

Single  house 

High  house  

Centre  of  town 

Extreme  point 

Town 

do 

N.E.  bluff. 


Point. 

Islet 

Point  Abu -rasas 

Point  Ras  Ye 

Extreme  point 

Maskat  Point 

E.  islet 

Fort 

S.  E.  tower  of  town-hall. 

W.  end  of  village 

N.  end  of  island 

Centre 


High  tower  with  flag-staff. 

Fort  flag-staff 

Nessah  Point 

N.  W.  point 

Portuguese  fort 

Custom-house  flag-staff  _. 

N.  end  of  town 

Fort  flag-staff 

Residency  flag-staff 

E. end  

N.  E.  point 


Lat.  N. 

2  46  40 

22     o 

24  50 

28  45 

57  50 
20  10 

31   15 

4  43  50 
4  49    o 

4  54  40 

5  12     o 
5  38    o 


16 

30 

0 

16 

59 

0 

17 

32  45 

17 

53 

15 

19 

0 

25 

20 

10 

0 

20 

31 

30 

22 

32 

40 

23 

38 

0 

23 

52 

0 

23 

51 

30 

24 

21 

50 

25 

21 

0 

26 

24 

13 

26 

30 

0 

25 

21 

34 

24 

29 

2 

25 

17 

28 

26 

10 

55 

26 

13 

53 

30 

32 

0 

29 

22 

5t) 

29 

15 

25 

28 

59 

7 

26 

47 

40 

26 

33 

37 

Long. 

E. 

44 

58   58 

45 

40  50 

46 

26 

35 

46 

39 

0 

48 

9 

0 

48  56  45 

49 

7 

35 

49  35 

5 

49  57 

5 

50 

16 

35 

51 

10 

30 

52 

14 

20 

52 

48 

0 

54  43 

29 

56 

3 

5 

•7e 

57  51  35 

58  38  35 

58  58  35 

59  48  35 
58  30  50 
58  8  o 
57  26  o 
56  46  12 
56  21  54 
56  32  22 
56  31  29 

55  24  12 
54  22  14 
51  31  37 
51   13  46 

50  32  17 

47  SI  23 

48  o  23 
50  21   II 

SO  50  35 

53  23  36 

54  2  21 


Ellis. 

Comdr.  Haines,  I.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Grieve,  I.  N. 

Do. 

Do. 
Capt.  Haines,  I.  N. 

Do. 
Capt.  Grieve,  I.  N, 

Do. 

Do. 

Do. 

Do. 
Indian  survey. 

Do. 
Comdr.  Constable,  I.  N. 

Do. 

Do. 
Indian  survey. 

Do. 
Capt.  Haines,  I.  N. 
Lieut.  Guy,  I.  N. 
Indian  survey. 
Mr.  Chapman,  I.  N. 
Indian  survey. 
Lieut.  (Juy,  I.  N. 
Comdr.  Constable,  I.  N. 

Do. 

Do. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

SOUTH  COAST  OF  ASIA— Continued. 


[Page  567 


o 
O 


Places. 


3 


w 
e 
0 

pq 


e 

•9 


Basiduh 

Haujam  Islet 
Kishm 


a 


Tashak  Bay  _ . 
kubKalat._. 
Chahbar  Bay. 
Gwatar  Bay  . 
Gwadar  Bay . 

Pasni 

Amara 

Sunmiyani 

Cape  Monze  . 


Kurrachee 

Do 

Mandavi ._. 

Beyt,  or  Bet 

Dwarka 

Do 

Porebander 

Mangarol 

Diu  Island 

Mowa 

Perim  Island 

Cambay 

Surat  River 

Surat 

Bassein 

Bombay  (time-ball) 

Bankot 

Ratnagherry 

Viziadroog 

Cape  Ramas 

Goa 

Do 

Vingorla 

Vingorla  Rocks 

Sedishigar  Bay 

Coompta 

Hinawar 

Cuadapur  

Mangalore 

Cananore  

Tellicherry 

Mahe  (French) 

Calicut 

Coclim 

Alipee 

Quilon 

Trevandrum 

Cape  Comorin 

Trichendore 

Tuticorin 

Paumben  Pass 


Manaar 

Colombo 

Dondra  Head 

Point  de  Galle 

Great  Bassas  Rocks . 
Little  Bassas  Rocks . 

Batticaloa 

Trincomalee 


Calymere  Point. 

Negapatam 

Pondicherry 


Exact  locations. 


Chapel 

Ruined  mosque 
Fort 


Telegraph  office 

High  peak,  1,680  feet 

Telegraph  office 

Islet 

Telegraph  office 

do 

do 

Jam's  House 

Peak 


Manora  light 

Observatory 

Light-house  

do 

do 

Temple  spire 

Light-house 

do  

Portuguese  fort 

Light-house 

do 

Flag-staff 

Tapti  light 

Minaret  Adrusah 

Centre  of  town 

Observatory 

Fort  Victoria 

Fort 

Fort  flag-staff 

W.  bastion  of  fort 

St.  Denis  Church 

Agoada  light 

Signal-station 

Light-house 

Oyster  Rock  light 

Light-house 

Monument 

Custom-house 

Light-house 

do 

do 

Flag-staff 

Light-house 

do 

do  

Flagstaff  on  W.  point 

Observatory 

Light  house 

Pagoda  on  point 

Liglit-house 

do 


Centre  of  town 

Government  flag-staff 

Extreme 

Light-house 

do 

do . 

do 

Dock-yard  llag-staff 


Light  house 

do  ._.. 

Flag-staff 


Lat.  N. 


// 


26 
26 
26 


39  12 

40  49 
57  27 


25  38  19 
25  29  45 
25  16  43 
25  3  17 
25  7  19 
25  15  52 
25  II  55 
25  25  19 
24  50  3 


24 

24 
22 
22 
22 
22 
21 
21 
20 
21 
21 
22 
21 
21 

9 
8 

7 
6 
6 
5 
5 
5 
5 
5 
4 
4 
4 

3 
2 

I 

I 

I 

I 

9 
9 
8 
8 
8 
8 
8 
9 


47  21 
49  49 
49  41 
29  o 


8  59  o 
6  55  40 
55  o 
I  25 
10  10 
22  55 
43  50 
33   30 


5 
6 

6 

6 

7 

8 


10  17  55 

10  45  30 

11  55  40 


Long.  E. 


55  16  47 

55  54  25 

56  17  37 

57  46  14 

59  40  32 

60  37  40 

61  26  24 

62  19  42 

63  28  37 

64  37  2 
66  35  39 
66  39  58 

66  58  47 

67  I  33 
69  20  51 
69  5  2 


14  0 

68  57  32 

14  3 

68  58  54 

37  10 

69  35  32 

6  0 

70  7  2 

42  40 

70  59  29 

2  21 

71  50  2 

35  54 

72  21  9 

17  0 

72  35  10 

5  20 

72  38  40 

12  19 

72  49  27 

20  10 

72  48  44 

53  45 

72  48  58 

58  19 

73  2  31 

59  42 

73  16  13 

33   32 

73  19  15 

5  12 

73  54  57 

21  24 

73  54  0 

29  26 

73  46  10 

51  14 

73  37    0 

53  16 

73  2;  17 

49  0 

74  3  40 

25  20 

74  23  40 

17  28 

74  26  40 

37   28 

74  40  10 

52  17 

74  50  40 

51  10 

75  22  17 

44  50 

75  29  2 

42  10 

75  31  44 

15  5 

75  46  40 

57  47 

76  14  17 

30  0 

76  20  40 

53  25 

76  35  30 

30  47 

76  56  45 

4  0 

77  33   II 

29  55 

78  7  47 

47  10 

78  II  52 

17  14 

79  13  10 

Authorities. 


79  53   52 

79  50  29 

80  34  12 

80  13  4 

81  28  32 
81  43  44 
81  41  52 
81  13  42 

79  52  2 
79  50  52 
79  50  10 


Comdr.  Constable,  I.  N. 
Capt.  Brucks,  I.  N. 
Comdr.  Constable,  I.N. 

Lieut.  Stiffe,  I.  N. 
Indian  survey. 
Capt.  Brucks,  I.  N. 
Capt.  Haines,  I.  N. 
Lieut.  Stiffe,  I.  N. 
Indian  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Ethersey,  I.  N. 
Indian  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  A.  D.  Taylor,  I.  N. 
Indian  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  A.  D.  Taylor,  L  N. 
Indian  survey. 

Do. 

Do. 

Do. 
Capt.  A.  D.Taylor,  I.N. 
Indian  survey. 

Do. 

Do. 
Capt.  A.  D.  Taylor,  I.  N. 

Do. 
Indian  survey. 

Do. 

Do. 

Do. 

Do. 
Lt.  Col.  Tupman,  R.  M.  A. 
Indian  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 

Lieut.  Fleuriais,  Fr.  N. 


Page  568] 


TABLE  49. 

MARITIME  POSITIONS. 

SOUTH  COAST  OF  ASIA— Continued. 


o 


a 

m 
h 

s 

n 


ei 

X 
ft 

S 


Places. 


Madras  (time  ball) ... 

Palicat 

Armogham 

Point  Divy 

Masulipatam 

Coconada  

Vizagapatam 

Calingapatam 

Gopaulpore 

Gaujam 

J  iiggernath 

False  Point 

Balasore 

Saugor  Island 

Diamond  Harbor 

Calcutta  .. 


Chittacong 

Akyab 

Do 

Ramree  Island 

Chedubah  Island. 

Cape  Negrais 

Bassein  River 

Bassein 

Andaman  Islands,  Great 

Coco  Island. 
Andaman  Islands,   Port 

Cornwallis. 
Andaman  Is.,  Port  Blair 
Andaman  Islands,  Little 

Andaman  Island. 

Krishna  Shoal 

Rangoon  River  

Rangoon 

Maulmain 

Maulmain  River 

Double  Island 

Tavoy  River   

Mergui 

Tenasserim 

St.  Matthew  Island 

Pak  Chan  River  


Exact  locations. 


Observatory 

Light-house 

do 

do 

Flag-staff 

Light-house 

Fort  flag-staff , 

Flag-staff , 

Light-house 

Fort 

Great  Temple , 

Light-house 

Spire 

Light-house 

Flag-staff 

Fort  William  semaphore 


Judge's  Court 

Oyster  Reef  light  . 

Old  temple 

S.  point 

N.  W.  peak 

Extreme 

Alguada  Reef  light 
Port  Dalhousie  .  . . , 
Light- house 


Rock  in  entrance . 


Tonkah  Harbor,  Tunk- 
seylm  Island. 

Pulo  Penang 

Dinding  Island 

Cape  Rachada  

Malacca 

.Singapore  Strait 

Singapore 

Singapore  Strait     

Do 


Settlement 
S.  E.  point 


Light-house 

Grove  Point  light 

Great  Dagon  pagoda  .. 

Docks 

Amherst  Point  pagoda. 

Light-house 

Tavoy  Point  pagoda  . . . 
Pagoda  


Hasting's  Harbor 
Victoria  Point 


Rhio  Straits 

Do 

Do 

Rhio,  l]intang  Island.. 

Pitong  Island 

Abang  ISesar  Island 


Lingga  Island  . 
Singkep  Island 
Menaloe  Island 


Harbormaster's  office.. .. 

Fort  Cornwallis 

Port  Pancore 

Light  house 

Flag-staff 

Coney  Island  light 

P'ullerton  P>attery 

Pedra  Bianca  light     .... 
Summit     Bintang    great 
hill,  1,253  feet. 

Pulo  San  light 

Terkolei  light 

Little  (iarras  light 

Residency  flag-staff 

Peak 

N.  point 


Flag-staff 

Mountain  summit 
N.  point     


Nicobar     Islands,    Car 

Nicoliar. 


N.  point 


Lat.N. 


13  4  6 
13  25  15 
13  52  50 

15  58  44 

16  9     8 

17  o  40 

17  41  34 

18  20  36 

19  13  o 
19  22  30 

19  48  17 

20  20  15 

21  30  12 

21  38  43 

22  II     ID 

22    33    25 


22    21      3 

20  5  O 
20  8  53 
18  51     O 

18  50  30 
16       I    30 

15  42    14 

16  I    30 

14  12   30 

13    18   40 

11  41    13 

10  27     O 

15  36    30 

16  30       I 

16  46  o 
16  26  o 
16    4  44 

15  52  30 
13  32    o 

12  26  45 
12     6     o 

10    5     5 
9  51  30 


5  24  30 
4  13  19 
2  24  8 
2  II  30 

I  9  51 
I   17  II 

I  J9  57 
I     4  20 

I  3  13 
o  57  21 
o  44  30 

o  55  50 
o  36  52 
o  36  30 

Lat.  S. 
O    12   34 

o  26  13 

o  57  51 
Lat.  N. 
9  15  40 


Long.  E. 


80  14  51 
8q  19  38 


80 
81 
81 

82 
83 
84 


12   15 

9  21 

9    8 

17    2 

17  42 

.     7  29 

84  52    o 

85  3  29 

85  49    9 

86  47  30 
86  55  46 
88  2  32 
88  II  7 
88  20  II 

91  50  14 

92  39  o 

92  52  40 

93  56  30 

93  31  o 

94  13 
94  12 
94  23  o 
93  22  47 


16 

7 


Authorities. 


Indian  survey. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 
Capt.  Ilalstead,  R.  N. 

Do. 
English  survey. 
Indian  survey. 
Capt.  Ward,  R.  N. 
Indian  survey. 


92  57  10     Lieut.  Blair,  R.  N. 

92  45   14  j  Indian  survey. 
92  31   10  i  Lieut.  Blair,  R.N. 


95  29 

96  23 

96  7 
9738 

97  33 

97  35 

98  12 

9835 
99 
98 
97 


3 

ID 


45 
19 

30 
o 

3 

8 

o 
o 
o 

15 

o 


Capt.  Ward,  R.  N. 
Indian  survey. 
English  survey. 

Do. 
Lieut   Jarrad,  R.  N. 
Indian  survey. 
English  survey. 

Do. 

Do. 

Do. 

Do. 


7  51   12       98  24    o     Com.  de  Richelieu,  Siam  N. 


9 

8 


100  20 

100  34 

loi  51  2 

102  15  33 

103  44  47 

103  51  15 

104  24  27 
104  27  21 

104  10  8 
104  19  34 
104  21  19 
104  25  43 
104  4  24 
104  II  13 

104  35  56 

104  30  15 

105  38  2 

92  48  o 


China  Pilot. 
Capt.  Napier,  R.  N. 
Indian  survey. 
Capt.  Ward,  R.  N. 
Com.  Reed,  R.  N. 
Lt.  Comdr.  Green,  U.  S.  N. 
Comdr.  Reed,  R.  N. 
Do. 

Netherlands  Ilyd.  Office. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 

Capt.VonW^iUenstoff,  Aus.N, 


tJ 


TABLE  49. 

MARITIME  POSITIONS. 

SOUTH  COAST  OF  ASIA— Continued. 


[Page  569 


a 
o 
O 


s 

g 


Places. 


3 


Nicobar  Islands,  Nan- 
cowry  Harbor. 

Nicobar  Islands,  Great 
Nicobar. 

Acheen  Head 

Do..... 

Diamond  Point 


Exact  locations. 


Naval  Point 

W,  point  of  Galathea  Bay. 


Pulo  Brasse  light 

N.  extreme 

Light -house 


Cape  Baroe , 

Cape  Bon  

Mocara  Kanpeh.. 

Djambi 

Palembang 

Lampong  Bay  . . . 

Blimbing  Bay 

Kroe 

Engano  Island.. 

Bintfjean 

Mega  Island 

Benkoelen 

Bantal 

Indiapaera  Point 

Pisang 

Padang  

Siberoet  Island  .. 

Katiagam 

Batoe  Islands 

Do 


Extreme 

do  

Fort 

Flag-staff  of  fort  ... 
Residency  flag-staff. 
Telok  Betong  light  . 


Ayer  Bangis 

Natal 

Nias  Island 

Do 

Do 

Siboga 

Singkel 

Banyak  Islands 


Village 

Barhoe  anchorage  . . 

River  mouth 

N.  point 

Fort  Marlborough  . 

Village 

Extreme 

Summit  of  islet 

Apenberg  flag-staff . 
Sigeb  Point 


N.  point  of  Simoe  Islet 
Summit  of  Telle 


Fort  flag-staff.. 

do   

Lagoendi  Bay  . 
Goenong  Sitoli , 

Lapan  

Flag-staff 


Simaloe  Island.. 
Tampat  Toewon 

Analaboe 

Batve  Toetong.. 


Cameleon  Bay,  Bankaru 
Islet. 

N.  W.poirt 

Flag-staff 


Landing-place 


Lat.  N. 

o    /      " 
8    2  10 

6  46  20 


5  44  55 
5  34  40 
5  15  58 

Lat.  S. 

0  O  32 

1  O  55 
I    23    13 

1  35  33 

2  59  26 
5  28    o 

5  55  2 
5  II  24 

5  18  50 
4  48  35 

3  59  25 
3  47  28 
2  44  54 
2  10  35 
o  59  46 
o  58     I 

o  53  58 
o     7  41 

o  3  13 
o     2  56 

Lat.  N. 
O  II  41 

O  33    II 

0  34  47 

1  17  36 
I  24  16 

1  44  24 

2  16  47 


2  51  30 

3  14  59 

4  8  14 

4  38  21 


Long. 

E. 

0 

1 

II 

93  29  42 

93  49 

20 

95 

4  33 

95 

19 

0 

97  29  53 

103  47  40 

104 

21 

12 

103 

58  56  1 

103 

3t> 

23 

104  45 

lb 

105 

lb 

0 

104 

32 

30 

103 

55  42  1 

102 

7 

10 

103 

20 

0 

lOI 

0 

40 

102 

14 

27 

lOI 

17 

25 

100 

49 

48 

100 

19 

48 

100 

20 

13 

98 

53  40  1 

99  45 

2 

98 

5 

55 

98 

16 

25 

99 

22 

9 

99 

6 

15 

97  43 

25 

97  36 

28 

97 

12 

28 

98  45 

50 

97  44 

48 

97 

b 

35 

95  56 

2 

97 

9  55  1 

96 

7 

5 

95  34 

II 

Authorities. 


Capt. Von  Wullenstoff,  Aus.  N, 
Do. 


Indian  survey. 
English  survey. 
Netherlands  H yd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 


EAST  COAST  OF  ASIA. 


e 
fa 

£ 

A 

m 

SQ 


es 

m 

£ 
a 

B. 

■ 
d 


Java  Head 

Sunda  Strait 

North  Watcher  Island 

Bangka  Strait 

Bangka  Island 

Do 

Bangka  Strait 

Bangka  Island 

Do 

Do 

Gaspar  Strait 

Do 

Do 

Billiton  Island 

Do 

Gaspar  Island 


First  Point  light 

Krakatoa  Island  peak 

Liglit-liouse 

Lucepara  Island  beacon.. 

Toljol  Ali  Fort  

Brekat  Point  light  (pro- 
posed). 
Nangka  Island,  W.  rock. . 

Mintok  light 

Blinyoe 

Crassok  Point 


Lat.  S. 
6  44  30 
8  46 

13  30 

13    5 

o  48 

3348 


Shoalwater   Island   (pro 
posed  light). 

Bulo  Lepar  light 

Pulo  Jelaka  light 

Tandjong  Pandan  tl  ig  staff 

Bienga  Point  light  (pro- 
posed). 

Peak 


2  22  53 

2  4  18 
I  38  26 
I  29    O 

3  18  15 


56  14 
51  48 
•44  40 
35  30 


Long.  E. 
105  II  48 

105  26  58 

106  26  20 
106  12  44 
106  27  22 
106  50  40 

105  45  21 
105   9  12 

105  46  10 

106  57  30 

107  13  3 

106  54  30 

107  o  55 
107  38  28 
107  38  16 


2  24  30     107    3  ^2 


Netherlands  Hyd,  Office. 

Do. 

Do. 

Do. 
English  survey. 
Netherlands  Hyd.  Office. 

English  survey. 
Netherlands  Hyd.  Office. 

Do. 
Various. 

Netherlands  Hyd.  Office. 

Do. 
Do. 
Do. 
Do. 

English  survey. 


Page  570] 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  ASIA— Continued. 


o 

o 


Places. 


C8 

» 
s 

d 

8 

fa 
w 


li 


u 

e 


Si 

V 

ac 
es 

•H 

Jl 


cs 

a 

•N 

.a 
s 

•pa 

.a 
e 


a 
a 

•m 
Ji 


Carimata  Island . 

Pulo  Eu 

Pulo  Aor  .. 


St.  Barbe  Island  . 
Direction  Island  . 

Data  Island 

St.  Julian  Island  . 
Tambelan  Island. 

Do 

Victory  Island 

Anamba  Islands  . 

Do 

Do 

St.  Pierre  Rock  . . 
Natuna  Islands  . . 

Do 


Pulo  Varela 

Pulo  Brala 

Tringano  River 

Great  Redang  Harbor 

Kalantan 

Cape  Patani 

Singora 

Koh  Krah  Islet , 

Bangkok  

Cape  Liant 


Chentabun   River 

Koh  Chang 

Koh  Kong 

Kusrovie  Rock  . . . 
Koh  Tang  Rocks 
Panjang  Island  ... 

Oby  Islands 

Saigon 

Mitho 

Cape  St.  James  . . . 
Cape  Padarau  . .  . . 

Cape  Varela , 

Quin  Hon 


Condore  Islands 


Safatu  Island 

Ceicer  de  !vler  Island.. 
Natuna  Islands,  Murun- 

dum  Island. 
Natuna     Islands,    Low 

Island. 


Canton  Pulo 

Cham-Callao  Islet. 

Touron  Bay  

Hon-ne 


Nam-Dinh 

Hon  Dan  Island 


Hai-Phong 

Hai-Duong 

Ha-Noi 

Pak-Hoi 

Guei-chow  Island 

Hainan  I.,  Cape  Bastion 
Hainan  I.,  CJaalong  l!ay 
Hainan  I.,  Tinhosa  I . .. 


Exact  locations. 


Sharp  peak 

Centre 

S. peak,  1,805  feet. 


Centre  of  W.  side 

S.  point 

N  E.  part 

do   

S.  point 

Tamban  I.  obs.  station 

S.  point 

White  rock 

Pulo  Repon 

Pulo  Domar 

.S.  point 

Pyramidal  rocks 

Semione  Island , 


Centre 

do  , 

N.  point 

Bukit  Maria  Island .... 

Entrance  small  river 

N.  E.  point 

S.  W.  point  of  Ticos  Island 

S.  E.  point 

Old  British  Factory 

N.  W.  rock  of  Koh  Mesan 

Entrance,  Bar  Island 

Small  island  on  W.  side. 
S.  point  of  river  entrance 

Centre 

S.  W.  rock  of  group 

N.W.  coiner  of  S.  W.  bay 
Square  rock  on  S.W.  point 

Observatory 

S.  gate  of  citadel 

Light-house , 

Extreme 


do .. 

Battery  flag-staff 


Largest  island,   landing- 
place  in  Great  Bay. 

Summit 

S.  W.hill 

S.  E.  point 


Centre 

Watering-place , 

Observation  island  . . 
Island     at     entrance 
Loch- Day. 

Citadel  tower 

Light-house 


of 


Observation  pagoda 

Citadel  tower 

do    


Lat.  S. 


1  33  24 

270 

2  26  30 

Lat.  N. 
O     7  26 
O  14  19 
o     8  II 

o  55  22 
o  56  52 
o  27 

34  41 
20    o 

25     o 

45     o 

51  42 

3    o 


^i 


4 

5 

5 
6 


Custom-house  flag-staff  . 


Summit 

Extreme  . 
E.  Brother 
S.  hill 


49  o 
21  40 

44  21 

"  53 

6  58  I 

7  13  54 

8  24  47 

13  44  20 
12  35  8 

12  27  43 
12  I  20 

II  33  o 
II  6  25 
10  21  20 

9  18  14 
8  25  37 

10  46  47 

10  21  16 

10  19  51 

11  21  o 

12  53  40 

13  45  23 

8  40  57 

9  58  23 
10  32  36 

2  2  55 


15  24  o 

15  57  10 
1670 

19  54  39 

20  25  30 
20  40  3 

20  51  43 

20  56  29 

21  I  57 
21  29  o 
21  I  15 
18  9  30 
18  II  30 

18  39  45 


Long^.  E. 


o   /  // 

oS  55  13 
04  17  o 

04  34  25 


37 

47 

7 


07  II 

08  I 
08  36 

06  43  57 

07  32  29 

07  24  7 

06  18  27 

05  34  o 

05  52  o 

05  25  o 

08  38  55 

07  21  40 
07  42  30 


03  38  o 
03  38  o 
03  8  o 

03  I  39 
02  20  47 

01  18  39 
00  36  12 
00  45  27 
00  28  42 

GO    56    52 

02  4    19 

02  15  49 
02  57  14 
02  47  49 

02  56  34 

03  29  14 

04  48  49 
06  42  10 

06  20  38 

07  4  55 

08  58  o 

09  ?3  42 
09  14  52 

06  36  10 

09  6  o 

08  56  27 

09  6  10 

07  48  o 


09  6  o 
08  32  47 

08  17  o 

05  58  48 

06  8  41 
06  47  9 

06  39  22 
q6  17  56 
05  48  40 

09  6  o 
09    6  30 

09  33  30 

09  41  30 

10  28    o 


Authorities. 


Dutch  survey. 
English  survey. 
China  Sea  Dirictorv. 

Do. 

Do. 

Do. 

Do. 
Netherlands  I  lyd.  Office. 
Com.  Reed,  K.  N. 
China  Sea  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Richards,  R.  N. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do, 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
French  survey. 
Lt.  Comdr.  Green,  U.  S.  N. 

Do. 
China  Sea  Directory. 

Do. 
French  survey. 

Com.  Reed,  R.  N. 

Do. 
Do. 
China  Sea  Directory. 

Do. 


Do. 

French  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Napier,  R.  N. 
Capt.  Napier,  R.  N. 
China  Sea  Directory. 
Capt.  Ross,  I.  N. 
China  Sea  Directory. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OP  ASIA— Continued. 


[Page  571 


Places. 


Hainan  Island 

Hainan  Island 

Paracel  Islands 

Do    

Do 

Do 

Pratas  Island 

Ty-fung-kyoh  Island  ... 

Tien-pak  Harbor 

Song-yui  Point 

Hui-lang-san  Harbor... 

Mandarin's  Cap 

Hawcheun  Island 

Macao 

Do 

Canton 

Raleigh  Rock 

Gap  Rock 

Hong  Kong 

Do 

Lema  Island 

Nine-pin  Rock 

Tuni-ang  Island 

Single  Island 

Mendoza  Island 

Rank  I'iah  Rock 

Pedra  Blanco  Rock 

Chino  Peak 

Cupchi  Point 

Breaker  Point 

Cape  of  Good  Hope 

Swatow 

Lamok  Island 

Brothers  Islets 

Tong-eang  Plarbor 

Chapel  Island 

Amoy 

Dodd  Island 

Chinchin  Harbor 

Pyramid  Point 

Ockseu  Island 

Sorrel  Rock 

Lamyit  Island 

Hungwha  Channel 

Turnabout  Island 

White  Dogs  Island 

Min  River 

Do 

Alligator  Island 

Tung-ying  Islands 

Cony  Island 

Double  Peak  Island 

Pih-seang  Island 

Dangerous  Rock 

Tae  Islands 

Nam-quan    I  larbor 

Ping-fong  Island 

Pih-quan  Peak 

Port  Namki 

Pih-ki-shan  Island 

Pe-shan  Islands 

Tung- chuh  Islet 

Kweshan  Islands 

Nimrod  Sound    

Tong-ting  Islet 

Chin-liai 

Ning-po  

Chusan  Islands 


Exact  locations. 


Lat.  N. 


Hoi-how  Fort 

Hainan  I  lead 

Triton  Island 

Observation  bank 

Lincoln  Island,  S.  E.  point 

Woody  Island 

N.  E.  part 

Centre 21 

Pauk  Pyah  Islet j  21 

Extreme !  21 

Mamechow  Islet j  21 

Summit,  200  feet j  21 

S.  W.  point 21 

Fort  Guia  light 22 

Fort  San  Francisco 22 

Dutch  Fally  light 

Centre 

do 

Cathtdral 

Wellington  Battery 

Lema  Head 

Centre 22 

Summit ,  22 

E.  summit   22 

Summit 22 


20  3 
20  12 

15  46 

16  36 
16  39 
16  50 
20  42 

22 
24 

31 

34 
28 

35 
II 

II 

6 

2 

49 
16 
16 


.....do  

Summit,  130  feet. 

do 

Hill 

Extreme 

do 


3 
15 

27 

24 
30 
22  32 
22  18 
22  44 
22  48 

22  56 

23  14 

British  Consulate 23  20 

Light-House 23   14 

S.  1-".  islet 23  32 

Fall  Peak 2347 

Light-house 24  10 

Signal  staff,  Kulangseu  I..  24  26 

Summit 24  26 

Pisai  Islet 24  49 

Extreme 2452 

Light-house 2459 

Summit 25     2 

High  Cone  Peak 25  12 

Sentry  Island 25   16 

Light-house 25  26 

do  . 25  58 

Pagoda,  Losing  Island  ..I  25  59 

Temple  Point !  26     8 

Summit ,  26     9 

Peak 26  23 

Summit 1  26  30 

Highest  peak 26  36 

Town  Island '  26  42 

Summit    26  53 

E.  islet   [  26  59 

Bate  Island .27     9 

Summit 27     9 

do 27  18 

E.  horn 2726 

Summit 2737 

do 28     5 

Summit,  700  feet 28  42 

Patahecock  .    29  2 1 

Middle  islet 29  34 

Summit I  29  51 

Citadel   !  29  57 

Tiger  Island  light .'  29  57 

Ting-hai  Harbor 30     o 


Long.  E. 


II 

10 

o 

o 

O 
34 
30 

30 

IS 
o 

o 

o 

o 

o 

24 

35 
o 

o 

52 

23 
40 

45 

6 

6 
42 
54 
30 
24 

7 

o 

o 
43 
50 
30 

15 
18 
46 
16 

13 
12 

o 

18 

o 

30 

o 

20 

o 

26 

o 

12 
O 

6 

30 

o 

12 

20    I 

42 
48 
18 
18 

30 

12 

54 
20 

42 
8 

43 
25 


10  19 

10  44 

11  II 

11  40 

12  44 
12  19 

16  43 
II   10 

"  15 
II  38 

11  46 

12  21 

12  31 

13  7>l 
13  II 
13  16 

13  47 

13  56 

14  9 
14  10 
14  19 
14  22 
14  36 
14  39 
14  50 


15 
15 


15  46 

16  4 
16  27 
16  47 

16  40 

17  17 
17  42 

17  36 

18  13 
18  4 
18  29 
18  41 

18  58 

19  27 
19  10 
19  35 
19  45 

19  5^ 

20  2 
19  27 

19  37 

20  26 
20  31 
20  10 
20  II 
20  22 
20  34 
20  43 
20  25 
20  32 

20  28 

21  6 


21 
21 
21 

22 


12 

31 

5 


21  43 

22  35 
21  43 
21  43 
22 


30 
o 
o 

30 

20 

o 

22 

30 
25 
30 

43 
30 
30 
30  1 
25 

34 
o 

25 

31 

2 

25 
7 

45 
12 

o 

.0 

54 
50 
26 

45 
o 

22 

30 
o 

48 

30 

4 
4 
o 
o 

30 

36 

o 
o 

42 

20 
16 

35 
o 
o 
o 

12 
42 
18 
48 

50 
42 
42 
36 
18 
48 
56 
42 

15 

48 

6 

51 
18 


Authorities. 


Capt.  Napier,  R.  N. 
China  Sea  Directory. 
Capt.  Ross,  I.  N. 

Do. 
Com.  Ward,  R.  N. 
Capt.  Ross,  I.  N. 
Capt.  Richards,  R.  N. 
Capt.  Ross,  I.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 
Capt.  Bate,  R.  N. 

Do. 
Capt.  CoUinson,  R.  N. 
Lt.  Comdr.  Green,  U.  S.  N. 

Do. 
Capt.  CoUinson,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lt.  Comdr.  Green,  U.  S.  N. 
Capt.  CoUinson,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light- House  List. 

Do. 
Capt.  Richards,  R.  N. 
Capt.  Bate,  R.  N. 
Capt.  CoUinson,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 
Capt.  CoUinson,  R.  N. 


»U 


Page  672] 


TABLE  49. 

MARITIME  POSITIONS, 

EAST  COAST  OF  ASIA— Continued. 


a) 
O 
O 


Places. 


a 
g 


c 

H 
h 

e 


S 


a 

»m 


ft 


Video  Island , 

West  Volcano  Island 

Chapu  

Gutzlaff  Islands 

Saddle  Islands , 

Barren  Islands 

Shanghai 


Woosung 

Shaweishan  Island 

Pescadores  Island. 
Do 


Formosa  Island 

Formosa  Island,  Takau  . 

Formosa  Island    

FormosaIsland,Tam-sui 

Harbor. 
Formosa  Island,  Kelung 

Harbor. 
Formosa  I.,  San-o  Bay.. 
Botel  Tobago  Sima 


Cape 


Tanjong  Datu 

Sarawak 

Cape  Sirik 

Tanjong  Barram  . 

Bruni  River 

Labuan  Island,  Victoria 
Harbor. 

Balabac  Island 

Palawan    Island, 

Bovliluyan. 
Palawan  Island  . 
Palawan  I.,  Port  Royalist 
Palawan  Island,  Tai-Tai. 
Palawan  I.,  Port  Barton . 
Palawan  I.,  Cabuli  I 


Cuyo  Islet , 

Agutaya  Islet 

Quiniluban  Islet 

Culion  Island 

Busuanga  Island  , 

Apo  Islet  . 

Caluya  Island  . ., 

Semerara  Island . . 

Mindoro  Island  . . 

Do 


Do 

Do 

Do 

Do 

Do 

Luzon  I.,  Loro  Peak  . . . 

Luzon  L,  Caballo  I 

Luzon  I.,  Corregidor  Islet 
Luzon  I.,  Port  Cavite. 

Luzon  I.,  Manila 

Do 

Luzon  I.,  Port  Salanguin 
Luzon  I.,  Capones  islet 
Luzon  I.,  Yba  Point... 
Luzon  I.,  Ports  Masing 

loe  and  Mataloi. 
Luzon  I.,  Silaqui  Islet  . 


Exact  locations. 


Summit 

Light-house 

Battery 

Light-house 

N.  Saddle  light 

Centre,  50  feet 

English     consulate 

staff. 

Light-house  (left  bank) 
Light-house 


flag- 


Fisher  Island  light 

Second  point  on  N.  side 
of  Makung  Harbor. 

S.  cape   

Saracen  Head 

Port  Heongsan 

White  Fort 


S.  shore. 


Beach  near  village 
S.  extreme 


P^  Point  light 


Palace 

Raussey  Point  flag-staff. 


Peak 

S.  extreme 


Victoria  Peak,  5,680  feet. 

Tide  Pole  point !     943 


Lat.  N. 


30  20  25 
30  36     o 

30  47  38 
30  50  20 

30  43     o 

31  14  42 

31  23  22 
31  24  30 

23  32  53 

23  32  54 

21  55    o 

22  36  14 

24  46    o 

25  10  24 

25     8  25 

24  35  28 
22     I  40 

2    5  15 

1  43  50 

2  46    o 

2  3*J  15 

4  52  40 

5  16  33 


7  55  50 

8  20  25 

9  22  30 


Fort. 

Bubon  Point 

Summit,  N.  extreme. 


Town 

Summit  of  Mt.  Aguade 

Summit 

Culion  village 

Mt.  Tundalara , 

Summit 

do   

N.W.  bluff , 

Manguiram  Beach 

Sablayan  Point 

Monte  Calavite 

Port  Galera 

Point  1  )umaly , 

Vhn  Island   , 

Lubang  Island,  PortTulig 

Summit,  3,985  feet 

Light-house , 

do , 

Naval  headquarters 

Passig  light-house 

Cathedral .. 

Farallon 

Summit 

Extreme 

Bani  Point 


N.  E.  point. 


o  50 

0  29 

1  26 


43 
o 

19 

25 


o  51  27 

9    9 

25  47 

53  53 
2    9 

39  46 
5428 

5  38 
21  20 

50  15 
28  40 
31  28 

6  5 
17  IS 

49  30 
13  3 
4  22  30 
4  23  3 
4  28  55 
4  35  41 
4  35  31 
4  45  41 

4  55  33 

5  20  40 

5  34  48 
16  27  8 


Long.  E. 


o   /  // 

22  46   O 

21  51  45 

21  3   O 

22  ID   O 

22  40   O 

23  7  14 

21  28  55 

21  29  35 

22  14  15 

19  28   7 

19  30  12 

20  50  30 
20  16  33 

20  55  o 

21  25  o 

21  45  23 

21  49  27 

21  39  45 

09  39  7 

10  30  30 

11  21  o 

13  58  57 

14  55  15 

15  15  15 


17  3  o 

17  9  35 

18  17  30 

18  43  o 

19  30  55 
19  5  25 

19  29  55 

20  59  43 
20  56  26 
20  45  38 
20  o  18 
20  12  II 

20  27  18 

21  30  24 
21  19  3 
21  3  48 

20  43  59 
20  22  33 

20  57  24 

21  29  20 

21  I  53 

20  9  58 

20  37  14 
20  35  34 
20  33  46 

20  54  49 
20  57  18 
20  58  3 
20  2  54 

19  59  II 
19  55  46 
19  53  28 

119  55    6 


Authorities. 


Capt.  CoUinson,  R.  N. 

Do. 

Do. 
Light- House  List. 

Do. 
Capt.  CoUinson,  R.  N. 
Lt.  Comdr.  Green,  U.  S.  N. 

Light- House  List. 
Do. 

Do. 
Capt.  CoUinson,  R.  N. 

Mr.  Wilds,  R.  N. 
Capt.  Richards,  R.  N. 
Lieut  Brooker,  R.  N. 
Do. 

Capt.  CoUinson,  R.  N. 

Comdr.  Brooker,  R.  N. 
Capt.  Beechey,  R.  N. 

Comdr.  Reed,  R.  N. 
Light-House  List. 
Lieut.  Raper,  R.  N. 
Comdr.  Reed,  R.  N. 
Capt.  Gordon,  R.  N. 
Capt.  Belcher,  R.  N. 


Comdr.  Reed,  R.  N. 
Capt.  Bate,  R.  N. 

Do. 
Do. 
Do. 
Do. 
Do. 

Spanish  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lt.  Comdr.  Green,  U.  S.  N. 
Spanish  Hyd.  Office. 

Do. 

Do. 
Spanish  survey. 

Spanish  Hyd.  Office. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OP  ASIA— Continued. 


[Page  673 


O 

O 


X 


Places. 


Luzon  I.,  Port  San  Fer- 
nando. 

Luzon  I.,  Port  Santiago. 

Luzon  I,  Salomague  I  .. 

Luzon  I.,  Capa  Bojeador 

Luzon  I.,  Mairaira  Point 

Luzon  I.,  Cagayan  River 

Luzon  I.,  Port  San  Vi- 
cente. 

Luzon  I.,  Cape  Engano 

Luzon  I.,  Camiguin  I  .. 

Luzon  I.,  Fuga  Island.. 

Luzon  L.Dalupiri  Island 

Calayan  Island 

Babayan  Claro  Island..  . 

Balingtang  Islands 

Batan  Island ; 

Ibayat  Island 

Y'ami  Island 

Luzon  I.,  Port  Dimasa- 
lasan. 

Luzon  I.,  Polillo  Island. 

Luzon  I.,  .San  Miguel  I  . 

Luzon  I.,  Cautanduanco 
Islands. 

Do    

Luzon  I.,  Point  Calaan  . 

Luzon  I.,  Port  Sorsogon 

Masbate  Island 

Masbate  I.,  Camasusu  I. 

Masbate  I.,  Tintolo  Point 

Burias  Island 

Marinduque  Island 

Maestro  de  Campo  Isl- 
and, Port  Concepcion. 

Banton  Island 

Tablas  Island 

Do 

Carabao  Island , 

Runblon  Island 

Do 

Sibuyan  Island 

Samar  Island 

Samar  I.,  Cabatlogan  .. . 

Maripipi  Island 

Leyte  Island,  Palompon. 

Bojol  I,  Lapiniu  Island  . 

Cebu  Island,  Cebu 

Siquiquor  Island,   Port 
Canoan. 

Negros      Island,     Port 
Bunbonon.  j 

Negros  Island 

Negros  Island,  Bacalod  . 
Guimaras  Island,  Inam- 
pulugan  Island. 

Panay  Island 

Do 


Exact  locations. 


N.  point  of  entrance. 


Remarkable  tree  S.  of  port 

Summit 

Extreme , 

Semaphore 

E.  point  of  mouth 

San  \'icente  Islet 


Roiia  Islet 

Summit 

W.  summit 
Peak  ....    . 
N.  E.  point 
W.  point  . . 


Mount  Irada 

Mount  Santa  Rosa 
Islet  off  S.  W.  part 
Entrance 


Port  Polillo 

N.  point 

N.  islet 


S.  extreme 

do    

Tinacos  Islet 

Point  Bugui 

Summit 

Extreme 

Summit  of  mount 

Summit  of  Mount  Catala  . 
Point  Fernandez 

Banton  Mountain 

Tablas  Head 

Sanguilan  Point 

W.  point 

Sabang  Point  light 

.Summit  over  port  .. 

.Summit 

.S.  extreme 

Fort , 

.Summit 

Church .. 

Mount  Basiao , 

Fort , 

S.  point  of  entrance 


Lat.  N. 


E.  point  of  entrance . 


Volcano    of 
8,192  feet. 

Town 

S.  W.  point . . 


Malaspina, 


Do 

Panay  I.,  Batbatan  Island 
Panay  I.,  Pucio  Point  .. 
Panay  I.,  Port  Batan  .. . 
Siargao  I.,  Port  Sapao  .. 

Gibdo  I  sland 1 

Bncas  Island 1 

Mindanao  Island 

Do 


Ilo-Ilo  Fort   

San  Jose 

Pan  de  Azucar 

Summit 

Extreme 

Village   

Semaphore 

do    

E.  point  of  Port  Sibanga  . 

Surigao 

Cape  St.  Augustin 


16  37  40 

17  16  55 

17  47  49 

18  29  30 
18  39  2 
18  21  43 
18  28  32 

18  32  2 
18  50  26 

18  52  54 

19  3  3 
19  22  o 
19  30  o 

19  58  30 

20  28  30 

20  48  o 

21  4  56 
17  20  17 

4  51  o 
3  23  40 
490 


30 
II  35  40 
10  II 

9  53 
9 
9 
6 


26 
o 

41  34 
47  53 
14  30 


Long.  E. 


28  30 
31  20 

52  20 

36  56 
10  3 

56  9 
50  36 
18  10 

54  3 


15 
o 

3i 


2  56  56 
2  38  42 

2  33  44 

-> 

36 
35 

24  55 
o  o 

46  44 

I  47  30 
I  2  37 
o  3  22 

o  17  35 
9  15  17 


9  3  37 
10  24  35 

10  40  21 

10  26  38 

ID  41  32 

ID  44  8 

11  16  47 
II  28  20 
II  45 


o  /   // 
120  16  o 

20  25  7 
20  22  33 
20  32  25 

20  50  S3 

21  34  34 

22  4  14 

22  5  49 

21  48  26 

21  15  42 
21  II  28 

21  32   O 

21  52   O 

22  14  O 
22  I  20 
21  52  30 

21  58  24 

22  19  20 

21  54  48 

23  43  18 

24  6  48 


Authorities. 


448 
4  18 
49  22 
13  45 
13  35 
7  34 
15  57 
21  54  33 
21  43    8 


24 

24 

23 

23 

23 

23 
22 


22  4  48 
22  8  38 
21  58  32 
21  53  53 
17  8 
16  26 
33  23 
4 
37 
IS 
7 


22 

22 

22 

25  44 
24  51 
24  18 
24  22 
24  3^  35 
23  54  8 
23  34  26 


Spanish  Ilyd.  Office. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 
Spanish  survey. 

Do. 

Do. 

Do. 

Do. 

Do. 
Spanish  Hyd.  Office. 

Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Spanish,  survey. 

Spanish  Ilyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Spanish  survey. 


23     6     9     Spanish  Ilyd.  Office. 


23     7    5 

22  55  42 
22  40  20 

22  34  32 

21  54  27 

22  9    9 
21  52  36 

21  58  59 

22  28  50 
26    2  53 

25  31   17 
25  58  22 

25  28  30 

25  47  48 


Do. 

Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  574] 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  ASIA— Continued. 


o 
U 


Places. 


•a 
a 


a 

•m 

A 


•0 

a 


e 
0 

e 
e 


e 
a 
e 
M 

e 

■ 

e 


(8 


m 
V 
.A 
« 


Mindanao  Island,  Davao 
Mindanao  I.,  Saranguni 

Islets. 
Mindanao  I.,  Basianang 

Bay. 

Mindanao  I.,  Pollok 

Mindanao  I.,  Santa  Cruz 

Islands. 
Mindanao    I.,    Zumbo- 

omga. 
Mindanao  I.,  Sibuco  Bay 
Mindanao  I.,  Port  Sta. 

Maria. 

Mindanao  Island 

Mindanao  Island,   Port 
Misamis. 

Camiguin  Island 

Sombrero  Rock 

Piedra  Blanca 

Cagayanes  Islands . 


Exact  locations. 


Mole  . . . 
W.  islet. 


San  Miguel  Isles. 


Cagayan  de  Sulu  Island. 

Omapui  Island 

Sibutu  Island 

Simonor  Island 

Bahaltolis  Island 

Bongalao  Island 

Keenapoussan  Island... 

Bubuan  Island 

Cuad  Basang  Island  ... . 

Lamenusa  Island 

Bulipongpong  Island  . .  . 

Tapul  Island 

Sulu  Island 


Pearl  Bank 

Doc-can  Islet 

Sulu  Island,  Dalrymple 
Harbor. 

Sulu  Island 

Pangitaran  Island 

Basilan  Island 


Sandakin  Harbor 

Unsang 

Cape  Kaniongan  . 


Pamaroong  Island. 


Pulo  Laut 

Cape  Selatan 

Banjermasin 


Celebes  I.,  Port  Laykan 
Celebes  I.,  Macassar  ..  , 
Celebes  I.,  Palos  Bay.. . 

Celebes  I.,  Cape  Rivers, 
Celebes  I.,  Gorontalo.. . 

Celebes  Island 

Do 

Celebes  I.,  Bajuren  I  ..  , 
Celebes  I.,  Tagulanda  I. 
Celebes  I.,  Seao  Island 
Celebes  I.,  Sauguir  I .. 


N.  point  of  Donauang  I . . 

Small  hill  back  of  town  . . 
S.E.  islet 


Mole 


Hill  S.  of  beach. 
Fort 


Dapitan  Village 
Fort 


Mount  Camiguin 

Centre 

do  

Rocky  islet  between  two 

larger  islands. 
E.  point  of  Manuk  Ma- 

nukan. 

Middle  of  W.  coast 

N.  W.  extreme   

Hill  on  E.  coast 

N.W.  point 

Sandakan  Harbor  , 

S.  point 

Centre 

Lagoon  entrance 

S.  W.  point 

E.  point 

Centre  hill 

Centre  hill,  i  ,676  feet  . . . . 
Maimbun  Anchorage,  dry 

bank. 

W.  islet 

W.  extreme 

Tulyan  Islet 


Sulu  light-house 

S.  W.  point 

La  Isabela 


Bahalatolis  Island.. 

Anchorage 

E.  point  of  Borneo  , 


E.   point  of  delta  River 
Koetei. 

S.  point  Koengit  Islet 

Extreme  of  Sita  Point  .. . 
Residency  flag-staff 


S.  \V.  point  of  Celebes 
F"ort  flag-staff. 


Village  at  head . 


N.  E.  Cape,  Slime  Islet  .. 

Fort  Liato 

Menado  Fort 

N.  Cape 

Summit 

Peak 

Conical  peak 

S.  point  Cape  Palumbatu. 


Lat.  N. 


o      '  " 

7     I  22 

5  22  30 

6  28  50 

7  21  15 
6  52  15 

6  54  20 

7  18  5 
7  45  41 


8  40  15 

8  855 

9  10  19 
10  43  o 
10  27    o 

9  35  30 

7  43    o 


7 
4 
4 
4 
5 
5 
5 
5  25 


o  38 

54  10 

49  30 

55  30 

50  o 
o  30 

13    o 


15 
5  27  10 

5  33  o 
5  41  30 
5  44  30 
5  54  45 


50  45 
52  30 

2  30 

3  40 
15  15 

42  43 


5  50    o 
5  16  30 
I     4    o 
Lat.  S. 
o  45     O 

4    5  42 

4  10  40 

3  18  55 

5  36    o 
588 

0  57    o 
Lat.  N. 

I 
o 
I 

1  45 

2  7 
2  22 

2  44 

3  21 


Long.  E. 


20     o 

29  41 

29  39 

5 
o 

o 

o 

o 


25  34  35 
25  13  48 

23  57  37 

24  II  42 
22    4    o 


22 


29 


22     3  18 
22    4  58 


23  23  13 

23  48  43 

24  42  50 
21  33  o 
2130 
21  23  30 

18  27    o 

18  26    6 

19  22  45 
19  48  o 
19  46  45 

18  II     o 

19  44  15 

20  40  45 
20  35  o 
20  II  30 
20  56  35 
20  49  45 

20  55     o 

21  O   40 

19  37  30 

19  44    o 

21   18  20 

20  58  40 

20  29  30 

21  56  50 

18  II      o 

19  16     o 

18  56    o 

17  37    o 

16  I  40 
14  42  18 
14  34  56 

19  26  o 
19  23  59 

19  47  30 

20  43  30 

23  2  50 

24  49  44 

24  39  24 

25  22     o 

25  24  30 
25  26  o 
25  39    o 


Authorities. 


Spanish  Hyd.  Office. 
Do. 

Spanish  survey. 

Do. 
Do. 

Spanish  Hyd.  Office. 

Spanish  survey. 
Do. 


Spanish  Hyd.  Office. 
Spanish  survey. 

Spanish  Hyd.  Office. 
Spanish  survey. 

Do. 

Do. 

L>o. 

Capt.  Chimmo,  R.  N. 

Do. 

Do. 

Do. 
Spanish  survey, 
Capt.  Chimmo,  R.  N. 

Do. 

Do. 

Do. 
Spanish  survey. 
Capt.  Chimmo,  R.  N. 

Do. 
Spanish  survey. 

Capt.  Chimmo,  R.  N, 
Do. 
Do. 

Light-House  List. 
Capt.  Chimmo,  R.  N. 
Spanish  Hyd.  Office. 

Spanish  charts. 
Capt.  Chimmo,  R.  N. 
Chart. 

Chart. 

Netherlands  Hyd.  Office. 
Do. 
Do. 

Sir  E.  Belcher. 
Dutch  H.  O. 
Van  Loo. 

Sir  E.  Belcher. 
Netherlands  Hyd.  Office. 

Do. 

Do. 
Spanish  survey. 

Do. 

Do. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  ASIA— Continued. 


[Page  575 


d 
o 


Places. 


.fi 


Celebes  I.,  Taluat  I 

Celebes  I.,  CapeFlesko. 

Celebes  I.,  Cape  Talabo. 
Celebes  I.,  Wowoni  I  .. 
Celebes  I.,  Bouten  Is  .. 

Do 

Do 

Celebes 
Celebes 

Do 


Cape  Lassa 
Salayar  I  .  . 


Anjer  (time-ball) . . . 

Bantam 

Batavia  (time- ball) 

Buitenzorg 

Boompjeo  Island... 

Chenboa  

Tegal  Mountain 

Pekalongan 

Samarang 

Rembang 

Sourabaya   

Do 

Pasveroean 

Madura  Island 

Do 

Bezoekie 

Cape  Sedano     

Banjowangie 

Banliman 

Barung  Island    

Kambangan  Island. 
Cape  Anjoe  .    


Exact  locations. 


Kabruang  I. 
Extreme 


S.  E.  point. 


E. end  

N.  point  . . . 

do  ... 

E.  point 

S.  W.  point . 

Extreme 

N.  point 

S.  point 


Fourth  Point  light . . . 

Flag-staff 

Observatory 

Palace  tower 

Racket  Island  light . . 

Light-house    ... 

Peak 

Light  \V.  of  entrance 

Lookout  station 

Residency  flag-staff. . 

Citadel  Tower 

Time-ball  station 

Flag-staff  on  beach  . . 

Bangkalau 

Soemenep  flag-staff. . 

Flag-staff 

N.  E.  point  of  Java  . . 

Flag-staff 

S.  point  of  Java 

S.  point 

Light-house , 

Extreme , 


Karimon  Djawa  Island 

Bawean  Island 

Great  Solombo  Island  . 
Arentes  Island 


Kangeang  Island 

Bali  Island 

Do ... 

Bali  I.,  Bali  Badong  Bay. 
Lombok  Island 

Do 

Sumbawa  Island 

Sumbawa  Island,  Tam- 
bora  \^olcano. 

Sumbawa  Island 

Pastilion  Islands 

Do 

Ardassier  Islands 

Brill  Reef.    

Hegadis  Island 

Token  Bessi  Island 

Do 

Gunong  Api 

Lucipari  Islands 

Flores  Island 

Do 

Do 

Kamba  Island 

Adenara  Island 

Lombata  Island 

Pantar  Island 

Ornbay  Island 

Timor  Island 

Do 


Flag-staff 

Sangkapoera  flag-staff  . .. 

N.  W.  point 

S.  point 

N.  W.  point 

Billing  light 

Peak.  11,326  feet 

Kotta  village 

Peak,  12,379  feet 

Ampanam  flag- staff 

Sumbawa  village 

Summit,  E.  side  of  crater. 

Bima  flag-staff 

N.  island 

Maria  Reigersbergen  I.. . 

S.  one 

Light-house 


Lat.  N. 


Long.  E. 


3  49 

o  27 

Lat.  S 
O  46 

3  58 

4  23  , 

5 
5 
5 
5 
6 


15 
41 

35 
47 
26 


30 

30 

2 

18 


43  45 
49  o 
8  12  50 
8  47  o 
8  32    o 

7  46  30 
7  25    o 


8  27 

631 
7  30 


Wangi-Wangi,  N.W.  point 

Binongko,  S.  point 

\  olcano 

N.  islet 

Reo  village 

Ende  village 

Flores  Head,  extreme  . . . 

Peak,  S.  part  . 

Summit,  Mount  Woka  ... - 

Mount  Lamararap 

S.  peak  of  saddle  on  S.  pt 

Dololo  anchorage 

Deli  custom-house 

Atapoepoe  


7 
6 
6 

5 
6 

6 

5 


o 
o 
o 
o 

50 

o 
o 
o 
o 


35 

5 

7 
15 
17 

43 

28  30 
8  16  15 
8  50  55 

8    4  45 

7  48    o 

8  20  30 

8  33  o 
8  34  o 
8  12  o 
8  34  o 
900 


o 
0 

o 
o 

30 

o 
20 
o 
o 
o 

4  18 
I  20 
7  40 


6 
6 
6 

6  35  45 

5  54  40 

6  42    o 

13 

54 
58 
42 


13  34 
12  10 

37  50 
I  30  ! 
o 


52  57 
51  18 
32  28 

5  46 
50  30 

4  o 
8  21  o 
8  42  30 
8  23    o 

8  34  15 
8  32  o 
8  12  30 


27    2  30 
24  26     o 


23  27 


o 
o 
o 
o 

30 

o 
o 


23  4 
23  16 
22  26 
20  29 
20  30 
20  28  30 

05  52  30 

06  8  20 
06  48  25 
06  47  22 
08  22  50 

08  34 

09  13 

09  39 

10  25 

11  20  13 

12  44  15 
12  43  40 
12  54  46 

12  44  28 

13  53  45 

13  38  o 

14  26  53 
14  22  50 
14  25  13 

13  15  o 

09  I  55 
06  24  30 

10  25  II 
12  38  52 

14  23  42 

14  35  o 

15  12  o 

15  5  50 
15  28  o 

15  8  47 

16  27  30 

16  3  40 

17  20  ^^ 

17  57  o 

18  43  55 
18  43  o 
17  56  o 

17  22   O 

18  56  50 
22  40   O 


Authorities. 


23 


32  o 
23  59  o 

26  43  30 

27  30  o 

20  29  55 

21  38  40 

22  52  o 

23  34 

23  15 

23  22 

24  6 

24  23 

25  33  39 
24  47  7 


Spanish  survey. 
China  Sea  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 
Sir  J.  Brooke. 
Chart. 

Do. 

Netherlands  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
China  Sea  Directory. 
Netherlands  Hyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
China  Sea  Directory. 

Do. 
Netherlands  Hyd.  Office. 
China  Pilot. 

Do. 
Netherlands  Hyd.  Office. 
China  Pilot. 

Netherlands  Hyd.  Office. 

Do. 
Chart,  1883. 

Do. 
China  Pilot. 

Netherlands  Hyd.  Office. 
Rietveld. 

Netherlands  Hyd.  Office. 
Dutch  survey. 
Netherlands  Plyd.  Office. 

Do. 
Dutch  survey. 

Netherlands  Hyd.  Oflfice. 
Chart. 

Do. 

Do. 
Nether' ands  Hyd.  Office. 
China  Pilot. 
Chart. 

Do. 

Do. 

Do. 
Netherlands  Hyd.  Office. 

Do. 
Dutch  survey. 
China  Pilot. 
Dutch  iurvey. 

Do. 

Do. 

Do. 
Netherlands  Hyd.  Office. 

Do. 


Page  576] 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  ASIA— Continued. 


V 

"9 
B 


Places. 


el 
a 


Timor  Island 

Rotti  Island 

Saru  Island 

Sandalwood  Island . . 

Wetter  Island     

Roma  Island 

Moa  Island 

Sermalta  Island 

Damma  Island 

Nila  Island   

Mano  or  Bird  Island. 
Timer  Laut  Island  .  . 

Vordate  Island 

Mulu  Island 


Exact  locations. 


Arru  Islands 

Do 

Great  Ki  Island 

Tello  Islands 

Tehor  Island 

Matabella  Islands 

Goram  Islands 

Banda  Island 

Boero  Island,  Kajeli 

Ceram  Island   

Amboina  Island 

XuUa  Is.,  Taliabo  I -land 
XuUa  Is.,  Mangola  I  .  . . 
Xulla  Is.,  Besi  Island  .. 

Oby  Major  Island 

Popa  Island 

Mysole  Island 


Geby  Islands 


Koepang,  Fort  Concordia 

W.  point 

Seba  Bay,  on  N,  W.  side  . 

Nangamessie    

Sanw  village 

W.  point 

Buffalo  Peak,  4,100  feet.. 

N.  E.  point 

Kulewatta  Harbor,  N.  pt 

Centre 

, do    

( 'lilet,  on  E.  coast 

S.  point 

N.  point 

.S.  island 

N.  point  . 

S.  point 

S.  island,  summit 

N.  E.  point 

Kukur . 

Goram,  S.  E.  point 

Mole 

Fort  Defensie  

Kawa 

Fort  flag-staff 

N.  W.  point 

S.  E.  point 

do   

W.  point 

S.  H.  point 

Elbe  Harbor 


N.  W.  point 


Gillolo  Island S.  point 


Gillolo  I.,  Cape  Tabo. . . 
Gillolo  I.,  Cape  Salawag  [ 
Gillolo  I.,  Derrick  Point 
Molucca  Is.,  Makkian  I. 
Molucca  Is.,  Ternate  I  . 


E.  extreme 

N.  E.  point 

N.  extreme 

Fort  Reeburgh 

Residency  flag-staff. 


Molucca  Is.,  Batchian  I. '  P^ort  Barneveld 


Port 


Tai- 


Meiaco-Sima  Is.,  Kumi  I 
Meiaco-Sima    Islands, 

Broughton  Bay 
Meiaco-Sima    Is., 

Haddington. 
Meiaco-Sima    Is., 

pin-san. 

Raleigh  Rock 

Ti-ao-usu  Island 

Hoa-pin-su  Island 

Lu-Chuls.,  Gt.  Lu  Chu. 

Do 

Lu-Chu  Islands 

Do 

Lu-Chu  Is.,  Kakirouma 
Lu-Chu  Is.,  Iwo  sima  .. 
Lu-Chu  Is.,  Oho-sinia  .. 
Lu-Chu  Is.,  Kikai-sima  . 


N.  beach 

Landing-place  . 

Hamilton  point 

I.W.Bay 


Summit,  270  feet 

Summit,  600  feet 

N.  face  

Nafa-Kiang 

Oonting  village 

Yori-sima,  413  feet    

Yerabu-sima  peak,  687 feet 

Summit,  2,207  feet 

Volcano,  541  feet 

N.  extreme 

.Summit,  867  feet 


Lat.  S. 


Wang-kia-tia  Bay |  Langwang  Temple 

Staunton  Island Landing-place,  N.  side. . 

Shantung  Promontory  . .     Extreme 


Che-Foo 
Che-foo  Harbor. 


Light  house 

Fort  in  village  bay 


10  9  49 
10  46  o 
10  29  o 

9  35  3 
7  56 

7  38 

8  12 
8  14 

-% 

44 
33 

55 
4 

35 
10 
20 

56 
20 

44 

33 

4 


7 
6 

5 
7 
7 
6 

7 
5 
5 
5 
4 
4 
4 
4 

3 

2 

3 
I 

I 

2 

I 

I 

2 


o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 
o 

31  53 

22  48 

55  52 
41  30 
44  o 
55  30 
28  o 
30  o 
12  o 

4  o 
Lat.  N. 
022 
Lat.  S. 
O  50  O 
Lat.  N. 

0  II  O 

1  26  O 

2  12   O 

o  24  o 

o  47  13 
Lat.  S. 
o  37  o 
Lat.  N. 
24  26  O 
24  21  30 

24  25  O 
24  43  35 


25  55  o 
25  58  30 

25  47  7 

26  12  25 

26  40  42 

27  2  o 

27  21  o 

27  44  o 

27  53  o 

28  31  40 
28  18  o 


Long.  E. 


35  39  o 

36  45  29 

37  24  30 
37  34  10 
37  36  o 


23  33  39 
22  52  o 
21  46  o 
20  14  30 

26  24 

27  19 

28  I 

29  o 

28  28 

29  29 

30  20 

31  23  30 

31  55  o 

31  40 
34  24 
34  40 

32  54 
31  58 
31  47 
31  50 


30 


o 
o 
o 
o 
o 
o 
o 
o 
o 

18 
46 


29  53 

27  6 

28  6 

28  10  17 
22  20  o 
26  14 

26  I 

27  18 

29  50 

30  12 


29  17  30 
28  23  o 

28  52  o 
28  37  o 
28  3  30 
27  21  o 
27  22  21 

27  25  30 

22  56  o 
24  17  40 

24  6  40 

25  17  49 


10 


24  35 
23  40 

23  30 

27  40 

28  o  o 
28  25  24 
28  33  10 
28  59  o 

28  14  30 

29  42  30 
29  59  o 


19  51  30 
22  16  48 
22  42  30 
21  31  30 
21  26  21 


Authorities. 


Dutch  survey. 
De  Vrieze. 
Dutch  survey. 
Netherlands  Hyd.  Office. 
Dutch  survey. 

Do. 
Owen  Stanley. 

Do. 
Chart. 

Do. 

Do. 
Owen  Stanley. 

Do. 
Chart. 

Do. 

Do. 
Owen  Stanley. 
Chart. 

Do. 

Do. 

Do. 
Netherlands  Hyd.  Office. 

Do. 

Do. 

Do. 
Chart. 

Do. 

Do. 

Do. 
Findlay. 
Forrest. 

Duperry. 

Dutch  chart. 

Do. 

Do. 
Netherlands  Hyd.  Office. 
Chart. 
Netherlands  Hyd.  Office. 

Chart. 

Capt.  Belcher,  R.  N. 
Do. 

China  Sea  Directory. 

Capt.  Belcher,  R.  N. 

H.  M.  S.  Serpent. 
China  Sea  Directory, 
Capt.  Belcher,  R.  N. 
U.  S. survey. 
Capt.  Hall,  R.  N. 
China  Sea  Directory. 

Do. 

Do. 

Do. 
U.  S.  survey. 
China  Sea  Directory. 

Mr.  Bullock,  R.  N. 
Mr.  Wilds,  R.  N, 
Capt.  Ward,  R.  N. 
Light-House  List. 
Capt.  Ward,  R.  N. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  CO  ft-ST  OF  ASIA  -Continued. 


[Page  577 


Places. 


Miautao  Island 
Pei-IIo  River.. 
Tientsin 


Shalaitien  Island 

N  ewchang 

Hulu-shan  Bay 

Port  Adams 

Lian-ti-shan  Promontory 

Ta-lienwhan  Bay 

Round  Island 

Thornton    Haven,   Ilai- 
yun-tan  Island. 

Choda  Island   

Sir  James  Hall  Islands.. 

Marjoribanks  Harbor 

Tas  de  foin  Islet 

Wai  ian-do  Island 

Guerin  Island 

Kokoun-tan  Islands 

Barren  Island 

Sea  Rock  

Modeste  Island 

Ross  Island 

Kuper  Harbor 

Port  Hamilton 

Bate  Islands 

Montravel  Island 

Quelpart  Islands 


Exact  locations. 


Peak  of  N.  island 

S.  Taku  Fort,  S.  Cavalier  . 
Shore  opposite  N.E.  angle 

o*"  wall. 

Joss  House 

Pagoda  

N.  side 

Entry  Island 

S.W.  point 

Isthmus  on  S.  Sanshan  I  .' 

Summit 

Beach    opposite   Temple 

Point. 


Lat.  N. 

0     / 

II 

3823 
3858 
39    9 

16 
0 

Observation  Island 

Sentinel  Island 

Broughton  Head 

Tsan-liang-hai  Harbor 
Tsu-sima  


Iki  Sima 

Oro  No  Sima . 

Kosime  No  'Jsima 

Yeboshisima 

Yobuko  Harbor . . . 

Hirado  Sima 

Goto  Island 

Pallas  Rocks 

Meac  Sima 

Nagasaki 

Kutchinotsu 

Kagoshima 

Tsukarase  Rocks  . 

Udsi  Sima 

Yamagawa  Harbor 

Satano  Misaki 

Lin.schoten    Is., 

kaki  Sima. 
Linschoten    Is. 

Sima. 
Linschoten   Is., 

Sima. 
Linschoten     Is. 

Simp. 
Linschoten  Is.,  Use  Islet 
Lirschnieii  Is.,  Kowose 

kocks. 
Linschoten  Is.,  Yakuno 

hima. 
Linschoten    Is.,    Firase 

Rocks. 

37    ^ 


Kusa- 
Kuro 

Ivvoga 
Take 


S.  point 

N.  island 

Manzoc  Islet 

Centre 

....   do   

Summit,  969  feet 

Camp  Islet    

Centre,  600  feet 

Centre,  160  feet 

N.  peak,  1 ,  228  feet 

Peak,  1,920  feet 

N.  E.  e.xtreme  of  Josling  I 
W.  point  of  ( )bs.  Island  . . 
Summit  Thornton  Islet  .. 

Centre,  1,041  feet 

Beaufort    Island,    middle 
of  \V.  side.  ! 

Point  of  W.  arm ! 

Summit,  400  feet 

Extreme 1 

N.  point  of  Deer  Island  . . ' 
Observation  rock 

.Summit,  S.  end  of  island. 

Summit,  277  feet 

Summit  ^^"ilson  Island..  . 

Light-house 

Bluff  opposite  Nicoya 

Taske  light 

Ose  Saki  light 

S.  rock  

Ears  Peak 

Minage  Point 

Light- house 

Iheakw ater  light 

Summit,  96  feet 

High  peak,  1,097  feet 

Spit  \.  of  town 

Light  house 

Ingersoll  Rocks,  530  feet 

2,160  feet 


38  53     o 
40  43  12 

39  40  46 
39  16    o 

38  43    o 
38  52  38 

38  40     o 

39  4    o 


38  27  o 
37  58  o 
36  26  45 
36  24  30 

36  15  45 
36     7    " 

35  48 
35  21  o 
34  42  o 
34  42  30 
34  6  o 
17  20 
I  23 
33  57  o 
33  59  o 
3i   29  40 


34 
34 


34  39 
34  33 

34  48 

35  6 
34  18 

33  44 
22,  52 
?,?>  53 
2i   41 


o 
6 

55 

30 
10 

50 


J  J 


33 

32  36  45 
32  13  12 
32  3  o 
32  44  28 
32  36 

31  32 

20 

12  o 

_   12  43 

30  58  (0)i 
30  51  o 


31 


5 

5 
o 


31 


Long.  E. 


O   /   /; 

120  55  O 

117  42  48 

117  II  44 

118  32  30 
122  14  14 

121  17  34 

121  35  59 

121   8  o 

121  51  59 

122  II  30 

123  10  34 


124  34  40 


124  34 
126  28 
126  24 
126  9 
126  I 


8   126  -,i 


o 
o 

50 
9 
o 

125  58  o 

126  19  45 
125  16  o 

125  7  o 

126  35  28 

127  18  34 
126  18  o 
126  55  o 
126  58  25 

128  14  o 
128  40  o 

128  44  o 

129  I  49 
129  13  6 


129  42 

130  2 


50  25 


30 
o 

20 

129  58  50 
129  52  43 

129  33  33 
^,6  ' 


6 

39 
o 

18 

40 


128  ^ 
128  "4 

128  25 

129  51 

130  13 
130  30  21 

129  46  20 

129  29 

130  37 
130  40 

129  28 


0 
o 

(«) 
o 


Peak,  2,469  feet. 
Peak,  816  feet  .. 


Peak,  206  feet 
Peak,  15  feet  . 


Mount  Malomi,  6252  feet. 
Highest,  92  feet 


30  50 

0 

129  57    0 

Do. 

30  48 

0 

130  19    0 

Do. 

30  49 

0 

130  26  30 

Do. 

30  44 
30  43 

0 

0 

130     7    0 
130  22    0 

U. 

Do. 
S.  S.  Powhatan. 

Authorities. 


Capt.Ward,R.N. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
English  survey. 
Lieut.  Buttock,  R.  N. 


French  frigate  Virginie. 
Com.  Shufeldt,  U.S.  N. 
French  frigate  Virginie. 

Do. 

Do. 

Do. 

Do. 
Capt.  Hall,  R.  N. 
Com.  Wilds,  R.  N. 
Capt.  Hall,  R.  N. 
Capt.  Bullock,  R.  N. 
Com.  WMs,  R.  N. 
Capt.  Richards,  R.  N. 
Com.  Wilds,  R.N. 

Do. 
Capt.  Belcher,  R.  N. 

Capt.  Bullock.  R.  N. 

Do. 
Com.  Wilds,  R.  N. 
Com.  Ward,  R.  N. 

Do. 

Com.  Brooker,  R.  N. 

Do. 
Com.  Ward,  R.  N. 
Light-House  List. 
Com.  Brooker,  R.  N. 

Do. 
Light-House  List. 
Comdr.  Perkins,  U.  S.  N. 
Capt.  Richards,  R.  N. 
Lt.  Comdr.  Green,  U.  S.  N 
Light- House  List. 

Do. 
H.  M.  S.  Retribution. 
French  survey. 
Japanese  survey. 
Light-House  List. 
China  Sea  Directory. 


30  21     o      130  29    o 
30     5     o      130     3     o 


China  Sea  Directory. 
Do. 


Page  578] 


o 
O 


Si 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  ASIA— Continued. 


Places. 


Kutsino 


Is.,    Hebi 


Is.,    Naka 


Is.,  Sunago 
Is.,  Tokara 


Linschoten  Is 

Sima. 
Linschoten 

.Sima. 
Linschoten 

Sima. 
Linscho:.en 

Sima. 

Linschoten  Is., Fira Sima 
Linschoten    Is  ,    Suwa 

Sima. 
Linschoten  Is.,  Aknisi 

Sima. 
Linschoten 

Islets. 
Linschoten 

Sima. 
Linschoten  Is.,  Yoke  Sima 

Tokio 

Simonoseki  _. 

Rockuren  Island 

Shirasu  Reef 

Susaki  

Tomo  Roads   

Port  Okoyama 

Wusimado  Port 

Akashi-no-seto   

Hiogo 

Kob^ 

Osaka  

Sakai    

Osaki  Bay 

Yura  No  Uchi 

Tanabe  Bay  

Oosima  Haibor 

Ura-kami  Harbor 

Owase  Bay 

Goza  Harbor    

Matoya  Harbor 

Omoi-saki 

Simidsu  Bay 

Mikomoto  Island 

Simoda  Harbor 

Yokoska  Harbor    

Yokohama 

No  Sima-saki    

Vries  Island  (Go  Simaj  . 

Kosu  Sima  Volcano 

Miaki  Sima 

Redfield  Rocks 

Mikura  Island 

Broughton  Rocks 

Fatsizio  Island 

Aogo  Sima 

Bayonnai^t.  Island   

.Smith  I  sland 

PonafitHn  Island 

Lot's  Wife  Rock 

Inu-Bo-Ye  Saki 

Kiuk  Wasan  Island 

Kama-i-shi  Harbor 

Yamada  Harbor 

Siriya  .Saki 

Toriwi  Saki 

Awomori   

Tatsupi  Saki     

Bittern  Rocks 

Tabu  Sima 


Exact  locations. 


Summit,  2,230  feet 
Summit,  1,687  feet 


Is.,  Kohebi      Summit,  996  feet. 


Peak,  3,400  feet 

Summit,  812  feet 
Volcano,  2,706  feet  . 


Summit,  1,978  feet 
Highest,  372  feet... 


.Summit,  860  feet 


Lat.  N. 


o     /     // 
29  59    o 

29  54  o 
29  53  o 
29  52    o 


29  41 

29  38 


.Summit,  1,700  feet 

Naval  Observatory 

Mozo  Saki,  S.  part 

Light-house 

do   

S.  W.liattery 

'I'amatz  Sima 

Tak^  Sima  temple 

W'usim.-ido  Peak  (548  feet) 

Maiko  Fort 

Wada  Misaki  light 

W.  Oamber 

Fort  'I'emplosan  light     . . 

Pier  liead  light 

Tree  Islet,  S.  point 

Pier 


18 
o 

35  12 
7  42 


Fossil  Point    

Kashinosaki light,  E.  point 

Village  point 

Hikimoto 

O.  Sima  Islet 

Anori-saki  light 

Light-house 

Mound  on  point   ... 

Light-house 

Centre  Island 

Evi  Yama  Point 

Flag-staff  on  Eng.  S.  H.. 

Light-house 

S.  E.  point 

Summit,  2,000  feet 

Summit,  2,690  feet 

S.  rock 

Summit 

Summit,  60  feet 

Observation  spot 

Summit,  800  feet 

.Summit,  26  feet 

Summit,  250  feet 

Summit,  1,328  feet 

Summit,  300  feet 

Light-house 

do   

S.  E.  end  of  village 

Ko-sima,  90  feet 

Light-house 

Centre  of  Low  Islet  off . 

Light-house 

N.  side 

S.  W.  Rock 

E.  extreme 


29  27  o 
29  13  o 

29  8  o 

28  47  30 
35  39  17 
33  58  o 
33  58  53 
33  59  II 

33  23  19 

34  22  37 

34  35  5« 

34  37  27 

34  38  29 

34  40  o 

34  41 

34  40 

34 

34 

33   57  34 

33   41  14 

33  28  15 

33  33   37 

34  6  10 

34  13  52 
34  21  55 

34  35  46 

35  o  51 
34  34  20 

34  39  49 

35  17  30 
35  26  24 
34  53  20 
34  39  30 
34  13  15 

34  5  o 
33  56  50 
33  52  o 
33  39  o 
33  4  24 
32  37  30 
32  o  40 
31  18  o 

30  33    o 

29  47  o 

35  43  30 

38  19  o 

39  16  30 

39  27  17 
41  26  10 

41  33   34 

40  51  45 

41  16 

40  31 
39  II 


17 
o 

53 


Long.  E. 


o   /   // 

29  55  o 
29  33  o 
29  3.8  o 
29  52  30 

29  32  30 
29  43  o 

29  37  o 
29  21  o 
29  13  30 

29  I  30 

39  44  30 

30  58  24 
30  52  31 
3G  47  56 
33   17  o 


J.I 

34 
35 
35 
35 
35 
35 
35 
35 


35  23 

35  52 

35 

36 


23 
24 
21 

59 
o 

14 

o 

44 
19 
16 

4 
10 

54  25 

14  35 


59 
9 
I 

12 
II 

27 

27 

8 

7 


54  44 
I 


b   4S  51 
36 

38  . 
3831 
38  57 

38  57  30 

39  39  43 
39  39  13 
^-^  53 


28 

19 
10 


39  28 
39  8 
39  31 

38  48 

39  34 


57 
o 
o 
o 

15 

o 

39  17  45 
39  50  24 

39  37  30 

40  o  o 

39  52  o 

40  15  o 
40  22  30 

40  53  30 

41  31  o 

52  50 
59  o 

29  25 
40  56 

40  45 
40  22  37 

39  31  o 

39  34  17 


41 
41 

41 


15 


Authorities. 


China  Sea  Directory. 

Do. 

Do. 

Do. 

Do. 
Do. 

Do. 

Do. 

Do. 

Do. 
Tokio  Hyd.  Bureau. 
Com.  Ward,  R.  N. 
Light- House  List. 

Do. 
Com.  St.  John,  R.  N. 
Lieut.  Bullock,  R.N. 
Prcnch  survey. 

J'o. 
Lieut.  Maxwell,  R.  N. 
Light- House  List. 
Japanese  Hyd.  Office. 

Liglit-I  louse  List. 
Lieut,  liullock,  R.  N. 

Do. 

Do. 
Light- House  List. 
Com.  Ward,  R.  N. 
Com.  St.  John,  R.  N. 

Do. 
Light-House  List. 

Do. 
Com.  Ward,  R.  N. 
Light-House  List. 
Lieut.  Brooke,  U.  S.  N. 
Lieut.  Banare,  Fr.  N. 
Lt.  Comdr.  Green,  U.  S.  N. 
Light- House  List. 
Com. Ward,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
U.  S. survey. 
H.  M.  S.  Tribune. 
U.  .S.  survey. 
U.  S.  S.  Macedonian. 
Light- House  List. 

Do. 
Capt.  \  anagi,  J.  N, 
Com.  St.  John,  R.  N. 
Light- House  List. 
Capt.  Richards,  R.  N. 
Light -House  List. 
Capt.  Richards,  R.  N. 

Do. 
Com.  Ward,  R.N. 


TABLE  49. 

MARITIME  POSITIONS. 

EAST  COAST  OF  ASIA— Continued. 


[Page  579 


o 

u 


Places. 


a 

OS 


e 

iS 


s 

e 


Awa  Sima 

Sack)  Island 

Fusliiki  Harbor. 
Cape  Roigen  . . . 

Niigata     

^[ana  Sima    


Exact  locations. 


Manao  I  larl^or 

Tsuruga  

Oki  Islands 

Taka  \'ama(Cape  Louisa) 

Ai  Sima „  . 

Mine  Sima    

Kadosinia  Island 

I  lakodadi    

Endernio  Harbor  

Akishi  Bay 


Noshiap  Saki 

Nemero   

Notske  Anchorage 

(."ape  Nossyah 

Risiri  Islet 


N.  E.  extreme 

\'a  Saki 

Light-house 

Extreme 

Buddhist  temple 

Summit,  200  feet 

Sorenjo  Point 

Town 

N.  point 

Extreme 

Summit,  300  feet 

Summit,  492  feet 

Tsuno  Shuna  light 

Entrance  to  Kamida  Creek 

Bluff  on  E.  side 

Sand  spit  N.  of  Aino  Vil- 
lage. 

Light-house 

Benten  Sima  light 

Village     

Extreme    

Peak,  5,713  feet 


Lat.  N. 


38  29  36 

38  19  55 

36  47  47 

37  28    o 

37  55  H 
37  35  o 
37    2  37 

35  40  24 

36  30    o 
34  40 
34  32 
34  48 
34  21 

41  47    s 

42  19  54 

43  2  22 


point , 


Kunashir  Island 

Iturup  Island 

Urup  Island 

Broughton  Island 

Simusir  Island 

Ketoy  Island 

Matana  Island Peak 

.Shiash-Kotan  Is-land Centre 

Kharim-Kotan  Island 

(Xme-Kotan  Island 

Moukon  rushi  Island  . 

Poro  musir  Island 

Soumshu  Island 


St.  Anthony's  Peak 44  20  o 

N.  E.  point 45  38  30 

Cape  Vanderlind 45  37  o 

Summit '  46  42  30 

Prevost  Peak '  47     2  50 


43  23 
43  20 
43  33 
45  25  50 
45  II  o 


Peak 

S.  W.  point . 

Centre 

Fool's  Peak 


Cape  Clonard Extreme !  36 

Ping-hai  I  larbor ; i  36 

1  .iancourt  Rocks !   Summit,  410  feet '  37 

Matu  Sima ^ 

Port  Lazaref 


45 
o 

o 

Peak,  4,000  feet !  37  3°     o 

S.  i^  miles  from  the  S.      39   19   12 
end  of  Bontenef  Island. 


5 

36 
14 


Summit,  12  feet 

W.  point  of  entrance.  . . 
Lighthouse  (building) 


Light-house  (building) . 

do 

Orekhera  Point 


Wawoda  Rock 

Expedition  Bay , 

Port  Novogorod  . 

Wrangel  Bay    

Cape  Pavorotnoi  . . 

Port  Olga 

St.  Vladimir  Bay  . 

Shelter  Bay 

Sybillo  Bay , 

Pique  Bay 1 

Bullock  Bay I 

Luke  Point j  Extreme 

Cape  Disappointment . .  J do 

Cape  Suffren    ' do 

Imperial  Port Cape     Mouvarieff 

(building). 

Castires  Bay |  Quoin  Point  light 

Saghalien   Island,   Cape  [  S.  point 

Xotoro. 
-Saghalien    Island,  Cape 

(iiretoko. 
Saghalien   Island,   Cape 

I'-lizabeth. 

Nikalaevsk 1 

Great  Shantar  Island  . . 


light 


42  14  30 
42  37  22 
42  33  40 
42  44  18 

42  38  o 

43  22  o 

43  53  40 

44  30  o 

44  43  45 

44  46  15 

45  5  o 
45  19  30 

45  41  30 
47  20  o 
49  o  o 

51  26  o 

45  54  15 


Extreme '  46  i  20 


N.  point 


Cathedral 
N.  point  . 


54  24  30 


53 
55 


8 
II 


o 
o 
o 

30 


o 

o 

II 


47  17  30 

48  6  o 

48  52  o 

49  8  o 
49  19  o 

49  51  o 

50  15  36 


Centre 50  46  o 


Long.  E. 


7 
9 
42 
o 
I 
o 


39  16 

38  27 

37  3 
37  22 

39  3 
36  54 
36  58  24 

I  22 
2^  o 
o 
o 
o 
o 


36 

33  -j 
31  36 


31 
31 


18 
9 
30  50 
40  43  44 
40  59  33 

44  51  50 

45  48 


45 


o 
o 

45  18  o 

41  39  50 
41  19  o 

46  15  o 
49  14  o 

49  34  o 

50  28  30 

51  52  50 

52  24  o 

53  12  30 

54  8 
54  39 
54  44 


54  . 

56  15  20 

56  26  o 


29  33 

29  20 

31  55 

30  53 
27  32 


30 
o 
o 
o 

48 


37  17  o 

30  44  10 

31  10  o 

2  3 

o  30 

15  o 

27 

36  2 
36  22 
36  27  15 

36  44  o 

37  10  15 
3738 

38  58 
40  27 


33 

33 
35 
35 


19 

o 

^o 


15 

o 


40  52  o 

42  9  30 

43  26  30 
42  4^  30 

40  42  58 
37  40  o 


Authorities. 


Com.  Ward,  R.  N. 
Capt.  Richards,  R.  N. 
Lieut.  Kimotsuki,  J.  N. 
Capt.  Richards,  R.  N. 
Lieut.  Kimotsuki,  J.  N. 
Capt.  Richards,  R.  N. 
Com.  Bullock,  R.  N. 
Com.Goldsborough,  U. 
Capt.  Richards,  R.  N. 

Do. 

Do. 

Do. 
Light- House  List. 
Com.  St.  John,  R.  N. 

Do. 

Do. 

Light- House  List. 

Do. 
Com.  Yanagi,  J.  N. 
Com-.  Ward,  R,  N. 
Adm.  Krusenstern. 

Admiralty  chart. 

Do. 

Do. 
Golownin. 

Do. 

Do. 
Adm.  Krusenstern. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Russ.  frigate  Pallas. 

Do. 
Forsyth. 

Com.  Ward,  R.  N. 
Russian  frigate  Pallas. 


Russian  survey. 
H.  M.  S.  Winchester. 
Light- House  List. 
Russian  survey. 
Light-House  List. 

Do. 
Com.  Bullock,  R.  N. 
II.  M.  S.  Barracouta. 
China  Sea  Directory. 

Do. 
H.  M.  S.  Barracouta. 

Do. 

Do. 

Do. 
China  Sea  Directory. 

Light- House  List. 
Com.  Ward,  R.  N. 

Adm.  Krusenstern. 

Do. 

Russian  survey. 
H.  M.  S.  Hornet. 


S.N. 


Page  580] 


Wl 


TABLE  49. 

MARITIME  POSITIONS. 

BAST  COAST  OF  ASIA— Continued. 


Places. 


Exact  locations. 


Port  Aian Cape  Vneshni 

St.  Jona  Island Summit,  i ,  200  feet 

Okhotsk Battery 

Cape  Lopatka Extreme 

Petropaulovski Rakof  light 

Cape  Shipunski Extreme 


Behring  Island Cape  Khitroff 

Mednoi,  or  Copper  I  .  . .  S.  E.  extreme 

Cape  Kamchatka ... Extreme 

Karajinski  Island S.  point 

Cape  Olutovski Elxtreme,  2,480  feet  . . . . 

Cape  Navarin Extreme,  2,5 12  feet  .  . . . 


St.  Matthew  Island Cape  Upright,  S.  E.  point 

St.  Lawrence  Island N.  point 

Cape  Tchoukotskoi !  Extreme 

Port  Providence I  Emma  Harbor 

Cape  Chaplin    Extreme 

Arakam  Island i  Cape  Kiguinin 

Anadyr  River Mouth 


Lat.  N. 


59 
51 


Cape  Behring  . 
East  Cape 


Extreme 
do 


56  25  28 
56  22  30 

19  45 
2  o 

52  57  32 

53  6  o 

54  56  o 
54  32  24 
56  10  o 

58  28  o 

59  58  o 

62  16  o 

60  18  o 

63  12   O 

64  16  O 
64  25  55 
64.24  30 
64  46  0 

64  50  o 

65  o  30 

66  3  o 


Long.  E. 


138  25  50 
143  15  45 
143  7 
156  50 

158  43 
160  4 
166  43 

168  9 
163  25 
163  32 
170  28 

179  4 
Long.  W. 

172  4  O 

159  50 

173  10 

173  7 
172  14 
172  7 

Long.  E. 
178  40  O 
Long.  W. 

175  57    o 

169  44    o 


Authorities. 


14 
o 

n 

o 
o 
o 
o 
o 
o 

30 


o 
o 

15 

0 

o 


Russian  survey. 
H.  M.  S.  Hornet. 
Krasilnikofif. 
Adm.  Lutkd. 
Light- House  List. 
Adm.  Lutk^. 

Do. 
Galownin. 
Adm,  Lutk^. 

Do. 

Do. 

Do. 

Do. 

Schischmareff. 
Adm.  Lutke. 
Com.  Moore,  R.  N. 
Adm.  Lutkd 
Do. 

Russian  survey. 

Adm.  Lutkd. 

Capt.  Beechey,  R.  N. 


ISLANDS  OF  THE  NORTH  PACIFIC. 


Malpelo   Island 
Cocos  Island  . . . 


Summit,  1,200  feet :     4 

Head  of  Chatham  Bay  .  . .      5  j 


2  57 


81  36    o     Com.  iVldham,  R.  N. 
86  59  17  !  Sir  E.  Belcher,  R.  N. 


Galapagos  Is.,  Redondo  j  Summit,  85  feet i  c  13  30 

Rock.  !  I 

(Jalapagos  Is.,  Towers' I !  W.  cliff '  o  20  o 

Galapagos  Is.,  Bindloe  I-i  S.  summit o  18  50 

Galapagos  Is.,  Abingdon  I    Summit,  1,950  feet o  34  25 


91 


o     Capt.  Eitzroy,  R.  N, 


Galapagos  Is.,Wenman  I 
Galapagos  Is.,  Culpepper 
Island. 


Christmas  Island. 
Eanning's  Island. 


Washington  Island. 

Palmyra  Islet 

Baker  Islet 

Howland  Islands . . . 


N.  W.  summit,  830  feet  ..      i  39 
Summit,  550  feet i  22  59 


Gilbert    Is.,    Arorai   or 

Hurd's  Island. 

Gilbert  Is.,  Tamana  I 

Gilbert  Is.,  Onvatoa  I  .. 
Gilbert  Is.,  Tapouteona 

or  Urummond  Island. 
Gilbert  Is.,  Nukunan  or 

Byron  Island. 
Gilbert     Is.,      Peru     or 

Francis  Island. 
Gilbert  Is.,  Nononti  or 

Sydenham  I.  land. 
Gilbert  Is.,  Aranuka  or 

Henderville  Island. 
Gilbert  Is.,  Apamana  or 

Hoppers  Island. 
Gilbert  Is.,  Mariana  I  .. 

Gilbert  Is.,  Tarawa  I 

Gilbert  Is.,  Apiang  I 


N.  point  of  Cook  Islet  . .. 
Flag-staff,     entrance     to 
English  Harbor. 

Village,  W.  end 

S.E.  islet 

Centre 

Centre  island 


-S.  point 


Centre 

do  .. 

S.  E.  point 


do  ... 

N.  W.  point 


Entrance  islet 


S.  point 

N.  E.  point . 
S.  point 


1  57  17 

3  51  26 

4  41   10 

5  49     4 

o  13  30 

0  49    o 

Lat.  S. 

2  40  54 

2  35     o 

1  50    o 

I  29  14 

I  23  42 
I  17  14 

o  36    o 

Lat.  N. 
o   II      o 


o  23     o      173  52 


0  51  30 

1  38  45  I 
I  44  15 


89  58  43  Do. 

90  30    8  Do. 

90  44  23  i  Do. 
92     o  43  '  Do. 

91  49  43  j  Do. 


157  27  46  :  Capt.  Skerrett,  U.S.N. 
'59  23  35      English  survey. 

160  18     5      Capt.  Skerrett,  U.  S.  N. 

162  10  32  Do. 

1 76  30  45      Capt.  Meade,  U.  S.  N. 

176  41   15  Do. 
Long.  E.      ' 

177  I    13  I   Findlay. 

176     7     o  j  Do. 

175  39     o  Do. 

175  12  20  I  Com.  Meade,  U.S.N. 

176  31  II  I  Do. 
17s  57  9  Do. 
174  24    o     Findlay. 

173  39  20     Com.  Wilkes,  U.  S.  N. 

Com.  Challis,  R.  N. 

173     330     Com.  Wilkes,  U.  S.  N. 
173     3     o  [  Do. 

173     7    o  .    Do. 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  NORTH  PACIFIC— Continued. 


[Page  581 


O 

o 


Places. 


Exact  locations. 


Gilbert  Is.,  Maraki  I  . 
Gilbert  Is.,  Taritari  I. 

Marshall  Is.,  Ebon  Atoll. 
Marshall   Is.,   Jaluit  or 

Bonham  Islands. 
Marshall  Is.,  Mulgravels 

Marshall  Is.,  Majuro  or  1 

Arrowsmith  Islands. 
Marshall  Is.,  Arhno  Atollj 
Marshall  Is.,  Odia  Is  .. . 
Marshall  Is.,  Namu  Is.. 
Marshall  Is.,  Jabwat  I.. 
Marshall    Is.,  Aurh  or 

Ibbetson  Island. 
Marshall  Is.,  MaloclabIs 
Marshall  Is.,  Wotje  or 

Romanzoff  Islands. 
Marshall  Is.,  Litkieh  I.. 
Marshall  Is.,  Ailuk  Is  .. 
Marshall  Is.,  Bigar  Islet. 
Marshall  Is.,  Kongelab 

or  Pescadores  Is. 
Marshall  Is.,  Rongerik 

or  Radakala  Islands. 
Marshall  Is.,  Ailinginae 

Island. 
Marshall  Is.,  Bikini  or 

Eschscholtz  Islands. 
Marshall  Is.,  Wottho  or 

Schanz  Island. 
Marshall  Is.,  Enivvetok 

Islands. 
Marshall  Is.,  Ujilong  or 

Providence  Island. 

Greenwich  Island 


Caroline  Is.,  Matelotas 

Group. 
Caroline  Is.,  Yap  Island 
Caroline  Is.,  Eau  Island. 
Caroline  Is.,   Uluthi  or 

Mackenzie  Islands. 
Caroline    Is.,    Feys    or 

Tromelin  Island. 
Caroline    Is.,    Sorol  or 

Philip  Islands. 
Caroline    Is.,    Eauripik 

or  Kama  Islands. 
Caroline  Is.,  Oleai  Group 
Caroline   Is.,    Ifalik   or 

Wilson  Islets. 
Caroline  Is.,  Faraulep  I. 
Caroline  Is.,  W.  Faiu  Islet 
Caroline   Is.,    Olimarao 

Islet. 
Caroline  Is.,  Toass  I  . .. 
Caroline  Is.,  Satawal  I.. 
Caroline  Is.,  Coquille  or 

Pikelot  Island. 
Caroline     Is.,    Suk    or 

Pulvsuk  Island. 
Caroline  Is.,  LosMartires 
Caroline  Is.,  Namounito 

Islands. 
Caroline  Is.,  Hall  Island 


N.  point 
S.  point  . 


Rube  Point . . . . 
N.  W,  extreme . 


Port   Rhin,   N.  point  of 

entrance. 
S.  E.  point 


N.  E.  point , 

S.  islet , 

do , 

Centre 

N.  E.  end ;  anchorage  . . . 

N.  W.  end  Karen  islet  . . 
Christmas  Harbor , 


N.  W.  point 

Capeniur  Islet  .. 

Centre 

Centre  of  group. 


E.  point 

S.W.  extreme 

W.  extreme 

Centre 

North,  or  Arthur  Island 
Centre  of  Atoll 


Northern  islet 


Easternmost  of  the  S.  isl- 
ands. 
Harbor  in  Torrid  Bay . . . 

Centre 

Mogmog  Islet 


E.  extreme 

Centre 

E.  islet 


Raur  Islet,  N.  point  . 
N.  end 


S.  end  . . 
Centre .  . 
do 


do 

do 

-do 

.do 


Ollap  Islet,  N.  point. 
Magur  Islet 


Namuine  Islet . 


Lat.  N. 


O      I       II 

230 

3  I  30 

4  35  25 

5  55  29 

6  14    D 
750 

7  9  17 
7  15    o 

7  46    o 

8  27    o 
8  19    o 

8  54  21 

9  28    9 

10    3  40 

10  17  25 

11  48     o 
II  19  21 

II  26  45 

II    8  20 

II  40    o 

10  5    o 

11  40    o 
9  39    o 


140 

8  18  30 

9  29  42 

9  52  30 
10    6    o 

9  46    o 

860 

6  40    o 

7  21  15 
7  15    o 

835    o 
830 

7  43  30 

7  29  30 

7  22    o 
890 

6  40    o 

738    o 

8  59  45 


Long.  £. 


73  25  30 
72  45  40 

68  41  31 

69  39  19 

71  46    o 
71  23  54 


71  55  51 
68  46  o 
68  23  o 
68  26  o 
71    9    o 


70  49 
70  16 


69    I  57 

69  59  20 

70  7    o 
67  24  57 

67  14  20 

66  26  30 

66  24  25 

66    4    o 

62  15    o 

61    8  30 

54  47  55 

37  33  30 

38  10  54 

39  42    o 

39  46    o 

40  35    o 

40  52    o 

43  "     o 

43  56  45 

44  31     o 

44  36    o 

46  50    o 

45  55  45 

46  24  30 

47  6  48 

47  42    o 

49  16    o 

49  27  30 

50  14  30 


Authorities. 


8  25  30     151  49  15 


Com.  Wilkes,  U.  S.  N. 
Do. 

Com.  Meade,  U.  S.  N. 
Lieut.  W.  U.  Moore,  R.  N, 

Capt.  Bdrard,  Fr.  N. 

Com.  Wilkes,  U.  S.  N. 

Com.  Meade,  U.  S.  N. 
Chramtschenko. 

Do. 
French  survey. 
Findlay. 

Kotzebue. 
Do. 

Do. 
Do. 
Do. 
Do. 

Do. 

Findlay. 

Kotzebue. 

Findlay. 

Do. 

Do. 

Tardy  de  Montreval. 

Capt,  Knorr,  Ger.  N. 

Do. 
Do, 

Adm.  Lutk^. 

Do. 

Do. 

Do. 

Capt.  Knorr,  Ger.  N. 
Adm.  Lutke. 

Do. 
Do. 
Do. 

Do. 
German  survey. 
Adm.  Lutke, 

Lieut.  Raper,  R,  N. 

German  survey. 
Adm.  Lutk^. 

Do. 


Page  582] 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  NORTH  PACIFIC— Continued. 


si 
O 

o 


Places. 


Exact  locations. 


Lat.  N. 


Long.  E. 


Authorities. 


Caroline     Is.,    Hogoen 

Group. 
Caroline  Is. ,  Namolouk  Is 
Caroline  Is.,  Mortlock  Is 
Caroline  Is.,  Nukuor  or 

Monteverde  Islands. 
Caroline  Is.,  Oraluk  or 

Borolelaise  Island. 
Caroline  Is.,  Ngatik  or 

Valientes  Islands. 
Caroline  Is.,  Ponapi  I  .. 
Caroline   Is.,    Mokil  or 

Duperry  Islands. 
Caroline  Is.,   Pingelasp 

or  Mac  Askill  Islands. 
Caroline  Is.,   Ualan  or 

Strong  Island. 

Pelew  Is.,  Angaiir  Island 
Pelew  Is.,  Pelelew  Island 
Pelew  Is.,  Errakong  or 

Akamokan  Island. 
Pelew  Is.,  Korror  Islands 

Pelew  Is.,  Baubeltaub  I 
Pelew  Is.,  Kyangle Islets 

Tabi  or  Lord  North  I . . . 

Mariana  Is.,  Guam  I 


Mariana  Is. 
Mariana  Is. 
Mariana  Is. 
Do... 
Mariana  Is. 
Mariana  Is. 
Mariana  Is. 
Mariana  Is. 

Island. 
Mariana  Is. 
Mariana  Is. 
Mariana  Is. 
Mariana  Is. 
Mariana  Is. 

Pajaros. 


Rota  Island 
Tinian  I.. 
Saypan  I  . 


,  Anataxan  I . 
,  Sariguan  I. 
,  Guguan  I . . 
,,  Alamaguan 

,  Pagan  I  . . . 
.,  Agrigan  I  . 
,  Asuncion  I . 
,,  Urracos  I.. 
,  Farralon  de 


Wake  Island 

Caspar  Rico  Reef . 


Johnston  or  Cornwallis  I 
Clipperton  Island , 


Sandwich  Is.,  Hawaii  I 


Do, 
Do, 
Do. 


Do 

Sandwich    Is.,    Kahoo- 

lawe  Island. 
Sandwich  Is.,  Maui  I.. 

Do 

Sandwich  Is.,  Molokai  I 
.Sandwich  Is.,  Oahu  I.. 

Do 

Do 


N.  end  of  Tsis  Islet . 


N.W.islet , 

Lukanor,  Port  Chamisso 
E.  point ... 


Centre . 

E.  extreme 


Kiti  Harbor,  Narmaur  I . 
Aoura,  N.  E.  point 


o     /     // 
7  18  30 

5  55  o 
5  29  20 
3  51     o 

7  39    o 

5  47  30 

6  47  o 
6  41  45 

6  12  50 

5  21  20 

6  53  55 
720 
780 

7  19    o 

7  40  30 
880 

380 

13  25  48 

14  7  30 
Sunharon  village    |   14  59  22 


N.  islet 

Coquille  Harbor 


S.  W.  point 

S.  point 

Centre 


Korror  Harbor,  Malakal 
pier. 

Cape  Artingal 

Centre  of  largest , 


Centre . 


Fort  Sta.  Cruz, 

d'xVpra. 
Summit 


San  Luis 


Magicienne  Bay,  landing 
Tanapag  Harbor,  Garapag 
Centre 

do  

do  

do 


S.  W.  point 

S.  E.  point 

Crater,  2,600  feet 

Largest  islet 

S.  end  


Centre 

N.  clump  of  rocks 


Flag-staff  on  W.  island . 
Centre 


15 
15 
16  20 

16  41 

17  17 
17  36 


17  10 
o 
o 
o 
o 


15     4     o 

18  46  20 

19  45     o 

20  6  35 
20  32  54 


19  10  54 
14  41     o 

16  44  48 

ID    17      O 


Hilo,  mouth  of  Waiaken  19  43  51 

Creek. 

Hilo  Bay  light 19  45 

Kawaihae  light I  20     i 

Keulakeakua  Bay,  Cook's  !  19  28 

monument. 

Kailua,  stone  church '  19  38 

Summit 20  33 


Maku  landing-pier 20  38 

Lahaina  court-house 20  52 

E.  point  Halawa  station.. ,  21  9 

E.  point  Makapun  station.    21  i8 

Diamond  Head 21  15 

Honolulu,  Tr.  of  V.  Obs..     21  17 


o 
o 
o 

26 
39 

o 

4 

I 

16 

21 

57 


O         '        // 

151  56  30 


Capt.  Simpson,  R.  N. 


53  13  30  j  Adm.  Lutk^. 

53  58     o  I  Do. 

55     o  54     Adm.d'Urville. 

55     5     o  I  Saliz. 

57  32     o     Adm.  Lutk6. 

58  19     o     Lieut.  Reynolds,  R.  N. 

59  50     0  !  Capt.  Duperrey,  Fr.  N. 

60  47  20  Do. 
63     I     o               Do. 


34     5  24  Adm.  D'Urville,  Fr.  N. 

53  iS    3  I>o- 

34  27    o  Capt.  Knorr,  Ger.  N. 

34  31  45  Mr.  Grovener,  R.  N. 

34  39  30  Capt.  Knorr,  Ger.  N. 

34  17     o  Douglas. 

31     8     01  Findlay. 

44  39  30  Capt.  Knorr,  Ger.  N. 

45  13     4  Admiralty  chart. 
45  36  20  j  Do. 

45  43  55  '  Mr.  Harvey,  R.  N. 

45  42  50  German  survey. 

45  39     o  Capt.  Freycinet,  Fr.  N. 

45  47     o  :  Capt.  Sanchez,  Sp.  N. 

45   57     o  Capt.  Knorr,  Ger.  N. 
45  55     o  '  Do. 


45  52  o 
45  41  45 
45  30  o 
45  20  o 
44  48  30 


66  31  30 

68  54  28 
Long.  W. 

69  31  53 
09  10     o 


Do. 
Com.  Wilkes,  U.  S.  N. 
Capt.  Sanchez,  Sp.  N. 
Capt.  Freycinet,  Fr.  N. 
Capt.  Knorr,  Ger.  N. 


Findlay. 

Lieut.  Brooke,  U.  S.  N. 

Do. 
Sir  E.  Belcher,  R,  N. 


55     I     o  Com.  J.  Rodgers,  U.  S.  N. 

55     5     o  Light-House  List. 
55  43    o  ,  Do. 

55  55     o  Lieut.  Child,  R.  N. 

56  o  15  j  Major  Tupman,  R.  M.  A. 
56  35  21  Hawaiian  Gov't  survey. 

56  22     o  Lieut.  Clapp,  R.  N. 

56  40  51  Hawaiian  Clov't  survey. 

56  43  44  1  1*<^- 

57  39  20  Do. 
57  48  52                Do. 

57  51  34  Major  Tupman,  R.  M.  A. 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  NORTH  PACIFIC— Continued. 


[Page  583 


o 
O 


Places. 


Saiulwich  Is.,  Oahu  I  .. 
Sainlwich  Is.,  Kauai  I_. 

Do 

Bird  Island... 

Necker  Island    

French  Frigate  Shoal  .. 

Gardiner  Island 

Maro  Reef 

Laysan  Island 

Lisiansky  Island  

Pearl  and  Hermes  Reef. 
Midway  or  Brooks  Is  . . 

Do 

Ocean  Island 


Marcus  Island  

Bonin  Is.,  Parry's  Group. 

Bonin  Is.,  Kater  Island   . 

Bonin  Is.,  Peel  Island  _. 

Volcano  Is.,  .San  Ales- 
sandro  or  North  I. 

Volcano  Is.,  Sulphur  I_. 

Volcano    Is.,    San   Au- 
gustine Island. 

Rosario  Island 

Douglass  Rocks 

Borodino  Islands  ... 
Do 

Rasa  Island 


Exact  locations. 


Honolulu,  Reef  light 

Hanalei,  Charlton's  farm. 

Waimea,  stone  church 

Centre 

do  

Islet  (120  feet) 

Centre .. 

N.  W.  point 

Centre _. 

do  

N.  E.  extreme 

S.  W.  end  of  Sand  Island. 
Welles  Harbor  anchorage 
Sand  Islet ... 


Lat.  N. 


21 

22 
21 

o  > 
'-J 

23 

23 

25 

25 


14 

57 
5 


55 
o 

17 

50 


35  18 
46     o 


40 
o 


Centre  . 
N. rock 


Port  Lloyd,  observatory 
Centre . 


Centre 


Centre,  148  feet 

Centre 

Centre  of  N.  island . . . 
Centre  of  S.  island  ... 
Centre 


25  47  47 

26  o  o 

27  56  30 

28  12  22 
28  14  o 
28  24  45 


24  14 

27  45 
27  31 
27  5 

25  14 

24  48 
24  14 


o 
o 
o 

37 
o 

o 
o 


Long.  W. 


157  52  O 

159  27  30 

159  40  8 

161  58  17 
164  40  47 

166  17  57 

168  o  52 

170  39  20 

171  44  17 

173  57  o 

175  46  o 

177  22  23 

177  23  15 

178  27  45 

Long.  E. 

153  58  o 

142  6  53 

142  II  53 

142  II  23 

141  II  o 


141  '3 
141  20 


27  15  32  ;  140  50  28 

20  30  o  136  10  o 

25  59  38  131  19  30 

25  52  45  131  12  17 

24  27  o  131  I  50 


Authorities. 


Major  Tupman»  R.  M.  A. 
Capt.  Reynolds,  U.  S.  N. 
Major  Tupman,  R.  M.  A. 
Lieut.  Brooke,  U.  S.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 
Brooks. 

Capt.  Reynolds,  U.  S.  N. 
Comdr.  Sicard,  U.  S.  N. 
Capt.  Reynolds,  U.  S.  N. 

Do. 

Capt.  Belknap,  U.  S.  N. 
Capt.  Beechey,  R.  N. 

Do. 
Com.  Rodgers,  U.  S.  N. 
Capt.  King,  R.  N. 

Do. 
Adm.  Krusenstern. 

Com.  Rodgers,  U.  S.  N. 

Fiudlay. 

Com.  Rodgers,  U.  S.  N. 

Do. 
Findlay. 


ISLANDS  OF  THE  SOUTH  PACIFIC. 


Galapagos  Is.,  Albe- 
marle Island. 

Galapagos  Is.,  Marl- 
borough Island. 

Galapagos  Is.,  James  I.. 

Galapagos  Is.,Jervis  I.. 

Galapagos  Is.,  Duncan  I. 

Galapagos  Is.,  Indefati- 
gable Island. 

Galapagos  Is.,  Barring- 
ton  Island. 

Galapagos  Is.,  Charles  I. 

Galapagos  Is.,  Hood  I ._ 

Galapagos  Is.,  Chatham 
Island. 

Marquesas  Is.,  Fatou 
Hiva  Island. 

Marquesas  Is.,  Motane 
Island. 

Marquesas  Is.,  Taou- 
ata  Island. 

Marquesas  Is.,  O-Hiva- 
Oa  Island. 

Marquesas  Is.,  Fetou 
Hougo  Island. 

Marquesas  Is.,  Roa  Poua 
Island. 

Marquesas  Is.,  Nuka- 
Hiva  Island. 

Marquesas  Is.,  Hiaou  or 
E.-Iao  Island. 

Marquesas  Is.,  Motu-ili 
Island. 


Iguana  Cove 

Cape  Hammond 

Sugarloaf,  1,200  feet 

Summit 

Centre  hill.      .        .      __ 

N.  W.  l)ay 

W.  summit,  900  feet 

Summit,  1,780  feet 

E.  summit,  640  feet 

Mount  I'itt,  800  feet 

S.  point 

S.  S.  E.  point 

Port    Resolution,   water- 
ing-place. 
E.  point 

Centre 

Obelisk  Islet 

Port  Tai-o-hae,  house  of 

resident  ofticial. 
S.  point 

Summit,  130  feet  . 


Lat.  S. 

O  59  O 

o  31  O 

o  15  20 

o  25  o 

o  36  30 

o  33  25 

0  50  30 

1  19  o 

I  25  o 

o  45  15 

10  30  40 

10  o  40 

9  56  o 

9  43  30 

9  25  o 

9  29  30 

8  55  49 

8  3  30 

8  44  o 


Long.  W. 
91  29  12 

91  36  O 

90  52  S3 
90  43  30 
90  41  o 

90  33  58 
90  6  13 

90  28  13 

89  40  S 
89  16  45 

138  43  15 

138  49  30 

139  9  o 
138  50  o 

138  57  45 

140  4  45 
140  4  45 
140  44  o 
140  38  30 


Capt.  Fitzroy,  R.  N. 

Do. 

Do. 
Do. 
Do. 
Do. 

Do. 

Do. 
Do. 
Do. 

M.  de  Tessan. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut,  le  Pord,  Fr.  N. 
M.  de  Tessan. 

Do. 


Page  584] 


TABLE  49. 

MARITIME  POSITIONS. 
ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


d 

o 


Places. 


Marquesas  Is.,  Ua-Hu- 
ka  or  Ua-Una  Island. 
Marquesas    Is.,    Fetou- 
houhou  Island. 

Caroline  Islands 

Vostok  Island 

Flint  Island 

Maiden  Island 

Starbuck  Island 

Penrhyn  or  Tongarewa  I 

Jarvis  Island 

Reirson  Island 

Humphrey  Island 

Union  or  Tokalau  Islands 

Do 


Do 


Phoenix   Is.,  Canton  or 

Mary  Island. 
Phcenix  Is.,  Enderby  I.. 
Phoenix  Is.,  Phoenix  I  _. 
Phoenix  Is.,  Birney's  I  _. 
Phoenix  Is.,  Gardner's  I. 
Phoenix  Is.,  McKean  I._ 
Phcenix  Is.,  Hull's  I   ._, 

Ellice    Is.,  Mukulaelae 
or  Mitchell's  Island. 
Ellice   Is.,  Funafuti  or 

Ellice  Island. 
Ellice  Is.,  Nukufetau  or 

De  Peyster's  Island. 
Ellice  Is.,  Oaitupu  Island 
Ellice  Is.,  Nui  or  Low- 

endahl  Island. 
Ellice  Is.,  Nauomaga  I. 
Ellice  Is.,  Niutao  Island. 
Ellice  Is.,  Nauomea  I  ._ 
Ocean  or  Paanapa  Island 

Pleasant  Island 

Indispensable  Reefs 

Rennel  Island 

Do 

Solomon  Is.,  San  Chris- 

toval  Island, 
Solomon  Is.,  Guadalcana 

Island. 
Solomon  Is.,  Florida  I.. 
Solomon  Is.,  Malayta  I  . 
Solomon  Is.,  Stewart  Is. 

Solomon  Is.,  Isabel  I 

Solomon   Is.,   Kese   or 

Shark  Island. 
Solomon  Is.,  Choiseul  I. 
Solomon  Is.,  Treasury  Is 
Solomon   Is.,  Bougain- 
ville Island. 
Solomon  Is.,  Bouka  I  ._ 
Solomon  Is.,  I^ord  Ilowe 
Group. 

Do 

Do 

New  Britain,  Blanche  Bay 

Duke  of  York  Island 

New  Ireland 


Exact  locations. 


N.  point. 


N.  E.  point 


Solar  Eclipse  Transit  Pier . 

Centre 

do 

Flag-staff,  W.  side 

do 

N.  N.  W.  point 

Centre 

Church 

N.  point 

S.  point  Fakaafo  or  Bow- 
ditch  Island. 
Nuko-nono,  or  S.  E.  isl'd, 

Duke  of  Clarence  I. 
Clump  on  S.  isl'd,  Oatafu 
or  Duke  of  York  Island. 
N.  point 


Centre 

do  ._. 

do  ... 

do  ... 

do  ... 

N.  W.  point. 


S.  point . 
E.  point . 
S.  point . 
S.  end  .. 


Centre  ... 

do 

do 

do 

do 

S.  point  of  S.  reef 

S.  E.  extreme  . 

W.  end 

Hada  or  Recherche  Bay, 

S.  end  of  gravel  beach. 

Wanderer  Bay,  mouth  of 

Boyd  Creek. 
Mboli  Harbor,  Tree  Islet. 
Village  Mary  I.,PortAdam 

Largest  islet 

N.  side  of  Cockatoo  Islet 
E. end  


Choiseul  Bay  entrance. .. 

Centre 

N.  E.  point ., 


Lat.  S. 


Summit  . 

Centre,  small  S.  W.  islet. 

t 

Centre,  small  N.  E.  islet.. 
N.W.  point  of  Hammond  I 
Matupi  I.,  N.  E.  point ... 
Port  Hunter,  Mitchell  Pt. 
Carteret  Harbor,  Cocoa- 
Nut  Island. 


8  54     o 
7  55     o 


o 
5 


25  43 
I     o 

38     o 

55  15 
22  ^^ 


10 
10 
II 

4 

5 

8 

o 

10    2    o 
10  20  30 

9  28    o 

9  13  6 
8  39  40 
2  44  20 


9    o 

47'  o 

34  15 
37  42 

35  10 
29  48 


9  18    o 

8  31  20 

842 

7  32    o 
7  13  20 


6  12  o 
680 

5  36  30 

o  52    2 

o  25    o 

12  50  15 

"  52  15 

II  33  45 
10  15  20 

9  41  47 

9  I  30 
9  30  o 
8  24  24 

8  30  50 
8     5  40 

700 

7  20  30 
■;  -lo    o 


5  16 
5  38 


5  18  o 
5  18  o 
4  13  20 

4  6  30 
4  41  26 


Lonsr.  W. 


o      /      // 

39  33  30 

40  34  40 

50  14  30 
52  23     o 

51  48 

54  57 

55  55 

58  7 

59  54  II 
61     5 
61     I 
71     9 


30 
12 

20 


71  44  40 

72  28  10 

71  43  15 

71     8    o 

70  44  15 

71  33    o 

74  40  18 
74  17  26 

72  20  52 
Long.  E. 
79  50    o 

79  21     3 

78  28  50 

78  46  o 
77  14  30 

76  16  30 

77  22  o 
76  10  o 
68  24  25 
67  5  o 
60  26    o 

60  40  o 
59  55    o 

61  15  15 

59  39  34 

60  27  20 

61  27  40 
63  2  o 
59  38  20 
56  50    o 


56  25  o 
55  26  o 
55     7  14 


54  39 
59  21 


59  34  o 
59  17  o 
52.10  18 
52  29  25 
52  42  25 


Authorities. 


M.  de  Tessan. 
Do. 

U.  S.  Solar  Eclipse  Exp. 

Do. 
An  der  Hydrographie. 
Lieut.  Chanoiniere,  Fr.  N. 

Do. 
Com.  Wilkes,  U.  S.  N. 

Do. 
Capt.  Richards,  R.  N. 

Do. 
Com.  Wilkes,  U.  S.  N. 

H.  M.  S.  Alert,  1880. 

Do. 

Com.  Meade,  U.  S.  N. 

Do. 
Do. 
Com.  Wilkes,  U.  S.  N. 
Do. 
Do. 
Do. 

Peters. 

U.  S.  Ex.  Exp. 

Do. 

Do. 
Capt.  Chramtschenko. 

Findlay. 

Do. 

Do. 
Dutaillis. 

Capt.  Cheyne,  R.  N. 
H.  M.  S.  Renard. 

Do. 

Do. 
Mr.  Tilly,  R.  N. 

Capt.  Denham,  R.  N. 

Mr.  Scudamore,  R.  N. 

Mr.  Hilliard,  R.  N. 

Findlay. 

Mr.  Tilly,  R.  N. 

English  survey. 

Adm.  Krusenstern. 

Capt.  V.  Schleinitz,  Ger.  N. 

Adm.  d'Urville. 

Findlay. 
Rosengren. 

Do. 

Do. 
German  survey. 
Lieut.  Bradley,  R.  N. 
Capt.  Belcher,  R.  N. 


en 

US 

O 

o 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


[Page  585 


Places. 


New  Ireland 

Do 

New  Hanover  Island  . .. 

Do 

St.  Matthias  Island 

Admiralty  Is.,  Admiralty 

Island. 
Admiralty  Is.,    St.  An- 
drew Island. 
Admiralty     Is.,     Jesus 

Maria  Island. 
Admiralty  Is.,  Commer- 

son  Island. 
Admiralty  Is.,  Anchorite 

Island. 
Admiralty   Is.,    Hermit 

or  I^oaf  Island. 
Admiralty  Is.,  Purdy  Is. 
New      Guinea,      Point 

d'Urville. 
New  Guinea,  Drei  Cap 

Peninsula. 
New  Guinea,  Triton  Bay 
New  Guinea,  Cape  Wal- 

sche. 
New  Guinea,  Fly  River. 
New      Guinea,      Port 

Moresby. 
New  Guinea,  Cape  Rod- 
ney. 
New  Guinea,  South  Cape 
New  Guinea,  Hayter  I.. 
New  ( iuinea,  Cape  Cretin 
Louisiade    Arch.,    Tro- 

briand  Islands. 
Louisiade  Arch.,  Wood- 
lark  Islands. 
Louisiade  Arch.,  D'En- 

trecasteaux  Islands. 

Do 

Do 

Louisiade  Arch.,  St.  Aig- 

nan  Island. 
Louisiade  Arch.,  Renard 

Islands. 
Louisiade  Arch.,  Rossel 

Island. 
Louisiade  Arch.,  Adele  I 
Coral  Sea  Arch.,  Coringa 

Islands. 
Coral  Sea  Arch.,  Herald 

Cays. 
Coral   .Sea   Arch.,  Tre- 

gosse  Islands. 
Coral  Sea  .\rch.,  Lahou  ; 

Reef.  ' 

Coral  Sea  Arch.,  Mellish 

Reef. 
Coral  Sea  Arch.,  Bamp- 

ton  Island. 
Coral  Sea  Arch.,  Renard 

Island. 
Coral  Sea  Arch.,  Wreck 

Reef. 
Coral  Sea  Arch.,  Cato  I . 
Santa  Cruz  Is.,  Duff  or 

Wilson  Group.  ' 


Exact  locations. 


Katharine  Haven 

Holz  Haven,  E.  side 

Water  Haven,  mouth  of 

creek. 
North  Haven  anchorage  . 

Centre 

Nares  Harbor,  obs.  islet . 

Violet  Islet,  60  feet 

S.  E.  point 

Centre  of  largest  islet. . . . 

N.  point 

Pemd  Islet 


Lat.  S. 


Mole  Islet 
Extreme  . . 


Wass  Islet 


Port  au  Bus 
Extreme  .  . . . 


Free  Islet,  S.  point 

N.  end  of  Jane  Island 


Extreme 


do 

W.  end 

Cretin  Islets 

N.  E.  point.  Cape  Denis  . 

Wari-ai  Islet 

Ferguson  I. .S.W.  extreme 

Well  Island,  E.  point 

Normanby  I.,  obs.  islet.. 
Summit 


W.  point 
E,  point . . 


S.  extreme  . . 
Chilcott  Islet 


N.  E.  Cay 

S.  islet 

Observation  Cay 
Cay  beacon 


Centre . . . . 

Bird  Islet 

Centr;  . . 
N.  i;  land. 


3  II   o 

2  47  30  ' 
2  33  43  t 

2  26  30 
I  40  o 

1  55  10 

2  25  40 
2  22  o 
o  44  o 

0  53  15 

1  28  o 

2  51  o 

1  25  40 

2  44  o 

3  46  o 
8  22  o 

8  41  o 

9  25  30 

10  14  30 

10  43  30 

10  37  o 

6  43  o 

8  24  o 

9  10  30 
9  38  o 

9  41  o 

9  43  53 
10  42  o 

10  52  40 

11  23  25 

II  29  10 
16  50  o 

16  55  52 

17  43  o 
17  7  20 
17  24  39 
19  8  o 

19  13  35 

22  10  30 

23  15  2 
9  45  o 


Long.  E. 


51  35  30 

50  57  35 
50  4  33 

49  55  36 

49  40  o 

46  40  56 

47  28  35 
47  55  o 
45  18  o 

45  33  4 

45  8  o 

46  15  o 
35  28  12 

32  4  o 

34  4  o 
37  40  o 

43  36  4 

47  7  4 

48  30  30 

50  13  4 

50  40  34 

47  53  20 

51  I  24 

52  53  30 
50  30  o 

50  58  o 

50  44  43 
52  42  4 

52  47  12 

54  8  o 

54  25  14 

49  58  o 

49  12  56 

50  42  4 
52  6  20 

55  52  24 
58  36  35 
58  56  40 
55  28  24 

55  33    4 

67  4  o 


Authorities. 


German  survey. 
Do, 
Do. 

Do. 
Findlay. 
Capt.  Thomson,  R.  N. 

Lieut.  Bower,  R.  N. 

H.  M.  S.  Alacrity. 

,Von.  Schleinitz,  Gr.  N. 

Do. 

H.  M.  S.  Challenger. 

Bristow. 

Conn,  des  Temps. 

Findlay. 

Do. 
Do. 

Macfarlane. 

Lieut.  Moardyan,  R.  N. 

Conn,  des  Temps. 

Capt.  Moresby,  R.  N. 

Do. 

Do. 
Findlay. 

Capt.  Loring,  R.  N. 

Capt.  Moresby,  R.  N. 

Findlay. 
Do. 
Australia  Directory. 

Findlay. 

Do. 

Capt.  Stokes,  R.  N. 
Australia  Directory. 

Capt.  Denham,  R.  N. 

Findlay. 

Capt.  Denham,  R.  N. 

Do. 
Lieut.  Richards,  R.  N. 

Do. 

Capt.  Denham,  R.  N. 

Australia  Directory. 
Lieut.  Suckling,  R.  N. 


Page  586j 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


o 
O 


Places. 


Santa  Cruz  Is.,  Matema 

or  Swallow  Group. 
Santa  Cruz  Is.,  Tinakula  I 
Santa  Cruz  Is.,  Nitendi  I 
Santa  Cruz  Is.,  Tapona  I 

Santa  Cruz  Is.,  Vanikoro 
New  Hebrides  Is.,  Torres 

or  Ababa  Island. 
New  Hebrides  Is.,Vanua 

Lava  Island. 
New  Hebrides  Is.,  Santa 

Maria  Island. 
New  Hebrides  Is.,  Au- 
rora Island. 
New  Hebrides  Is.,  Mal- 

licollo  Island. 
New  Hebrides  Is.,  Vate 

or  Sandwich  Island. 
New  Hebrides  Is.,  Er- 

romango  Island. 
New  Hebrides  Is.,Tanna 

Island. 
New  Hebrides  Is.,  Er- 

ronan  or  Footoona  I. 
New  Hebrides  Is.,  Anei- 

tum  Island. 
New      Hebrides      Is., 

Matthew  Island. 
New  Hebrides  Is.,  Hun- 
ter Island. 
New  Hebrides  Is.,  Wal- 

pole  Island. 

Mitre  Island 

Rotumah  Island 

Fiji  Is.,  Kantavu  Island. 

Do 

Do 


Exact  locations. 


Nimanu  Islet 

Summit,  2,200  feet 

N.  E.  point,  Cape  Byron. 
Basilsk  Harbor,  S.  point 
of  entrance. 

Ocili  village 

Hayter  Bay,  Middle  I .._ 

Port  Patterson,  Nusa  Pt.. 

Lasolara  Anchorage 

Laka-rere 


Lat.  S. 


Port  Sandwich,  point  on 

E.  side. 
Havannah  Harbor,  Mata- 

pou  Bay  flag-staff. 
Dillon  Bay,  S.  point  of 

creek  entrance. 
Port  Resolution,  Mission. 

N.W.  point 

Port  Aniteum,  Sand  Islet. 

Peak,  465  feet 

Peak,  974  feet 

S.  point 


Fiji  Is.,  Vatu  Lele  Island 

Fiji  Is.,Ovalau  Island.. 

Fiji  Is.,  Viti  Levu  Island 

Do ' 

FijiIs.,MbegaorMbenga! 
Island.  I 

Fiji  Is.,  Matuku  Island.' 
Fiji  Is.,  Moala  Island  .. 
Fiji  Is.,  Ngau  Island  .  .  . 
Fiji  Is.,  Wakaya  Island. 
Fiji  Is.,  Makongai  Island 

Fiji  Is.,  Goro  Island 

Fiji  Is.,  Vanua  Levu  I.. 


Do. 
Do. 


Do.._ _ 

Fiji  Is.,  Taoiuni  Island  . 

Fiji  Is.,  Thikombia  I 

Fiji  Is.,  Naitamba  Island 

Fiji  Is.,  Vatu  Vera  I 

Fiji  Is.,  Kanathea  Island 
Fiji  Is., Vanua  Mbalavu  I 
Fiji  Is.,  Mango  Island.. 
Fiji  Is.,  Thithea  Island 
Fiji  Is.,  Tabutha  Island. 
Fiji  Is.,  Naian  Island  .. 


Centre 

Epipigi  Peak 

N.  rock  Astrolabe  Reef.. 
Mt.  Washington,  N.  peak. 
N'galoa    Harbor,    outer 

beacon. 

S.  point 

Levuka  school-house  pt.. 
Summit  of  Malolo  Islet.. 
Suva  Harbor,  Na-mbuka- 

lon  Church. 
Swan  Harbor,  Leaven  Pt. 

N.  side  of  Matuku  entrance 

Rocks  off  N.  point 

Herald  Bay,  N.  W.  side.. 

Rocky  Peak 

Dilliendreti  Peak 

N.  W.  point ._ 

Mbua  Bay,  Dimba-Dimba 

Point. 
Nandi,  obsei-vation  islet.. 
SavuSavu  Point;  extreme 


N.E.  Point 

Somu-Somu  town. 

E.  hummock 

Centre 


S.  point 

N.  W.  point 

S.  E.  point 

do 

N.W.  peak 

Summit,  5S0  feet 


O       I       II 

10  21     o 

10  23  30 

10  40    o 

11  17  30 

II  39  30 
13  15     o 

13  48     o 

14  II      o 
14  58    o 

16  25  30 

17  34  49 

18  47  30 

19  31   17 

19  31  20 

20  15   17 
22  20  12 

22  24     2 
22  38     7 

1  55     o 

2  30  10 

8  37  47 

9  7  9 
9    5  30 

8  36  o 
7  40  45 

7  44  45 

8  823 

8  22     I 

9  9  38 
8  32  49 

7  59  32 
7  37  II 
7  27  14 
7  15  21 
6  48  10 

6  57  53 
6  49  2 

680 
6  46  o 

5  44  45 
730 
29  o 
17  20 
10  o 
o 
o 
?o 


29 

48 

37 
59 


Long.  E. 


Oil! 

166  17  o 

65  47  30 

66  o  30 
66  32  14 

66  55  10 

66  33  o 

67  30  31 

67  30  o 

68  2  o 

67  45  o 

68  16  5 

68  58  o 

69  27  30 

70  II  13 

69  44  44 

71  20  30 

72  5  15 
68  56  45 

70  10  o 

77  4  39 

78  31  3 

77  57  9 

78  10  34 

77  38  o 

78  50  4 

77  9  o 

78  26  4 

78  6  53 

79  44  27 
79  56  29 
79  14  8 
78  59  29 

78  57  46 

79  20  44 
78  26  14 

78  47  35 

79  16  54 
Long.  W. 
79  58  46 
79  51  o 
79  54  26 
79  17  o 
79  34  o 
79  10  o 

79  5  45 
79  10  o 

79  19  <=> 

78  42  o 

79  4  o 


Authorities. 


Lieut.  Tilly,  R.  N. 

Do. 

Do. 

Capt.  d'Urville. 

Do. 

Capt.  Moresby,  R.  N. 

Mr.  Kerr,  R.  N. 
Lieut.  Tilly,  R.N. 

Do. 
Lieut.  Hilliard,  R.  N. 
Lieut.  Richards,  R.  N. 
Lieut.  Tilly,  R..N. 
Capt.  Denham,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Admiralty. 

Capt.  Ponetheir,  Fr.  N. 

Lieut.  Moore,  R.  N. 

Do. 
Capt.  Nares,  R.  N. 

English  survey. 

Do. 

Do. 
Lieut.  Dawson,  R.  N. 

Lieut.  Moore,  R.  N. 

Capt.  Denham,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Com.  Goodenough,  R.  N. 
Findlay. 

Capt.  Denham,  R.  N. 
H.  M.  S.  Alacrity. 

Findlav. 

Do. 
Lieut.  Moore,  R.  N. 
Findlay. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


[Page  687 


Places. 


Exact  locations. 


Fiji  Is.,  Lakemba  Island 
Fiji  Is.,  Oneata  Island.. 
Fiji  Is.,  Mothe  Island  __ 
P'iji  Is.,  Mamuka  Island 
Fiji  Is.,  Kambara  Island 
Fiji  Is.,  Totoya  Island.. 
Fiji  Is.,  Fulanga  Island. 
Fiji  Is.,Ongea  Levu  I_. 
Fiji  Is.,  Vatoa  or  Turtle  I 

Fiji  Is.,  Ono  Islands 

Fiji  Is.,  Michaeloft' I 

Fiji  Is.,  Simonoff  I 

Foutouna  or  Home  Is  .. 
Urea  or  Wallis  Island  .  . 
Niua-Fu  or  Good  Hope  I 

Keppel  Island 

Boscawen  Island 

Samoan  Is.,  Savaii  I  . 
Samoan  Is.,  Upolu  I 

Samoan  Is.,  Tutuila  I  .. 

Samoan  Is.,  Manua  I 

Samoan  Is.,  Rose  I 

Iniue  or  Sarage  I 

Danger  Is.,  or  Bernardo 
Suwarrow  or  Souwaroff  I 

Palmerston  Islands 

Scilly  Islands 

Bellingshausen  Island  _. 
Mopelia  (Lord  Howe)  I 

Society  Is.,  Maitea  I 

Society  Is.,  Tahiti  I 

Society  Is.,  Tubuai-Ma- 

nu  or  Maia-iti  I. 

Society  Is.,  Eimeo  I 

Society  Is.,  Huaheine  I. 

Society  Is.,  Ulietea  I 

Society  Is.,  Tahoa  I 

Society  Is.,  Bola-Bola  I. 
Society    Is.,    Tubal   or 

Motu-iti  Island. 
Society   Is.,    Marua   or 

Maupili  Island. 
Paumotu  or  Low  Arch., 

Dacie  Island. 
Paumotu  or  Low  Arch., 

Pitcairn  Island. 
Paumotu  or  Low  Arch., 

Henderson  or  Eliza- 
beth Island. 
Paumotu  or  Low  Arch., 

Oeno  Island. 
Paumotu  or  Low  Arch., 

Timoe  or  Crescent  I. 
Paumotu  or  Low  Arch., 

Mauga  reva  or  Gam- 
bier's  Island. 
Paumotu  or  Low  Arch., 

Marutea  or  Lord 

Hood's  Island. 
Paumotu  or  Low  Arch., 

Maria  or  Moerenhout 

Island. 
Paumotu  or  Low  Arch., 

Matureivavao  Island. 
Paumotu  or  Low  Arch., 

Vohanga  Island. 


Kendi  Point 

Summit  of  Loa  Island 

Summit .. 

Centre,  260  feet 

Highest  peak 

Black  Rock  Bay,  W.  side. 

W.  bluff 

Centre 

Hummock 

Peak 

Centre 

do 

Mount  Schouten 

Fenua-fu  Islet 

N.  W.  extreme 

Centre 

do 

Paluale  village  . 

Apia     Harbor,     Rage's 

Wharf. 

PagoPago,  obs.  point 

Village,  N.  W.  side 

Centre 

S.  point 

Middle  rock 

Cocoa  Nut  Islet 

W.  islet 

E.  islet 

Centre 

do 

Summit 

Papiete  Harbor,  centre  of 

Motuuta  Island. 
N.  point 


Lat.  S. 


Talu  Har.,  Vincennes  Pt. 

Owaharre  Harbor  bar 

Regent  Point 

Centre 

Otea-Vanua  village 

N.  point  of  reef 


Centre 


N.  E.  entrance 

Village 

Centre 


N.  point 

N.  W.  point. 
Flag-staff 


Centre 


.do 


N.  point. 
W.  point 


18  14  10 
18  25  46 
18  38  56 
18  46  o 
18  56  15 

18  58  57 

19  3  o 
19  4  o 

19  49  II 

20  39  10 

21  o  9 
21  I  39 


14  20 

23  35 
o 
o 
5  58  o 
3  45  o 
3  48  56 


5  34 
5  52 


Long.  W. 


178 
178 
178 
178 
178 
179 
178 
178 
178 
178 
178 
178 
178 
176 

175 

173 

173 
172 


52  o 

27  4 
30  54 

44  o 
59  5 
52  58 
47  25 
33  25 
15  38 

45  27 

46  3 

51  47 
7  o 

II  47 
40  40 

52  o 
52  o 
17  o 


Authorities. 


18 

19 

32 
10 

52 


6 
o 
o 
o 

47 


14  30 


5 
28 

48 

52 

53 
^2 


50 
o 

o 

o 

o 

II 


7  38  41 

7  29  23 
6  42  49 
6  50  o 
6  35     o 

6  31  35 
611     o 

16  26     o 


25     3  37      130     8  23 
24  21   20  I  128  19     o 


24  I  20 
23  19  o 
23     7  36 

21  30  50 

21  58  30 

21  25  o 
21   18     o 


170  42 

31 

169  32 

0 

168  9 

0 

169  50 

0 

165  51 

30 

163  4 

10 

163  10 

0 

154  30 

0 

154  31 

0 

154  0 

0 

148  5 

0 

149  34 

16 

150  35 

51 

149  50 

30 

151  7 

36 

151  27 

21 

151  35 

0 

151  46 

0 

151  48 

0 

152  12 

0  i 

124  48 

0 

130  41     o 

134  28  48 

134  57  32 


135  33  19 


136  13  46 


136  24  46 
136  38  53 


Findlay. 

Do. 

Do. 

Do. 

Do. 
Capt.  Denham,  R.  N. 
Findlay. 

Do. 
Capt.  Denham,  R.  N. 

Do. 

Do. 

Do. 
Findlay. 

Do. 

Do. 
Admiralty. 

Do. 
Com.  Wilkes,  U.  S.  N. 
Capt.  Richards,  R.  N. 

Comdr.  Miller,  U.  S.  N. 
Com.  Wilkes,  U.  S.  N. 
Sir  E.  Belcher. 
Findlay. 

Comdr.  Miller,  U.  S.  N. 
Com.  Rodgers,  U.  S.  N. 
French  survey. 
Lieut.  Palmer,  R.  N. 
De  la  Chauvinidre. 


Adam  Kulczycki. 

Le  Clerc. 

English  survey. 
Mr.  Rowe,  R.  N. 
French  survey. 
Findlay. 

Do. 

Do. 

Do. 


Do. 
Findlay. 

Capt.  Beechey,  R.  N. 
Conn,  des  Temps. 
Do. 

Capt.  Beechey,  R.  N. 

Conn,  des  Temps. 

Do. 
Do. 


I 


Page  588] 


.      TABLE  49. 
MARITIME  POSITIONS. 
ISLANDS  OP  THE  SOUTH  PACIFIC— Continued. 


o 

U 


Places. 


Exact  locations. 


Lat.  S. 


Long.  W. 


Authorities. 


Paumotu  or  Low  Arch., 

Tenaranga  Island. 
Paumotu  or  Low  Arch., 

Tenararo  Island. 
Paumotu  or  Low  Arch., 

Morane  or  Cadmus  I. 
Paumotu  or  Low  Arch., 

Tareia  or  Carysfort  I. 
Paumotu  or  Low  Arch., 

Mururea     or     Osna- 

burg    Island. 
Paumotu  or  Low  Arch., 

Ahunui  or  Cockburn 

Island. 
Paumotu  or  Low  Arch., 

Tematongi  or  Blighl. 
Paumotu  or  Low  Arch., 

Mukutipipi    or    Mar- 
garet Island. 
Paumotu  or  Low  Arch., 

Anu  Aruaro  Island. 
Paumotu  or  Lo  a'  Arch., 

Hereheretna    or    St. 

Paul  Island. 
Paumotu  or  Low  Arch., 

Vana  Vana  or  Barrow 

Island. 
Paumotu  or  Low  Arch., 

Vairaatea  Island. 
Paumotu  or  Low  Arch., 

Nukutuvake  or  Whit- 
sunday Island. 
Paiunotu  or  Low  Arch., 

Pukaruhaor  Clermont 

Tonnerre  Island. 
Paumotu  or  Low  Arch., 

Reao  or  Series  Island. 
Paumotu  or  Low  Arch., 

Vahitahi  Island. 
Paumotu  or  Low  Arch., 

Pinaki  or  Byam  Mar- 
tin Island. 
Paumotu  or  Low  Arch., 

Aki-Aki  or  Lancier  I. 
Paumotu  or  Low  Arch., 

Nukutapipi  Island. 
Paumotu  or  1  ow  Arch., 

Tatakoto   or    Narcis- 
sus Island. 
Paumotu  or  Low  Arch., 

Amanu  or  Moller  I. 
Paumotu  or  Low  Arch., 

Hao  or  Bow  Island. 
Paumotu  or  Low  Arch., 

Paroa  or  Gloucester  I. 
Paumotu  or  Low  Arch., 

Manuwangi  or  Cum- 
berland Island. 
Paumotu  or  Low  Arch., 

Nengo-nengo  Island. 
Paumotu  or  Low  Arch., 

Ravahere  Island. 
Paumotu  or  Low  Arch., 

Marokau  Islets. 
Paumotu  or  Low  Arch., 

Tekokota  Island. 
Paumotu  or  Low  Arch., 

Reitoraor  Bird  I. 


W.  point. 

Centre 

E.  point  . 
Entrance . 


N.  E.  point 


N.  point 

S.  W.  point. 

W.  point  . . . 
do  ... 


.do 


W.  point  of  reef . 
N.  W.  point 


Centre . 


N.  W.  point 

W.  point 

N.  W.  point . 


Centre 

E.  point  

Flag-staff  on  western  coast 

S.  W.  point 

N.  W.  pass 


Centre 


S.  W.  point 

S.  point 

S.  S.  E.  passage  . 

W.  part   

N.  be.-xch , 


o     /      /' 
21   18  30 

21  18    o 
23     7  50 

20  44  53 

21  50    o 

22  12  25 

21  37  41 
20  42    8 

20  25  17 

19  53  17 

20  46    7 

9  20  o 
9  23  38 

8  33  42 

8  16    o 

8  43  19 

9  40  22 

8  30    8 

9  17  40 
7  19  30 

7  53  20 
^  5  45 
9    8  44 


8  45  53 
8  18  30 

8    5     I 

7  20  16 

7  49  35 


136  32  20 

136  45  46 

137  8  52 

138  20  53 
138  55  49 

138  41  48 

140  40  o 
143    5  57 

143  33  58 
145     7    o 

139  5  34 

139  15  55 
138  41  46 

136  20    o 

137  4  15 

138  52  46 

140  24  23 

139  13  46 
138  48  16 
138  26  26 

140  50  26 

140  59  7 

141  42  46 


9  10  19  !  141  12  47 


141  46  39 

142  II  31 
142  13   2 

142  36  20 

143  5  23 


Conn,  des  Temps. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 

Do. 

Do. 
Do. 

Do. 

Do. 
Do. 

Capt.  Duperrey,  Fr.  N. 

Conn,  des  Temps. 
Do. 
Do. 

Do. 
Do. 
Lieut.  Ingouf,  Fr.  N. 

Conn,  des  Temps. 
Do. 
Do. 
Do.  ■ 

Do. 
Do. 
Do. 
Do. 
Do. 


TABLE  49. 

MARITIME  POSITIONS. 

ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


[Page  589 


Places. 


Paumotu  or  Low  Arch., 

1  [ikiiero  or  Melville  I. 
Paumotu  or  Low  Arch., 

Tauere  Island. 
Paumotu  or  Low  Arch., 

Puka-puka  Island. 
Paumotu  or  Low  Arch., 

Napuka  Island. 
Paumotu  or  Low  Arch., 

Angatan  or  Aratcheff 

Island. 
Paumotu  or  Low  Arch., 

Takume  or  Volonsky 

Island. 
Paumotu  or  Low  Arch., 

Tuanske  or  Reid  I. 
Paumotu  or  Low  Arch., 

Hiti  Island, 
Paumotu  or  Low  Arch., 

Nihiru  Island. 
Paumotu  or  Low  Arch., 

Marutea    or     P'urne- 

aux  Island. 
Paumotu  or  Low  Arch., 

Tahanea  Island. 
Paumotu  or  Low  Arch., 

Anaa  Island. 
Paumotu  or  Low  Arch., 

Tepoto  Island. 
Paumotu  or  Low  Arch., 

Haraiki  or  Croker  I. 
Paumotu  or  Low  Arch., 

Motu-tunga  Island. 
Paumotu  or  Low  Arch., 

]\Iakuimu  or  Phillips 

Island. 
Paumotu  or  Low  Arch., 

Katiu  or  Sacken  I. 
Paumotu  or  Low  Arch., 

Faaite     or     Milordo- 

witch  Island. 
Paumotu  or  Low  Arch., 

Fakarawa     or     Witt- 
genstein Island. 
Paumotu  or  Low  Arch., 

Raraka  Island. 
Paumotu  or  Low  Arch., 

Taiero  or  King's  I. 
Paumotu  or  Low  Arch., 

Aratika  Island. 
Paumotu  or  Low  Arch., 

Kavahi  Island. 
Paumotu  or  Low  Arch., 

Toau  or  Elizabeth  I. 
Paumotu  or  Low  Arch., 

Niau  or  Greig  Island. 
Paumotu  or  Low  Arch., 

Raukura  Island. 
Paumotu  or  Low  Arch., 

Arutua  Island. 
Paumotu  or  Low  Arch., 

Tikei  or  Romanzoff  I. 
Paumotu  or  Low  Arch., 

Tokapoto  Island. 
Paumotu  or  Low  Arch., 

Manhii  Island. 
Paumotu  or  Low  Arch., 

Ahii  Island. 


Exact  locations. 


E.  point , 

N.  W.  point 

E.  point , 

W.  point 

do  

N.  W.  point 

do  

do  

S.  W.  point 

W.  point 

N.  W.  point 

Islet  in  N.  pass 

N.  point 

S.  W.  point 

N.  pass 

W.  pass 


S.  W.  pass . . 
W.  extreme 

S.  E.  pass  . . 


Lat. 

s. 

0   / 

II 

17  35 

28 

17  20 

30 

14  56 

0 

14  12 

0 

15  50 

0 

15  44 

20 

16  38 

42 

16  42 

14 

16  44 

30 

16  54  46 

Long.  W. 


16  46  46 

17  20  20 

16  47  49 

17  28  42 

17      2    16 

16  26     9 

16  22  37 
16  41  32 

16  30  55 


N.  W.  pass 

Middle  of  W.  shore  . . . 

E.  point 

S.  W.  pass 

N.  pass 

N.  W.  point 

N.  W.  pass 

E.  pass  

Centre 

S.  point 

E.  side  of  entrance |   14  27  46 

S.  W.  point 14  34  40 


16    4  59 

15  43  15 

15  27  40 

15  55     5 

15  51     o 

16  8    o 

15  38  47 
15  18  o 
14  57  o 
14  44  10 


o       /       // 

142  35  16 

141  29  43 
138  42  31 

141  15  n 

140  53  31 

142  8  40 

144  14  45 
144    8  20 

142  53  34 

143  19    3 

144  58    o 

145  30  54 
144  17  i8 

143  31   17 

144  22  48 

143  57  59 

144  27  31 

145  22  13 

145  22  23 

144  57  19 

144  38  34 

145  16  16 

145  9  16 

146  3  16 
146  24  II 
146  48  1 1 
146  40  1 1 
144  42  16 

M5  13  16 
146  4  42 
146  25  II 


Authorities. 


Conn,  des  Temps. 
Do. 
Do. 
Do. 
Do. 

Do. 

Do. 
Do. 
Do. 
Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 

Do. 
Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  590] 


TABLE  49. 

MARITIME  rOSITIONS. 

ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


o 
O 


Places. 


Exact  locations. 


Paumotu  or  Low  Arch., 
Rairoa  or  Vliegen  I. 

Paumotu  or  Low  Arch., 
Makatea  Island. 

Paumotu  or  Low  Arch., 
Matahiva  Island. 

Juan  Fernandez  Island. 

Mas-a-fuera  Island 

St.  Ambrose  Island 

St.  Felix  Island 

Sala  y  Gomez 

Easter  Island 

Rapa  or  Oparo  Island . . 

Bass  Islets  (Morotiri)  . 

Tubuai  or   Austral  Is., 
Vavitoa  Island. 

Tubuai  or  Austral  Is., 
Toubai  Island. 

Tubuai  or  Austral  Is., 
Rurutii  Island. 

Tubuai   or  Austral  Is., 
Rimitara  Island. 

Cook  Is.,  Hull  Island  . 

Cook  Is.,  Mangara  I  .. 

Cook  Is.,  Rarotonga  I . 

Cook  Is.,  Mauki  or  Par- 
ry Island. 

Cook  Is.,  Mitiero  Island 

Cook  Is.,  Vatiu  or  Atiu  I . ' 

Cook  Is.,  Hervey  Islets. 

Cook  Is.,  Aitutaki  Island 

Friendly  [s.,  Vavao  I-..i 

Friendly  Is.,  Kao  Island. 

Friendly  Is.,  Tofua  I  . . . 

Friendly     Is.,     Tonga- 
tabu  Island. 

Minerva  Reefs,  N.   Mi- 
nerva. 

Minerva  Reefs,  S.   Mi- 
nerva. 

Kerniadec  Is.,  Raoul  or  1 
Sunday  Island.  I 

Kermadec  Is.,  Macauley 
Island. 

Kermadec  Is.,  Curtis  I . .  i 


S.  E.  point 
W.  point  .. 
do  .. 


Fort  S.  Juan  Babtista 

Summit,  4,000  feet 

Summit , 

Centre 

N.  W.  point 

Cook's  Bay,  mission 

Tauna  Islet 

S.  E.  islet,  344  feet 

Centre 


Flag-staff,  N.  side . 

N.  point 

Centre 


N.  W.  point 

Centre 

N.  W.  point 
Centre   


.do 
.do 
.do 
.do 


Port  Valdes,  Sandy  Point, 

Summit,  5,000  feet 

Summit,  2,800  feet 

Nakalofa,  King's  garden 

N.  E.  side 

S.  side  of  entrance 

Denham  Bay  flag-staff.. 

Centre 

do  


Lat.  S. 


Long.  W. 


Conway  Reef 

Loyalty  Is.,  Ueaor  Hal- 

gan  Island. 
Loyalty  Is.,  Lifou  Island 
Loyalty    Is.,    Mare    or 

Britannia  Island. 
New     Caledonia,    Port 

Kanala. 
New  Caledonia,  Port  St. 

Vincent. 
New  Caledonia,  Noumea 

New  Caledonia,   Balari 

Pass. 
New     Caledonia,    Port 

Alcmene. 

Norfolk  Island 

Elizabeth  Reef 

Lord  Howe  Island 

Ball's  Pyramid 

Macquarie  Island 

Auckland  Islands 


.do 


Bishop  Sound,  Oidiy  Islet- 

Wreck  Bay,  N.  W.  shore. 
S.  point 

Observatory 

Marceau  Island 


Light  at  office  of  captain 

of  port. 
Amedee  Island  light . 


Alcmene  Island 


Lower  flag-staff  at  jetty  .. 

Centre 

S.  end  of  middle  beach . . 

Summit,  1,816  feet 

N.  point 

Port  Ross,  Terror  Cove., 


15  18  7 

15  50  30 


o   '  /' 
147  15  33 


148  16  46 
14  53  o  ;  148  43  36 


33  37  36 
33  46  o 
26  21  o 
26  16  o 

26  27  41 

27  10  o 
27  35  46 
27  55  30 
23  55  o 

23  21  45 

22  29  o 

22  45  o 

21  47  O 
21  49   O 

21  II  35 

20  17  o 


20  1  o 

20  4  o 
19  18  o 
18  54  o 

18  39  2 

19  41  35 
19  45  o 

21  8  20 


23  37  19 
23  56  22 

29  15  30 

30  16  o 

30  36  o 
21  45  o 

20  28   O 

20  46  O 

21  42   O 

21  29  12 

22  O  10 
22  16  20 
22  28  44 
22  42  30 
29  3  45 

29  56  o 

31  31  38 

31  45  10 
54  19  o 
50  32  30 


78  49  45 
80  46  o 

79  40  30 

80  6  56 
105  28  o 
109  26  o 
144  17  21 
143  28  21 
147  48  o 

149  35  35 

151  23  41 

152  55  o 


154  51 
157  56 
159  47 
157  23 


Authorities. 


157  34  0 

158  8  0 

158  54  0 

159  32  0 
174  I  0 

174  59  50 

175  3  0 

175  8  7 

178  49  39 

179  4  57 

177  54  52 

178  32 

0 

178  37  0 
Long.  E. 

174  37  0 

166  28  0 

167  2 

168  0 

30 
0 

165  58  50 

166   5 

0 

166  27 

8 

166  28 

50 

167  27  55 

16758 
159  4 
159  5 

T  CO  Tf\ 

6 

30 
58 
10 

158  56     o 

166    12    34 


Conn,  des  Temps. 

Do. 

Do. 

English  survey. 

H.  M.  S.  Albatross. 

Ca]-)t.  Bruce. 

Adm.  du  Petit  Thouars. 

Chilean  survey. 

Do. 
French  survey. 

Do, 
O'Neill 

French  survey. 

Kulczyki. 

Lieut.  Lebleux,  Fr,  N. 

Do. 
Lieut.  Quentin,  Fr.  N. 
Findlay. 
Capt.  Scheibner,  Ger.  N. 

Findlay. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 
Lieut.  Heath,  R.  N. 
Adm.  d'Urville. 

Do. 
Lieut.  Heath,  R.  N. 

Capt.  Denham,  R,  N. 

Do. 

Do. 

Findlay. 

Adm.  d'Urville,  Fr.N. 

Lieut.  Moore,  R.  N. 
Com.  Oliver,  K.  N. 

Lieut.  Hilliard,  R.  N. 
Adm.  d'Urville,  Fr.N. 

French  survey. 

Do. 
Light- House  List. 

Do. 

Capt.  Denham,  R.  N. 

Do. 
Do. 
Do. 
Do. 

Lieut.  Raper,  R.  N. 
Capt.  Ross,  R.  N. 


TABLE  49. 

MARITIME  POSITIONS, 

ISLANDS  OF  THE  SOUTH  PACIFIC— Continued. 


[Page  591 


o 

u 


Places. 


Campbell  Island. 

Antipodes  Island 

Bounty  Islands 

Chatham  Island,  Whare 
Kauri  Island. 

Do.. 


Exact  locations. 


S.  harbor,  Shoal  Point . 

Summit,  600  feet 

E.  islet 


PortWaitangi,  Point  Han- 
son. 
Port  Hutt,  Gordon  Point  _ 


Lat.  S. 


O      /       li 

52  33  26 
49  42  o 
47  46    o 

43  57  24 

43  49     3 


Long.  E. 


169     8  41 

178  43     5 
178  56  44 

Long.  W. 
176  32   15 

176  42     o 


Authorities. 


Capt.  Ross,  R.  N. 
Conn,  des  Temps. 


Lieut.  Dennis,  R.  N. 

U.  S.  Transit  of  Venus  Exp. 


AUSTRALIA. 


Cape  York 

Mount  Adolphus  

Travers  Isles 

Prince  of  Wales  Island.. 

Booby  Island 

Flinders  River 

Albert  River 

Sweers  Island 

Groate  Eylandt 

Bickerton  Island 

Cape  Arnheim 

Cape  Wilberforce 

C:.pj  Weasel 

Dale  r-i'-t 

Cape  Stc\.  art 

Liverpool  River 

Cape  Croker 

Port  Essington 

Melville  Island 

Bathhurst  Island 

Adelaide  River 

Port  Darwin 

Port  Patterson 

Port  Keats 

Pearce  Point 

Victoria  River 

Cape  Dussejour 

Cape  Londonderry  

Cape  Bougainville 

Cassini  Island 

Cape  Voltaire 

Barker  Islets 

Montalivet  Islands 

Maret  Islets 

Colbert  Islet 

Prince  Regent  River 

Port  Nelson 

De  Freycinet  Islets 

Red  Islet 

Cockell  Islet 

MacLeay  Islets 

Port  Usborne 

Fitz  Roy  River 

Cape  L'Eveque 

Lacepede  Island 

Cape  Baskerville 

Cape  Latouche  Treville. 

Turtle  Isles 

Cape  Lambert '__. 

Legendre  Island 

Rosemary  Island 

Enderby  Island 

Montebello  Island 

Barrow  Island 

North  West  Cape 

Cape  Cuvier 


Sextant  Rock 

Summit 

Centre 

Cape  Cornwall,  extreme. 

Centre 

Entrance 

Kangaroo  Point 

Inscription  Point 

S.  E.  point 

Summit 

Extreme 

E.  extreme 

Extreme 

do 

do 

Haul  Round  Islet 

Extreme 

Smith  Point 

Cape  Van  Diemen 

Cape  Fourcroy 

E.  entrance  point 

Emery  Point 

Quail  Islet . 

Tree  Point 

Extreme 

Water  Valley 

Rock  off  cape 

Extreme 

do 

Centre 

Flat  Hill 

Centre ,_. 

W.  islet 

N.  islet 

Centre 

Mount  Trafalgar 

Careening  Beach 

W. islet 

Centre 

W.  point 

Rock  off"  N.  end 

S.  point 

Escape  Point 

Extreme 

N.W.  islet 

Extreme 

do 

Centre  of  N.  isle 

Extreme 

N.  W.  extreme 

W.  summit 

Rocky  Head .. 

N.  extreme  of  reef 

N.  point 

Extreme 

do _. 


o  41 

o  37 
o  22 
o  46 

36 
36 

35 

6 

16 

45 
14 
53 

0  59 

1  36 

I  57 
I  54 

0  58 

1  7 
I  8 

51 
I 


27 

30 

59 

25 

13 
42 

44 
52 
55 
15 
55 
14 
23 
51 
16 
6 
o 

13 

5  46 

52 


39 
24 
23 
50 
9 

8  29 

9  54 
20  36 
20  19 
20  27 

20  35 
20  16 

20  40 

21  47 

24  o 


45 
o 

o 

5 
40 

10 

50 
o 
o 
o 
o 
o 
o 
o 
o 
o 

23 

o 

o 

20 

45 

53 
o 

50 

45 
o 

o 

o 

o 

o 

o 

o 

o 

o 

36 

o 

o 

15 

o 

o 

25 
25 

o 
o 
o 
o 
o 
o 
o 
o 
o 
45 

40 
40 

o 


42  2^  20 
42  39  20 
42  21  19 
42  10  50 

41  53  49 
40  37  6 

39  45  56 
39  38  36 
36  58  o 

36  15 

37  o 
36  34 
36  46 

36  7 
34  45 
34  12 
32  37  30 
32  10  37 

30  19  o 

29  58  o 

31  16  30 

30  50  45 
30  27  o 

29  37  o 
29  20  42 
29  48  14 
28  10 
26  57 
26  12 
25  45 
25  39 

24  55 

25  12 

25  o 

24  42 

25  7 
25  I 
24  36 
24  14 
24  4 

23  45 
23  36  27 

23  39  47 

22  55  45 
22  5  30 
22  15 

21  54 
18  48 
17  II 
16  45 
16  30 
16  23 
15  22 

15  27  45 
14  2  45 
i^  21     o 


Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Australia  Directory. 
Lieut.  Raper,  R.  N. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 
Australia  Directory. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Australia  Directory. 
Lieut.  Raper,  R.  N. 
Australia  Directory. 

Do. 

Do. 
British  survey. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 
Australia  Directory. 
British  survey. 

Do. 

Do. 

Do. 

Do. 
Australia  Directory. 

Do. 
Lieut.  Raper,  R.  N. 


^^ 


Page  592] 


O 

o 


TABLE  49. 

MARITIME  POSITIONS. 

AUSTRALIA— Continued. 


Places. 


Cape  Inscription 

Houtman  Rocks 

Port  Gregory 

Cape  Leschenault 

Rottenest  Island 

Perth.,. 

Peel 

Cape  Naturaliste    

Cape  Leuwin  . 

D'Entrecasteaux  Point. 

Nuyts  Point 

West  Cape  Howe 

Eclipse  Islets 

King  George  Sound 

Bald  Isle 

Hood  Point 

Recherche  Archipelago. 

Culver  Point 

Dover  Point 

Fowler  Point 

Streaker  Bay 

Coffin  Bay 

Cape  Catastrophe 

Neptune  Isles 

Port  Lincoln 

F"ranklin  Harbor 

Port  Augusta 

Port  Victoria 

Cape  Spencer 

Investigator  Strait 

Port  Wakefield 

Port  Adelaide. 

Cape  Jervis 

Cape  Borda 

Cape  Willoughby 

Port  Victor  . 

Cape  Jaffa 

Cape  Northumberland.. 

Cape  Nelson 

Portland  Bay 

Port  Fairy 

Cape  Otway 

King  Island 

Port  Phillip 

Geelong 

Melbourne 

Cape  Schanck 

Port  Western 

Wilson  Promontory 

Kent  Island 

Flinders  Island 

Goose  Island 

Banks  Strait 

Port  Albert 

Gabo  Island 

Cape  Howe  (east) 

Cape  Green  

Twofold  Bay 

Dromedary  Mountain  .. 

Montague  Island 

Bateman  Bay 

UlladuUa 

Jervis  Bay 

Kiama  Harbor 

WoUongong 

Sydney  

Port  Jackson 


Exact  locations. 


Extreme 

N.  islet.. 


Extreme 

Light-house 

Arthur  Head  light 

Robert  Point .    

Extreme 


Summit 

Extreme  ... 

do 

do 

Summit  of  largest 

Commissariat  house  near 
Albany  jetty. 

Centre 

Doubtful  Isles 

Termination  Isle 

Extreme 

do 

do 

Port  Blanche 

Mount  Dutton 

W.  point  . 

S.E.  islet 

.English  Church 

Observation  spot  

Flag-staff 

Wardang  Island  hut. 

S.  point 

Troubridge  light 

Inner  end  of  Clinton  jetty. 

Snapper  Point 

Light-house . 

do _ 

do 

Flag-staff 

Margaret  Brock  It. -house. 

Light-house 

S.  extreme 

Lawrence  Rock 

Griffith  Island  summit 

Light-house 

Cape  Wickham  light 

Point  Lonsdale  light 

Custom-house 

Observatory 

Light-house 

Extreme  of  W.  head 

Light,  S.  E.  point 

Deal  Island  light 

Strzelecki  Peaks,  S.  E.peak 

Light  on  S.  end 

Swan  Island  light 

Light-house.. 

do 

Extreme 

S.  E.  point. 

Lookout  Point  light 

Summit  . 

S.  point 

Observation  head 

Inner  end  of  pier 

Light-house 

Duter  extreme  of  S.  head 

Summit  of  head . 

Observatory 

Outer  S.  head  light 


Lat.  S. 


32 
32 


25  29  19 
28  18  5 
28  12 
.^l  18 
o 

3 

32  27 

33  32 

34  19 

34  52 

35  5 
35  9 
35  II  54 
35  2  20 


o 
o 
20 
12 
o 
o 
o 
o 
o 
o 


o 
o 
o 
o 
o 

30 

o 


34  55 
34  24 
34  30 
32  57 
32  34 
32  I 

32  48 

34  29  29 

35  o  30 
35  20  30 

34  43  22 

33  44  8 
32  29  42 

34  28  25 

35  18  21 

35  7  31 
34  13  59 
34  46  50 


45 

30 

o 

6 


35  36 
35  45 
35  51 

35  34 

36  57  o 
38  4  18 
38  26  o 
38  24  39 
38  23  47 

38  51  45 

39  35  35 
38  17  40 

38  8  52 

37  49  53 

38  29  42 

38  29  15 

39  8  o 

39  29  45 

40  II  45 
40  18  40 
40  43  20 
3845  6 
37  34  15 
37  30  10 
37  15  40 
37  4  18 
36  18  30 

36  15  40 
35  43  58 
35  21  41 
35  9  15 
34  40  25 
34  25  30 
33  51  41 
33   51  30 


Long.  E. 


o 

112 

113 
114 

115 
115 
115 
115 
115 
115 
116 
116 
117 


57 
35 
14 
30 
30 
45 
44 

o 

6 

I 

38 
40 

117  53  45 
117  54  o 


9 
33 
30 

o 
12 

3 
o 

15 
o 

o 

o 

o 


118  27 

119  34 
121  58 

124  39 

125  30 


o 
o 
o 
o 
o 
132  33    o 

134  13  40 

135  24  56 

135  56  30 

136  7  o 

135  51  3 

136  57  22 

137  45  24 
137  22  21 

136  53  30 

137  49  39 

138  I  37 
138  30  39 
138  5  50 
136  35  o 
138  7  45 

138  37  9 

139  39  39 

140  39  40 

141  32  39 

141  40  2 

142  14  37 

143  30  39 

143  56  39 

144  36  58 
144  21  47 
144  58  32 
144  52  51 


145 

I 

34 

146 

25 

16 

147 

18 

39 

148 

4 

0 

147  47 

39 

148 

7 

24 

146  37 

43 

149  55 

10 

149 

58 

39 

150 

3 

4 

149  54  45  1 

150 

I 

34 

150 

13 

44 

150 

12 

34 

150 

29 

29 

150 

46 

26 

150 

52 

19 

150  55 

14 

151 

12 

23 

151 

18 

15 

Authorities. 


Australia  Directory. 

Do. 

Do. 

Do. 
Light-House  List. 

Do. 
Australia  Directory. 
British  survey. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
British  survey. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
British  survey. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
British  Admiralty. 
Australia  Directory. 


3 

o 


TABLE  49. 

MARITIME  POSITIONS. 

AUSTRALIA— Continued 


[Page  593 


Places. 


Broken  Ray 

Newcastle 

Port  Stephen 

Sugar  Loaf  Point 

Port  Macquarie 

Solitary  Islands 

Clarence  River 

Richmond  River 

Lookout  Point  .    

Cape  Moreton 

Double  Island  Point  _ 

Indian  Head 

Sandy  Cape 

Burnett  River 

Lady  Elliot  Islet 

Bustard  Head  

Rodd  Bay 

Port  Curtis 

Cape  Capricorn 

Port  Bowen 

Percy  Isles 

Northumberland  Isles . 

Cape  Palmerston 

Cape  Conway 

Port  MoUe 

Cumberland  Island 

Port  Denison 


Gloucester  Island 

Holborne  Islet 

Cape  Bowling  Green 

Cape  Cleveland 

Palm  Islands 

Rockingham  Bay 

Barnard  Island 

Frankland  Island 

Cape  Tribulation 

Hope  Island 

Cook  Mountain 

Cape  Bedford 

Murdock  Point 

Cape  Melville 

Flinders  Island 

Claremont  Point 

Cape  Sidmouth 

Cape  Direction 

Cape  Grenville 

Sir  Charles  Hardy  Island 

Bird  Island 

Hannibal  Isles 


Exact  locations. 


Baranjo  Head 

Nobby  Head  light 

Point  Stephen's  light 

Light-house 

Entrance 

S.  isle  light 

S.  head  light 

N.  head  light 

Extreme 

Light-house 

E.  extreme 

Extreme 

Light-house 

S.  head 

Centre 

Light-house 

Spit  end 

Gatcombe  Head 

Light-house 

Observation  rock 

Pine  Peak  

Summit  of  Prudhoe  Island 

N.  extreme 

S.  E.  point 

S.  side  of  entrance .. 

Wliitsunday  Island,  sum- 
mit on  W.  side. 
Observation  point  on  W. 

side  of  Stone  Isle. 
Summit  near  N.  end  ._  .. 

Centre 

Light-house 

N.  W.  extreme 

S.  E.  point  of  S.  E.  island. 

Peak  of  Goold  Isle 

Outer  N.  isle 

High  islet 

Extreme 

S.  islet  

Summit 

S.  E.  extreme 

Extreme 

N.  E.  extreme 

N.  extreme  of  N.  island.. 

Extreme 

do 

N.  E.  extreme 

Extreme 

N.  extreme  of  S.  E.  isle  .. 

N.  W.  isle 

E.  isle 


Lat.  S. 


33  35  o 
32  55  15 
32  45  10 
32  26  10 
31  25  30 
30  12  o 
29  25  30 
28  51  30 
27  26  20 
27  2  10 

25  55  50 
25  o  15 
24  43  20 

24  45  o 
24  7  o 
24  I  20 
24  I  20 
23  52  50 
23  29  30 
22  31  40 
21  31  30 
21  19  15 
21  32  o 
20  32  20 
20  18  50 

20  15  30 

20  o  50 

9  57  30 
9  41  50 
9  19  20 

9  II  15 

8  45  30 
8  9  30 
40  30 

9  45 
4  20 

45  o 
29  45 
16  30 

37 
10 

7 
o 


IS 
o 

45 
30 
24  45 
51  o 

58  15 
55  o 
46  30 

36  30 


Long.  E. 


51  20  30 

51  48  19 

52  12  24 

52  33  20 

52  55  19 

53  16  4 
53  23  10 
53  35  45 
53  33  50 
53  28  4 
53  12  50 
53  23  o 
53  13  40 
52  25  20 
52  45  30 
51  41  4 
51  37  15 
51  23  40 
51  14  4 
50  45  44 
50  8  45 
49  43  30 
49  31  4 
48  58  o 

48  53  15 

49  o  o 

48  16  54 

48  27  34 


48 
47 
47 

46  42  50 
46  II  4 
46  12 
46  2 
45  29  34 
45  28  30 
45  17  30 
45  23  15 
44  57  30 
44  32  34 
15 


23  o 

27  40 

I  10 


0^ 
30 


44 

43  42 
43  36 
43  34 
43  15 
43  29 
43  6  o 

42  56  19 


19 

15 

19 

o 

15 
o 


Authorities. 


Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Light-House  List. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


TASMANIA. 


Cape  Portland 

Port  Dalrymple  ._ 

Port  Sorrell 

Port  Frederick 

i.even  River 

Emu  Bay .    _ 

Hunter  Island 

Cape  Grim 

Albatross  Islet 

.\rthur  River 

i'ieninn  River 

Mr.c  luarie  Harbor 


N.  W.  point 

Low  head  light 

N.  W.  entrance  head  .. 

Entrance 

W.  entrance  head 

Blackman  Point 

N.  point 

Outer  Doughboy  Islet  . 

N .  point 

Entrance 

Rocks  close  to  entrance 
Entrance  Islet 


40 
41 
41 
41 
41 
41 
40 
40 
40 
41 
41 
42 


44  o 

3  25 

7  5 

10  o 

8  30 
2  50 

23  40 

40  10 
22  o 

4  o 

41  o 

11  37 


147 

55 

40 

146 

47 

54 

146 

33 

30 

146 

24 

30 

146 

12 

0 

145 

56 

39 

144  47 

45 

144 

39 

44 

144 

39 

19 

144 

44 

0 

144 

57 

0 

145 

12 

34  { 

Australia  Directory. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  694J 


TABLE  49. 

MARITIME  POSITIONS. 

TASMANIA— Continued. 


o 


Places. 


Cape  Sorrell 

Port  Davey 

South  West  Cape 

Mewstone  Rock 

Cape  Bruny 

Bruny  Island 

Hobart  Town 

Do 

Cape  Pillar 

Cape  Frederik  Hendrik 

Freycinet  Peninsula 

St.  Patrick  Head 

Eddystone  Point 


Exact  locations. 


N.  W.  extreme 

Pollard  on  N.  head 

Extreme  point 

Centre 

Light-house . 

Penguin  Islet 

Transit  of  Venus  station 

Fort  Mulgrave 

Tasman  Islet 

Extreme 

Summit 

N.  point 

Extreme 


Lat.  S. 


42  II    30 

43  19  o 
43  33  30 
43  44  30 
43  29  40 
43  21     o 

42  53  25 

42  53  32 

43  14 
42  52 

42  13 
41  34 
40  59 


Lonsr.  E. 


145  10  o 

145  53  o 

146  I  4 

146  22  4 

147  8  49 
147  23  40 
147  20  7 

147  20  17 
14S  2  o 

148  o  o 
148  18  4 
148  19  30 
148  20  o 


Authorities. 


Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 
Prof.  Harkness,  U.  S.  N. 
Australia  Directory. 

Do. 

Do. 

Do. 

Do. 

Do. 


NEW  ZEALAND. 


Three  Kings  Island 

North  Cape 

Parenga-renga  Harbor. . 

Monganui  Harbor  . 

Wangaroa  Harbor 

Bay  of  Islands 

Wangaruru  Harbor 

Wangar,i  Harbor  . . 

Great  Barrier  Island 

Auckland  Harbor _ 

Coromandel  Harbor 

Cape  Colville 

Cuvier  Island 

Tauranga  Harbor 

White  Island 

Cape  Runaway 

East  Cape 

Tolaga  Bay 

Mahia  Peninsula 

Ahurivi  Harbor 

Kidnapper's  Cape 

Cape  Palliser 

PortNicholson(timeball) 

Mana-watu  River 

Wanganui  River 

Egmont  Mountain 

New  Plymouth 

Kawhia  Harbor.. 

Aotea  Harbor 

Whaingaroa  Harbor 

Manukau  Harbor 

Kaipara  Harbor 

Hokianga  River 

Cape  Campbell 

Port  Cooper 

Akaroa  Island 

Ashburton  River 

Waitangi  River 

Otago  Harbor 

Molyneux  Bay 

Nugget  Point 

Bluff  Harbor 

Tewalwae  Bay 

Solander  Islands .. 

Preservation  Inlet  

West  Cape  . 

Queenstown 

Milford  Sound 

Cascade  Point 


N.  E.  extreme  of  N.  E 
island. 

Cape  Islet 

Kohan  Point ... . 

White's  Point 

Peach  Islet 

Motu  Mea  Islet 

Grove  Point 

Loot  Point 

Aiguilles  Point 

Depot  Point 

Tuhnia  Island 

N.  point 

Highest  peak 

Mount  Monganui,  860  feet 

Summit,  863  feet 

Extreme 

Islet,  420  feet 

Matu-heka  Islet 

S.  extreme  of  Portland  I_. 

Maori  Pah 

Extreme  .    , 

do 

Pencarrow  light 

Light-house 

N.  head 

Summit,  8,270  feet 

Flag-staff 

S.  head 

do 

S.  entrance  point 

Paratutai  flag-staff 

S.  head 

Flag-staff  at  entrance..   . 

Light-house 

Lyttleton  custom-house.. 

Light-house 

N.  entrance  point 

N.  entrance  head 

Taivoa  Head  light 

Landing  place 

Light-house 

Point  near  anchorage 

Pallia  Point 

Summit,  1,100  feet 

Cuttle  Cove 

Extreme . 

U.  S.  Tr.  of  Venus  station 

Freshwater  Basin _. 

N.  extreme 


34  6  20  '  172  8  49 


34  28 

34  31 

35  o 


30 

o 

20 


35 
35 
35 
35  51 


I  44 
17  o 
23  48 


I 


9 
15 

36  50  5 
36  48  35 
36  28  20 

36  26  20 

37  36  25 
37  30  o 
37  30  45 

37  40  o 

38  20  50 

39  17  40 

39  28  44 

39  38  o 
41  36  50 
41  21  40 

40  27 
39  57 
39 
39 
38 


I! 


3 

4 

37  59  35 
37  46  22 
37  3 

25 
32 


36 
35 


o 
10 

5 
41  44  o 

43  46  42 

43  54  o 

44  4  50 

44  54  50 

45  47  o 

46  24 
46  27 
46  36 
46  20  40 

6  o 


5 
15 
17 


ID 

20 

O 

35 
50 


46 

46  4 

45  54 
45  2 
44  40  20 
44  o  30 


30 
20 

7 


24 
14 


73  4  30 
73  o  54 
73  32  39 

73  45  48 

74  6  6 

74  21 

74  31 

75  25  34 

74  48  14 

75  24  34 
75  21  4 

75  47  24 

76  10  14 

77  10  49 

77  59  34 

78  35  9 
78  20  14 

77  52  0 

76  55  10 

77  7  40 
75  16  24 

74  51  4 

75  13  44 
74  59  44 
74  3 
74  4 
74  48 
74  50 


59 

35 

4 

4 

74  52  19 


74  31 
74  13 


73  21 

74  17 


14 

37 

59 

14 

44  17 


1^ 

73  o  20 
71  48  34 
71  II  14 
70  44  2 

69  47  53 
69  50  4 

68  21  55 

67  42  19 
66  54  4 
66  39  42 

66  25  49 

68  40  6 

67  54  45 

68  21  34 


Capt.  B.  Drury,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.  •», 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Stokes,  R.  N. 
New  Zealand  Pilot. 
Light- House  List. 
Capt.  Stokes,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Raymond,  U.  S.  A. 
Capt.  Stokes,  R.  N. 

Do. 


TABLE  49. 

MARITIME  POSITIONS. 

NEW  ZEALAND— Continued. 


[Page  595 


Places. 


Grey  River 

Hokitika .. 

Cape  Foulwind.. 
Cape  Farewell  .. 

Nelson 

D'Urvillc  Island 

Port  Gore 

Wellington  . 

Port  Underwood 
Port  William  ... 
Paterson's  Inlet  . 
Port  Adventure  . 

Port  Pegasus 

Codfish  Island  ._ 
Snares  Islands  ._ 


Exact  locations. 


N.  shore  light 

Entrance 

Extreme  . 

do 

Bowlder  Bank  light 

Port  Hardy 

Head  of  Melville  Cove  .. 

Observatory 

Flag  Point 

Howell's  House 

Glory  Cove  

White  Beach,  S.  end 

Cove  abreast  Anchorage  I 

N.  W.  extreme 

S.W.  islet _. 


Lat. 

s. 

0 

/ 

II 

42 

30 

0 

42 

42 

20 

41 

45 

30 

40  29 

50 

41 

15 

5 

40 

46 

35 

41 

I 

55 

41 

lb 

57 

41 

20 

28 

46  50 

30 

46  58 

30 

47 

3 

52 

47 

II 

AO 

46  45 

45 

48 

6 

43 

Long. 

E. 

0 

/ 

// 

171 

II 

0 

170  59 

30 

171 

34 

30 

172 

41 

4 

173 

16 

2 

173 

54 

4 

174 

II 

22 

174 

46 

22 

174 

8 

24 

168 

5 

34 

168 

9 

54 

168 

10 

57 

167 

40 

51 

167  36 

49 

166 

27 

44 

Authorities. 


Light-house  List. 

Ho. 
Capt.  Stokes,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Messrs.  Adams  and  Russell, 
Capt.  Stokes,  R.  N. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 


THE  ARCTIC  REGIONS. 


Cape  Walsingham 

Miles  Island 

Marble  Island 

Cape  Kendall 

Iglooik  Island  .  _. 

Victoria  Harbor 

Elizabeth  Harbor 

Magnetic  Pole,  1831  ... 

Port  Neill 

Port  Bowen. 

Batty  Bay 

Port  Leopold 

Carey's  Islands 

Thank  God  Harbor 

Discovery  Harbor 

Cape  Breevort .. 

Alert's  Winter  Quarters. 

Cape  Joseph  Henry 

Cape  Hecla 

Cape  Columbia 

Melville  Island 

North  Cape 


Extreme 
N.  point. 
E.  end  ... 
Extreme  , 
E.  point. 
N.  shore  . 
Entrance . 


N.  point  of  entrance. 

N.  cove 

S.  point  of  entrance  . 
Whaler  Point 


Liakhov  Islands... 
Cape  Tscheljuskin . 

Novaya  Zembla 

Do 

Franz  Josef  Land., 
Mezen 


Morjovetz  Island  .. 

Archangel 

Jighinsk  Lsland 

Onega 

Salovetski 

Sviatoi  Nos,  Cape  . 

Bear  Island 

Spitzbergen  Island. 

Do 

Do 


Extreme 


Lat.  N. 
66     o     o 

64     7 

62  33 

63  42 

69  21 

70  9  17 
70  38  14 


70 

73 

73 

73 

73  50 
76  49 

81  38 


13 


13  39 

13    o 

5 
o 


91 
87 
81 


Long.  W 
69   28 

77  50 
6 

15 
31 

91  30  33 

92  10  56 
96  47     o 

89  o  54 
88  54  48 
91     8    o 

90  12 
73  10 


81 
82 


N.  extreme 

do 

Extreme 

Winter  Harbor. 


82  27 
82  40 

82  54 

83  7 
74  47 
68  55 


40 
o 
o 
o 
o 
o 

10 
o 


E.  point  of  New  Siberia. . 

E.  point 

Vaigat's  Island,  N.  point. 
N.  E.  point,  Cape  Desire. 

Wilczek  Island 

Epiphany  Church 

Light-house 

Trinity  Church 

Light-house 

St.  Michael's  Church 

Light-house 

do    


75  10    o 

77  41  o 

70  25  o 

76  58  o 
79  55  o 

65  50  18 

66  45  so 
64  32     6 

12 


o 
o 
o 
o 
o 
o 
o 
o 
o 

15 

o 


S.  cape 

Cloven  Cliff 

Treusenberg  Bay,  Hecla 
Cove. 


65 

63  53 
65 
68 

74  30 
76  35 
79  50 
79  55 


17 

36 

7  o 

8  51 


o 
18 


61  44 

64  45 
61  20 
61    18 

63  38 

64  45 
70  20 

no  48 

179  57 

Long.  E. 
150  30     O 
104     I     o 

59  10 
76  4.0 

58  45 
44  17 
42  30 

40  33  30 

36  51  30 

38  8  30 
35  37     o 

39  48  54 
20  o  o 
17  23     o 

II  40  30 
II  40  30 


Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 

Do. 
Admiralty. 

Do. 
Lieut.  Raper,  R.  N. 
Admiralty. 
Admiralty  chart. 
Admiralty. 
Admiralty  chart. 
Lieut.  Raper,  R.  N. 
C.  F.  Hall. 
Lieut.  Archer,  R.  N. 
C.  F.  Hall. 
Sir  G.  S.  Nares,  R.  N. 

Do. 

Do. 

Do. 
Admiralty. 
Lieut.  Raper,  R.  N. 

Do. 
Nordenskjold. 
Lieut.  Raper,  R.  N. 

Do. 
Lieut.  Payer,  Aus.  N. 
Lieut.  Raper,  R.  N. 
Light-House  List. 
Lieut.  Raper,  R.  N. 
Light-House  List. 
Lieut.  Raper,  R.  N. 
Light- House  List. 

Do. 
Lieut.  Raper,  R.  N. 

Do. 

Do. 

Do. 


GREENLAND. 


Ca]ie  York 

Uiicrna .  ik_ 


Extreme 

Flag-.staff 


Lat.  N. 

75  55     o 

72  47  4S 


Long.  W. 
65    30     O 

55  53  4^ 


I   Lieut.  Raper,  R.  N. 
I  Danish  Hyd.  Office. 


Page  596]  TABLE  49. 

MARITIME  POSITIONS. 
THE  ARCTIC  REGIONS— GREENLAND— Continued. 


o 
O 


Places. 


Proven   

Omenak  Island  ... 

Godhavn  

Jacobshavn 

Claiishavn    

Chiistianshaab 

Egedesmunde 

Whalefish  Island . . 

Holsteinberg , 

Kangainint 

Ny  Sukkertop  .... 

Godthaab 

Sermelik  Fjord 

Fiskernaes 

Jensen's  Nunatak  . 

Ravn's  Storo 

Frederikshaab 

Kangarssuk  Havn 

Arsuk , 

Kajartalik  Island   . , 

Ivigtuk 

Bang's  Ilavn 

Aurora  I  larbor  ... 

Julianshaali 

Neunortalik 

Frederiksthal 

Cape  P'arewell  ..  ... 

Aleuk  Islands 

C'a])e  Tordenskjold 

Cape  Hille 

Cape  J  iiel 

Cape  Lovenorn  ... 
Danneborg  Island  ., 

Ingolfsfjeld 

Rigny  Mount 

Pendulum  Islands.. 
Cape  Philip  Broke 
Cape  Bismark 


Jan  Mayen  Island 
Do 


Exact  locations. 


\'illage    . 
, do 


Lat.  N. 


do    .. 

do   .. 

do   .. 

....    do  .. 

do  . . 

Boat  Inlet 
Village  ... 


72  20  42 

70  40    o 

14 

7 


69 
69 
69 


4 
12 


Village 

Flag  staff 

Kasuk  Peak  . . 

Village 

Peak 

do   

Church 

Village   

Pin  go  Beacon 

Summit 

House 

Anchorage 


68  49  6 
68  42  30 
68  58  30 

66  55  . 
65  48  42 

65 

64 

63  29 

5 

50 

62  42  36 

61  59  36 
28  20 
10  24 

9  42 
12  12 


63 
6 


54 
42 
24  30 
10  36 
12 
12 
o 


61 
61 
61 
61 


Village 

do   ... 

do   ... 

Staten  Iluk 

Centre 

Extreme 

do  ... 

do   ... 

do  ... 

Beacon  


60  47  30 
60  48  36 

60  43  7 
60  8  12 
60  o  o 
o 
o 
o 
o 
o 
o 
o 
2 


Summit . 


Extreme 


59  49 

60  9 

61  25 

62  I 

63  14 

64  30 

65  18 

66  19 
69  o  12 
74  40  o 
74  55  o 
76  47    o 


Mt.  Beerenberg,  6,870  ft 
Young's      F"oreland,     or 
Cape  Northeast. 


71 
71 


Lonsr.  W. 


55   20     o 

51  59  o 
53  24  7 
50  56  30 

50  55  30 

51  o    o 

52  46    o 

53  27  o 
53  40  18 
53  23  o 
52  54  o 
51  45  48 
51   10  48 

5"  43  36 

48  57  o 
50  20  48 

49  44  o 
48  51  o 
48  26  o 
48  30  42 
48  10  30 

47  52  o 
47  46  48 
46  I  o 
45  16 
44  40 
44  I 
42  55 
42  15 
42  o 
40  50 

39  30 
8  30 

II 

10  24 
17    o 

17  33    o 

18  40     o 


Authorities. 


35 
26 

18 


o 
o 

42 

o 
o 
o 
o 
o 
o 
o 


7  36 
7  26 


Danish  Ilyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 
Capt.  Parry,  R.  N. 
Danish  Ilyd.  Office. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.      • 

Do. 

Do. 

Do. 
Lieut.  Raper,  R.  N. 

Do. 
Koldewey. 

Lieut.  Raper,  R.  N. 
Do. 


ICELAND. 


Langanes  Point 

Gunolfsvik  Tr.  Station.. 

Rissnaes  I'omt 

Grimsey  Noiddranger  -- 

Akureyi  i .    

Sigelfjird  Hoaneyri 

Skagataas  Point 

Skagestrands 

Bordeyri 

Hafa  Fjeld 

Kalfatindr ' 

Flatey _.. 

Stykkisholm 

Slraums  Naes  Point 

Onundar  Fjord 

Fugle  or  Staabjerg  Huk. 

Snefjelds  \'okul 

Hjortsey 

Akrafjeld 

Reykiavik 

Cape  Skagen 

Reykianaes 


Tr.  Station 

do... 

Church 


Flag-staff 

Pier 

Tr.  Station  _    _ 

do 

Church   

Sugandisey  Beacon 


Flateyri  flag  staff 

Point 

Tr.  Station 

do 

do 

Observatory 

Extreme 

I  .iirht-house 


66 
66 
66 
66 

65 
66 

66 

65 

65 

65 
66 

65 

65 
66 

65 

65 
64 

64 
64 
64 
64 

63 


22  45 

8  46 

32  40 

33  42 
40  28 

9  35 
7  30 

50  o 

13  50 
54  31 
27  29 

22  25  j 

4  44 
26  30 

3  27 

3c  15 

48  4 


50 

o 

40 

5  o 
48  18 


19 
8 


14  30  46 

15  3  30 

16  10  24 

17  57  36 
3  16 

53  30 
5  26 

20  18  20 

21  7  16 
30  42 

23  4 

22  54  26 

22  41   2 

23  8 
,0 


18 
18 
20 


21 

22 


23 

24  31 


o 
22 
26 


22  18  34 
21  56  16 

21  55  o 

22  40  35 
22  41  35 


Danish  Hyd.  Office. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


TABLE  49. 

MARITIME  POSITIONS. 

THE  ARCTIC  REGIONS— ICELAND— Continued. 


[Page  597 


o 
U 


Places. 


Exact  locations. 


Strandar Church  . . . 

Lapstadir do   . . 

Westnianey  Heimaklettr     Tr.  Station 

Portland  Uyrholarey do 

Hjorleifs  Hofdi do 


Lat.  N. 


63  49  50 
63  48  18 

63  26  53 
63  23  59 
63  24  56 


Kirkjuboejar  Heidi do   63  47 


60 
64 


48   19 
17  40 


Irgolfstrofdi do 

Vestra  Horn  Point 

Papey  Island Tr.  Station j  64  35  42 

Djupavog  Bondavarde c'o   |  64  39  32 

Reydar  Fjeld [ do  64  55  27 


Seydis  Fjord 
Dia  Fjeld 


Pier 

Tr.  Station 


65   18 
65  45 


Long.  W. 


21  40  30 
20  53  ID 
20  13  46 

19  5  54 
18  42  42 

18  2  24 
16  36  13 
14  54  40 

14  8  31 
14  14  38 
13  41  10 

13  51  30 

14  23  35 


Authorities. 


Danish  Hyd.  Office. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 
Do. 


Page  598] 


■MlfldailiHaMHaliir 


INDEX  TO  TABLE  49. 


Page. 

Aalborg 553 

Aarhus 553 

Ababa  Island 586 

Abaco  Island 532 

Abang  Besar  Island 568 

Abbeville 553 

Abd-al-Kuri  Island 563 

Aberdeen 545 

Abervach 554 

Aberystwith 544 

Abingdc  n  Island 580 

Abo  . 549 

Aboukir  Bay 560 

Abreojos  Point 530 

Abrolhos  Island 537 

Absecum  Inlet 524 

Abu  Thabi 566 

Acajulta 531 

Acapulco 531 

Accra 561 

Acheen  Head 569 

Aconcagua  Mount 540 

Acre  560 

Adakh  Island 528 

Adalia 560 

Adams  Point 529 

Port 576 

Addu  Atoll 564 

Adelaide,  Port 592 

River 591 

Ad^le  Island 585 

Aden 566 

Adenara  Island 575 

Admiralty  Head 529 

Island     585 

Adolphus  Mountain 591 

Adventure,  Port 595 

^gina.... 559 

Aero  Island 552 

Africa  Rock 556 

Agalegas  Island 565 

Agdenoes 547 

Agiabampo 531 

Agrigan  Island ..  582 

Aguadilla  Bay 534 

Aguja  Point 542 

Agulhas  Cape 562 

Agutaya  Islands 572 

Ahii 589 

Ahunai  Island 587 

Ahuriri 594 

Aiari 580 

Aignan,  St.,  Island 585 

Aigues  Mortes 556 

Ailinginae  Islands 581 

Ailly  Cape 553 

Aillick  Harbor 520 

Ailuk  Islands 581 

Aisima   579 

Aitutaki  Island 590 

Aix  Island 554 

yVjaccio 556 

Ajano 560 

Akamokan  Island 582 

Akaroa  Island 594 

Akashi-no-seto 578 


Page. 

Aki-Aki  Island 588 

Akishi 579 

Akpatok  Island 520 

Akrafjeld   596 

Akuisi  Sima 571 

Akureyri 596 

Akyab  Harbor 568 

Alacrane  Reef 526 

Alamaguan  Island 582 

Aland  Island 549 

Alagarte  Reef 527 

Albany 523 

Albatross  Island 593 

Albemarle  Island 583 

Albert,  Port 592 

River 591 

Alboran  Island 560 

Albuquerque  Bank 527 

Alcatrasses  Islands 537 

Alcmene 590 

Alcoba9a 537 

Aldabra  Island 565 

Alden 547 

Alegranza  Island 543 

Alegre,  Porto 537 

Alert's  winter  quarters 595 

Alessandro,  S.,  Island 583 

Aleuk  Islands   596 

Alexander,  Port 529 

British  America 529 

Alexandretta 560 

Alexandria  .  .  .■ 560 

Alfaques,  Port 555 

Alfred,  Port 562 

Algeciras   555 

Algiers 560 

Algoden  Bay 541 

Ali-Agha 560 

Alicante     555 

Alijos  Rocks 530 

Alipee 567 

Alligator  Reef 525 

Rock 571 

Almadie  Point 561 

Almeria 555 

Alphonse  Island 565 

Altata 531 

Alta  Vela 534 

Altea 555 

Altona 552 

Alvarado 525 

Amager  Island 552 

.\manu 588 

Amber  Cape 565 

Amboina  Island 576 

Ambrose,  St. ,  Island 590 

Amchitka  Island 528 

Amelia  Island 524 

Ameni  Island 564 

.■\mherst  Island 521 

Amirante  Islands 564 

Amour  Point 521 

Amoy 571 

Amsterdam 553 

Island 566 

Ana,  Sta.,  Lagoon 526 


Page. 

Anaa 589 

Anacapa  Island 530 

Anadyr  River 580 

Analaboe 569 

Anamba  Islands 570 

Anataxan  Island 582 

Anchorite  Island 585 

Anclam 550 

Ancona 557 

Andamans 568 

Andenas 547 

Andrava  Bay 565 

Andrea,  St.,  Rock 558 

Andrew,  St.,  Cape 565 

Island 527 

Andrews,  St 522 

Island 527 

Andros  Island 532 

Bahamas 532 

Grecian  Arch 559 

Anegada    534 

Aneiteum  Island 586 

Angatan 589 

Angeles  Bay 531 

Los   . 530 

Port 531 

Angelos,  Port 529 

Anghris  Head 546 

Angour  Island 582 

Angoxa  Island 563 

Angra  dos  Reis 537 

Pequena 562 

Anguilla 534 

Anhatomirim 538 

Anholt  Island 552 

Animas,  Las 531 

Anjer 575 

Anjoe  Cape 575 

Ann  Cape 523 

Ann's,  St , 544 

Bay 533 

Harbor 522 

Anna,  St.,  Island 536 

N.  Brazil 1.  536 

S.  Brazil 537 

Annapolis    524 

Harbor 522 

Anne,  St. ,  Island 523 

Annisquam 523 

Anno  Bon  Island 561 

Anowik  Island 528 

Antareh,  Ras 563 

Antibes    556 

Anticosti  Island 521 

Antigua 534 

Antipodes  Island 591 

Antivari , 558 

Antofagasta 541 

Antonina 537 

Antonio,  Port   533 

.San,  Port 538 

St.,  Cape 538 

Buei.os  Ayres 538 

Cuba    533 

Mt    and  Island 543 

Antonio,  St.,  Port 540 


INDEX  TO  TABLE  49. 


[Page  599 


Page. 

Antonio,  St.,  Sierra 538 

Antwerp 553 

Ann  Aruvaro  Island 588 

Aogo  Siina 5 78 

Aor,  l*iilo 5  70 

Aotea 594 

Apalacliicola. 525 

Apaniima  . 5S0 

ApLnrade  551 

Apiang  Island 580 

Apo  Island 572 

Apostle  Rocks    539 

Arago  Cape 529 

Araish,  El 560 

Arakam  Island 580 

Arakchayeff  Island 589 

Aran  Island 546 

Aransas  Pass 5-5 

Aranuka  Island 5S0 

Aratica  Island 589 

Arcadius  Islands 533 

Areas  Cays 526 

Archangel 595 

Arcona 550 

Ardassier  Islet 575 

Ardrossan 545 

Arena  de  la  Ventana 530 

Arena  Point 530 

California 529 

Guatemala 53° 

Arenas  Cay 5-^ 

Arendal  Inlet 547 

Arentes  Island 575 

Argentina 538 

Argostoli,  Port 558 

Arhno  Atoll 581 

Arica 541 

Arichat  Harbor 522 

Armagon 568 

Arnheim  Cape 591 

Arorai  Island 580 

Arran  Islands 546 

Arrowsmith  Islands 5^' 

Arru  Islands 5  76 

Arsuk 596 

Artaki  Bay 560 

Arthur  River    593 

Arutua  Island 5^9 

Arvoredo  Island 533 

Ascension  liay 526 

Island 530 

L.  California 530 

S.  Atlantic 543 

Ashburton  River 594 

Ashrafi  Island 563 

Asia  Rock 541 

Aspinvvall 535 

Assateague  Island 524 

Assel 551 

Assens   532 

Assumption  Island 565 

Astoria 529 

Asuncion 582 

Atalaia  Point 536 

Athens     559 

Atico 541 

Atiu  Island 590 

Atka  Island 528 

Atkinson  Point 529 

Attu  Island 528 

Auckland     594 

Islands 590 

Audieme 554 

Augusta 522 

Augusta,  Port 522 


Page. 

Azgusti,  Port  Sicily 557 

Australia 592 

Augustenberg 551 

Augu^tin,  St.,  P>ay 565 

Augustin,  St.,  Cape 536 

Brazil 536 

Philippines 573 

Augustine,  St.,  Harbor 524 

Island   583 

Augosto,  Port 539 

Aunivak  I>lar.d 527 

Aurh  Island 581 

Aurora 596 

Island 586 

Avarena  Point 534 

Aves  Island 534 

Aviles 554 

Avlona 558 

Axim  Bay 561 

Awasima 5  79 

Awomore 578 

Ayamcnte 555 

Ayer  Bangis 569 

Ayr 545 

Azores .  542 

Baago  Island 552 

Babayan  Claro  Island 573 

Baccalieu  Island 520 

Bagamoyo   563 

Bahama  Island   532 

Bahatolis  Island 5  74 

Bahia 536 

de  Cadiz  Cay 533 

Bahia  Honda 531 

Guatemala 531 

New  Grenada 535 

Bahrain  Island    566 

Bajaren  Island 574 

Baker's  Island 522 

Maine,  U.  S 522 

N.  Pacific 580 

Baklar 559 

Balabac  Island 572 

Balaklava  Bay 559 

Balari  Pass 590 

Balasore 568 

Bald  Island 592 

Ba-L.-Hof 566 

Balfour  Rock 566 

]ali  Lsland      575 

^alintang  Islands 573 

Ball's  Pyramid 590 

3allones  Cape 565 

fellycottin 547 

5allum 551 

Balstrum 552 

"Jalta  Island 545 

Jaltic,  Port 549 

Jaltimore    524 

iiamiJton  Shoal 585 

jan(la  Islands 576 

ianderburum    5^6 

iangka  Strait 569 

Island   569 

bang's  Ilavn 596 

iangor     522 

janjar  Massin    5  74 

ianjowangie 5  75 

5ankok 570 

iankot     ..      567 

jank's  Strait 592 

Jantal 569 

Bantam 575 

Bantaman 575 


Page. 

Banton  Island 573 

Bantry  Bay 545 

Banyak  Islands 569 

Baracoa 532 

Baratoube  Bay 565 

Barbadoes  Island 535 

Baibara,  Santa 530 

California 536 

Mexico 531 

Barbara,  ,Sta. ,  Island 530 

I'o't 540 

Barbe,  St ,  Island 570 

Barbuda 534 

Bartelo  Bay 539 

Barcelona    555 

^Pain 555 

Ven?zuela 535 

Barcbey  Island 544 

Bartleur  Cape 553 

Bari    : 557 

Barker  Islands    591 

Barnard  Islands 593 

Barnegat  Inlet 524 

Barnevelet  Islands 539 

Barnstable 523 

Baroe  Cape 569 

Barra  Head 545 

Barra,  Sao  Joao   537 

Barrataria  Bay 525 

Barren  Island 577 

Islands 572 

Ba' rier.  Great,  Islands 594 

Barrington  Island 583 

Barrow  Island 591 

■  Australia 591 

Low  Arch 588 

Barrow  Point 527 

Barth 550 

Bartholomew,  St.,  Cape 538 

-^Port 534 

Bai  tolome  San •  530 

Barton,  Port 572 

Barung  Islands 575 

Bas  c  e.  Island 554 

Basdorf 550 

Basidieh 566 

Bafilau  Ldand 574 

Basianang  Bay 574 

BasI  erville  Cape 591 

Basrah 566 

Bass  Islancb      590 

Bassa,  Grand    561 

Bassas  Rocks    567 

da  India   565 

Bassein 568 

Burmah 568 

llindoostan 567 

River 568 

Basse  Terre 534 

Bastia 556 

Bastion  ( 'ape 5  70 

Basto 548 

Bataban  Island 573 

Batalden  Island 547 

Batan  Island 573 

Batang  Port 5  73 

Batavia    575 

Batchian  Island 5  76 

Bate  Island 577 

Bath  522 

Bateman's  Bay 592 

Bathurst 561 

Island 591 

Batoe  Islands 569 

Batoum  559 


Page  6001 


INDEX  TO  TABLE  49. 


Page. 

Batticaloa 567 

Battle  Islands   520 

Battoe  Toetong 569 

Batty  Bay 595 

Baudeltaob 582 

Bauld  Cape 520 

Bavvean  Islands 5  75 

Baxo  Nuevo 526 

Gulf  of  Mexico 533 

Pedro  Bank 526 

Bay  of  Islands 594 

Bayne's  Sound 529 

Bayonnaise  Island 578 

Bayonne 554 

Bazarou to  Island 562 

Beachy  Head 544 

Beale  Cape 528 

Bear  Island 595 

Beam  Cape 555 

Beata  Island '. 533 

Beaufort 562 

Africa 562 

N.Carolina 524 

S.  Carolina 524 

524 

Beaver  Harbor 529 

Beaver-tail  Light 523 

Bee  du  Raz 554 

Bedaa,  Al 566 

Bedford  Cape 593 

New 523 

Bees,  St 545 

Beeves  Rocks 546 

Behring  Cape 580 

Island 580 

Beirut 560 

Bel  Air 565 

Belfast 522 

Lough 546 

Belgrano 538 

Belize 526 

Bell  Island 520 

Bell,  Scotland 545 

Bellavista  Cape 556 

Belle  Isle 520 

France 554 

Labrador 520 

Bellingshausen  Island 587 

Benbane  Head 546 

Bender  Erekli 560 

Benicia 529 

Benedicto  San  Island 531 

Benevente   537 

Ben  Ghazi 560 

Benguela 562 

Benidonne 5c c 

Benin  River 561 

Benito,  San,  Island 530 

Benkeelen 569 

Bento,  San,  River 561 

Benzert 560 

Bequia  Island 535 

Bequico  Island 535 

Berbereh ^63 

Berdiansk 559 

Bergen „ 547 

Norway 547 

Prussia 550 

Berlin 552 

Bermudas 543 

Bernal  Chico 525 

Bernardo  Islands 537 

Berwick cac 

Besuki c  7c 

Betra  i'ar  Island 564 


Page. 

Beverly 523 

Beyt 567 

Bezookie 575 

Bianche  Point 557 

Biarritz 554 

Bickerton  Island 591 

Bideford 544 

Bidestone 544 

Bi gar  Islands 581 

Bikini  Islands 581 

Bilbao 554 

Bille  Cape 596 

Billiton  Island 569 

Bindloe  Island 580 

Bintang  Hill 568 

Bintoean 569 

Bird  Island 593 

Banda  Sea 576 

Bahamas 532 

Low  Arch 588 

Sandwich  Islands  . .   583 

Seychelles 569 

W.Africa  561 

Bird  Islands 583 

Australia 593 

E.  Africa 562 

Magdalen  Islands . .   521 

Birney's  Island 584 

Bismark  Cape 596 

Bittern  Rocks 5  78 

Bjorneborg 549 

Bjuro 549 

Blaabjerg 553 

Black  Head 520 

Point  Bay 562 

Blacksod  Bay 546 

Blackstairs  Mountain 546 

Blair,  Port 568 

Blaize,  St 562 

Blanco  Cape 561 

N.  Africa 561 

S.Africa 561 

Oregon 529 

Peru 542 

Blanco  Peak 527 

Point 527 

Blankenberg 553 

Bias,  St.,  Cape 525 

San 531 

Harbor  and  Bay  . . .   538 

Blasket  Islands 545 

Blewfield 527 

Bligh  Island 588 

Bligh's  Cape 566 

Blimbing  Bay 569 

Blinyoe 569 

Block  Island 523 

Blocksberg 550 

Bloody  Foreland 546 

Bluff  Harbor 594 

Bobara  Rock 558 

Body's  Island 524 

Boero  Island 576 

Bogense 552 

Bogskaren 549 

Bohnsack 550 

Bojol  Island 573 

Bojador  Cape 561 

Bojeador  Cape 573 

Bola- Bola  Island 587 

Bom  Abrigo  Island 537 

Bombay 567 

Bon  Cape 569 

Barbary 560 

Sumatra 569 


Page. 

Bona 560 

Bonacca  Island 526 

Bonaive  Island 535 

Bonaventura  Head 520 

Island 521 

Bonavista  Cape 520 

Island 543 

Bongalae  Island 574 

Bongaroni  Cape 560 

Bonifacio 556 

Bonham  Island 581 

Bonin  Islands 583 

Bonn 552 

Boobjerg 553 

Booby  Island 534 

Leeward  Islands  .  .. 534 

S.  Pacific 591 

Booleelooyan  Point 5  72 

Boompjes 575 

Boon  Island 522 

Borda  Cape 592 

Bordeaux 554 

Bordelaise  Island 582 

Bordeyri 596 

Borgia  Bay . 539 

Bornholm 552 

Borodino  Islands 583 

Boscawen  Island 587 

Bosphorus 559 

Boston 523 

Botel  Tobago 5  72 

Bougainville  Cape 591 

Island 584 

Bouka  Island 584 

Boulougne 553 

Bounty  Islands 59' 

Bourbon  Cape 566 

Bouton  Island 5  75 

Bouvets  Island 544 

Bow  Island 5^^ 

Bowditch  Island 584 

Bowen,  Port 593 

Australia 593 

Baffin's  Bay 595 

Bowling  Green  Cape 593 

Boyanna  Bay 565 

Boyne  River 546 

Bradore  Hills 521 

Brala,  Pulo 570 

Brandenberg 55° 

Brangman's  Bluff 527 

Bransberg 55° 

Brass  River 5^* 

Brasse,  Pulo 543 

Brava 543 

C.  Verd  Islands 543 

E.  Africa 563 

Brazos  Santiago 525 

Bray  Head 546 

Braye 547 

Breaker  Point 571 

Brekat  Point 569 

Bremerhaven 55-^ 

Brest 554 

Brevoort  Cape 595 

Brewer's  Lagoon 5^7 

Bridgeport 523 

Brielle 553 

Brill  Shoal 575 

Brindisi   . .    557 

Bristol 544 

England   , . .  544 

Rhode  Island 523 

Brittania  Island 590 

Broadhaveii 


j7- 


INDEX  TO  TABLE  49. 


[Page  601 


Page. 

Broken  Bay 593 

Brooks  Island 583 

Brothers 571 

China 571 

Red  Sea   563 

Broughton  Bay 57^ 

Head 577 

Island   579 

Rocks 578 

Brunet  Island 520 

Bruni  River 5  72 

Brunswick 524 

Georgia 524 

Maine 522 

Bruny  Cape 594 

Island  594 

Brussels 553 

Brustevort 550 

Bryer's  Island 522 

Bubuan  Island 574 

Bucas  Island 573 

Buchanness 545 

Buddenness 545 

Budrum 560 

Budua 558 

Buenaventura 542 

San 530 

Buenos  Ayres 538 

Buhalmen 547 

Buitenzorg 575 

Bulipong  Pong  Island 574 

Bulk 551 

Bull  Harbor 529 

Bullock  Bay 579 

Burgeo  Island 525 

l^urghaz 559 

Burias  Island 573 

Burin  Harbor 520 

Burlingo 555 

Burnett  River 593 

Burrard  Inlet 529 

Busies 537 

Islands 537 

Bustard  Head 593 

Busuanga  Island 572 

Busum   551 

Butt  of  Lewis 545 

Button  Island 520 

Butzfloth 551 

Byam  Martin  Island 588 

Byron  Island 580 

Caballo  Island 572 

Cabeceira  Cape 563 

Cabeza  de  Vaca 541 

Cabrera  Island 556 

Cabron  Cape 533 

Cabrut  Island 564 

Cabuli  Island 572 

Cadaqu^s 555 

Cadiz 555 

Cadmus 588 

Caen 553 

Cagayan  Sooloo  Islands 574 

Cagayanes  Islands 574 

Caguyan  River 573 

Cagliari    556 

Caifara 536 

Caicos,  W.  Cay 532 

Island 532 

Calaan  Point 5  73 

Calais 553 

France 553 

Calais,  Maine 522 

Calavite  Mountain 572 


Page. 

Calayan  Island 5  73 

Calbuco 540 

Calcasieu  Pass 525 

Calcutta 568 

Caldera    534 

Caldy  Island 544 

Calebar  River,  New 561 

Old 561 

Caledonia 535 

Calicut 567 

Calf  of  Man 545 

Rock 545 

Calingapatam 568 

Callao 541 

Calpe 555 

Caluya  Island 572 

Calvi 556 

Calymere  Point 567 

Camamu 537 

Camaron  Cape 527 

Cambay 567 

Cambridge 523 

England  544 

U.S 523 

Cambriu 537 

Camiguin  Island 574 

Babuyanes    5  74 

Philippines 573 

Cammin 550 

Campbell  Cape 594 

Island   591 

Campeche 526 

Campobello  Island 522 

Cananore 567 

Canary  Island,  Grand 543 

Canaveral  Cape 524 

Cancun  Island 526 

Candia  Island 558 

Cannes  550 

Cannonier  Point 564 

Canoas  Point 530 

Canso  Cape 522 

Gut 522 

Cautanduanco  Islands 573 

Canton 571 

Island  584 

Pulo 570 

Cantyre 545 

Cape  Breton  Island 522 

Cape  Town 562 

C!ape  Verde  Islands 543 

Capel  Island 547 

Cape  d'lstria 557 

Capones  Point 5  72 

Capraia  Island 556 

Caprera  Island 556 

Capri  Island 556 

Capricorn  Cape 593 

Carabane   561 

Carabas  Island 573 

Caraccas  Bay 542 

Caraccas 535 

Carataska  Lagoon 527 

Caravellas  537 

Carbon  Cape  . 560 

Carbonera  Cape 556 

Cardamum  Island 564 

Cardiff 544 

Carey's  Islands 595 

Cargados  Carajos 564 

Caribana  Point 535 

Carimare  Mountain 536 

Carimata  Island 5  70 

Carlingford  Lough 546 

Carlopago 557 


Page. 

Carlos,  San,  Bay 540 

Point 530 

Port   540 

Carmen  Island 526 

Car  Nicobar 568 

Caroline  Islands   501 

N.Pacific 581 

S.  Pacific 584 

Carousel  Islands 521 

Carreta  Point 527 

Port 535 

Mountain 541 

Carrisal,  Port 541 

Cartagena 535 

N.  Grenada 535 

Spain 555 

Cartago  Mountain  527 

Carteret  Cape 554 

Port 584 

Cartwright  Harbor 520 

Carupano 535 

Gary  jfort  Island 588 

Reef 524 

Cascade  Point 594 

Caskets 553 

Cassini  Island 591 

Castillos 538 

Castle  Island 532 

Castries  Bay 579 

Castro 540 

Urdiales 554 

Cat  Island 525 

Catalana  Harbor    520 

Catalina,  Sta.,  Island 530 

Catania 557 

Catastrophe  Cape 592 

Catharine,  St 544 

Point  539 

Island 538 

Cato  Bank 585 

Catoche  Cape 526 

Cattaro 558 

Cavite 5  72 

Caxones 527 

Cayenne 536 

Cayeux 553 

Caymans 533 

Cazza  Island 55^ 

Ceara 536 

Cebu  Island 573 

Cedar  Cays 525 

Cedeiro 555 

Ceicer  de  Mer  Island 570 

Celebes 5  74 

Centinella  Island 535 

Ceram  Island 576 

Cerros  Island 530 

Cestos 561 

Cette 556 

Ceuta 560 

Ceylon  567 

Chahbar  Island 567 

Chacachacare  Island 536 

Chacopata 535 

Chagos  Arch 564 

Chala  Point 541 

Chaleur  Bay 521 

Challenger  Cape 5^^ 

Chama  Bay 561 

Cham-CoUao  Island 570 

Cham6  I^oint 542 

Chamisso  Island 527 

Champerico 53' 

Chandeleur  Islands 5^5 

Chaneral  Bay 541 


Page  602] 


INDEX  TO  TABLE  49. 


Page. 

Chaneral  Island 540 

Chao  Island 542 

Chapel  Island 571 

Chaplin  Cape 580 

Chapii 572 

Charles  Cape 524 

Charles  Island 520 

Galapagos 5^3 

Hudson  St 539 

Charleston 524 

Charlotte  Town 521 

Chateau  Bay 521 

Chatham  Harbor 523 

Island 583 

Islands 591 

Chatte  Cape 521 

ChaumeLa... 554 

Chausy  Islands 554 

Cheduba  Island 568 

Che-foo 5  76 

Chentabun    River 5  70 

Chepillo  Island 542 

Cherbourg 553 

Cheribon     575 

Cherso 557 

Chiachi  Islands 528 

Chicarene  Point 531 

Chidleigh  Cape  . 520 

Chignecto  Cape 522 

Chignik  Bay 528 

Chilca  Point 541 

Chimba  Bay   541 

Chimbote 542 

Chincha  Islands   541 

Chin-chin 571 

Chinchorro  Bank 526 

Chin-Hai 571 

Chino  Peak 571 

Chirambiri  Point 542 

Chirikoff  Island 528 

Chittae  Island 564 

Chittagong  River 568 

Choda  Island.    577 

Choiseul  Island. 584 

-^ Port 565 

Chorras  Islands 540 

Christian,  Pass 525 

Christiana  Island 559 

Christiana 548 

Christianefield 551 

Chri;tiansand   547 

Chiistianshaab 596 

Christianso  Island   552 

Christianstad 534 

Christiansund   547 

Christmas  Cove 540 

Harbor 566 

Christmas  Island 566 

Indian  Ocean 566 

N.Pacific 580 

Christopher,  St 534 

Christoval,  St. ,  Island  . 584 

Chuapa  River 540 

Chuluvvan 562 

Chupat  River 538 

Churruca,  Port 539 

Chusan  Islands 571 

Chute  d'Eau  Island 536 

Ciaris  Island 531 

Cica,  Mount 558 

Cienfuegos 533 

Ciotat 556 

Cispata  Harbor 535 

Citta  Nuova 557 

Civita  Vecchia 556 


Page. 

Clara,  Sta    529 

Clare  Island 546 

Claremont  Point 593 

Clarence,  Port 527 

532 

R.America 527 

Clarence  River 593 

Clarion  Island 531 

Claushavn 596 

Clear  Cape 545 

Clearwater  Point 521 

Cleveland  Cape 593 

Cleremont  Tonnere  Island  . . .   588 

Clifden  Bay 546 

Clipperton  Island 531 

Rock 582 

Qonard  Cape 579 

Coast  Castle,  Cape 561 

Coatzucoalcos  526 

Cobbler  Rocks 527 

Cobija  - 541 

Cobre  Bay 541 

Cochon 534 

Cockburn  Island 588 

Cockell's  Islands 591 

Cockscomb  Mountain 526 

Coco,  Great,  Island 568 

Cocos  Island 532 

N.Pacific 566 

Panama 532 

Cod  Cape 523 

Cod  Roy  Island 521 

Codera  Cape 585 

Codfish  Island 595 

Coetivy  Island 565 

Coffin  Bay 592 

Coffin  Island 522 

Madagascar 565 

Nova  Scotia 522 

Cofre  del  Perote  Mt 525 

Coiba  Island 531 

Colberg 550 

Colbert  Island 591 

Coles' Point 541 

Colina  Redonda 542 

Colnett  Bay 530 

Colombo 567 

Colonia 538 

Colonne  Cape 557 

Colonna  Cape 559 

Colorado  Reefs 533 

Columbia  Cape 595 

Columbretes  Islands 555 

Columbus  Island 527 

Colville  Cape 594 

Coman  Inlet 540 

Comandatuba 537 

Commerson  Island 585 

Comorin  Cape 567 

Comoro  Island 565 

Conceifao 537 

Conception  Island 532 

Point 530 

Coconada 568 

Cond^ , 536 

Condor  Cove 540 

Condore  Islands 570 

Conducia 5^3 

Conejo,  El,  Point 530 

Coney  Island 571 

Confites  Cay 533 

Congo  River 562 

Congrehay  Peak 526 

Connetable  Island 536 

Constantinople 559 


Page. 

Constitution  Cove 541 

Contas 537 

Conte  Port 556 

Contoy  Island 526 

Conway  Cape 593 

Reef 590 

Cook  Cape 528 

Mountain 593 

Island 540 

Cookra  Hill 527 

Coomptah 567 

Cooper,  Port 594 

Copeland  Islands 546 

Copenhagen 552 

Copiapo 541 

Copper  Island 580 

Coquet  Island 545 

Coquille  Island 581 

Coquimbo 540 

Coral  Island 538 

-; — Islet 537 

Corcovado  Vole 540 

Cordovan  Point 554 

Corfu 558 

Coringa  Shoal 585 

Cork 547 

Cormorant  Island 529 

Corn  Islands 527 

Cornwallis  Islands 582 

Port 568 

Coro,  Tela  de 535 

Coromandel  Harbor 594 

Corona  Point 540 

Coronation  Island 544 

Corregidor  Island 572 

Corrientes  Cape  538 

B.  Ayres 538 

Mexico 531 

Panama 542 

S.  Africa 562 

Corsarios  Bay 535 

Corseules,  Port 553 

Corso  Cape 55O 

Island   540 

~  Mountain 540 

Corti 556 

Coruna 555 

Corvo  Island 542 

Coslin 550 

Cosmoledo  Island 565 

Cotinguiba 536 

Cotrone 557 

Country  Harbor 522 

Courbe,  Point  de  la 554 

C'ourtown  Bank 527 

Coutances 554 

Cove  Rock 562 

Cow  Head 521 

Coy  Inlet 538 

Cozumel  Island 526 

Cracker  Bay 53^ 

Crassock  Point 569 

Crescent  City 529 

Island   5S7 

Cretin  Islands 585 

(  reux  Cape 555 

Croisie 554 

Croker  Island 589 

Cape 591 

Crooked  Island 532 

Crookhaven 545 

Crozet  Islands 566 

Cruz  Cape 533 

Sta 530 

Brazil 537 


INDEX  TO  TABLE  49. 


[Page  603 


Page. 

Cruz  Sta,  California 530 

Lee\var(i  Islands.. .  534 

Island 530 

^California 530 

S.  Pacific 585 

Islands 574 

Port 538 

Cuad  Basong  Island 574 

Cnba 532 

Culebra 531 

Island   534 

Culion  Island 572 

CuUera  Cape 555 

Culpepper  Island 580 

Culver  Point 592 

Cumana 535 

Cumberland  Island ....  593 

Georgia 524 

Low  Arch 588 

Islands 593 

Cundapore 5^7 

Cunioleewas  Harbor 528 

Cup-chi  Point 57' 

Cupica  Bay 542 

Cura9oa  Island 535 

-; Little 535 

Currituck  Beach 524 

Curtis  Islands 590 

Port 593 

Curzola  Island 558 

Cuttyhunk  Light 523 

Cuvier  Cape 591 

Island 594 

Cuxhaven 551 

Cuyos  Islands 572 

Cyprus 560 

Dsedalus  Shoal 563 

Dago  Island 549 

Dakar  Cape 561 

Dalcahue  540 

Dale  Point 591 

I  )alryniple,  Port 593 

Dalupiri  Island 5  73 

Damghot 566 

Damma  Islands 576 

Danger  Island 587 

Dangerous  Rock 571 

Dantzig 555 

Danube  River 559 

Danneborg  Island 596 

Dardanelles 559 

Dar  el  Beida  Cape 560 

Dar  es  Salaam 563 

Darien 542 

C.  America 542 

Georgia,  U.  S 524 

Darsserort 550 

Darwin,  Port 591 

Datu  Island 570 

Dauphin,  Fort 565 

Davao 5  74 

Davey  Port 594 

iJeadman  Island 521 

Deception  Island 544 

Deimaniyet 566 

Delagoa  Bay 562 

1  )elgada  Point 539 

Delgado  Cape 563 

Point 538 

Demerara 536 

Denia 555 

Denis,  St 564 

Denison,  Port 593 

D'Entrecasteaux  Islands 585 


Page. 

D'Entrecasteaux  Point   592 

De  Peyster  Islands   584 

Deseado  Cape 539 

Desert  Mt.,  Rock 522 

Desertas 543 

Desirade 534 

Desire,  Port 538 

Desolation  Cape 539 

Dia  Fjeld    597 

1  )iamond  Harbor 568 

Point 569 

Diedrichshagen 550 

Diego  Garcia 564 

Ramirez  Islands 539 

San 530 

Cape 528 

Dieppe 553 

Digges  Islands 520 

Dimasalasan,  Port 573 

Dinding  Island 568 

Dingle  Bay 545 

Diomede  Islands 527 

Direction  Cape 593 

Island 570 

Disappointment  Cape 579 

Siberia 579 

W.  Territory 529 

Discovery  Harbor 595 

Disei  Island 563 

Diu  Island 567 

Divy  Point 568 

Dix  Cove  .    561 

Djambi 569 

Djuparog  Bondavarde 597 

Djursten 548 

Dnieper  Bay 559 

Doc-can  Islet 574 

Dodd  Island 571 

Dog  Island 534 

Domar,  Pulo 5  70 

Dome  Ness 549 

Domingo,  St.,  City 534 

Cay 532 

Point 530 

Dominica 534 

Donaghadee 546 

Dondra  Head 567 

Donegal  Bay 546 

Double  Island 593 

Australia 593 

Gulf  of  Martaban..  568 

Peak  Island 571 

Douglass  Rocks 583 

Douvres  Rocks 554 

Dover  Point 592 

Dounpatrick  Head 546 

Drepano 558 

Drei  Cap  Peninsula 585 

Drobak 548 

Drochtersen 551 

Dromedary  Mountain 592 

Drummond  Island 580 

Dublin       546 

Ducie  Island 587 

Duff  Islands 585 

Duke  of  Clarence  Island 584 

Duke  of  York  Island 584 

New  Britain .  584 

S.  Pacific 584 

Duke  Gulf 526 

River 526 

1  )ulcigno 558 

Dumali  Point 572 

1  >uncan  Island 583 

Dundee  Rock 540 


Page. 

Dundrum  Bay 546 

Dungarvan 547 

Dungeness 544 

New 529 

Point 539 

Dunkerque ^ 553 

Dunnet  Head 545 

Dilnnau         550 

Duperrey  Islands 582 

Duppel 551 

Durazzo 558 

Dumford  Point 562 

Port  563 

D'Urville  Island   595 

Point 585 

Dussdjour  Cape 591 

Dwarica 567 

Eagle  Island 546 

East  Cape 565 

Madagascar 565 

New  Zealand 594 

Siberia 580 

East  Island 521 

Eastport 522 

Eau  Island 581 

Eauripik  Islands 5^1 

Ebou  Atoll 581 

Eckemforde 551 

Eclipse  Harbor 520 

Islands 592 

Eddystone 544 

Point 594 

Eden  Harbor 539 

Edensaw  Cape 528 

Edenton 524 

I'^dinburgh 545 

Egedesmunde 596 

Eggrunds  Islands 548 

E^mont  Mountain 594 

Port 544 

Eimeo  Island 587 

Eldiolm  Island 549 

Elba 556 

Elbing 550 

Elches,  Port 528 

Elena,  St.,  Point 542 

Port 538 

Elephant  Bay 562 

Eleuthera  Island 532 

Elias,  St.,  Mount 528 

lilizabeth  Bay 562 


Cape. 
City  ... 
Harbor 
Reef... 


522 
524 

595 
590 

Elizabeth  Island 539 

Low  Arch 589 

Magellan  Straits...   539 


EUice  Islands 584 

Elmschenhagen 55' 

Emden 552 

Emma,  Great,  Island 532 

p:mu  Bay 593 

Eu,  Pulo 570 

Enanger    .   54^ 

Endelave  Island 552 

Enderby  Island 591 

Australia 591 

S.  Pacific 584 

Endermo 579 

Enfant  Perdu  Island 536 

Engano  Capo 533 

Indian  Arch 573 

St.  Domingo 533 


Page  604] 


INDEX  TO  TABLE  49. 


I 

I 


Page. 

Engano  Island 569 

Engelholm 548 

English  Cay 526 

Eniwetok  Islands 581 

Enrag^  Cape 522 

Enseuada 530 

Entry  Island 521 

Errakong  Island 5S2 

Erramango  Island 586 

Erronau  Island 586 

Escarseo  Point 535 

Escholtz  Islands 581 

Escudo  Island 527 

Escumenac  Point 521 

Esdu  Island 564 

Esens 552 

Esmeralda  Island 535 

River 542 

Espada  Point 535 

N.  Grenada 535 

Hayti    534 

Esperanza  Inlet 528 

Espiritu,  Santo,  Bay 537 

rCape 539 

Esquimault 529 

Essington,  Port 591 

Estaca  Point 554 

Estangues  Point 535 

Estevan  Point 528 

Etang  Harbor 522 

Eten  Hill 542 

Eureka 529 

Euripo 559 

Europa  Island 565 

Eustatius  St 534 

Evangelist  Islands 539 

Evaristo,  San 530 

Expedition  Bay 579 

Faero  Islands 542 

Fain  W.,  Island 581 

Fair  Island 545 

Fairy,  Port 592 

Faiti  589 

Faka'afo 584 

Fakarawa  Island 589 

Falkenberg 548 

Falkland  Islands -  - 544 

Falmouth 533 

Harbor 544 

False  Cape  Horn .  539 

Point 568 

Falster  Island 552 

Falsterbo 548 

Famagousta 560 

Famine,  Port 539 

Fanad  Point 546 

Fanning's  Island 580 

Fane  Island 558 

Adriatic 558 

Denmark 553 

Farallon  de  Pajaros 529 

Faraulep  Island 581 

Farevi^ell  Cape 596 

Davis' Strait 596 

New  Zealand 594 

Farina  Cape 560 

Farisan  Island 564 

Earn  Island 545 

Faro  Island 556 

Mediterranean 556 

Sweden 548 

Farquhar  Islands 565 

Farralon  Islands 582 

Farral  Rock 527 


Page. 

Farlak  Ras 566 

Fastnet  Rock 545 

Father  Point 521 

Fatou-hiva 583 

Fatsizio  Island 578 

Fayal  Island 542 

Fe'camp 553 

Federal  Point 524 

Felipe,  San,  Cays 533 

Point 531 

Felix,  St.,  Island 590 

N.  W.  America 590 

Chile 541 

Fenerive  Point 565 

Fernandina 524 

Fernando  Noronha 543 

Po 561 

San,  River 525 

r.P°^^ 573 

Trinidad 536 

536 

Ferro  Island 543 

Ferrol 555 

Ferrolle  Point 521 

Fetou-houhou  Island 584 

Feys  Island 581 

Fidonisi  Island 559 

Figari  Cape 556 

Fiji  Islands 586 

Filsand  Island 549 

Finisterre  Cape 555 

Firase  Rocks 577 

Fira  Sima 5  78 

Fire  Island 523 

Firmin,  San 531 

Firmino  Point 530 

Fish,  Great  Bay 562 

Little  Bay 562 

Fischhausen 550 

Fiskernaes 596 

Fitz  Roy  River 591 

Fiume 557 

Five  Fathom  Bank 524 

Flamborough 545 

Flamenco 541 

Flamenes  Island 542 

Flat  Hill 591 

Flatey 596 

Flattery  Cape 529 

Flensberg 551 

Flesko  Cape 575 

Flinders 592 

Island 592 

River 591 

Flint  Island 584 

Florence .   556 

Flores  Island 538 

Azores 542 

Indian  Arch 575 

River  Plate 538 

Florida  Island 584 

Flower  Cove 521 

Flushing 553 

Fly  River 585 

Foerder  Island 548 

Fogo  Island 543 

Fohr 551 

Footoona  Island 586 

Foreland,  North 544 

South 544 

Formigas  Islands 543 

Shoal 533 

Formosa  Island 572 

Fornceo 553 

Forsmark 548 


Page. 

Forsyth  Point 528 

Forth  Mountain 546 

Fortune  Island 532 

Foulwind  Cape 594 

Four,  Le,  Rock 554 

Fourchu  Cape 522 

Foutouna 587 

Fowey  Rocks 524 

Fowler  Point 592 

Francis  Islands 580 

Francis,  St.,  Cape 520 

C.  Colony 562 

Newfoundland 520 

Francisco,  San 529 

St.,  Cape 542 

Harbor 529 

Island 537 

River 53(> 

Frankland  Islands  593 

Franklin  Harbor 592 

Franz  Josef  Land 595 

Eraser  River 529 

Frauenberg 550 

Frayle  Rock 534 

Frayles  Point 541 

Frederick,  Port 593 

Frederik  Henry,  Cape 594 

Frederikshaab 596 

Frederikstahl 596 

Fredriksten  548 

Frederiksvaern 548 

Freels  Cape 520 

Frehel  Cape 554 

Freiburg 551 

Freikallen 547 

French  Cay 532 

French  Frigate  Shoal 583 

Freycinet  De 591 

Peninsula 594 

Frio  Cape 537 

Brazil 537 

W.  Africa 562 

Port 537 

Froward  Cape 539 

Fru  Island 547 

Frying  Pan  Shoals 524 

Fuenterabia 554 

Fuerte  Island 535 

Fuerteventura  Island 543 

Fuga  Island 573 

Fugle  Huk  Point 596 

Fuglebock 548 

Funafuti  Islands 584 

Funk  Island 520 

Funkenhagen  550 

Furen  Island 547 

Furneaux  Island 589 

Fushiki 579 

Gaalong  Bay 570 

Gabo  Island 592 

Gabriel  Mountain 545 

Gaeta 556 

Gafor  Island   564 

Galapagos  Islands 580 

Galera  Point 542 

Colombia 542 

Trinidad 536 

Galera,  Port 5  72 

Galgenberg 551 

Galiola  Rock 557 

Galita  Island 560 

Gallant,  Port 539 

Galle,  Point  ae 567 

Gallegos,  Cape  and  Port 538 


INDEX  TO  TABLE  49. 


[Page  605 


Page. 

Galley  Head 547 

Gallinas  River   561 

Gallipoli .  557 

Naples 557 

Turkey 559 

Galloway,  Mull  of 545 

Galveston 525 

Galway 5^6 

Gambler's  Islands 58 7 

Ganjam 5^^ 

Gannet,  Outer,  Island 520 

Rock 522 

Gap  Rock 571 

Garcia  d' Avila 536 

Gardiner's  Island 523 

Gardiner  Island 5S3 

N.Pacific 583 

S.  Pacific 584 

Garras,  Little 568 

Gaspar,  Island  and  Strait 569 

Rico 582 

Gasp^  Cape 521 

Gata,  Cape  de 555 

Gay  Head 523 

Geby 576 

Geelong 592 

Gefle 548 

Geltorf 551 

Genoa 55*^ 

George,  Fort,  Cay 532 

George's  Island 531 

St.,  Cay 526 

George,  St.,  Cape 521 

Nova  Scotia 522 

Florida 525 

Newfoundland 521 

Island 528 

Azores 542 

Russ.  America 528 

Georgetown 524 

Georgia,  South,  Island 544 

Geronimo,  San,  Island 530 

Geyser  Reef 565 

Gharib,  Ras 563 

Ghir  Cape 561 

Gibdo  Island 573 

Gibraltar 555 

Giglio  Island 556 

Gijon 554 

Gilbert  Arch 580 

Gilolo  Island 576 

Ginger  Cay   532 

Girgenti 557 

Gizau 564 

Glasgow 545 

Glashedy  Head 546 

Glenan  Islands 554 

Glorioso  Island 565 

Gloucester 523 

Island 523 

Australia 593 

Low  Arch 588 

Glover  Reef 526 

Gnarp 548 

Goa 567 

Godthaab ". 596 

Goedereede 553 

Golam  Head 546 

Gollenburg 550 

Gomenitza 558 

Gomera  Island 543 

Gomnitzberg 551 

Gonave  Island 533 

Gonalves 533 

Good  Hope  Cape 562 


Page. 

Good  Hope,  Africa 562 

China 571 

Island 587 

Good  Success  Bay 538 

Goose  Island 592 

Gopaulpore 568 

Goram  Island 5  76 

Gorda  Cay 527 

Point 541 

Gore,  Port 595 

Goree  Island 561 

Road 538 

Gorgona  Island 542 

Goro  Island 586 

Gorontalo 574 

Gotha 552 

Gottland  Island 548 

Gottenburg 548 

Gottingen 552 

Goto  Islands 577 

Gough's  Island 544 

Gracias  a  Dios  Cape 527 

Goza 578 

Gozo  Island 557 

Graciosa  Island 543 

Grade ..   557 

Grand  Manan  Island 522 

Grand,  Port 564 

Grande  Point „ 541 

Grange  Point . . . , 533 

Granitz ,„. 550 

Granville 554 

Grappler,  Port 539 

Grave,  Pte  de 554 

Gravelines 553 

Grady  Harbor 520 

Great  Rock  Head 527 

Green  Cape 592 

Green  Island 520 

Hudson  Strait 520 

Newfoundland 521 

Greenly  Island 527 

Greenspond  Island 520 

Greenwich 544 

Island   581 

Gregory  Cape 529 

Port 592 

Greig  Island 589 

Grenada 535 

Greenville  Cape 593 

Grey  River 595 

Griefswald 550 

Griefs walder  Oie 550 

Grim  Cape 593 

Grimsey  Norddranger 596 

Grip   547 

Grisnez  Cape 553 

Groix,  Island  de 554 

Groote  Eylandt 591 

Gross  Horst 550 

Grouin  du  CouPoint 554 

Gruizzo  Rock   557 

Gryto 547 

Guadalcanar  Island 584 

Guadalupe 534 

Guadeloupe 534 

( iuaianneco  Islands 540 

Guam  Island 582 

Guanape  Islands 542 

Guanica  Point 534 

Guano,  Little,  Cay 532 

Guantanamo 533 

Guarapiri  Islets 537 

Guaratiba  Cape 537 

( juardafui  Cape 563 


Page. 

Guarmey  542 

Guascama  Point 542 

Guatulco,  Port 531 

Guayaquil 542 

Guaymas   551 

Guayra,  La_ 535 

Guei  Chow  Island 570 

Guerande 554 

Guerin  Island 577 

Guguan  Island 582 

Guimaras  Island 573 

Guldager 553 

Gull  Island,  Little 523 

Gun  Cay 532 

Gunershang 547 

Gunalfswick 596 

Gunong  Api  Island 575 

Gutzlaff  Islands 5  72 

Gwadar  Bay 567 

Gwatar  Bay 567 

Habibas  Islands 560 

Hacha,  Rio  de  la 535 

Haddington,  Port 576 

Hadersleben 551 

Haelva 555 

Hafa  P'jeld 596 

Hafun,  Ras 563 

Hagermeister  Island  527 

Hague 553 

Capela 553 

Hai-Duong 570 

Haifa 560 

Hainan  Head 571 

Island 570 

Haipong  Island 5  70 

Hai-yun-tan 577 

Hakodadi    5  79 

Half-Moon  Cay 526 

Shoal 526 

Half-Port  Bay 539 

Halgan  Island 590 

Halifax 522 

Haliguen,  Port 554 

Hall  Island 5S1 

Islands,  Sir  J.,  Group  ..  577 

HRllo  Island 548 

Halmstadt 548 

Hals 553 

HaltBay 539 

Halten  Island 547 

Hamburg 552 

Hamilton  Mountain 529 

Port 577 

Hammamet  Bay 560 

Hammerfest 547 

Hammelworden 551 

Hampton 523 

Hamrange 54^ 

Hanalae  Bay 583 

Handewith 55° 

Hunfelah  Bay  563 

?Iangklip  Cape 562 

Hango 549 

Hanjam  Island 567 

Hannibal  Islands 593 

Hano  Island 548 

Ha-Noi 5  70 

Hao  Island- , 53S 

Haradskar  Islet 548 

Haraiki  Island 589 

Harbor  Grace 520 

Harburg 552 

Hardy,  Sir  C,  Islands 593 

Harrison  Cape 520 


Page  606] 


INDEX  TO  TABLE  49. 


Page. 

Hartlepool 545 

Harvey,  Port 529 

Harwich 545 

Hatteras  Cape    524 

Haustholm 553 

Haute  Island    522 

Havana 533 

Havre 553 

Cape  le 522 

Hawaii 582 

Hawcheun  Island 571 

Hayten  Island 585 

Hayti 533 

Haytien  Cape 533 

Heard  Island 566 

Heart's  Content 520 

Heaux  de  Brehat 554 

Heawandu  Island 564 

Hebi  Sima 528 

Hecla  Cape 595 

Hecate  Bay 528 

Cove 529 

Hed,  Ras  al 566 

Hee-tah-doo  Island 564 

Hegadis  Island 575 

Heiligen  Creutz 550 

Hekkingen 547 

Hela 550 

Helena,  St.,  Island 543 

Helgoland 551 

Heller's  St 547 

Helleso 547 

Hellyer's  Rocks 540 

Helsinborg 548 

Helsingfors 549 

Helvick  Head 547 

Helvoetsluis 553 

Henderson  Island 587 

Henderville  Island 580 

Henlopen  Cape 524 

Henry  Cape 524 

Port 540 

Heongsan 5  72 

Herald  Cays 585 

Hereheretua 588 

Hermes  Cape 562 

Hermit  Islands 585 

Hermite  Island 539 

Hervey  Islands 590 

Hesquiat  Harbor 528 

Hesselo  Island 552 

Hessenstein 551 

Hestskjoer 547 

Heve,  Cape  la 553 

Hiaou  Island 583 

Hikuero  Island 589 

Hillswickness 545 

Hilo   582 

Himmittee  Island 564 

Hiogo 578 

Hirado  Sima 577 

Hitchinbroke  Cape 522 

Hiti  Island 589 

Hiva-Oa 583 

Hjelm  Island 553 

Hjertholm 547 

Hjoerringga  Mountain 547 

Hjorleis  Hofdi 597 

Hjortsey 596 

Hoa-pin-su  Island 5  76 

Hobart  Town 594 

Hodeidah 564 

Hoedic  Island 554 

Hog  Island 524 

Virginia 524 


Page. 
Hog  Island,  Indian  Ocean  . . .   566 

Islands 526 

Hogland  Island 549 

Hogolen  Islands 582 

Hogsty  Reef 532 

Hohenschonberg 551 

Hoheweg 552 

Hoi-how 571 

Hokianga  River 594 

Hokitika 594 

Holborne  Island 593 

Hole-in-the-Wall 562 

Holmestrand 548 

Holmo  Gadd 549 

Holsteinberg 596 

Holyhead 544 

Homborg 552 

Honawar 567 

Hondan  Island 570 

Hondeklip  Bay 562 

Honfleur 553 

Hong  Kong 571 

Hon-ne 570 

Honolulu 582 

Hood  Island 583 

Lord,  Island 587 

Port 522 

Australia 592 

522 

Hope  Island 593 

Hope's  Advance  Cape 520 

Hopedale  Harbor 520 

Hopper  Island 580 

Horn,  Cape 539 

Head 546 

Island  525 

Home  Islands 587 

Hornelen  Mountain 547 

Horsens  Island 552 

Horten 548 

Hospital  Bight 526 

Hougue,  La,  Cape 553 

Houtman  Rocks 592 

Howaiyuh 566 

Howe,  Lord,  Island 587 

Islands. 584 

Island 584 

Cape 591 

W.  Australia 591 

E.  Australia 592 

Sound 529 

Howland  Islands 580 

Howth  Bailey  Light 546 

Huafo  Island 540 

Huaheine  Island 587 

Huanchaco  Point 542 

Huasco 541 

Hudiksvall 548 

Hligeberg 551 

Hui-lang-san 571 

HuUIsland 584 

Islands 590 

Hulu-shan  Bay 577 

Humber  River 545 

Humboldt 529 

:  Harbor 528 

Humphrey  Island 584 

Hungwha 571 

Hunter  Island 586 

New  Hebrides  ....   586 

V.  Dieman's  Land  .   593 

Hurd  Island 580 

Hurst  Castle 544 

Hushals 553 

Husum 551 


Page. 

Hvitingso 547 

Hy^res  Islands 556 

Ibayat  Island 5  73 

Ibbetson  Islands 581 

Icacos  Point 526 

Honduras 526 

Trinidad 536 

Ichabo  Island 562 

Icy  Cape 527 

leraka    ..  559 

Ifahk  Islands 581 

Igloolik  Island 595 

Ignacio,  San,  Point 530 

Iguape 537 

Ildefonso  Islands 539 

Ilha  G)ande 537 

Ilheos 537 

Imperial,  Port 5/9 

Inaccessible  Islands 543 

Inagua  Islands 532 

Inch  Keith  Rocks 545 

Indefatigable  Island 583 

Indian  Harbor 520 

Head 593 

Tickle 520 

Iiidianola 525 

Indiapoera  Point 569 

Indio  Point 538 

Indispensable  Reef 584 

Ingolfstrof di 597 

Ingolsfjdd 596 

Inhambane  Bay 562 

Inine  Island 587 

Innishbofhn 546 

Innishawen  Head 546 

InnistrahuU 546 

Inishturk  Island 546 

Inscription  Cape 591 

Inu  bo-ya  saki 578 

Investigator  Strait 592 

Ipswich 523 

Iquique 54I 

Ireland 543 

Isaac,  Great,  Cay 532 

Isabel  Cape 540 

Lland 584 

Point 525 

Isene   559 

Isidro,  San,  Cape 539 

Isla  Grande 531 

Island  H:,.-bor 528 

Islay 541 

Isle  of  Glass  545 

Man 545 

May 545 

Wight 544 

Isola 557 

Isolette  Cape 566 

Itacolomi  Island 537 

Itacaloni  Point   536 

Itapacoroya  Point 537 

Ita,)arica 536 

Ilapemerim   537 

Iturup  Island 579 

Ivigtuk 596 

Iviza 556 

Iwo-sima 576 

Iwoga-sima 577 

Jabvvat  Island 581 

Jackson,  Port   592 

Jacksonville 524 

Jacmel 533 

[acohshavn 59^ 


INDEX  TO  TABLE  49. 


[Page  607 


Page. 
Jaffa  Cape 59e 

Jago,  St.,  Island 543 

JagLiarybe  River 536 

(aluit  Island   581 

Jamaica 533 

janics  Island 5^3 

James,  St.,  Cape  528 

Vancouver  I . .   528 

Cochin  China.   570 

Jan  May  en  Islands 596 

Jara  Head 541 

Jarea 555 

Jar  vis  Island 5^4 

J  asenitz   550 

JashakBay 507 

J  ava   569 

Head 569 

Jean,  St.,  de  Luz 554 

Jebel  Zukur  Island 564 

"1  elaka  Pule 569 

Jelalil 564 

Jensen's  Nunatak 59() 

Jeremie    533 

Jershoft   550 

J  ervis  Bay 592 

Cape  592 

Island 583 

Jesus  Maria  Island 565 

J  iddah 564 

J ijghinsk  Island 595 

Joao,  San,  da  Barra 537 

Johanna  Island 565 

John,  St.,  Cape 520 

Newfoundland  520 

Tier  del  i^  uego  538 

John's,  St 534 

N.  Brunswick  ....   522 

— Newfoundland 520 

Island 534 

Red  Sea 503 

Virgin  Islands  534 

River 524 

Johnston's  Island 582 

J  omfruland   548 

Jona,  St.,  Island 580 

Jose,  San,  de  Guatemala 53' 

del  Cabo .    530 

California 529 

Port 573 

J  oseph  Hem  y  Cape 595 

Juan,  St 535 

• I'ort 535 

J  uan,  San 541 

Point   526 

Port 529 

de  Nicaragua 527 

Fernandez    590 

Juanico,  San,  Point 530 

Juby  Cape 561 

Judith  Point 523 

Juel  Cape 596 

f uggernath 568 

■juist 552 

Julianshaab 596 

Julian,  St.,  Island 570 

Port 538 

Jupiter  Inlet 524 

Jura  Island   559 

Kabenda  Bay 561 

Kado  Sima 579 

Kago  Shima 577 

Kaholawe  Island 582 

Kaipara  Harbor 594 

Kais  566 


Page. 

Kajartalik  Island 596 

Kakirouma 576 

Kalama 529 

Kalantan  River 57° 

Kalbaden  Island 549 

Kalfatindr 596 

Kal  Farun  Island  . 563 

Kalibia 560 

Kalpen  Islands 564 

Kama-i-shi 578 

Kamaran  Bay 564 

Kambangan  Island 575 

Kambara  Island 587 

Kama  Islands 581 

Kamchatka  Cape 580 

Kanala,  Port 590 

Kandeliusa  Island  559 

Kangarssuk  Havn 596 

Kangeang  Island 575 

Kaniongun  Point 574 

Kantavu 586 

Kao  Island 590 

Kappeln... 551 

Karabournu  Cape 559 

Karaghinsky  Island 580 

Karimon  Djawi  Island 575 

Karlscrona 54^ 

Karlshamn 548 

Kasko 549 

Katakolo  Bay 558 

Kater  Island 583 

Katiagam 569 

Katie  Rock 558 

Katiu  589 

Kauai  Island 583 

Kaugamiut 59^ 

Kavahi  Island 589 

Kawhia  Harbor   594 

Keat's,  Port 591 

Keelah  Island 564 

Keeling  Islands 566 

Keenapoussan  Island 574 

Keitum 551 

Kelung 572 

Kendall  Cape 595 

Kent  Islands 592 

Keppel  Island 587 

Kerguelen  Islands 566 

Kermadec  Islands 590 

Kertch 559 

Kese  Island    584 

Ketoy  Island 579 

Key  West 525 

Kharamtkoan  Island 579 

Kharig  Island 566 

Khaur  Fakan  Bay 566 

KheU 559 

Khios  Island 559 

Khor  Nahud 564 

Nowarat 563 

Ki  Islands 5  76 

Kiama  Harbor 592 

Kidnapper's  Cape 594 

Kiel i 551 

Kiefali  Cape 558 

Kikai  sima 5  76 

Killiney  Hill 546 

Kilwa  Kisiwani 563 

Kimbeedo  Island 5^4 

King  George's  Sound 59^ 

King  Island 5^7 

King  Island,  Bass  Strait 592 

Russ.  America  ....  527 

King's  Island 589 

Kingston 533 


Page. 

Kingstown 546 

Kinkwasan 578 

Kino 549 

Point 531 

Kinsale 547 

Kirkwall 545 

Kirkjuboejar  Heidi 597 

Kishm 567 

Kismayo  Bay 563 

Kiswere 563 

Kittan  Island 564 

Kjorge 552 

Klutz 551 

Knirsberg 551 

Knocklane 546 

Knockmealdown  Mountain  . . .  547 

Knocknavea 546 

Knox  Bay 529 

Cape 528 

Knysna 562 

Kobe 578 

Koh  Chang 5  70 

Kohebi  sima 5  78 

Koh  Kong  Island 570 

Koh  Krah  Island  . 570 

Koh-  tang  Rocks 5  70 

Kokountan  Islands 577 

Kokskar 549 

Kolding 552 

Komba  Island 5  75 

Kompas  Mountain 547 

Kongelab  Islands 581 

Konigsberg 550 

Koniushi  Island 528 

Koora  Rythi  Point 565 

Koprino  Harbor 529 

Koroni 558 

Korror  Island 582 

Kos 559 

Kosair 566 

566 

RedSea 566 

Ko-sima 5  78 

Ko-sima  No  Sima 577 

Koster 548 

Kosu  Sima  Mountain 578 

Kowose  Rocks 577 

Krakatoa  Island 569 

Krishna  Shoal 568 

Kroe 569 

Kronberg 552 

Kronstadt 549 

Krusenstein  Cape 527 

Kubkalat  567 

Kullen  Point 548 

Kumfidah 564 

Kumi  Island 576 

Kunashir  Island 579 

Kuper 528 

^—  Port 577 

Kurrachee  567 

Kuria  Muria  Islands 566 

Kuro  Sima 577 

Kutchinotsu 577 

Kusakaki  Sima 577 

Kusrovie  Rock 570 

Kusterjeh 559 

Kutsino  .Sima 578 

Kuweit 566 

Kwee-han  Islands 571 

Kyangle  I  slets 582 

Kynquot  .Sound 528 

Kyska  Island 528 

Labiau  549 


Page  608] 


INDEX  TO  TABLE  49. 


Page. 

Labuan  Island 5  72 

Labyrinth  Head 538 

Lacadivh  Islands 564 

Lacepede  Islands 591 

Lady  Elliot  Island 593 

Francis  Port 565 

Lagartos 526 

Laghi  Cape 55^ 

Lagoon  Head 530 

Lagos 561 

Africa 561 

Portugal 55s 

Lagosta  Island 558 

Lagostine  Island 558 

Lahou  Shoal 585 

Lakemba  Island 587 

Lamaka 560 

Lambayeque 542 

Lambert  Cape 591 

Laraehuapi  Cove 540 

Lamenusa  Island 574 

Lamo  Bay 563 

Lampedusa  Island 557 

Lampong  Bay 569 

Lam-yit  Island 571 

Lancier  Island 588 

Landfall  Island 539 

Landhammar 548 

Land's  End 544 

Landskrona 548 

Landsort 54^ 

Langanaes  Cape 596 

Langeland  Island 55- 

Langeoog 552 

Langesund 54^ 

Langford,  Port 528 

Langotangen 548 

Langwarden 552 

Lanzarote  Island 543 

Lapstader 597 

Laptan 549 

Larne  Lough 546 

Lassa  Cape 575 

Lassan   550 

Latakiyah 560 

Latouch  Tr^ville  Cape 591 

Laun 520 

Laurie  Island 544 

Laut,  Pulo 5  74 

Lavaca 525 

Lavata 541 

Lawrence,  St.,  Island ,  580 

Russ.  America  527 

....  527 

Laykan  Point . . '. 5  74 

Laysan  Island 583 

Lazarefif,  Port   5  79 

Lazaro,  St.,  Cape 530 

Leander  Shoal 521 

Leba 550 

Leer 552 

Legendre  Island 591 

Leghorn 556 

Leipzig 552 

Lema  Island 571 

Lemnos  Island 559 

Lengua  de  Vaca  Point    540 

Lennox  Cove 538 

Leones  Island 538 

Leopold,  Port 595 

Lepar,  Pulo 569 

Lepreau  Cape 522 

Lerma 526 

Lerwick   545 

Leschenhault  Cape 591 


Page. 

Lessina  Island 558 

Leiibu  River 540 

Leuwin  Cape 592 

Leven  Island 565 

Port. 565 

River 593 

L'Eveque  Cape 591 

Lewis,  St.,  Cape 520 

Leyden 553 

Leyte  Island 573 

Liakhov-  Islands 595 

Liancourt  Rocks 579 

Liant  Cape 5 70 

Lian-ti-shan 577 

Libau  549 

Libertad 531 

Guatemala 531 

Mexico  531 

Lifou  Island 590 

Lighthouse  Rocks 528 

Limasol   560 

Limerick 546 

Lincoln  Island 571 

Port 592 

Lindisnoes 547 

Lindo 559 

Lindi  River 563 

Lingga  Island 568 

Linguetta  Cape .  558 

Linosa  Island 557 

Lipari  Islands 556 

Lisbon 555 

Lisburne  Cape 527 

Lisiansky  Island 583 

Lissa  Island 558 

List 551 

Lith 564 

Litkieh  Islaud 581 

Lituya  Bay 528 

Little  Hope  Island 522 

Liverpool 544 

Port 565 

River 591 

Lizard 544 

Llico 540 

Loa  River  541 

Loango  Bay 562 

Lobito  Point 562 

Lobos  Point 541 

N.Peru 541 

S.  Peru 541 

Cay 525 

Bahamas 532 

■■ Mexico 525 

de  Afuera  Islands 542 

Tierra 542 

Island 538 

Canaries 543 

River  Plate 537 

Lofoten  Islands 547 

Loheyyah 564 

Loma  Point 530 

Lomas  Point 541 

Lombata  Island 575 

Lombok  Island 5  75 

Lomok  Island 571 

London  (E.  Africa) 562 

Londonderry 54^ 

Londonderry  Cape 591 

Long  Island 53^ 

Bahamas  .. .  532 

United  States 523 

Look^,  Port 565 

Lookout  Cape 524 

Point 524 


Page. 

Lookout  Point,  Australia 593 

N.  Carolina 524 

Lopatka  Cape 580 

Lopez  Cape 561 

Lorenzo,  San,  Island 541 

St.,  Cape 542 

Loreto 530 

Loro,  Mount 572 

Lorstakken  Mountain 547 

Los,  Islands  de 561 

Lota  540 

Lot's  Wife 578 

Louis,  Port 534 

Falkland  Islands . . .  544 

Mauritius 564 

St 561 

Louisburg 522 

Loune 553 

Louisiade  Arch ' 585 

Lovenorn  Cape 59° 

Low  Arch... 587 

Island 570 

Port 540 

Lowendal  Island 584 

Lowestoft 545 

Loyalty  Islands 590 

Lubang  Island 5  72 

Lubeck 551 

Lucar,  San 555 

Lucas,  San 53° 

Lucepara  Island 575 

Lu-chu  Islands 576 

Lucia,  Sta 533 

Island 543 

Cape 562 

Kafferland 562 

Jamaica 533 

Windward  Islands  .  535 

Lucrecia  Point 533 

Lucrietta  Rock 557 

Liidingworth 551 

Liiis,  San,  Island 531 

Luke  Point 579 

Lundy  Island   544 

Lungo 548 

Lupona  Point 530 

Lurio  Bay 563 

Lussin  Piccolo 557 

Lutjenberg 55' 

Luzon  Island 572 

Lyo  Island 552 

Lysabbel 551 

Macahe 537 

Macao 571 

Mac  Askill  Islands 582 

Macassar 574 

Macauley  Island 590 

Maceio 536 

Machias   522 

Island 522 

Machikora 565 

M'Kean  Island 584 

Mackenzie  Islands 5^1 

Mac  Leay  Islands 591 

Macquarrie  Harbor 593 

Island 590 

Port 593 

Macquereau  Point 521 

Madagascar 565 

Reef 526 

Africa 562 

Gulf  of  Mexico 526 

Madame  Island .  522 

Madeira 543 


INDEX  TO  TABLE  49. 


[Page  609 


Page. 

^[adras 568 

Madryn,  Port 538 

Madura  Island 575 

Maestro  de  Campo  Island 573 

Mafamale  Island 563 

Magadoxa 563 

Magdalen  Cape 521 

Islands 521 

Magdalena  Bay 530 

River 535 

Magnetic  Pole 595 

Magoari  Cape 53*^ 

Mahanuru 5^5 

Mahe 567 

Malikoondoo  Island 564 

Mahia  Penin 594 

Mahon,  Port 556 

Maiden  Rocks 546 

Mairaira  P£)int 573 

Maitea  Island   587 

Maitencillo  Cove 540 

Majambo  Bay 565 

Majorca    556 

Majunga 565 

Majuro  Islands 5^1 

Makkian  Island 5  76 

Makongai  Island 586 

Makalleh  Bay 566 

Makarska 558 

Makawawa  Island 563 

Maker's  Ledge,  South 521 

^fakry 559 

Makuimu 589 

Makumba  Island 565 

Mala  Point 532 

Malabrigo  Bay 542 

Malacca   568 

Malaga 555 

Malamocco 557 

Mala  Pasqua  Cape 534 

Malaspina,  Port 538 

Malay ta  Island 584 

Maiden  Island , 584 

Maldonado 531 

Mexico 531 

Buenos  Ayres 538 

Male  Atoll 564 

Malemba  Bay 562 

Malin  Head 546 

Mallicollo  Island 586 

Malmo    548 

Malo,  St 554 

Maloelab  Islands 581 

Maloren 549 

Malpelo  Island 580 

Galapagos 580 

Panama 532 

Malta   557 

Manaar 567 

Mana  Sima 579 

Manda  Roads 563 

Mandarin's  Cap 571 

Mandavi 567 

Manfredonia 557 

Manga 587 

Mangara  Island 590 

Mangalore 567 

Mangaratiba 537 

Mangarol 567 

Mangles  Point 542 

Mango  Island 586 

Manguirim  Port 572 

Manhegan  I  sland 522 

Manheim ^52 

Manhii 589 

39  B 


Page. 

Manila 572 

Mano  Island 5  76 

Denmark 553 

-• 576 

Manoel  Cape 561 

Manta  Bay 542 

Man ua  Island 587 

Manukan  I  larbor 594 

Manuwangi 588 

Manuwatu  River 594 

Manvers,  Port 520 

Manzanilla  Bay 531 

Point 533 

Maracas  Mountain 536 

Maracaybo 535 

Maraki  Island 581 

Marambaya  Island 537 

Maranham 536 

Marble  Island 595 

Marblehead 523 

Marcial,  San,  Point 530 

Marcos,  St.,  Island 530 

Marcus  Island 583 

Mare  Harbor 544 

Mare  Island 590 

California 529 

590 

Maret  Islands 591 

Margaret  Island 588 

Bay 522 

Margate  Head 562 

Maria  di  Leuca,  St.,  Cape 557 

Maria  Island 587 

Port 533 

Madre  Island 531 

Sta.,  Cape 555 

Portugal  ....  555 

Uruguay 537 

Cove 530 

Island 540 

Azores 543 

Chile    540 

S.  Pacific ....  586 

Port 574 

Mariana  Island 580 

Islands 582 

Maricas  Islands 537 

Marie  Galante 534 

Marienleuchte 55 1 

Mariguana  Island 532 

Marinduque  Island 5  73 

Marion  Island 566 

Maripipi  Islands 573 

Maritmio  Island 557 

Marjoribank 577 

Marks,  St 525 

Marlborough  Island. 583 

Marmora  Island 560 

Marmorice 559 

Marne 551 

Maro  Reef 583 

Marokan  Islands 588 

Maroni  River 536 

Marquesas 583 

Marsala 557 

Marseilles 556 

Marshall 561 

Marshall  Islands 581 

Marsow 550 

Marstenen  Island 547 

Marta,  Sta 535 

. Cape 537 

Martin  de  la  Arena,  San 554 

Martin,  St.,  Island 530 

L.  California. .  530 


Page. 
Martin,  St.,  I.,  Leeward  Is...   534 

Garcia  Island 538 

\  as  Rocks 543 

Martinique 534 

Martyr's  Islands 581 

Marua  Island 587 

Marutea  Island 589 

Mary  Island    584 

Mary,  St.,  Cape    520 

Madagascar  . .  .565 

New  Ireland..   584 

Nova  Scotia  . .   522 

W.Africa 561 

Island 565 

Rocks 521 

Mary's,  St 524 

Marzo  Cape 542 

Masafuera  Island 590 

Masbate  Island 573 

.Masingloe  ...    572 

Masirah  Island ,  566 

Maskat 566 

Masset  Harbor 528 

Masulipatam 568 

Matabella  Islands 576 

Matacong  Island 561 

Matagorda 525 

Matahiva  Island 590 

Matamoras  Cove 541 

Matana  Island 579 

Matanzas  Peak 533 

Matatane 565 

Matelotas  Islands 581 

Matema  Islands 586 

.Maternillas  Point 533 

Mathew,  Island 586 

.Mathias,  St.,  Island 585 

.Matinicus  Rock 522 

Matoya 5  78 

Matthew  Island 580 

Matthew's,  St.,  Island 580 

Russ.  Amer  ..    527 

568 

Matuku  Island 586 

Matureivavas  Island 5S7 

Matu  Sima 5  79 

Mauger  Cay 526 

.Maui  Island 582 

Mauki  Island 590 

Maulmain 568 

River 568 

Maupiti  Island 587 

•Mauritius    564 

May  Cape 524 

Mayaguez 534 

May6  Mountain 536 

Mayne  Harbor 539 

Mountain   540 

Mayo  Island 543 

Mayo  ta  Island 565 

Maysi  Cape 532 

Mayumba  Bay 5*^^ 

Mazatlan 531 

Mazemba  River 562 

Mazarron 555 

Mbenga, Island 586 

Mchinga  Bay 5^3 

Meac  Sima 577 

Mecate  Mountain 5^5 

Mecatina  Islands 521 

Medanas  Point 538 

Mednoi  [.-land 5S0 

Mega  Island 569 

Megalo  Kastron 558 

Mehediah 560 


Page  610] 


INDEX  TO  TABLE  49. 


Page. 

Meia-co-sima  Islands 5  76 

Mejia  Island 531 

Mel,  Ilhado 537 

Melbourne 592 

Melle  Cape 556 

Meleda  Island 558 

Melinda 563 

Mellish  Cays 585 

Melmore  Point 546 

Melo,  Port 538 

Melville  Cape 593 

Island 595 

Australia 591 

Barrow's  Strait 595 

Low  Arch 589 

Memel 549 

Memory  Rock 532 

Menaloe  Island 568 

Mendocino  Cape 529 

Mendoza  Island 571 

Mentchikoff  Cape 528 

Merbat 566 

Mercy  Harbor 539 

M  rgui 568 

Mesa  de  Dona  Maria 541 

Messina 557 

Mesurado  Cape 561 

Meurka 563 

Mewstone  Rock 594 

Mexican  Boundary 530 

Mexico,  City  of 525 

Mexillon  Bay 541 

Mexillones  Mountain 541 

Meyet  Island 563 

Mezen 595 

Mgan  Mwania 563 

Miaki  Sima 578 

Miatao  Islands 577 

Michael,  St.,  Island 543 

Michaelovski 527 

Middleton  Island 528 

Midway  Island 583 

Miguel,  San,  Island 574 

California 530 

■ Luzon 573 

Islands 5  74 

Mikhailoff 587 

Mikinduri 563 

Miko-moto  Island 578 

Mikura  Island 578 

Milagro  Cove 540 

Milazzo 556 

Milford  Sound 594 

Miles  Island 595 

Milolsland 559 

Miloradovitch  Island 589 

Min  River 571 

Mina  Bay,  El   561 

Minchinmandom  Mountain. ..    540 

Mindanao  Island 573 

Mindoro  Island 572 

Mine  Head   547 

Minerva  Reef 590 

Minicoy  Island 564 

Minorca 556 

Mino  Sima 579 

Minow 565 

Minsener-old-Oog 552 

Mintok 569 

Miramichi  Bay 521 

Miscow  Island 521 

Mississippi  River,  mouth 525 

t'ity 525 

Misteriosa  Bank 526 

Mita  Point 531 


Page. 

Mitchell  Group 584 

Mitho 570 

Miti^ro  Island 590 

Mitre  Island 586 

Mityleni  Island 559 

Mizen  Hill 545 

Moa  Island 576 

Cayo,  Port 532 

Moala  Island 586 

Mobile 525 

Point 525 

Mocamba,  Port 563 

Mocara  Kampeh 569 

Mocha 564 

Island 540 

Moco  Moco  Point 536 

Modeste  Island 577 

Moen  Island 552 

Moerenhout  Island 587 

Mogador 561 

Mohillah  Island ". 565 

Mokatein 566 

Mokil  Islands   582 

Molle,  Port 593 

Mollendo 541 

Moller  Island 588 

Port 528 

Molloy  Point 566 

Molokai  Island 582 

Molonta  Penin 558 

Moloque  Atoll 564 

Molucca  Islands 576 

Molyneux  Bay 594 

Sound 540 

Mombaza 563 

Mona  Island 534 

Monastir 560 

Mondego  Cape 555 

Monfalcone 557 

Monfia  Island 563 

Monganui  Harbor 594 

Monjes 535 

Monkonrushy  Island 579 

Monomoy  Point 523 

Monrovia 561 

Montague  Island 592 

Montalivet  Islands 591 

Montauk  Point 523 

Montebello  Islands 591 

Monte  Video 538 

Montecristo  Island 556 

Montego  Bay 533 

Montepio 525 

Monterey 530 

Monteverde  Islands 582 

Mnntravel  Island 577 

Montreal   521 

Monte,  Point  de 521 

Montserrat 534 

Monze  Cape 567 

Mopelia  Island 587 

Moresby,  Port 563 

Morant  Cays 533 

Point 533 

Morayra 555 

Morecambe  Bay 545 

Moreno  Mountain 541 

Morane  Island 588 

Moreton  Cape 593 

Morgan  Cape 562 

Morjovetz  Island 595 

Morlaix 553 

Moro-tiri  Islands 590 

Morro  Ayuca 531 

Petaltan 531 


Page. 

Morro  Solar 541 

St.  Paulo 536 

Mortlock  Islands 582 

Mosquito  Cays 527 

Motane  Island.. 583 

Mothe  Island 587 

Mothoni 558 

Motou-iti     587 

Motu-iti  Island 583 

Motutunga 589 

Moudros 559 

Mount  Cape 561 

Mourondava 565 

Moville 546 

Mowa 567 

Mozambique 563 

Msimbati 563 

Mugeres  Island 526 

Muilcalpue  Cove 540 

Mukulaetae  Island 584 

Mukutupipi  Island 588 

Muleje  530 

Mulgrave  Islands 581 

Port 528 

Mulu  Island 576 

Munich 552 

Murderer's  Bay 565 

Murdock  Point 593 

Murat  Hill 563 

Murundum  Island 57o 

Mururea  Island 588 

Musawwa 563 

Musendum,  Ras 566 

Mussel  Bay 539 

Mysole  Island 576 

Nachoack  Bay 520 

Nagai  Island 52^8 

Nagasaki   577 

Nain 520 

Nairn  Cay 532 

Naitamba  Island 586 

Naiau  Island 586 

Naka-sima 5  78 

Nakkehoved 552 

Namdinh 570 

JSamki 571 

Namolouk  Islands 582 

Namoun  Group 581 

Nam-quan 571 

Namu  Islands 581 

Namuka  Island 590 

Nanaimo 529 

Nanka  Islands 569 

Nanoose  Harbor 529 

Nantes 554 

Nantucket  Island 523 

S.  Shoal 523 

Naples  556 

Napuka  Island 589 

Naranjo,  Port   533 

Narcissus  Island 588 

Nareenda  Bay 565 

Nar  Force  Island 564 

Nargen  Island 549 

Narva 549 

Nasca  Point 541 

Nasparti  Inlet 528 

Nassau 532 

Natal 569 

Africa 562 

Bay  569 

Natal,  Port 562 

Natashquan  Point 521 

Natuna  Islands 570 


INDEX  TO  TABLE  49. 


[Page  611 


Page. 

Naturaliste 592 

Nauomaga  Island 584 

Nauomea  Island 584 

Nauset  Beach  523 

Navachista 531 

Navalo,  Port 554 

Navarin  Cape 5S0 

Navassa  Island 533 

Navesink  Highlands 524 

Navidad  Bank 532 

Bay   531 

Navire  Bay  566 

Naxos  Island 559 

Nazaire,  St.,  Port 554 

Necker  Island 583 

Needles  Rocks 544 

Negapatam 567 

Negrais  Cape   568 

Negro  River 538 

Negros  Island 5  73 

Neil],  Port 595 

Nelson 595 

Port 591 

Nelson's  Cape 592 

Nemero 5  79 

Nengo-Nengo  Island 588 

Neptune  Islands 592 

Nera  Point 557 

Neunortalik 596 

Nevvwerke 551 

Neville,  Port 529 

Nevis 534 

N  ew  Britain 584 

Caledonia  . 590 

Guinea 585 

Hanover 585 

Haven 523 

Hebrides   586 

Ireland 584 

Bank 526 

London 523 

Orkneys   544 

Orleans 525 

S.  Shetland 544 

Vork 523 

Newbern 524 

Newburyport 523 

Newcastle 593 

Newchang 577 

Newfoundland 520 

Newport 523 

Ireland 546 

Rhode  Island 523 

Newton  Head,  Great 547 

Ngan  Island 586 

Ngarik 582 

Nias  Island 569 

Niau  Island 589 

Nice  556 

Nicholson,  Port 594 

Nickerie  River 536 

Nicobar  Islands  568 

Great,  Island 569 

Nicolas,  St.,  Island 530 

Cape  Verde  Islands  543 

Nicolas,  Mole 533 

Nidingen  Island 548 

Nieuport   553 

Niewe  Diep ..  553 

Nihiru  Island 589 

Niigata 579 

Nikalaevsk 579 

Nikalao,  St.,  Island  . 559 

Nikalo,  St 559 

Nila  Island 576 


Page. 

Nile  River 560 

Nimrod  Sound 571 

Ninepin  Rock 571 

Ning-Po 571 

Nipe,  Port 533 

Nina-foou 587 

Noir  Cape,  Island 539 

Noirmoutier  Island 554 

Nolloth,  Port 562 

Nome  Cape 527 

Noncowry  Island 569 

Nonati  Island 580 

Nootka  Sound 528 

Norden 552 

Nordeny 552 

Nord  Koster  Island 548 

Norfolk 524 

Island 590 

Norman  Cape 520 

Norrkoping 548 

Norrtelge 548 

Norskar  Island 549 

North  Cape 595 

Amazon 536 

Asia 595 

Norway 547 

N.  Zealand 594 

Harbor 528 

Island  583 

Vancouver 528 

Volcano  Islands  .- .  583 

Lord,  Island 582 

Standing  Creek ^26 

Northumberland  Cape 592 

Islands 593 

Northwest  Cape 591 

Norwalk  Island 523 

No  Sima  Saki 5  78 

Noshiap  Saki    579 

Nossi  Bell  Island 565 

Nossyah  Cape 5  79 

Nostra  Senhora  de  Deserto..  -  538 

Notch  Cape 539 

Notske 5  79 

Nottingham  Island 520 

Noumea 590 

Noun  Cape 561 

Nouvelle,  Port 556 

Novaya  Zembla 595 

Novogorod,  Port 5  79 

Nuevitas,  Port  533 

Nuevo,  Port 531 

Nugget  Point 594 

Nui  Island 584 

Nukahiva 583 

Nukufetau 584 

Nukunar  Island   580 

Nukunono 584 

Nukutapipi  Island 588 

Nukutuvake  Island 588 

Nukuor  - 582 

Numba  Island 563 

N  unez  River 561 

Nurse  Channel  Cay 532 

Nykjobing 552 

Nuyts  Point 592 

^^yberg 552 

Ny  Sukkertop 596 

Nystad 549 

Oahu 582 

Oaitupu  584 

Oatafu 584 

Oban 545 


Page. 

Obispo  Shoal 526 

Obristadbroekke 547 

Observation  Island 577 

Oby  Islands 570 

Major 576 

Occasional  Harbor 520 

Ocean  Island 583 

N.Pacific 583 

S.  Pacific 584 

Ockseu  Islands 571 

Ocracoke 524 

Oddensby 552 

Odensholm 549 

Odessa 559 

Odia  Island 581 

Oederquart 551 

Oeno  Island  .    587 

Offer  Wadham 520 

Oho  Sima 576 

Oki  Islands 5  79 

Okotsk 580 

Okoyama,  Port 5  78 

Okso 547 

Oland  Island 548 

Old  Fort  Island 521 

Point  Comfort 524 

Providence 527 

Oldenberg 551 

Oleai  Islands 581 

Oleron  Island 554 

Olga,  Port 579 

Olimarao  Islands 581 

Oiinda . . . 536 

Olipa  Rock 558 

Olivenfa 537 

Olutovsky  Cape 580 

Omapui  Island 5  74 

Ombay  Island 575 

Omenak  Island 596 

Omo  Island 552 

Omoa 526 

Omoi-saki    578 

Oneata  Island  . . ; 587 

Onega 595 

Ongeaevu  Island? 587 

Ono  Islands 587 

Onundar  Fjord 596 

Onvatoa  Islands 580 

Oparo  Island 590 

Opobo  River 561 

Oporto 555 

Oran 560 

Orange  Cape 536 

• Brazil 536 

Magellan  Strait 539 

Oranienbaum 549 

Orchila  Island 535 

Orfordness 545 

Orient,  L' 554 

Orizaba  Mountain 525 

Orkney  Islands 545 

Orlouk 5S2 

Oro-no-sima 577 

Oropesa 555 

Orrengrund 54S 

Orskiir  Rock 548 

Oruba  Island 535 

O  Sima  Island 578 

Od  Sima 5  78 

Osaka 5  78 

0.«aki  Bay   578 

Oscarsberg 54S 

Oscuro  Head 540 

Osnaburgh 588 

Ostend 553 


Page  612] 


INDEX  TO  TABLE  49. 


Page. 

Osterbruck 551 

Osthammar 548 

Ostro  Point 558 

Otago  Harbor 594 

Otranto,  Cape  and  Port 557 

Otierndorf 551 

Otway  Cape 592 

Port 540 

Ounekotan  Island 579 

Ouro  River   561 

Ovalan  Island 586 

Owase  Bay 578 

Oxhoft 550 

Oxford 544 

Paanapa  Island 5^4 

Pabellon  de  Pico 541 

Pacasmayo  Point 542 

Padang 569 

Padaran  Cape 5  70 

Padre,  Port 533 

Pagania 558 

Pagan  Island 582 

Paimboeuf 554 

Paix,  Port 533 

Pajaros  Islets 540 

Pak  Chan  River 567 

Pak-Hoi 570 

Palamos 555 

Palawan  Island 522 

Palembang .   569 

Palermo 556 

Port 558 

Pali  Cape 558 

Pallas  Rocks 577 

Palliser  Cape 594 

Palm  Island 593 

Palma 543 

Canaries 543 

Majorca 556 

Palmas  Bay 537 

Cape 561 

Point 526 

Palmerston  Cape 593 

Islands 587 

Palmyra 5^0 

Palmyra  Island 580 

Palos  Bay 5  74 

Pamaroong  Island 574 

Pampatar  Island 535 

Pan  de  Azucar 5  73 

Panama 532 

Panay  Island 573 

Pangituran 5  74 

Panjang,  Pulo 5  70 

Pank  piah  Rock 571 

Pantar  Island 5  75 

Papey  Island 597 

Paposo 541 

Para   ■ 536 

Paraca  Bay 541 

Paracel  Islands 571 

Parahyba  River  and  Port 536 

Paramaribo   536 

Parainagua 537 

Paranahyba  River 536 

Paraii 537 

Paredon  Grande  Cay 533 

Parenga-renga 594 

Parenzo 557 

Parga 558 

Parida 531 

Farinas  Point 542 

Paris 553 

Parker  Cape  539 


Page. 

Paroa  Island 588 

Paros  Island 559 

Parry  Island 590 

Parry's  Group 583 

Pasado  Cape 542 

Pasages,  Port 554 

Pascagoula,  East 525 

Pasni   567 

Pass  Christian  Light 525 

Passaro  I-;land 557 

Pasvervean    575 

Patache  Point 541 

I'atani  Cape '  57° 

Paternoster  Rock 548 

Paterson  Inlet 595 

Patook  River 527 

Patos  Island 53 1 

Patras 558 

Patrick,  St.,  Head 594 

Pauillac 554 

Paul  de  Loando 562 

St.  (Mauritius) 565 

Harbor 528 

Rocks 543 

Paul's,  St.,  Island 521 

Ind.  Ocean  . . .  566 

Low  Arch 588 

N.  America.. .  521 

Russ.  America  528 

Paumben  Pass 567 

Paxo  Island    558 

Payta 542 

Paypoton  Mountain 526 

Paz,  La 530 

Pearce  Point 591 

Pearl  Bank 5  74 

Cays 527 

Pearl  and  Hermes  Reef 583 

Pedra  Blanca 571 

Bianca 568 

de  Galha 561 

Pedro  Bank 533 

San 540 

Point   541 

-    Port 540 

Peel 592 

Island 583 

Pegasus,  Port 595 

Pei-ho  River 572 

Pekalongan  575 

Pelado  Island 542 

Pelagosa  Rock 558 

Pelelew  Island 582 

Pelew  Islands 582 

Peloro  Cape    557 

Pemba  Bay 563 

Pembroke  Cape 544 

Pena  Point 536 

Penang  Island 568 

Peiias  Cape   531 

Pendulum  Islands 596 

Penguin  Island 566 

Penha  Grande 561 

Peniche 555 

Penmarch  Rocks   554 

Penrhyn  Island 584 

Pensacola 525 

Pentland  Skerries 545 

Percy  Islands 593 

Perim  Island     564 

Arabia 564 

India 567 

Pernambuco 536 

Pernaux 549 

Peros  Banhos  Islands 564 


Page. 

Perth 592 

Peru  Island 580 

Perula  Bay 531 

Pescadores  Island 572 

Islands 541 

P'ormosa 541 

N.Pacific 581 

Point 541 

Pe-shan  Islands 571 

Petalidi  Bay 558 

Petali  Island 559 

Peter.St 551 

Port 554 

Peterhof 549 

Petersburg!!,  St  549 

Petersdorf 551 

Petit  Menan  Island 522 

Petite  Riviere 533 

Terre 534 

Petropaulovski   580 

Petropolis 537 

Pha-lee-doo  Atoll 564 

Phenix  Island 584 

Philadelphia 524 

Philip  Island 581 

Caroline  Islands  ...  581 

Low  Arch 589 

Philip  Brooke  Cape 596 

Philip's  Point 531 

Phillip,  Port   592 

Pianosa  Island 556 

Italy 556 

— . 556 

Pichidanque 540 

Pichilinque  Bay 530 

Pickle  Bank    533 

Pico  Island 542 

Pictou  Harbor 522 

Piedra  Blanca 574 

Piedras  Blancas 530 

Cay   533 

Cay  de 533 

Piedras  Point 538 

Pieman  River 593 

Pierre,  St 534 

Island 5  70 

Anambas 570 

Newfoundland  520 

Pietro  di  Nembo,  St.,  Island  .  55" 

Pigeon  Point 529 

Pih-ki-shan  Islands 571 

Pih-quan  Peak 571 

Pih-seang  Islands 571 

Pikelot  Island 581 

Pilier  Island 554 

Pillau 550 

Pillar  Cape    594 

Magellan  Strait 539 

V.  Dieman  Land  ..  594 

Pinakii  Island     588 

Pine  Cape . .    520 

Pines  Island 533 

Pines,  Island  of 533 

Pingelap  Island 582 

Ping-fong  Island 571 

Ping-hae  Bay 579 

Pinnacle  Island 527 

Pinos  Point 530 

Pique  Bay 5  79 

Piraeus 559 

Pirano    557 

Pisagua 541 

Pisang 569 

Pisco 541 

Pitcairn  Island 587 


INDEX  TO  TABLE 


49. 


[Page  613 


Page. 

Pitea    549 

Piton-^  Island 568 

I'lacentia  IIarl)or     520 

-  -Point 526 

I'la.lda  Tslnnd 545 

Piaiia  Cay    532 

Pl.mier  Rock  . .. 556 

Plata  l^,la^^l 542 

Poi-    .■ 533 

Platte  Island  . 564 

Playa  Colorado 531 

Maria  Bay 530 

Parda  Cove 539 

Pleasant  Island 584 

Pleltenburg  Bay 562 

Plum  Island 523 

Plymouth 544 

England 544 

Mass.,  U.S 523 

^'ew 594 

Poile  Bay 521 

Pokonj idol  Rock 558 

Pola 557 

Sta.,  Bay 555 

Polillo  Island 573 

Politz  550 

Pollard  Cove 539 

Pollock 5  74 

Porno  Rock 558 

Ponafidin  Island 578 

Ponapi  Island 582 

Pond  Mountain 539 

Pondicherry 567 

Ponga  River 561 

Ponza  Island 556 

Poolebeg 546 

Popa  Island 57*^ 

Porcos,  Grande,  Island 537 

Porebander 557 

Porman   555 

Poromonshir  Island 5  79 

Poros 559 

Port-au-Prince 533 

Portendik 561 

Porthcurnow 544 

Portland 544 

England   544 

Maine,  U.  S 522 

Bay    592 

t'ape 593 

Dyrholarey 597 

Port  Royal . 526 

Jamaica 533 

S.  Carolina 524 

Said 560 

Porto  Bello 535 

Cabello  535 

Re 557 

Rico  Island   534 

Sante  Island 536 

Island  and  Bay 536 

Leguro 537 

Porto  Vecchio 556 

Portsmouth 523 

England 544 

U.S 523 

Possession  Bay  and  Cape 539 

Island 506 

Postilion  Islands 575 

Potsdam  .      552 

Povorotnoi  Cape 5  79 

I'owenden 549 

Prado 537 

Pratas  Island 571 

Preniiera  Islands 563 


Page. 

Preservation  Inlet  594 

Prestenizza  Point 557 

Prevesa 558 

Prince  lulward  Island    521 

Islands 521 

Prince  of  Wales  Cape 527 

Island 591 

Sound   520 

Prince  Regent's  River 591 

Princes  Island    561 

Proestoe 552 

Progreso 526 

Promontore  Point    557 

Prosekin      551 

Proti  Passage 558 

Proven 595 

Providence 523 

Islands, 581 

Port 580 

Psara  Island 559 

Pucio  Point 573 

Puka  Puka  Island 589 

Pukaruha  Island 588 

Puhcat 567 

Pulkowa 549 

Pulosuk  Island 581 

Pulpito  Point 530 

Puna 542 

Purdy  Islar  ds 585 

Putzig 550 

Putziger  Ileisternest 550 

Pyramid  Point   571 

Pyramidal  Rocks 570 

Quaco 522 

(Juaebo  River 561 

Ouebec 521 

Queenstown 547 

Ireland 547 

N.  Zealand     594 

Queimada,  Grande  Island....  537 

(^)uelpart  Island      577 

nuentin,  San 530 

Querimba  Island 563 

Queule  Bay 540 

Quilca 541 

Quillan  Cape 540 

Quillimane 562 

River 562 

(^)uilon 567 

Ouinhon 570 

(^uinaluban  Islands 572 

Quintero  Point 540 

(^uito  Sueno  Point 527 

Quod  Cape 539 

Quoddy  Head 522 

Quoin  Point 562 

Great,  Island 566 

Race  Cape 520 

Island 529 

Rachada  Cape 568 

Radackala  Islands 5S1 

Radama 565 

Island   565 

Ragged  Island 532 

Ragusa  Rocks,  Pcttini  di   ....  558 

Rairoa  Island   590 

Raleigh  Rock  576 

China 571 

57<J 

Ramas  Cape 5(17 

Rame  Head 562 

Ramree  Island 568 

Randers 553 


Page. 

Rangoon    568 

River 568 

Ranu  Cove 540 

Rapa  Island 590 

Raper  Cape 540 

Raphti,  Port 559 

Raraka 589 

Rarotonga  Island 590 

Rasa  Island 583 

Rathlin  Island 546 

O'Birne  Island 546 

Ratnagberry 567 

Raukura  Island 589 

Ravahere  Island 588 

Ravn's  Storo 596 

Ray  Cape 521 

Kaza  Island 537 

L.  California 531 

-.- 543 

Razzali  Island 556 

Real 536 

Realejo 531 

Reao  Island 588 

Recherche  Archipelago 592 

Recif  Cape 562 

Redang,  Great,  Harbor 570 

Redfield  Rocks 578 

Red  Island 591 

Redonda  Island 534 

Rock 580 

Refuge  Cove 528 

Reichenberg 550 

Reid  Island 589 

Reikianes  Cape    596 

Reikiavik 596 

Reirson  Island 584 

Reitova 588 

Rekkin,  Ras   566 

Rembang „ 5  75 

Remedios  Bay 531 

Renard  Island 585 

Islands S'^S 

Rendj-burg 551 

Rennel  Island    5^4 

Renskar 549 

Repon  Islind 5  70 

Re:-olution  Island 520 

Reunion  Island 564 

Revel   549 

Rpy,  Isla  del 542 

Reydar  Fjeld    597 

Reyes  Head 541 

Point 529 

Rhe  Island 554 

Rhinns,  Isla  of 544 

Rhio 5O8 

Rhodes 559 

Ribe 553 

Ribnitz    550 

Rich  Point 521 

Richmond $24 

Bay   521 

Richmond  River 593 

Riga 549 

Rigny  Mountain 596 

Rimitara  Island    590 

Ringkjobin    553 

Rio  Frio,  I'ort 539 

Grande 525 

do  Norte 525 

do  Sul 538 

Janeiro 537 

Risiri  Island 579 

Rissnaes  Point 596 

Rivadeo 554 


Page  614] 


INDEX  TO  TABLE  49. 


Page. 

Rivadesella 554 

Rivers  Cape 574 

Rixhoft 550 

RoaPoja 583 

Robert's  Point 529 

Roca  Partida 525 

Mexico 525 

Vera  Cruz 526 

Rocas  Reef 543 

Rochefort 554 

Rochelle 554 

Rocka  Cape 555 

Rockabill ..   546 

Rockal  Island 542 

Rockingliam  Bay 593 

Rockland 522 

Rockiiren  Islets 578 

Rodd  Bay 593 

Rodkallen  Rocks 549 

Rodney  Cape 585 

Rodoni  Cape 558 

Rodriguez  Island 564 

Rodskar  Island 549 

Roeskilde 552 

Rogosnizza 557 

Roigen  Cape 5  79 

Roma  Island 576 

Roniain  Cape 524 

RomanzofF  Cape 5^7 

Island   581 

Low  Arch 589 

Marshall  Islands.. .   581 

Romblon  Island 573 

Rome   556 

Ronaldsha  N 545 

Roncador  Cay 527 

Rongerik  Islands 581 

Rodcwal  Bay 562 

Roque,  St. ,  Cape 536 

Roques  Islands 535 

Rosa,  Sta.,  Island 530 

Rosalind  Bank 527 

Rosario  Island 583 

Rose  Island 587 

Rosemary  Island 591 

Rose  Spit  Point 528 

Rosier  Cape 521 

Ross  Island 577 

Rossel  Island , 585 

Rostock 550 

Rota  Island 582 

Rotti  Island 5  76 

Rottenest  Island 592 

Rotterdam 553 

Rotumah  Island 586 

Round  Hill  Island 520 

Round  Island  577 

Rovigno 557 

Roxo  Cape 525 

Royalist,  Port 5  72 

Royal  Island 532 

Ruad  Island 560 

Ruatan  Island 526 

Rudau.... 550 

Rligenwalde 550 

Rum  Cay 532 

Runaway  Cape 594 

Runo  Island 549 

Rupert  Island 539 

Rurutu  Island 590 

Ruxtehude 551 

Ryvingen  Island 547 

Saba   534 

Sabanilla 535 


Page. 

Sabine  Pass 525 

Sabionello  Peninsula 558 

Sablayan  Point 5  72 

Sable  Cape 522 

Island   522 

Sacaluta 531 

Sacken   589 

Sacrificios  Island 525 

Point 531 

Saddle  Group 5  72 

Island 520 

Sado  Island 579 

Safaja  Island 563 

Safatu  Island 570 

Saghalien  Island 5  79 

Saida 560 

Saigon 570 

Saints,  The 534 

Sal  Island 543 

Cay. 533 

Salado  Bay    541 

Salanguin,  Port 5  72 

Salaya  Island 575 

Sala  y  Gc^mez 590 

Saldanha  Bay 562 

Salem 523 

Sali 560 

Salina  Cruz .   531 

Salinas  Bay 530 

C.America. 531 

L.  California 530 

Point 534 

Salisbury  Island 520 

Salomague  Island 573 

Salonika 559 

Saltee,  Great 546 

Salut  Islands 536 

Salvador,  San,  Islands 532 

Salvage  Islands 543 

Salvore  Point 557 

Sama,  Port  and  Peak 533 

Sainana 533 

Cay 532 

Samanco  Bay 542 

Samar  Island 5  73 

Samarang 575 

Sambro  Island 522 

Samoan  Islands 587 

vSamos  Strait 559 

Samso  Island 552 

San,  Pulo 568 

Sand  Key 525 

Island 583 

Sandakan  Bay 5  74 

Sandalo  Cape 556 

Sandalwood  Island 576 

Sandfly  Cay 526 

Sando 547 

.Sandwich  Island 586 

Islands 544 

■ N.Pacific 582 

Sandwich  Islands,  .S.  Atlantic.  544 

Sandy  Cape 593 

Hook 524 

Point 539 

Sangallan  Island 54' 

Sanguin  River 5^' 

Sanguir  Island 5  74 

Sankaty  Head 523 

San-o  Bay 572 

Santander 554 

River 525 

Santiago  Cape 540 

de  Chile 540 

Port 573 


Page. 

Santiago  de  Cuba 533 

Santona 554 

Santos 537 

Saona  Island 534 

Sapelo  Sound 5^4 

Sarangani  Islands 574 

Sarawak 5  7^ 

Sariguan  Island 582 

Sarstoon  River 526 

Sasseno  Island 558 

Satawal  Island 5^1 

Satano  Misaki - 577 

Saugor  Island 567 

Saunders,  Port 521 

Savage  Island 5S7 

Savaii  Island 57*^ 

Savannah 524 

la  Mar 533 

Savu  Island 57t) 

Saybrook     523 

.Saypan  Island 582 

Scalloway 545 

Scalp  Mountain 54*^ 

Scarries  River 5^1 

Scatary  Island 5-2 

Schaaken  549 

Schama  Mountain 541 

Schank  Cape 592 

Schanz  Islands 5*^1 

Schaprode 55° 

Scharhorn 55' 

Scheveningen 553 

Schillighorn 552 

Schleimunde 55 ' 

Schleswig 55' 

Schonbaum 55° 

Schonberg 55' 

Schrievenborn 55' 

Schwerin 55' 

Scilly  Islands 544 

England 544 

S.Pacific 587 

Scott  Cape 529 

Scutari 559 

Sea  Bear  Bay 53^^ 

Seaconnet  Point 5^3 

.Seal  Cays 52b 

Island 522 

Seao  Island -.  5 74 

Sea  Rock 577 

Seattle 529 

Sebastian,  St.,  Cape 562 

Madagascar  . .  565 

S.  Africa 562 

Spain 554 

■_ Island 537 

Sebenica 557 

Sedano  Cape 575 

Sedishigar  Bay 5^7 

Seguin  Island $^2 

Seiero  Island 55^ 

Sein,  I.  de 554 

Sejan,  Ras 5^3 

Selatan  Cape -  574 

Seldom-come-by  Harbor 520 

Semeny  River 55^ 

Semarara  Islands 572 

Semiahmoo  Bay 529 

Semione  Island 570 

Sentinel  Island 577 

Serle  Island 588 

Sermo  Island 559 

Sermatta  Island 57*' 

Sermelik  Fjord 596 

Serjana  liank 527 


INDEX  TO  TABLE  49. 


[Page  615 


Page. 

Serranilla  Bank 527 

Seskar  Islaid 549 

Setuval     555 

Seuheli  Par 564 

Seva<^topnol 559 

Seven  I  leads .  547 

Seychelle  Arch 564 

Seydis  Fjord 597 

Slug  Rocks 544 

Shahah 566 

Shaikh  Shuab  Island    566 

Sha-lui-tien  Island 577 

Sliaiighai   572 

Shannon  River 54^ 

Shantar  Islands 5  79 

Shantung 5  76 

Shar  Abu    566 

Shargeh 566 

Shark  Island 584 

Sharmeh 566 

Sha-wei-shan    57^ 

Shelburne  Harbor 522 

Shelter  Bay 579 

Shepherd's  Island    527 

Sherbedat,  Ras 566 

Sherbro  Island 561 

River 561 

Sherm  Hassejy 563 

Jaobbah 563 

Rabigh 564 

Wejh 563 

Yahar    563 

Shetland  Islands 545 

Shiashkotan  Island 579 

Shields,  North 545 

Shinnecock  Bay  . 523 

Ship  Island 525 

Shoal 525 

Shipunsky  Cape 5S0 

Shirasu  Reef 578 

Shoals,  Islands  of 523 

Shoal  water  Bay 529 

Island   569 

Siargao  Island 5  73 

Siberoet  Island 569 

Siboga   569 

Sibuco  Bay 524 

Sibuyan  Island 5  73 

Sibutu  Island 574 

Sidmouth  Cape 593 

Sierra  Leone 561 

Sighajik 560 

Sigelfjord  Hoanegri 596 

Sigri,  Port 559 

Sihuatenego 531 

Sihut 566 

Silam 526 

Silaqui  Island 5  72 

Silver  Bank 532 

Simaloe  Island 569 

Simeonoff  Island 528 

Simidsu  Bay 5  78 

Sinioda 5  78 

Simonoseki 5  78 

Simon's  Bay 562 

St.,  Island 524 

Simonoff  Island 587 

Simonor  Island 5  74 

Simusir  Island 579 

Singapore 568 

Single  Island 571 

Singkep  Island 568 

Singora 570 

Sinkel 569 

Sinon 561 


Page. 

Sinope 560 

Siphanto  Island. 559 

Siquiquor  Island 573 

Sirik  Point 571 

Siriyasaki 57^ 

Sisal   526 

Sitka 528 

Sittee  Point 526 

Skagataas  Point   596 

Skagestrands •596 

Skags  Head 548 

Skagen  Cape 596 

Skaw  Cape 553 

Skelligs 545 

Skerries 544 

Skerryvore  Rocks 545 

Skiathos  Island 559 

Skidegate  Bay    528 

Ski  Sima 577 

Skoorgaarde 551 

Skumbi  River 558 

Skyring  Mountain- 539 

Sligo  Bay 54^ 

Slyne  Head 546 

Small's  Rocks 544 

Smerwick 546 

Smith  Island 529 

Japan 5  78 

— — Wash.  Terr 529 

Smyrna 560 

Snares 595 

Sneefeldsyokel    596 

Society  Islands 587 

Socorro  Island 531 

Mexico 531 

Chile    540 

Socotra  Island 563 

Soderarm     54^ 

Soderhamm 548 

Soder  Skars 549 

Sofala 562 

Sohar 566 

Sola  Island 535 

Sobnder  Islands 594 

Solitary  Island 593 

Solombo,  Great,  Island 575 

Solomon  Islands 5^4 

Solovetski 595 

Solta  Island 558 

Sombrero 534 

Key 525 

Rock 574 

Sommars  Island 549 

Song-yui  Point 57^ 

Sooke  Inlet   529 

Sorell  Cape 594 

Port 593 

Rock 558 

Sorol  Islands 581 

SorriUe  Rocks 571 

Sorsoghon,  Port 573 

Souklioum 559 

Soumshou  Island 579 

Sourabaya 575 

Sourop     549 

South  Cape  585 

South  Rock 546 

Sea  Castle 544 

Southampton 544 

South  Water  Cay 526 

West  Cape 594 

Reef 525 

Spain,  Port 536 

Spalatro  Passage 558 

Port 558 


Page. 

SpanbergCape 527 

Spartel  Cape 560 

Spartivento  Cape 556 

Naples  .    557 

Sardinia 556 

Spencer  Cape 592 

Spezzia 556 

Spha.\ 560 

Spikeroog 552 

Spiridione,  St 558 

Spitzbergen 595 

Spodsbjerg 552 

Spurn  Head    . 545 

Square  Handkerchief  Bank.  ..    532 

Staalburghuk  Fugle 596 

Stack,  S . .   544 

Stade 551 

Stag  Rocks 547 

Stamp  Harbor 528 

Stampali  Island . 559 

Stanley,  Port 544 

Slarbuck  Island   584 

Start  Light 545 

Point 544 

Staunton  Island 576 

Stavanger 547 

Steegen 550 

Steenskar  Rock 549 

Steiiacoom 529 

Steinberg 551 

Steinkirchen 551 

Steinshesten 547 

Stephen,  Port 593 

Stettin  . 550 

Stewart  Cape  .    591 

Islands   584 

Stirrup  Cays 532 

Stii  s  Point 549 

Stockho'  m 548 

Stonington 523 

Stopelmiinde 550 

Stora 560 

Stornaway 545 

Stot  . 547 

Stralsund 550 

Strandar  .  , 597 

Strasburg 552 

Strati  Island  559 

Straums  Naes  Bay 596 

Streaker  Bay 592 

Streckelsberg 550 

Strogonaff  Cape 528 

Stromstad 548 

Strong  Island  582 

Strovathi  Islands 558 

Stuart  Island 527 

Stykkisholm 596 

Suakin   563 

Suda 558 

Sueik 566 

Suez   563 

Suffren  Cape 5  79 

Sugarloaf  Point 593 

Sugrah 566 

Suk  Island 581 

Sulphur  Island  . 5^3 

Sulu  Island 574 

Sumbawa  Island 575 

Sumburgh  Head 545 

Sunaga  Islets 577 

Sunda  Strait 5(^)9 

Sunderland 545 

Sundsvall 548 

Sunmayani 5^7 

Sup^ 542 


Page  616] 


INDEX  TO  TABLE  49. 


Page. 

Sur 560 

Surat 567 

River 567 

Surigas 573 

Susaki 578 

Suwarrow  Islands 587 

Suwa  Sima 578 

Svartklubben 548 

Svendborg 55^ 

Svenor 548 

Svinoen 547 

Sviatoi  Noss   595 

Swalfer  Ort 549 

Swallow  Bay 539 

Islands 586 

Swan  Islands 526 

Swansea 544 

Swatow 571 

Sweers  Island 591 

Swinemlinde 55° 

Sybille  Bay . 5  79 

Sydenham  Island 5^0 

Sydney 592 

Harbor 522 

Synesvarde  Mountain 547 

Syra  Island 559 

Syracuse 537 

Tabasco  River 526 

Tablas  Island 573 

Point 540 

Table  Bay 562 

Head 520 

Taboga  Island 532 

Tabou  River 561 

Tabu-sima 5  78 

Tabutha  Island 586 

Tacorady  Bay 561 

Tae  Islands 571 

Tagulando  Island 5  74 

Tahanea  Island 589 

Tahiti  ...    587 

Tahoa  Island 587 

Tai-pin-san   5 76 

Tairo  Island 589 

Tai-tai 5  72 

Tajer 557 

Takapoto  Island 589 

Takau 5  72 

Takagama 5  79 

Takhkona  Point 549 

Tak6  Sima 577 

Takume  Island 589 

Talabo  Cape 5  75 

Talcahuano   540 

Ta-lien- whan  Bay 577 

Talinay  Mountain 540 

Taltat,"Port 541 

Taluak  Island 575 

Taniana  Island 580 

Tamandare 536 

Tamar  Cape 539 

: Port 539 

Tamatave 565 

Tambelan  Island 569 

Tampa  Bay 525 

Tampat  Tuan  Point 569 

Tampico 525 

Tam-sui  Harbor 572 

Tanabe  Bay 578 

Tancook  Island 522 

Tanga  Bay 563 

Tangier 560 

Tangtang 565 

Tanjong  Barram 5  72 


Page. 

Tanjong  Datu 572 

Pandam    569 

Tanna  Island 586 

Tanzon  Cape 5^5 

Taormina  Cape 557 

Taou-ata  Island 5^3 

Tapona  Island 586 

Tapoute-ouea 580 

Tapul  Island 574 

Tara  Hill 546 

Tarawa  Island 580 

Tarbertness 545 

Taranto 557 

Tarifa 555 

Taritari  Island 581 

Tarpaulin  Cove 523 

Tarragona 555 

Tas  de  Foin  Island 577 

Tatakoto 588 

Tatsupisaki 578 

Tauranga  Harbor 594 

Tauere  Island 589 

Tavolara  Cape 556 

Tavoy  River 568 

Taytao  Cape 540 

Tchoukotskoi  Cape 580 

Tegal,  Mount 575 

Tehor  Island 576 

Tekokota 588 

Tello  Islands 5  76 

Tematongi  Island 588 

Tenavaro  Island 588 

Tenaranga  Island 588 

Tenasserim 568 

Tenedos  Island 560 

Tenerife  Island 543 

Tenez  Cape 560 

Tepoca  Cape 531 

Tepoto  Island 5S9 

Tequepa 531 

Tercera 543 

Terkolei 568 

Teresa,  Sta,  Bay 530 

Terminos  Lagoon 526 

Ternate  Island 576 

Tersteni  Rock 557 

Testa  Cape 556 

Testigos  Islands 535 

Tewaewae  Bay 594 

Thank  God  Harbor 595 

Thermia  Island 559 

Thikombia  Island 586 

Thithea  Island 586 

Thom^,  St..  Cape 537 

Thomas,  St.,  Island 534 

Bay  of  Biafra.    561 

West  Indies  . .   534 

Three  Kings 594 

Three  Points  Cape 526 

Br.  Honduras.   526 

Gold  Coast  ...   561 

Patagonia 538 

Ti-ao-usu  Island    5  76 

Tiburon  Island 531 

Tiegenhof 550 

Tiegenort 550 

Tientsin 577 

Tien  Pak 571 

Tikei  Island 589 

Tiilicherry 567 

Tilly  Bay 539 

Timbalier  Island 525 

Timoe  Island 587 

Timor  Island 575 

Laut  Island 576 


Page. 

Tinakula  Island 5S6 

Tinhosa  Islands 570 

Tinian  Island 582 

Tirby  Point 527 

Toass  Island 581 

Toan 589 

Tobago 535 

Tobi  Island 582 

Tobol  Ati 569 

To-doo  Island 564 

Todos  Santos    530 

Tofua  Island 590 

Tokalan  I  slands 584 

Tokara  Sima 578 

Token  Bessy  Islands 575 

Tokio  Naval  Observatory 578 

Tolaga  Bay 594 

Tolkemit 550 

Tomas,  Santo 530 

Tomkins,  Fort 523 

Tomo  Roads 578 

Tongare wa  Island 5  84 

Tongatabon  Island 590 

Tongeang 571 

Tongoy 540 

Tong-ting  Island 571 

Tonkah .   568 

Tonning 551 

Topolo  Bampo 531 

Torbjomskar 548 

Tordenskj  old  Cape 596 

Torganten   548 

Toriwisaki 528 

Tornea 549 

Torres  Island 586 

Point 538 

Port 556 

Tortola 534 

Tortosa 555 

Tortuga  Island 535 

Tortugas 525 

Tory  Hill 546 

Island 546 

Tosco  Cape 53° 

Totoia  Island 587 

Toubai  Island 590 

Toulinquet  Islands 520 

Toulon   556 

Touron  Bay 57° 

Towers'  Island 580 

Townsend  Cape 5^1 

Port 529 

Trafalgar  Cape .   555 

Tralee  Bay 54" 

Tiani 557 

Trapani 556 

Travemunde 55^ 

Travers'  Islands 591 

Treasury  Islands 5^4 

Trebizonde 5^0 

Tregosse  Islets  585 

Trelleborg 54^ 

Tremiti  Islands 557 

Tr^passy  Harbor 520 

Tres  Montes  Cape 540 

Puntas  Cape 536 

Venezuela 536 

540 

Treuvenberg 595 

Trevandrum 5^7 

Tre vose  1 1  ead 544 

Triangle  Island .   529 

Triangles 526 

Tribul.Ttion  Cape 593 

Trichindore 5*^7 


INDEX  TO  TABLE  49. 


[Page  617 


Page. 

Trieste    557 

Trincomalee 567 

Tringano  River 57° 

Trinidad 536 

Head 529 

Island 543 

Tripoli 560 

Africa 560 

Syria 560 

Tristan  d'Acurha 543 

Triton  Bay 585 

Island 571 

Trunfo  Cape 526 

Trobriand  Islands 585 

Tromelin  Island 565 

Carolines 581 

Mauritius 565 

Tromso 547 

Trondheim 547 

Troon 545 

Truxillo  526 

Tsan-liang-hai 577 

Tscheljuskin 595 

Tsmano 565 

Tsukarase  Rocks 577 

Tsuruga 579 

Tsu-sima 577 

Tuanske  Island 589 

Tubai  587 

Tubai-manu  Island 587 

Tucacas  Island 535 

Tucker's  Beach 524 

Tally  Mountain 546 

Tumaco 542 

Tumbez   542 

Tungchuh  Island 571 

Tung-ying  Islands 571 

Tuni  ang  Island 571 

Tunis 560 

Tund  Island 553 

Tupilco 526 

Turk's  Island 532 

Turnabout  Island 571 

Turo  Island 552 

Turtle  Island 587 

Islands 591 

Tuskar  Rock 546 

Tuspan  Shoal 525 

Tuticorin 567 

Tutoia 536 

Tutuila  Island 587 

Tuxtla  \'olcano 525 

Twelve  Islands 566 

Twofold  Bay 592 

Tybee  Island 524 

Ty-fung-kysh  Island 571 

Tynemouth   545 

Ua  Haka  Island 584 

Ualan  Island 582 

Ubatuba 537 

Udsi-sima 577 

Uea  Island 590 

Ujilong  Islands 581 

Uleaborg 549 

Ulietea  Island 587 

Ulko  Kalla  Rock 549 

UUaduUa 592 

Ulsire .  547 

Uluthi  Islands 581 

Umea 549 

Una..    537 

Unalaska  Island 528 

Unare  Bay 536 

Underut  Island 564 

Underw  ood,  Port 595 


Page. 

Unga  Island 528 

Unie  Island 557 

Union  Bay 538 

Islands 584 

Port  de  la 531 

Unsang  Point 574 

Upernavik 595 

Upolu  Island 587 

Upright  Cape  and  Port 539 

Upsala 548 

Ura  Kami 578 

Urea  Island 587 

Urracas  Islands 582 

Uruk  Island 579 

Usborne,  Port 591 

Usedom 550 

Use  Islet 577 

Ushant 554 

Ustica  Island 556 

Utila  Island 526 

Utrecht 553 

Uto  Island 549 

Vache  Island 533 

Vadso 547 

Vahitahi  Island 588 

Vaivaatea  Island 588 

Valdes  Island 529 

Valdez  Port 590 

Valdivia   540 

Valencia 555 

Valentia 545 

Valentine  Harbor  . 539 

Valentyn  Cape 539 

Valery  en  Caux  St 553 

Valiente  Peak 527 

Valientes  Island   582 

Valparaiso 540 

Vana  \'ana  Island 588 

Vancouver  Island 529 

Vanikoro  Island 586 

Vannes 554 

Vanua  Lava  Island 586 

Levou  Island 586 

Mbalavou  Island 586 

Varde 553 

Vardo 547 

Varela  Cape 570 

Pulo 570 

Varna 559 

Vate  Island  586 

Vathi    558 

Vatin  Island 590 

Vatoa  Island 587 

Vaton  Lele  Island 586 

Vera  Island 586 

Vavao 590 

Vavitou  Island 590 

Vaza  Barris  River 536 

Veglia 557 

Veiro  Island 552 

Vela  Cape 535 

Venangue  Be  Bay 565 

Vendres,  Port 555 

Venice 557 

Ver,  Point  de 553 

Vera  Cruz 525 

Verde  Cape 561 

Verde  Cay 532 

' Cuba   533 

Bahamas 532 

Vernieja  Head 538 

Vestra  I  lorn  Point 597 

Vestervik 548 

Viborg  Bay 549 


Page. 

Vicente,  San,  Cape 539 

Port 573 

Victor,  Port 592 

Victoria 529 

Harbor 595 

Port 592 

(Australia) 592 

River 591 

Victory  Cape 539 

Island 570 

Vidal  Cape 562 

Video  Island 572 

Vieques  Island 534 

Vieste 557 

Vigo  555 

Villa 547 

Joyose 555 

Nova  da  Princessa 537 

Ville  Tranche   556 

Vinaroz 555 

Vincent,  St.,  Island 535 

Cape  Verde  Is  543 

Windward  Is  .  535 

Cape 555 

Madagascar  ..  565 

— Portugal 555 

Vincent  de  la  Buquera,  San  ..  554 

Vineyard  Haven 523 

Vingorla 567 

Rocks   567 

Virgins  Cape 538 

Virgin  Gorda 534 

Viti  Levou 586 

Vizagapitam   568 

Viziadroog 567 

Vladimir,  St.,  Bay 579 

Vliegen  Island 589 

Vliko,  Port 558 

Vohanga  Island 587 

Vohemar 565 

Vojazza  River 558 

Volcano  Island 572 

Volkhousky  Island 589 

Volta  River 561 

Voltaire  Cape 591 

Vordate  Island 576 

Vordingberg 55^ 

Vostok  Island 584 

Vourlah 560 

Vries  Island 578 

Wadero  Island 548 

Wahdu  Island 564 

Wai-ian-do  Island 577 

Wai-mea ... 5^3 

Waitangi  River 594 

Wakaia  Island 586 

Wake  Island 582 

Wakefield,  Port 592 

Walker  Cay 532 

Wallir  . 550 

Wallis  Islands 5S7 

Walpole  Island 5^^ 

Walsche  Cape 585 

Walwich 563 

\\'anganui  River 594 

Wangari  Bay 594 

Wangaroa  H  arbor 594 

Wangaruru 594 

Wangeroog 552 

Wang-kia-tia  Bay 5  76 

Warberg 548 

Warnemunde 550 

Washington 524 

— — Island 580 


Page  618] 


INDEX  TO  TABLE  49. 


Page. 

Watch  Hill  Point 523 

Watcher,  North  569 

Waterfall  Bluff 562 

Waterford 546 

Waterloo  Bay 562 

WatHng's  Island 532 

Wawoda  Rock 579 

Wedge  Island 522 

Wegg's  Cape 520 

Weichselmunde 550 

Wellington 595 

Wenman  Island 580 

Wesselburen 551 

Wessel,  Cape 591 

West  Cape 594 

Western,  Port 592 

Westmaney  Heimakleter 597 

Westminster  Hall  Island 539 

New 529 

Westport  Bay 546 

Wetter  Island 576 

Wexford 546 

Whaingaroa  Harbor 594 

Whalefish  Islands 596 

Whale's  Back 523 

White  Dogs  Island 571 

White  Head  Island 522 

White  Island 594 

Rock 539 

Whitehaven 545 

Whitsunday  Island 588 

Whittle  Cape 521 

Wicklow 546 

Wilberforce  Cape 591 

Wilhelmshaven 552 

Willemstad 553 

William  Port 595 

Wilmington 524 


Page. 

Willoughby  Cape 592 

Wilson's  Island 585 

Islands 581 

Promontory 592 

Windau 549 

Winter  Harbor 595 

Wismar 551 

Wittgenstein  Island 589 

Wolgast 550 

Wollaston  Island 538 

Wollongong 592 

Wood  Island 521 

Labrador 521 

Maine,  U.  S 522 

Woodlark  Islands 585 

Woody  Islands 571 

Woosung 572 

Wostenholme  Cape 520 

Wotje  Islands 581 

Wowoni  Islands 5  75 

Wottho  Islands 581 

Wrangle  Bay 5  79 

Wrath  Cape 545 

Wreck  Reef   585 

Wusimado,  Port 578 

Wustrovv 550 

Xulla  Islands 576 

Bessey 576 

Mangola 576 

Xulla  Islands,  Talyabo 5  76 

Yakuno  Sima 577 

Yamagawha 577 

Yami  Island 5  73 

Yafiez 540 

Yap  Island 581 

Yaquina  Head 529 


Page. 

Yba  Point 572 

Yeboshi  Sima 577 

Yembo 563 

Yeu,  Island  de 554 

Ylin  Island 572 

Ylo 541 

Yniada 550 

Yobuko 577 

Yokohama  .. 5  78 

Yokoska 5  78 

Yokosima 5  78 

York  Cape 595 

Island 584 

York  Minster  Rock 539 

Youghal 547 

Ystad 548 

Ytapere  Bay 565 

Point 565 

Yuiada  Road 559 

Yura-No-Uchi 578 

Zafarina 563 

Zafarin  Islands 560 

Zambasi  River 562 

Zamboanga 5  74 

Zamowitz 550 

Zante 558 

Zanzibar 563 

Zapotellan  Pt 526 

Zara.. 557 

Vecchia 552 

Zempoala  Point 525 

Zengg 557 

Zeyla 563 

Zirona  Grande,  Island 557 

Zizow 550 


i» 

Page  619 

MAGNETIC    VARIATION. 

TABLE  50. 

THE  MAGNETIC  VARIATION  OF  THE  COMPASS. 

[In  Latitude  from  70°  N.  to  60°  S.] 

Longitude  West  of  Greenwich. 

Lat. 

« 

Lat. 

0° 

5° 

10°         15°         20° 

25° 

30° 

35°         40° 

45° 

70°  N. 

25.  oW. 

29.  2  W. 

33.  6  W.^  37.  8  W.   42.0  W.I  46.  oW. 

49.  9  W. 

53. 4  W.   56.  5  W. 

59.  6  W. 

70^  N. 

65 

22.  7 

26.6 

30-  7         34-  9         39-  0        42.  5      i  46. 9 

50.  4         53-  8 

57-2 

65 

60 

20.8 

24.  2 

27.9 

32.0         35.6         39.2         42.6 

45.  6         48.  2 

1  49.9 

60 

55 

19.5 

22.5 

25.8 

29-  3      ,  32. 4        35-  8         38.  3 

40.  5         42.  0 

43- 0 

55 

50 

45°  N. 

18.2 

20.  7 

23-4 

26.5      j  29.3 

31.6 

28. 4  W. 

33-4 

34-  6         35-  4 

t  35-5 

50 

1 7.  2  W. 

19.  5  W. 

21.  7  W.   24.  3  W.   26.  5  w. 

29.  6  W. 

29.  9  W.   30.  0  W. 

29. 4  W. 

45°  N. 

40 

16.3 

18.2 

20.  0 

22.0        24.0         25. 4        25.9 

25.8         25.2 

24.2 

40 

35 

15.6 

17.4 

18.9 

20.  5         22.  I         23.  3      1  23. 4 

22.8         21.8 

20.3 

35 

30 

15.2 

16.6 

18.0 

19,3         20.6        21.6         21.6 

20.5         18.9 

:    16.7 

30 

25 
20*^  N. 

15-2 

16.4 

17.6 

18. 8         19. 9         20.  +       20. 2 

18.7 

16.3 
14.  0  W. 

10.  8  W. 

25 

15- 4  W. 

16.  5  W. 

I7.6W. 

18.  7W.    19.  7W.   20.+W.!  19.  I  W.    16.8  W. 

20°  N. 

15 

15-9 

17.0 

18.2         19. 2         20.—       20. 5      i  17. 9 

15.2         12.0 

8.2 

15 

10 

16.6 

17.9 

19.0 

20. 0         20.  -f-        19.3         17. 0 

14.  I          10.4 

,     6.8 

10 

5 

17.6 

19.  I 

20.  2 

20.  7         20.  +        19.  I          16. 5 

13-4          9-5 

i     5.8 

5 

0 

19.2 

20.4 

21.3 

21. 5         20. 8         19.0 

16.3 

13.2 

9.1 

5-3 

0 

5°S. 

21.  2  W. 

22. 4  w. 

22.  8  W.   22. 4  W.   21.  I  W.'  18.  6  W. 

16.  2  W. 

13.  oW. 

9.0W. 

5. 1  W. 

5°  S. 

10 

23-4 

24.4 

24.4 

23.2         21.2       1  18. 5 

15.9          12.8           8.7 

4.8 

10 

15 

25.7 

26.  2 

25-4 

23.3         21.0         18.0         15.3         12.0           8.1 

4.3 

15 

20 

27.2 

27.0 

25- 3 

23.1      20.5      17.6    :  14. 7    1  II.  4       7.3 

3-6 

20 

25 

30'-  s. 

28.0 

26.6 

24.8 

22.6    1 20. 0    i  17. 0 

13.8 

10.  2      1     6.  2 

2.4 

25 

30°  s. 

27.  9  w. 

26.  3  w. 

24.  3  W.   21.  8  W.    19.  I  W.   J5.8W.    12.6           9.0W.     5.0W. 

i.oW. 

35 

27.6 

25.0 

23.5         21.0         17.9         14.6         II. 2           7.2           3.4 

0.  3E. 

35 

40 

27.1 

25.0 

22.5          19.9         16.4         13.0           9.8           5.7           1.7 

1.9 

40 

45 

26.  2 

24.0 

21.2      18.3      14.6      10.9    \   ^.^    13-6 

0.0 

3-8 

45 

50 

25-1 

23.  5  w. 

22.5 

19.8        16.2      i  12. 9         9.3      !    5-5          1.6 

1.9E, 

5.8 

50 

55°  S. 

20.  5  W. 

17.  5  W.    15.  oW.'  10.  5  W.     6.8W.i     2.  8W.     0.9E. 

4.3E. 

8.0E. 

55°  S. 

60 

21.7 

18.6 

15.1          II. 5   .    1     7.8           4.0      j     0.4      1     3.0 

6.8 

10. 0 

60 

45° 

50° 

55° 

60° 

65° 

70° 

75° 

80° 

85° 

90° 

70°  N. 

59.  6  W. 

64.  5  W. 

70.  oW.'  75.  oW. 

80.  oW. 

86.  oW. 

89.  oW. 

90. 0  W. 

90.  0  W. 

90. 0  W. 

70°  N. 

i^ 

57.2 

63.0 

65. 0     ;  66. 0 

67.0 

65.0        62.0         58.0 

55-0 

27-5 

65 

60 

49.9 

51-2 

51.8     1  51.7       50.5     ;  47.5       42.0     '  32.0 

20.0 

4.0 

60 

55 

43-0 

43-5 

42.8       41.8       38.8     \  34.0       27.0 

19.0 

9.0 

1.5E. 

55 

50 

35-5 

35-0 

33.6       31.6       28.5 

23-9 

17.5 

10. 0 

2.2 

4-7 

50 

45°  N. 

29. 4  W. 

28. 4  W. 

26.  6  W.I  24.oW.i  21.  oW. 

16.  oW, 

10.  5  W.     s.oW. 

0.8E. 

6.0E. 

45°  N. 

40 

24.2 

22.  6 

20.5 

17.8 

14.0 

10. 0           6.0           2.0 

2.4 

6.3 

40 

35 

20.3 

18.3 

16.  0 

12.9 

9.4 

6.3 

2.  9       1     0.  2  E. 

3-6 

6.4 

35 

30 

16.7 

14-3 

"•5 

8.5 

5-9 

3-3 

0.8           1.8 

4.2 

6.4 

30 

25 

13-7 

10.  7 

7-9 

5-5 

2.3           1.2 

0. 8  E.  1     2.  9 

4.6 

6.3 

25 

20°  N. 

10.  8  W. 

7.6W. 

5.2W.1    3.9W. 

1.2W.     0.6E. 

2.2E.'     3.7E. 

5.  IE. 

6.  +  E. 

200  N. 

15 

8.2 

5-4 

31 

I.O 

0.6E.      1.8 

3-2       I     4-3 

5-3 

6.+ 

15 

10 

6.8 

3-7 

1.4 

0. 6E.       1.9           3.  I 

4-2           5-3 

6.+ 

7-  — 

10 

5 

5.8 

2.8 

°-3^ 

i.'6           3.0 

4.2 

5-3 

6.3 

7.0 

7.4 

5 

0 

5-3 

2.3 

0.  4E. 

2.4      !     4.0 

5.3 

6.5 

7.7 

8.4 

8.5 

0 

5°S. 

S-iW. 

1.8W. 

i.oE. 

3.  2  E.      4. 9  E.  1     6. 4  E. 

8.0E. 

9.2E. 

9.9E. 

9.8E. 

5°S. 

10 

4.8 

1.4 

1.6 

4.0           5.9           7.8           9.4 

10.6 

II. 2 

II.  I 

10 

^5 

4-3 

0.7 

2.4 

50           7.1       19-3 

10.6 

II. 8 

12.3 

12.2 

15 

20 

3-6 

0.  lE. 

3-3 

6. 2           8. 5         10. 5 

12. 1 

13.2 

13.6 

13-3 

20 

25 

2.4 

1-5 

4.6 
6.0E. 

7.  6         10. 0 

12.  X      !  13. 7      1  14.7        14.9 

14.6 

16. 1  e: 

25 

30°  s. 

i.oW. 

2.  7E. 

8.8E.     11.4E. 

13.  6  E,!  15.  2  E,     16.  I  E.     16.  3  E. 

30°  s. 

35 

0.3E. 

4-3 

7-5 

10.4         12.7 

15.3       I  16.9         17.8 

18.0 

17.8 

35 

40 

1.9 

5-7 

9ro 

II. 6         14.0 

16.5 

18.3         19-3 

19.  6 

19-3 

40 

45 

3-^ 

7-4 

10.4 

13. 1       1  15.6 

18.2 

20.0        21.2 

21.5 

21. 2 

45 

50 

5-8 

9.1 

II. 8 

14.4         17.0 

19.6 

21.6        22.8 

23.4 

23-  3 

25.  7  e. 

50 
55    ^• 

55°  S. 

8.0E. 

10.  9  E. 

13.5E. '  16.  3  E.;  18.  8  E. 

21.  3  E.'  23.  6  E.    25.  oE. 

25.  7  E. 

60 

10. 0 

12.7 

15.3         18.0        20.6         23.4         25.9 

27.3 

28.0 

28.0 

60 

Page  620 

TABLE  50. 

THE  MAGNETIC  VARIATION  OF  THE  COMPASS. 

[In  Latitude  from  70°  N.  to  60°  S.] 

Longitude  West  of  Greenwich. 

Lat. 

Lat. 

90° 

95° 

100° 

105°    j    110°        115° 

120° 

125° 

130° 

135° 

70°  N. 

90.  0  W. 

80.  oW.'  65.  oE. 

73.  0  E. '  70.  0  E.  >  67. 0  E. 

63.  0  E. 

58.  0  E. 

53-  0  E. 

49. 0  E. 

70°  N. 

^5 

27.5 

5.  0  L.    30.  0 

39.0         43.5       !  45.0 

45- 0 

44.0 

43-5 

41.0 

65 

6o 

4.0 

II.  0         22.  5 

28.5         32.0       '  34.0 

34.0 

34- 0 

33- 0 

32.0 

60 

55 

1.5E. 

"•5 

.'7-3 

22. 5       ,  26. 0         27.0 

28.0 

28.2 

27.9 

27.4 

55 

50 

4-7 

II.  I 

15.8 

18.6      I  21. 0         22.  7 

23-4 

23-7 

23-7 

23  4 

50 

45°  N. 

6.0E. 

10,  5  E. 

14.  I  E. 

16.  7E.     18.4E.  1  19.  6  E. 

20.  7  p. 

20.  8  E. 

20.  6  E. 

20. 4  E. 

45°  N. 

40 

^•3 

9-9 

12.5 

14.8         16.2         17.  I 

17.7 

17.8 

17.7 

17-5 

40 

35 

6.4 

9.2 

II.  2 

12.8         13.9         14.6 

14.9 

15.  o 

15- I 

14.9 

j5 

30 

6.4 

8.6 

10.  I 

II.  3         12.0         12.3 

12.5 

12.6 

12.7 

12.6 

30 

25 

6.3 

7-9 
7.3E. 

9.2 

10. 0         10.5         10.6 

10.  7 

10.7 

10.7 

10.6 

25 

20°  N. 

6.+E. 

8.2E. 

8.  7  E.      8.  9  E. ,     8.  9  E. 

8.8E. 

8.8E. 

8.6E. 

8.  5E. 

20ON. 

15 

6.+ 

7-— 

7.5 

7.6           7.7      1     7.6 

7.4 

7.2 

7-1 

6.9 

15 

10 

7-- 

7-— 

7-- 

7--     ,     7-- 

6.5 

6-3 

6.0 

5-8 

5-7 

10 

5 

7-4 

^■5 

7-3 

7.-     j     6.5 

6.1 

5.5 

5.0 

5-0 

5-^ 

5 

0 

8.5 
9.8E. 

8.3 
9-3E. 

7-7 
8. 6"E. 

7-2          6.5 

5-9 

5-2 

5.0 

5-0 

5.0 

0 

5°S. 

7.8E. 

7.  2E. 

6.4E. 

5.6E. 

5.0E. 

5.  oE. 

5.0E. 

5°S. 

10 

II.  I 

10.3 

9-5 

8.7 

7-8 

7.2 

6.5 

5-9 

5-7 

5-7 

10 

15 

12.2 

"•3 

10.5 

9.6 

8.  7           7. 9 

7-4 

7-1 

6.8 

6.8 

15 

20 

13-3 

12.4         II. 4 

10.6 

9.  7           9.  0 

8.4 

8.1 

7.8 

7.8 

20 

25 

14.6 

13-5 

12.  6 

13. 8  e: 

II. 7 

ID.  8          10. 1 

9.4 

9.0 

8.8 

8.8 

25 

30°  S. 

16.  I  E. 

14.  9  E. 

12.  8  E.     II.  8  E.     1T.2E. 

10, 4  E. 

10.  0  E. 

9.  7  E. 

9.6E. 

30°  s. 

35 

17.8 

16.7      1  15.4 

14.2         13.2          12.3 

II. 6 

II.  I 

10.7 

10.6 

35 

40 

19.3 

17-3 

17.0 

15.7         14.4         13.5 

12.8 

12.  2 

II. 7 

II. 6 

40 

45 

21.  2 

20.3 

19.0 

17.6         16.3          15.0 

14.2 

13-5 

13-1 

12.8 

45 

50 

23.2 

22.4 

21. 2 

19.  7         18.2         16.8 

15-6 

14.8 
17.  oE. 

14-3 

14.2 

50 

55°  S. 

25.  7  E. 

25- 3  E. 

24.  3  e. 

22.  5  E.    20.  9  E.     19.  5  E. 

18.  2  E. 

16.  3  E. 

15.  8  E. 

55°  S. 

60 

28.0 

27.  5       !  26.  8 

25.8         24.3         22.8 

1                                 1 

21.3 

20.  I 

19.2 

18.5 

65 

70ON. 

135° 

49.  0  E. 

140°        145° 

i 

150°        155=        160° 

165° 

170° 

29.  I  E. 

1*5° 

180° 

47.  5  E. 

45. 0  E. 

42.  0  E. 

39.  0  E.    36.  5  E. 

33- oE. 

25.  8  E. 

22. 2  E. 

70°  N.  1 

65 

41.  0 

39- 0 

37- 0 

34- 0 

32.  0         29.  2 

26 

3 

22.7 

19.4 

16  6 

65 

60 

32.0 

30.6 

29-5 

28.1 

26.  3         24.  I 

21 

5 

18.8 

16.3 

13-6 

60 

55 

27.4 

26.6 

25-7 

24.6 

23.2         21.5 

19 

4 

17.  I 

14.9 

12.4 

55 

50 

23.4 

22.9 

22.3 

21.4 

20.4         19.2 

17 

5 

15-5 

13-5 
12.  6  E. 

"•5 
II. 2E. 

50 

45°  N. 

20.  4  E. 

20.  0  E.     19.  5  E. 

18.  8  E.     18.  oE.,  17.  oE. 

-15 

6E. 

14.  3  E. 

45°  N. 

40 

17-5 

17.  I 

16.8 

16.3         15.7         15.0 

14 

I 

13-2 

12.  I 

10.8 

40 

35 

14.9 

14.8 

14.  6 

14.3         13-8         13-5 

12 

9 

12.3 

II. 5 

10.  6 

35 

30 

12.  6 

12.5 

12.4 

12.  2         12.  0         II.  7 

II 

5 

"•3 

10.  9 

10.4 

^0 

25 

10.  6 

10.5 

10.4 

10.3         10.2         10.3 

10 

3 

10.3 

10.3 

10. — 

25 

20^  N. 

8.5E. 

8. 4  E.      8.  4  E. 

8.  3  E.      8.  4  E.  i     8.  6  E. 

8 

9E. 

9-+E. 

9-5E. 

10. — E. 

200  N. 

15 

6.9 

6.  8           6.  8 

6.  8           7.  2           7.  5 

7 

9 

8.5 

8.— 

9-+ 

15 

10 

5-7 

5-7 

5-8 

6.  I           6.  4           6.  8 

7 

4 

8.0 

8.5 

9-— 

10 

5 

5-0 

5-0 

5-0 

5.4           5.9           6.6 

7 

3 

7.8 

8.+ 

9-— 

5 

0 

5-0 

5-0 

5-0 

5.2       1     5-8 

6.7 
7.  2  E. 

7 

3 

7.8 

8.4 

9-— 

0 

5°S. 

5.0E. 

5.0E. 

5.0E. 

5.  7  E.      6.  4  E. 

7 

6E. 

8.2E. 

8.5E. 

8.  8  E. 

5°S. 

10 

5-7 

5-7 

6.1 

6.  6           7.  2           7.  6 

8 

2 

8-5 

8.8 

9-+ 

10 

15 

6.8 

6.8 

7.2 

7-5           7-9           ^-5 

8 

6 

9.0 

9-+ 

9-+ 

15 

20 

7.8 

7-9      i     8.2 

8.4 

8.6      1     8:8 

9 

3 

9-5 

9.6 

10. — 

20 

25 

8.8 

8.  8      1     8. 9 

9.2 

9-4 

9.6 

9 

8 

10. 1 

10.4 

10.6 

25 

30"  S. 

9.6E. 

9.  6  E.      9.  7  E, 

9. 8  E.     ID.  2  E. 

ID.  4  E. 

10 

7E. 

II.  oE. 

II. 4E. 

II. 7E. 

30°  s. 

35 

10.  6 

10.  5          10.  6 

10. 8         IX.  I          II.  4 

II 

7 

12.  2 

12.  5 

13.0 

35 

40 

II. 6 

II.  5          II.  6 

II. 8         12.2          12.5 

12 

8 

13-4 

13.8 

14-3 

40 

45 

12.8 

12.8         12.8 

13.2          13.4      1  13.8 

14 

3 

14.7 

15-4 

15.8 

45 

50 

55°  S. 

14.2 
15.  8  E. 

14.2 

14- 3 

14.4         14.7 

15.2 

15 

7 

16.3 
18. 2  E. 

16.9 

19.  3  E. 

50 
55°  S. 

15.  8  E. 

15.  8  E. 

16.  2  E.  1  16.  5  E. 

17.  I  E. 

17 

6E. 

18.  7  E. 

60 

18.5 

18.3 

18.3 

18.4         18.  7         19. 2 

19 

8 

20.4 

21.  0 

21.8 

60 

Page  622 

TABLE  50. 

THE  MAGNETIC  VARIATION  OF  THE  COMPASS. 

[In  Latitude  from  70°  N.  to  60°  S. 

Longitude  East  of  Greenwich. 

Lat. 

Lat. 

90° 

95° 

100° 

105° 

110° 

115° 

120° 

125° 

130° 

135° 

70°  N 

15.  oE. 

13-  5  E. 

II.  5  E. 

9.5E. 

9.0E. 

8.0E. 

7.0E. 

5.SE. 

5.0E. 

5. 0  E.    70°  N.  1 

65 

13-7 

II. 0 

8-5 

6-5 

4.0 

2.0 

1.0 

1.5W 

2.0W. 

2.  5  W.J  65         1 

60 

II. 4 

9.1 

6.5 

4.0 

1.4 

0.6W 

2.6W. 

4.2 

5-4 

6.2 

60 

55 

9.8 

7-5 

5-0 

2.3 

0.0 

1.8        !      3.6 

5-2 

6.3 

7.0 

55 

50 

f  0 

6.1 

3-7 

1-5 

0.5W. 

2-3 
2.4W 

!    3-9 

5.4 

6..5 

7.0 

50 

45°  N. 

6.-,E. 

5.2E. 

3.  IE. 

1.2E. 

0.6W. 

3-8W. 

5.3W. 

6.3W 

6.8W. 

45°  N. 

40 

5-f 

4-5 

2.9 

I.  2 

0.5 

2.0               3.4 

4.6 

5-5 

5-6 

40 

35 

4.8 

4.2 

2.9 

1.4 

0. 1 

1.4            2.6 

3-8 

4-4 

4.4 

35 

30 

4-3 

4.0 

3-1 

1.8 

0.5E. 

0.6 

1-7 

2.7 

3-3 

31 

30 

25 
20*^  N. 

3-5 

4.- 

3-+ 

2.2 

1.2 

0.  2  E. '    0.  8 

1. 5 

2,  I 

1.8 

25 

2.7E. 

1     3.+E. 

3-+E. 

2.6E. 

1.7E. 

0.  8  E.      0.  2  E. 

0.5W. 

0.  8  VV. 

0.  7W. 

20°  N. 

15 

2-5 

2.7 

3-+ 

3-0 

2. 2 

1.4           0.8 

0. 3  E. 

0.  I  E. 

0.  2E. 

15 

10 

2-3 

2   1 

3-- 

3-+ 

3-— 

2.0           1.4 

1.0 

I.  2 

1.0 

10 

5 

1.9 

2.^ 

2.6 

J- 

3.—        1       2.+         ;       2.— 

2. — 

2.— 

1.6 

5 

0 

1-5 

2.0 

2.+ 

2.+ 

2.+ 

2.+     i     2.+ 

2. — 

2.— 

2.  2 

0 

5°S. 

0.8E. 

i.2r 

1.7E. 

2.+E. 

2.  +  E. 

2.+E.        2.H-E. 

2.+E. 

2.+  E. 

2.6E. 

5°S. 

10 

0.4W. 

0.0 

0-5 

0.8 

I.  I 

1-3      1     1-5 

2. — 

2.  2 

2.8 

10 

15 

2-3 

1.9W. 

1.5W. 

I.  I  W. 

0.  5  W. 

0.  iW.     0.5 

1.2 

2.  0 

3-1 

15 

20 

4-7 

4. 1 

3-4 

2.6 

I.  8 

1.2       1     0. 4W. 

0.7 

1.8 

3-2 

20 

25 

8.1 
12.  2  W. 

7-4 
II.  oW. 

6.4 
9.6W. 

5-0 

3-5 

2.2           1.2 

0.0 

I- 5 

3-3 

25 

30°  -s. 

7.9W. 

5.7W. 

3.SW.      1.9W. 

0.4W. 

1.2E. 

3.4E. 

30°  s. 

35 

17.2 

15-7 

'3-8 

11.3 

8.9 

5-8      1    31 

1.2 

0.8 

3-4 

35 

40 

22.  2 

20.  9 

18.7 

16.  0 

12.6 

9.0          5.2 

2.  2 

0.3 

3-3 

40 

45 

28.0 

26.4 

*4.  2 

21.  I 

17-5 

13.4          8.9 

4.0 

0.  5W. 

3-0 

45 

50 

55°  S. 

33-8 

32.2 

29.9 
j6.  6  w: 

26.5 

22.4 

17.7         12.6 

6.8 

1.9 

2-5 

50 

41.  5  w. 

39-  5  W. 

33.  oW. 

28.  4  W. 

23.  oW.    17.  3  W. 

II. oW. 

4.5W. 

1.4E. 

55°  S. 

60 

50.  2 

48.1 

45.0 

41.  0 

35-7        30.0         23.3 

16.0 

8.2 

0.9W. 

60 

135° 

140° 

145° 

150° 

155°        160° 

165° 

no° 

175° 

180° 

70°  N. 

5.0E. 

6.uE. 

6.  5  E. 

8.0E. 

10.  2  E,     12.  oE. 

14. 0  E. 

16.  5  E. 

19.  0  E. 

22.  2  E. 

70°  N. 

65 

2. 5  w. 

2.  oW. 

i.oW. 

1.0 

3-0          5.5      !    8.0 

10.5 

13.2 

16.2 

65 

60 

6.2 

6.1 

5.0 

2.8W. 

0.3W. 

2.4 

51 

7-9 

10.7 

13-5 

60 

55 

7.0 

7.0 

6.0 

4.0 

1-5 

1-3 

4.2 

6.8 

9.6 

12.3 

55 

50 

7.0 

7.0 

5-8 

3-9 

1.4 

1-3 

4.0 

6.7 

9.3 

"•5 

50 

45°  N. 

6.8W. 

6.5W. 

5-3VV.I 

3-3W. 

0.  7  W. 

1.7E. 

4.3E. 

6.8E. 

9.2  E. 

II.  I  E. 

45°  N. 

40 

5-6 

5-3 

3-9 

1.8 

6.3E. 

2.6 

4.9 

7-3 

9-4 

10.  9 

40 

35 

4.4 

3-7 

2.5 

°-5 

1-4           3-4 

^•5 

7.6 

9.4 

10.  6 

35 

30 

3-1 

2.4 

1.0 

0.5  E. 

2.3           4. 2 

6.1 

7-9 

9-4 

10.4 

30 

25 
20°  N. 

1.8 

I.  2 

0.  I  E.  ' 

1-5 

3.2           5.0           6.6 

8.3 

9-  + 

10.- 

25 

0.  7  W. 

0.0 

I.  I  E. ' 

2. 4  E. ! 

4. 0  E. !     5.  6  E. 

7.2E. 

8.4E. 

9.-I-E. 

9-+E. 

200  N. 

15 

0.  2  E. 

0.8E. 

1.9 

3-3 

4.  8           6.  2 

7-5 

8.5 

9-+ 

9-+ 

IS 

10 

I.O 

1-7 

2.7 

4.1 

5-4           6.7 

7.8 

8.5 

9.4- 

9  - 

10 

5 

1.6 

2.4 

3-5 

4.8 

6.  I           7.  2 

8.1      ' 

8.6 

9.0 

9- 

5 

0 

2.2 
2.6E, 

2.9 

3.  5  E.  j 

4.2 

5-4 

6.  6           7.  6 

8.3 

9.2 

9-+ 

9-- 

0 

5°«- 

4.  8  E. 

6.0E. 

7.  2  E.      8. 1  E. 

8.6E. 

9-+E. 

9-+E.  j 

9.-E. 

5°S. 

10 

2.8 

4.0 

5-2 

6.5 

7.6           8.4 

9.0 

9-  + 

9.+      ! 

9-+ 

10 

15 

3-1 

4-5 

5-7 

7.2 

8.  I           8.  8 

9-+ 

9-+ 

9-  + 

9-+ 

15 

20 

3-2 

4.8 

6.3 

7.6 

8.5       '     9-2 

10. — 

10.— 

10. — 

10.— 

20 

25 

3-3 

5-3 

7.0 

8.2 

9.0      i  10. — 

10.  2 

10.  6 

10.7 

10.  6 

25 

30°  s. 

3.4E. 

5.9E. 

7.5E. 

8.  7E. 

9.5E. 

10.  4  E. 

II.  2  E. 

II.  8  E. 

11.9E. 

II. 8E. 

30°  s. 

35         1 

35 

3-4 

6.4 

8.2 

9.4 

10.5 

II-5 

12.  3 

13.0 

13-2        , 

13.0 

40 

3-3 

6.8 

8.8 

10.4 

II. 6         12.8 

13.8 

14.4 

14-5      1 

14.4 

40 
45 

45 

3-0 

7.0 

9-7 

II. 6 

13.  I          14.4 

15-4 

16.  2 

16.2      1 

15-9 

50 

2-5 

I.  41:. 

7.0 
6.  9  E. 

10.4 

ii.oEr 

12.8 
14.0  E. 

14.5          15.9         17.0 
16.  I  E.     17.  9  E.     19.2  E. 

17.8 

17.8 

17.4 
19.  2  E. 

50 

55°  S. 

jr-^- 

19.  7  E. 

19.  6E.  i 

0.  9  W. 

6.0 

"•5 

15-5 

18.5 

20.8        21.8      1 

22.3 

22.3 

21.8 

60 

DECIMAL    FRACTIONS.  623 


^iPiPEisriDix:. 


DECIMAL  FRACTIONS. 

It  is  to  be  supposed  that  the  fundamental  rules  of  common  arithmetic  are  clearly  understood,  but  there  may 
be  many  who,  in  beginning  the  study  of  Practical  Navigation,  have  not  become  familiar  with  the  use  of  decimal 
fractions ;  and  since  calculating  with  them  enters  so  largely  in  the  problems  of  Navigation,  it  has  been  deemed 
proper  to  append  the  following  brief  explanation  : 

Fractions,  or  ]~idgar  Fractions,  are  expressions  for  any  assignable  ])art  of  a  unit;  they  are  usually  denoted  by 
two  numbers,  placed  the  one  above  the  other,  with  a  line  between  them ;  thus  \  denotes  the  fraction  one-fourth,  or 
one  part  out  of  four  of  some  whole  quantity,  considered  as  divisible  mto  four  equal  parts.  The  lower  number,  4,  is 
called  the  Jenoniiiiator  o{  ihe  fraction,  showing  into  how  many  parts  the  whole  or  integer  is  divided;  and  the  upper 
number,  l,  is  called  the  numerator,  and  shows  how  many  of  those  equal  parts  are  contained  in  the  fraction.  And 
it  is  evident  that  if  the  numerator  and  denominator  be  varied  in  the  same  ratio,  the  value  of  the  fraction  will  remain 
unaltered;  thus,  if  the  numerator  and  denominator  of  the  fraction,  ^,  be  multiplied  by  2,  3,  or  4,  (Sic,  the  fractions 
arising  will  be  t,  -^,  -^^,  &c.,  which  are  evidently  equal  to  ^. 

A  Decimal  F) action  is  a  fraction  whose  denominator  is  always  a  unit  with  some  number  of  ciphers  annexed, 
and  the  numerator  any  number  whatever,  as,  -j-j,  -rf,^,  Ti'ifiir,  &c.  And  as  the  denominator  of  a  decimal  is  always 
one  of  the  numbers  10,  100,  1000,  (\:c.,  the  inconvenience  of  writing  the  denominator  may  be  avoided  by  placing  a 
point  between  the  integral  and  the  fractional  part  of  the  number;  thus,  -^q  is  wri  ten  .3,  and  xi/u  is  written  .14; 
the  mixed  number  3-1*0%,  consisting  of  a  whole  number  and  a  fractional  one,  is  written  3.14. 

In  setting  down  a  decimal  fraction,  the  numerator  must  consist  of  as  many  places  as  there  are  ciphers  in  the 
denominator ;  and  if  it  has  not  so  many  figures,  the  defect  must  be  supplied  by  placing  ciphers  before  it ;  thus, 
-,ijj|i-  =: .  16,  Ttmo  =  .016,  -nfrfoTT  =  .0016,  &c.  And  as  ciphers  on  the  right  hand  side  of  integers  increase  their  value 
in  a  tenfold  proportion,  as,  2,  20,  200,  &c.,  so,  when  set  on  the  left  hand  of  decimal  fractions,  ihey  decrease  their 
value  in  a  tenfold  proportion,  as,  .2,  .02,  .002,  &c. ;  but  ciphers  set  on  the  right  hand  of  these  fractions  make  no 
alteration  in  their  value,  neither  of  increase  or  decrease;  thus,  .2  is  the  same  as  .20  or  .200.  The  common  arith- 
metical operations  are  performed  the  same  way  in  decimals  as  they  are  in  integers;  regard  being  had  only  to  the 
particular  notation,  to  distinguish  the  integral  from  the  fractional  part  of  a  sum. 

ADDITION  OF  DECIMALS. 

Addition  of  decimals  is  performed  exactly  like  that  of  whole  numbeis,  placing  the  numbers  of  the  same  denom- 
ination under  each  other,  in  which  case  the  decimal  separating  points  will  lange  straight  in  one  column. 

Examples. 

Feet.  Inches. 

1.26  272.3267 

2.31  .0134 

I.  785  2.  1576 

2.0  31.4 


Mil 
26. 

es. 

7 

.32. 

IS 

H3- 

206 

• 

003 

Sum        202.059  7.355  305-8977 

SUBTRACTION  OF  DECIMALS. 

Subtraction  of  decimals  is  performed  in  the  same  manner  as  in  whole  numbers,  by  observing  to  set  the  figures 
of  the  same  denomination  and  the  separating  points  directly  under  each  other. 

Examples. 

From  31.267  36.7s  1-254  1364.2 

Take  2.63  .026  .316  25.163 

Difference         28. 637  36.  724  . 938  I339- 037 

MULTIPLICATION  OF  DECIMALS. 

Multiply  the  numbers  together  the  same  as  if  they  were  whole  numbers,  and  point  off  as  many  decimals  from 
the  right  hand  as  there  are  decimals  in  both  factors  together;  and  when  it  happens  that  there  are  not  so  many 
figures  in  the  product  as  there  must  be  decimals,  then  prefix  as  many  ciphers  to  the  left  hand  as  will  supply  the 
defect. 


Example  I. 
Multiply  3.25  by  4.5. 

3-25 
4-5 


1.625 
[^.00 


Answer        14. 625 


In  one  of  the  factors  is  one  decimal  and  in  the  other 
two;  their  sum,  3,  is  the  number  of  decimals  of  the 
product. 

Example  II. 

Multiply  0.5  by  0.7. 

0-5 
0.7 

Answer  o.  35 


624 


DECIMAL    FKACTIONS. 


Example  IIt. 

Multiply  3.25  by  .05. 

3-25 
.05 


Answer  .  1625 

Example  IV. 
Multiply  .17  by  .06. 


Answer 


.17 
,06 


,  0102 


In  each  of  the  factors  are  two  decimals ;  the  pro- 
duct ought  therefore  to  contain  4 ;  and,  there  being  only 
three  figures  in  the  product,  a  cipher  must  be  prefixed. 


Example  V. 
Multiply  .18  by  24. 

.18 
24 


72 
^,6 


Answer  4. 32 

Example  VI. 

Multiply  36. 1  by  2.5. 

.S6. 1 


2. 

5 

18. 

OS 

72. 

2 

Answer 


90.25 


DIVISION  OF  DECIMALS, 


Division  of  decimals  is  performed  in  the  same  manner  as  in  whole  numbers;  only  observir.g  Ihat  iht  number 
of  decimals  in  the  quotient  must  be  equal  to  the  excess  of  the  number  of  decimals  of  the  dividend  above  those  of 
the  divisor.  When  the  divisor  contains  more  decimals  than  the  dividend,  ciphers  must  be  affixed  to  the  right  hand 
of  the  latter  to  make  the  number  equal  or  exceed  that  of  the  divisor. 


Example  I. 

Divide  14.625  by  3.25. 

3.25)14.625(4.5 
1300 

1625 

1625 

In  this  example  there  are  two  decimals  in  the  divisor 
and  three  in  the  dividend ;  hence,  there  is  one  decimal 
in  the  quotient. 

Example  II. 

Divide  3.  i  by  .0062. 

Previous  to  the  division  affix  a  number  of  ciphers  to 
the  right  hand  of  3.1,  which  does  not  alter  its  value. 

.0062  )  3. 1 00000  C  500.00 
310 


Example  IV. 

Divide  9.6  by  .06. 
.06)9.60 


00000 
Therefore,  the  answer  is  500.00  or  500. 

Example  III. 

Divide  0.35  by  0.7. 

•7)-35(-5 
•35 


160  Answer. 

Here,  by  affixing  a  cipher  to  9.6,  it  becomes  9.60, 
and  has  then  two  decimals  in  it,  which  is  the  same 
number  as  is  in  the  divisor ;  therefore,  the  quotient  is  an 
integral  number. 

Example  V. 
Divide  17.256  by  1.16. 

1. 16)  i7.256oo(  14.875 
116 


464 

1016 
928 


880 
812 


680 
580 

100 


MULTIPLICATION  AND  DIVISION  OF  DECIMALS  BY  CONTRACTION. 

The  operations  of  multiplication  and  division  of  decimal  fractions  may  be  very  much  abbreviated  when  it  is 
required  to  retain  a  certain  order  or  place ;  and  this  will  constantly  occur  in  reducing  the  elements  talcen  from  the 
Nautical  Almanac,  from  Greenwich  noon  to  dales  later  or  earlier. 

Example.  Suppose  it  were  recpiired  to  muUiply  63.4285  by  75.25  to  retain  three  decimal  places  in  the 
product. 


By  ordinary  method 

63.4285 
75-25 


By  contraction. 

63.4285 
52-57 


3171425 
1268570 

3171425 

4439995 

4772.994625 


4439995 

317143 
12686 

3171 
4772.995 


DECIMAL    FRACTIONS. 


625 


RULE^  ••Reverse  the  order  of  the  muhiplier  and  arrange  it  in  such  a  manner  that  the  units  figure  will  he  under 
that  decimal  place  of  the  multiplicand,  which  is  to  be  the  last  place  retained  in  the  product. 

In  multiplying,  begin  with  that  figure  of  the  multiplicand  which  stands  directly  over  the  multiplying  figure 
(the  operation  to  be  performed  in  the  usual  ma.aier  from  right  to  left),  and  in  order  to  secure  correctness  add  to 
each  the  nearest  number  of  tens  that  would  arise  from  multiplying  the  rejected  right-hand  figure  of  the  multipli- 
cand. 

The  result  will  rarely  be  more  than  i  in  error  in  the  last  decimal  place.  In  the  example  given  above  it  is 
required  to  retain  three  places  of  decimals,  hence  5,  the  units  figure  of  the  multiplier,  is  placed  under  8,  the  third 
decimal  place  of  the  multiplicand,  and  the  order  of  the  multiplier  reversed. 

In  multiplying  by  5,  add  3  to  the  product  of  5  and  8,  since  5  times  5,  the  rejected  right-hand  figure,  equal  25, 
and  3  would  be  the  nearest  number  of  tens  if  there  were  still  another  figure  to  the  right  of  5,  the  rejected  figure. 

When  the  multiplicand  has  not  as  many  decimal  figures  as  are  required  in  the  product,  annex  o's  to  supply 
the  deficiency. 

ExAJiPi.E.  Required  to  reduce  the  sun's  hourly  difference  of  declination  =  —  58". 18  for  -j-  "f^  25'"  48%  where 
it  is  essential  to  retain  two  places  of  decimals. 

yh  25'"  48^  =  7''.43 
—       58.18 
+        34-7 


40726 
2327 

175 


—  432".28  =  —  7'  I2".28 

Example.   Suppose  it  were  required  to  divide  4772.994625  by  63.4285  to  retain  two  decimal  places  in  the 
quotient. 

63.4285  )  4772.994625  (  75.25 
44400 


3329 
3171 

126 

32 
32 


Rui.E.  First,  consider  how  many  figures  the  quotient  will  contain.  In  the  example  given  there  will  be  four 
figures  in  the  quotient — two  integral  figures  from  dividing  4772  by  63,  and  the  two  required  decimal  figures. 

Divide,  then,  by  as  many  figures  in  the  left  of  the  divisor  as  there  are  to  be  figures  in  the  quotient ;  and,  instead 
of  afiixing  the  next  figure  of  the  dividend  to  the  remainder  for  a  new  dividend,  reject  another  figure  in  the  divisor. 

In  multiplying  the  divisors  by  the  quotient  figures  it  is  necessary  to  add  the  tens  that  would  arise  from  multi- 
plying the  rejected  figure  on  the  right.  When  the  divisor  has  not  as  many  figures  as  are  required  in  the  quotient 
the  chvision  must  proceed  in  the  ordinary  method  until  the  figures  in  the  divisor  are  one  more  than  those  remain- 
ing to  be  found  in  the  quotient. 

REDUCTION  OF  DECIMALS. 

To  reduce  a  vulgar  fraction  to  a  decimal  add  any  number  of  ciphers  to  the  numerator  and  divide  it  by  the 
denominator ;  the  quotient  will  be  the  decimal  fraction  ;  the  decimal  point  must  be  so  placed  that  there  may  be  as 
many  figures  to  the  right  hand  of  it  as  there  were  added  ciphers  to  the  numerator ;  if  there  are  not  as  many  figures 
in  the  quotient  place  ciphers  to  the  left  hand  to  make  up  the  number. 


Example  I. 
Reduce  i  to  a  decimal. 

S)i-o 


.2  Answer. 


Example  II. 
Reduce  f  to  a  decimal. 

8 )  3.000 


.375  Answer. 


Example  III. 


Reduce  3  inches  to  the  decimal  of  a  foot. 
Since  12  inches  :=  i  foot  this  fraction  is  - 
12  )3.oo 


.25  Answer. 


10  B 


Example  IV. 
Reduce  3^  inches  to  the  decimal  of  a  foot. 


3i  = 


7  - 
2  > 


this 

divided  by  12 
24 )  7.000  ( 
48 

220 
216 

is  -i 
.291 

• 

Answer, 

nearly 

40 
24 

16 

Example 

V. 

is  A^ 


Reduce  i  foot  and  6  inches  to  the  decimal  of  a  yard. 

Here  i  foot  6  inches  =1  18  inches. 

And    I   yard  =  36  inches ;    therefore  this  fraction 

36  )  18.0  ( .5  Answer. 
180 


626 


LOGARITHMS. 


Having  any  decimal  fraction  it  is  easy  to  find  its  value  in  the  lower  denominations  of  the  same  quantity;  thus, 
if  the  fraction  was  the  decimal  of  a  yard,  by  multiplying  it  by  3  gives  its  value  in  feet  and  parts;  multiplying  this 
by  12,  the  product  is  its  value  in  inches  and  parts;  and  in  the  same  manner  the  values  may  be  obtained  in  other 
cases. 


Example  VI. 

Required  tb*;  value  of  3.25  yards. 
3-25 
3 


•75 
12 


Example  VII. 

Required  the  value  of  7.231  days. 

7.231 
24 


924 
462 

9-00  5-544 

Answer,  3  yards,  o  feet,  9  inches.  60 

32.640 
60 

38.400 

Answer,  7  days,  5  hours,  32  minutes,  38  seconds, 
I  and  4  tenths  of  a  second. 

LOGARITHMS. 

In  order  to  abbreviate  the  tedious  operations  of  multiplication  and  division  with  large  numbers,  a  series  of 
numbers,  called  Logarithms,  was  invented  by  Lord  Napier,  baron  of  Marchinston,  in  Scotland,  and  published  in 
Edinburgh  in  1614,  by  means  of  which  the  operation  of  multiplication  may  be  performed  by  addition  and  division 
by  subtraction.  Numbers  may  be  involved  to  any  power  by  simple  multiplication  and  the  root  of  any  power 
extracted  by  simple  division. 

In  Tal)le  42  are  given  the  logarithms  of  all  numl)ers,  from  i  to  9999;  to  each  one  must  be  prefixed  an  index, 
with  a  period  or  dot  to  separate  it  from  the  other  part,  as  in  decimal  fractions  ;  the  numbers  from  i  to  100  are 
published  in  that  table  with  their  indices;  but  from  100  to  9999  the  index  is  left  out  for  the  sake  of  brevity;  but  it 
may  be  supplied  Ijy  this  general  rule,  viz  :  The  index  of  the  logarithm  of  any  integer  or  mixed  ninnhet  is  always 
one  less  than  the  nn^nber  of  integral  places  in  the  natural  number.  Thus,  the  index  of  the  logarithm  of  any  number 
(integral  or  mixed)  between  10  and  100  is  I ;  from  100  to  looo  it  is  2 ;  from  looo  to  loooo  is  3,  &c.;  the  method 
of  finding  the  logarithms  from  this  table  will  be  evident  from  the  following  examples  : 

To  find  the  logarithm  of  any  number  less  than  loO. 

Rule.  Enter  the  first  page  of  the  table,  and  opposite  the  given  number  will  be  found  the  logarithm  with  its 
index  prefixed. 

Thus,  opposite  71  is  1.85 126,  which  is  its  logarithm.  ^ 

Tofitidthe  logarithm  of  any  miniber  between  100  ajid  1000. 

Rule.  Find  the  given  number  in  the  left-hand  column  of  the  table  of  logarithms,  and  immediately  under  o  in 
the  next  column  is  a  number,  to  which  must  be  prefixed  the  number  2  as  an  index  (because  the  number  consists 
of  three  places  of  figures)  and  the  sought  logarithm  will  be  found. 

Thus,  if  the  logarithm  of  149  was  required;  this  number  being  found  in  the  left-hand  column,  against  it,  in 
the  column  marked  o  at  the  top  (or  bottom)  is  found  1 7319,  to  which  prefixing  the  index  2,  we  have  the  logarithm 
of  149  =  2. 1 7319. 

To  find  the  logarithm  of  any  number  between  1000  and  loooo. 

Rule.  Find  the  three  left-liand  figures  of  the  given  number  in  the  left-hand  column  of  the  table  of  logarithms, 
opposite  to  which,  in  the  column  that  is  marked  at  the  top  (or  bottom)  with  the  fourth  figure,  is  to  be  found  the 
sought  logarithm;  to  which  must  be  prefixed  the  index  3,  because  the  number  contains  four  places  of  figures. 

Thus,  if  the  logarithm  of  1495  was  required;  opposite  to  149,  and  in  the  column  marked  5  at  the  top  (or 
bottom)  is  17464,  to  which  prefix  the  index  3,  and  we  have  the  sought  logarithm,  3.17464. 

To  find  the  logarithm  of  any  number  above  1 0000. 

Rule.  Find  the  three  first  figures  of  the  given  number  in  the  left-hand  column  of  the  table,  and  the  fourth 
figure  at  the  top  or  bottom,  and  take  out  the  corresponding  number  as  in  the  preceding  rule ;  take  also  the  differ- 
ence between  this  logarithm  and  the  next  greater,  and  multiply  it  by  the  given  number  exclusive  of  the  four  first 
figures;  cross  off",  at  the  right-hand  of  the  product,  as  many  figures  as  in  the  given  number  to  multiply  by;  then 
add  the  remaining  left-hand  figures  of  this  product  to  the  logarithm  taken  from  the  table,  and  to  the  sum  prefix  an 
index  equal  to  one  less  than  the  number  of  integral  figures  in  the  given  number,  and  the  sought  logarithm  will  be 
found.  To  facilitate  the  calculation  of  these  proportional  parts  several  small  tables  are  placed  in  the  margin,  which 
give  the  correction  corresponding  to  the  difference  D,  and  to  i\\.e  fifth  figure  of  the  proposed  number.  The  use  of 
these  tables  will  be  seen  in  the  following  examples : 

Thus,  if  the  logarithm  of  14957  was  required;  opposite  to  149,  and  under  5,  is  17464,  the  difference  between 
this  and  the  next  greater  number,  17493,  ^^  29,  the  difference  D;  this  multiplied  by  7  (the  last  figure  of  the  given 
numlier)  gives  203;  crossing  off  tlie  right-liand  figure  leaves  20.3  or  20  to  l)e  added  to  17464,  which  makes  174S4; 
to  this,  prefixing  the  index  4,  we  liave  the  sought  logarithm,  4. 174S4.  'I'his  correction,  20,  may  also  be  found  by 
inspection  in  the  small  table  in  the  margin,  marked  at  the  top  with  D  ^  29,  and  opposite  to  the  fifth  figure  of  the 
number,  namely  7,  at  the  side ;   the  corresponding  number  is  the  correction^20. 


LOGARITHMS.  627 

Again,  if  the  logarithm  of  1495738  was  required;  the  logarithm  corresponding  to  149  at  the  left,  and  5  at  the 
top,  is,  as  in  the  last  example,  17464;  the  difierence  between  this  and  the  next  greater  is  29;  multiplying  this  by 
738  (which  is  equal  to  the  given  number,  excluding  the  four  first  figures)  gives  21402  ;  crossing  off  the  three  right- 
liand  figures  of  this  product  (because  tlie  nuudier  738  consists  of  three  figures),  we  have  the  correction  21  to  be 
added  to  17464;  and  the  index  to  be  prefixed  is  6,  Ijecause  the  given  number  consists  of  7  places  of  figures  ;  there- 
fore tlie  sought  logarithm  is  6. 1 7485.  This  correction,  21,  may  be  found  as  above,'  by  means  of  the  marginal  table, 
marked  at  the  top  with  D  =  29,  and  at  the  side  7.38  or  7^  nearly,  to  which  corresponds  21,  as  before. 

To  find  the  logarithm  of  any  mixed  decimal  number. 

Rule.  Find  the  logarithm  of  the  number,  as  if  it  was  an  integer,  by  the  last  rule,  to  which  prefix  the  index 
of  the  integral  part  of  the  given  number. 

Thus,  if  the  logarithm  of  the  mixed  decimal  149.5738  was  required;  find  the  logarithm  of  1495738,  without 
noticing  the  decimal  point ;  this,  in  the  last  example,  was  found  to  be  1 7485  ;  to  this  prefix  the  index  2,  corre- 
sponding to  the  integral  part  149  ;  the  logarithm  sought  will  therefore  be  2.17485. 

To  find  the  logarithm  of  any  decimal  fraction  less  than  Jinity. 

The  index  of  the  logarithm  of  any  number  less  than  unity  is  negative ;  but,  to  avoid  the  mixture  of  positive 
and  negative  quantities,  it  is  common  to  borrow  10  or  100  in  the  index,  which  must  afterwards  be  neglected  in 
summing  them  with  other  indices ;  thus,  instead  of  writing  the  index  —  i,  it  is  usually  written  +9,  or  +99;  but 
in  general  it  is  sufficient  to  borrow  10  in  the  index  ;  a7ui  it  is  ivhat  we  shall  do  in  the  rest  of  this  work.  In  this 
way  we  may  find  the  logarithm  of  any  decimal  fraction  by  the  following  rule : 

Rule.  Rnd  the  logarithm  of  a  fraction  as  if  it  was  a  whole  number;  see  how  many  ciphers  precede  the  first 
figure  of  the  decimal  fraction,  subtract  that  number  from  9,  and  the  remainder  will  be  the  index  of  the  given  fraction. 

Thus  the  logarithm  of  0.0391  is  8.59218;  the  logarithm  of  0.25  is  9.39794;  the  logarithm  of  0.0000025  is 
4-39794,  &c. 

To  find  the  logarithm  of  a  vulgar  fraction. 

Rule.    Subtract  the  logarithm  of  the  denominator  from  the  logarithm  of  the  numerator  (borrowing  10  in  the 
index  when  the  denominator  is  the  greatest);   the  remainder  will  be  the  logarithm  of  the  fraction  sought. 


Example  I. 

Required  the  logarithm  of  \. 
From  log.  of  3 o.  4771 2 


Example  II. 

Required  the  logarithm  of  3J,  or  ^^. 
From  log.  of  13 i.  11394 


Take  log.  of  8 o.  90309      Take  log.  of  4 o.  60206 


Remainder,  log,  of  f  or  .375 9.  57403      Remainder,  log.  of  3^  or  3.25 o.  51 188 

To  find  the  number  corresponding  to  any  logarithm. 

Rule.  In  the  column  marked  o  at  the  top  (and  bottom)  of  the  table  seek  for  the  next  less  logarithm,  neglecting 
the  index;  note  the  number  against  it,  and  carry  the  eye  along  that  line  until  the  nearest  less  logarithm  to  the  given 
one  is  found  and  the  fourth  figure  of  the  required  number  will  be  at  the  top,  which  is  to  be  placed  to  the  right  of 
the  three  other  figures;  if  greater  accuracy  is  desired,  take  the  difference,  D,  between  this  tabular  logarithm  and 
the  next  greater,  also  the  difference,  d,  between  that  least  tabular  logarithm  and  the  given  one ;  to  the  latter  differ- 
ence, d,  annex  two  or  more  ciphers  at  the  right  hand,  and  divide  it  by  the  former  difference,  D,  and  place  the  quo- 
tient* to  the  right  hand  of  the  four  figures  already  found,  and  the  number  sought  will  be  given,  expressed  in  a 
mixed  decimal,  the  integral  part  of  which  will  consist  of  a  number  of  figures  (at  the  left  hand)  equal  to  the  index 
of  the  logarithm  increased  by  unity.t 

Thus,  if  the  number  corresponding  to  the  logarithm  1.52634  was  required,  find  52634  in  the  column  marked 
o  at  the  top  or  bottom,  and  opposite  to  it  is  336;  now,  the  index  being  i,  the  sought  numlDer  must  consist  of  two 
integral  places  ;   therefore  it  is  33.6. 

If  the  given  logarithm  was  2.32838,  we  find  that  32838  stands  in  the  column  marked  o  at  the  top  or  bottom, 
directly  opposite  to  213,  which  is  the  number  sought,  because,  the  index  being  2,  the  number  must  consist  of  three 
places  of  figures. 

If  the  number  corresponding  to  the  logarithm  2.57345  was  required,  look  in  the  column  o,  and  find  in  it, 
against  the  number  374,  the  logarithm  57287;  and,  guiding  the  eye  along  that  line,  find  the  given  logarithm, 
57345,  in  the  column  marked  5 ;  therefore  the  mixed  number  sought  is  3745 ;  and,  since  the  index  is  2,  the  integral 
part  must  consist  of  3  places  ;  therefore  the  number  sought  is  374  5.  If  the  index  be  i,  the  number  will  be  37.45; 
and  if  the  index  be  o,  the  number  will  be  3.745.  If  the  index  be  8,  corresponding  to  a  number  less  than  unity,  the 
answer  will  l)e  0.03745,  &c. 

Again,  if  the  numlier  corresponding  to  the  logaritlun  5.5781 1  was  required,  look  in  the  column  o,  and  find  in 
it,  against  378,  and  under  5,  the  logarithm  57807,  the  difference  between  this  and  the  next  greater  logarithm,  57818, 
being  11,  and  the  difference  between  57807  and  the  given  number,  5781 1,  being  4;  to  this  4  affix  two  ciphers, 
which  make  400,  and  divide  it  by  11 ;  the  cjuotient  is  36  nearly;  this  numlser,  being  connected  with  the  former 
four  figures,  makes  378536,  which  is  the  number  required,  since,  the  index  being  5,  the  number  must  consist  of 
six  places  of  figures. 

*This  quotient  must  consist  of  as  many  places  of  figures  as  there  were  ciphers  annexed,  conformable  to  the  rules  of  the 
division  of  decimals.  Thus,  if  the  divisor  was  40  and  the  number  to  which  two  ciphers  were  annexed  was  2,  making  2.00,  the 
quotient  must  not  be  estimated  as  5,  but  as  05,  and  then  two  hgures  must  be  placed  to  the  right  of  the  four  figures  Ireforc  found. 

t  If  tlic  index  corresponds  to  a  fraction  less  tlian  unity,  place  as  many  ciphers  to  the  left  of  that  number  as  are  ecjual  to  the 
index  subtracted  from  9,  the  decimal  point  being  placed  to  the  left  of  these  ciphers  ;  in  this  manner  the  sought  number  will  be 
founil. 

AVe  may  find  the  fifth  figure  of  the  required  number  by  means  of  the  marginal  tables,  by  enteruig  the  table  corresponding 
at  the  lop  to  the  proposed  value  of  D,  and  in  the  right-hand  column  with  d :  the  corresponding  number  is  the  fifth  figure  of  the 
required  natural  number. 


628 


LOGARITHMS. 


To  show,  at  one  view,  the  indices  corresponding  to  mixed  and  decimal  numbers,  see  the  following  table : 


Logarithms. 


Mixed  number. 

40943.  o Log.  4.  61218 

4094.  3 -. Log.  3.  61 2 18 

409.43 Log.  2.  61 218 

40.  943 I^og.   1 .  6 1 2 1 8 

4.0943 Log.  o.  61218 


Decimal  72umhcr.  Logarithms. 

o.  40943 Log.  9.  61 2 18 

o.  040943 Log.  8.  61 218 

0.0040943 Log.  7.  61218 

o.  00040943 Log.  6.  61 2 18 

o.  000040943 Log.  5.  61218 


MULTIPLICATION   BY  LOGARITHMS. 

Rule.    Add  the  logarithms  of  the  two  numbers  to  be  multiplied,  and  the  sum  will  be  the  logarithm  of  theii 
product. 


Example  I. 

Multiply  25  by  35. 

25 Log.  1.39794 

35 Log.  1.54407 

Product,  875 Log.  2.94201 

Example  II. 

Multiply  22.4  by  1.8. 

22.4 Log.  1.35025 

1.8 Log.  0.25527 

Product,  40.32 Log.  1.60552 


Example  III. 

Multiply  3.26  by  0.0025. 

3.  26 Log.  o.  51322 

0.0025 Log.  7.39794 


Product,  0.00815 Log.  7. 91 1 16 

Example  IV. 
Multiply  0.25  by  0.003. 

0.25 Log.  9.39794 

0.003 ^ Log.  7.47712 


Product,  o.  00075 Log.  6.  87506 


In  the  last  example  the  sum  of  the  two  indices  is  16;  but  since  10  was  borrowed  in  each  number,  we  have 
neglected  10  in  the  sum;  and  the  remainder,  6,  being  less  than  the  other  10,  is  evidently  the  index  of  the  logarithm 
of  a  fraction  less  than  unity. 

DIVISION  BY  LOGARITHMS. 

Rule.  From  the  logarithm  of  the  dividend  subtiact  the  logarithm  of  the  divisor;  the  remainder  will  be  the 
logarithm  of  the  quotient. 


Example  I. 

Divide  875  by  25. 

875 Log.  2.  94201 

25 Log.  1.39794 

Quotient,  35 Log.  1.54407 

Example  II. 

Divide  40.32  by  22.4. 

40. 32 Log.  I.  60552 

22.4..'. Log.  1.35025 

Quotient,  1.8 Log.  0.25527 


Example  III. 
Divide  0.00815  by  0.0025. 

0.00815 Log.  7.  91 1 16 

o.  0025 Log.  7.  39794 

Quotient,  3.  26    Log.  o.  51322 

Example  IV. 
Divide  0.00075  ^Y  0.025. 

o.  00075 Log.  6.  87506 

0.025 Log.  8.39794 

Quotient,  o.  03 Log.  8.  47712 


In  Example  III  both  the  divisor  and  dividend  are  fractions  less  than  unity,  and  the  divisor  is  the  least;  con- 
sequently the  quotient  is  greater  than  unity.  In  Example  IV  both  fractions  are  less  than  unity;  and,  since  the 
divisor  is  the  greatest,  its  logarithm  is  greater  than  that  of  the  dividend;  for  this  reason  it  is  necessary  to  borrow 
10  in  the  index  before  making  the  subtraction;   hence  the  quotient  is  less  than  unity. 


INVOLUTION  BY  LOGARITHMS. 

Rule.  Multiply  the  logarithm  of  the  number  given  by  the  index  of  the  power  to  which  the  quantity  is  to  be 
raised;  the  product  will  be  the  logarithm  of  the  power  sought.  But  in  raising  the  powers  of  any  decimal  fraction 
it  must  be  observed  that  the  first  significant  figure  of  the  power  must  be  put  as  many  places  below  the  place  of 
units  as  the  index  of  its  logarithm  wants  of  10  multiplied  by  the  index  of  the  power. 


Example  I. 

Required  the  square  of  18. 

18 Log.  1.25527 

2 


Answer,  324 Log.  2.  51054 


Example  II. 
Required  the  cube  of  13. 
13 Log.  I.  1 1394 


Answer,  2197 Log.  3.34182 


LOGAEITHMS. 


629 


.*  Example  III. 

Required  the  square  of  6.4. 
6.4 Log.  0.80618 


Example  IV. 

Required  the  cube  of  0.25. 
0.25 Log.    9.39794 


Answer,  40.96. 


Log.  I.  61236      Answer,  o.  015625 Log.  28.  19382 


In  the  last  example  the  index  28  wants  2  of  30  (the  product  of  10  by  the  power  3) ;  therefore  the  first  signifi- 
cant figure  of  the  answer,  viz  :    I,  is  placed  two  figures  distant  from  the  place  of  unity. 

EVOLUTION  BY  LOGARITHMS. 

Rule.  Divide  the  logarithm  of  the  number  by  the  index  of  the  power;  the  quotient  will  be  the  logarithm  of 
the  root  sought.  But  if  the  power  whose  root  is  to  be  extracted  is  a  decimal  fraction  less  than  unity,  prefix  to  the 
index  of  its  logarithm  a  figure  less  by  one  than  the  index  of  the  power,*  and  divide  the  whole  by  the  index  of  the 
power ;  the  quotient  will  be  tlie  logarithm  of  the  root  sought. 


Example  I. 
What  is  the  square  root  of  324? 

324 Log.  2)2.51055 

Answer,    18 Log.       1.25527 

Example  II. 
Required  the  cube  root  of  2197. 

2197 Log.  3)3-34183 

Answer,     13 Log.       1.11394 


Example  III. 

Required  the  square  root  of  40.96. 
40.  96 Log.  2)1.  61236 

Answer,  6.4    Log.       0.80618 

Example  IV. 

Required  the  cube  root  of  0.015625. 

o.  015625 Log.       8.19382 

Prefix  2  to  the  index 3 )  28.  19382 

Answer,  o.  25 Log.       9.  39794 


To  ivork  the  R^ile  of  Three  by  logarithms. 

When  three  numbers  are  given  to  find  a  fourth  proportional,  in  arithmetic,  make  a  statement,  and  say,  As  the 
first  number  is  to  the  second,  so  is  the  third  to  the  fourth  ;  and  by  multiplying  the  second  and  third  together,  and 
dividing  the  product  by  the  first,  we  obtain  the  fourth  number  sought.  To  obtain  the  same  result  by  logarithms 
add  the  logarithms  of  the  second  and  third  numbers  together,  and  from  the  sum  subtract  the  logarithm  of  the  first  num- 
ber; the  remainder  will  be  the  logarithm  of  the  sought  fourth  number. 


cost? 


Example  I. 
If  6  yards  of  cloth  cost  5  dollars,  what  will  20  yards 


As  6 Log.  o.  77815 


Is  to  5 Log  o.  69897 

So  is  20 Log.  I.  30103 

Sum  of  2d  and  3d 2.  00000 

Subtract  the  first o.  77815 

To  16.67 Log.  I.  22185 

The  answer,  therefore,  is  16  dollars  and  -i^q-q,  or  16 
dollars  and  67  cents. 


Example  II. 

If  a  ship  sails  20  miles  in  7  hours,  how  much  will 
she  sail  in  21  hours  at  the  same  rate? 

As  7 Log.  o.  845 10 

Is  to  20 Log.  I.  30103 

So  is  21 Log.  1.32222 

Sum  of  2d  and  3d . .    2.  62325 

Subtract  the  first 0.84510 


To  60 Log.  I.  77815 

The  answer  is  60  miles. 


To  calculate  compound  interest  by  logarithms. 

To  100  dollars  add  its  interest  for  one  year  ;  find  the  logarithm  of  this  sum,  and  reject  2  in  the  index ;  then 
multiply  it  by  the  number  of  years  and  parts  of  a  year  for  which  the  interest  is  to  be  calculated ;  to  the  product 
add  the  logarithm  of  the  sum  put  at  interest ;  the  sum  of  these  two  logarithms  will  be  the  logarithm  of  the  amount 
of  the  given  sum  for  the  given  time. 

Example. 

Required  the  amount  of  the  principal  and  interest  of  355  dollars,  at  6  per  cent,  compound  interest,  for  7  years. 

Adding  6  to  100  gives  106;  whose  logarithm,  rejecting  2  in  the  index,  is 0.02531 

Multiphed  by 7 

Product o.  1 771 7 

Principal,  355  dollars Log.  2.  55023 

Sum  gives  the  logarithm  of  533.83 Log.  2.  72740 

Therefore  the  amount  of  principal  and  interest  is  533  dollars  and  83  cents. 


*  In  this  rule  it  is  supposed  that  10  is  borrowed  in  finding  the  index  to  the  decimaL 


630 


LOGARITHMS. 


To  find  the  logarithm  of  the  sine,  tangent,  or  secant,  corresponding  to  any  mimher  of  degrees  and  minutes,  by  Table  44. 

The  given  number  of  degrees  must  be  found  at  the  bottom  of  the  page  when  between  45°  and  135°,  otherwise 
at  the  top ;  the  minutes  being  found  in  the  column  marked  M,  whicli  stands  on  the  side  of  the  page  on  which  the 
degrees  are  marked ;  thus,  if  the  degrees  arc  less  than  45,  the  /nliiiilcs  are  to  he  found  in  the  /eft-hand  column,  &c., 
and  it  must  he  noted  that  if  the  degrees  are  found  at  the  top,  the  names  of  hour,  sine,  cosine,  tangent,  i.\:c.,  must  also 
he  fo7ind  at  the  top  ;  and  if  the  degrees  are  found  at  the  bottom,  the  names  ^mQ,  cosine,  &c.,  must  also  he  found  at  the 
bottom.  Then  opposite  to  the  number  of  the  minutes  will  be  found  the  log.  sine,  log.  secant,  &c.,  in  the  columns 
marked  sine,  secant,  Sec,  respectively. 


Example  I. 

Required  the  log.  sine  of  28°  37'. 

Find  28°  at  the  top  of  the  page,  directly  below 
whi:h,  in  the  left-hand  column,  find  37';  against  which, 
in  the  column  marked  sine,  is  9.68029,  the  log.  sine  of 
the  given  number  of  degrees  ;  and  in  the  same  manner 
the  tangents,  &c.,  are  found. 


Example  II. 
Required  the  log.  secant  of  126*^ 


20 


Find  126°  at  the  bottom  of  the  page,  directly  above 
which,  in  the  left-hand  column,  find  20' ;  against  which, 
in  the  column  marked  seca/it,  is  10.22732  required. 


To  find  the  logai'ithm  of  the  sine,  cosine,  ^'c,  for  degrees,  minutes,  and  sccoiu/s,  by  Table  a^. 

Find  the  numbers  corresponding  to  the  even  minutes  next  above  and  below  the  given  degrees  and  minutes, 
and  take  their  difference,  D ;  then  say,  As  60"  is  to  the  number  of  seconds  in  the  proposed  number,  so  is  that 
difference,  D,  to  a  correction,  d,  to  be  applied  to  the  number  corresponding  to  the  least  number  of  degrees  and 
minutes  ;  additive  if  it  is  the  least  of  the  two  numbers  taken  from  the  table,  otherwise  subtractive. 


Example  III. 

Required  the  log.  sine  of  24°  16'  38". 

Sine  of  24°  16' Log.  9.  61382 

Sine  of  24°  17' Log.  9.  6141 1 

Difference D  =  29 

Then,  as  60"  :   38"  :  :  29  :  18,  which,  being  added 


Example  IV. 

Required  the  log.  secant  of  105°  20'  16  '. 

Secant  of  105°  20' Log.   10.  57768 

Secant  of  105°  21' Log.   10.  57722 


Difference  D 


46 


to  the  number  corresponding  to  24^ 
the  log.  sine  of  24'^  16'  38". 


16',  gives  9.61400, 


Then,  as  60"  :  16"  :  :  46  :  12,  which,  being  sub- 
tracted from  the  number  corresponding  to  105^  20', 
gives  10.57756,  the  log.  secant  of  105°  20'  16". 


If  the  given  seconds  be  \,  \,  \,  );,  or  \,  or  any  other  even  parts  of  a  minute,  the  like  parts  may  be  taken  of  the 
difference  of  the  logarithms,  and  added  or  subtracted  as  above,  which  may  be  frequently  done  by  inspection. 
These  proportional  parts  may  also  be  found  very  nearly  by  means  of  the  three  columns  of  differences  for  seconds, 
given,  for  the  first  time,  in  the  ninth  edition  of  this  work.  The  first  column  of  differences,  which  is  to  be  used 
with  the  two  columns  marked  A,  A,  is  placed  between  these  columns.  The  second  column  of  differences,  which 
is  to  be  used  with  the  two  columns  B,  B,  is  placed  between  these  two  columns.  In  like  manner  the  third  column 
of  differences,  between  the  columns  C,  C,  is  to  be  used  with  them.  The  correction  of  the  tabular  logarithms  in 
any  of  the  columns  A,  B,  C,  for  any  number  of  seconds,  is  found  by  entering  the  left-hand  column  of  the  table, 
nutrked  S'  at  the  top,  and  finding  the  number  of  seconds  ;  opposite  to  this,  in  the  column  of  differences,  will  be 
found  the  corresponding  correction.  Thus,  in  the  table,  page  215,  which  contains  the  log.  sines,  tangents,  &c.,  for 
30*^,  the  corrections  corresponding  to  25'',  are  9  for  the  columns  A,  A,  12  for  the  columns  B,  B,  3  for  the  columns 
C,  C;  so  that,  if  it  were  required  to  find  the  sine,  tangent,  or  secant  of  30"^  12'  25'',  we  must  add  these  corrections 
respectively  to  the  numbers  corresponding  to  30°  12';  thus — 


Col.  a. 

Logs,  for  30°  12' Sine  9.  70159 

Corrections  for  25"  in  S' .  -f-  9 


Col.  B. 


Tangent 


+ 


9-  76493 
12 

9.  76505 


Col.  C. 


Secant . 


...   10.06335 
+  3 


10.  06338 


Logs    for  30°  12'  25" 9.  70168 

These  corrections  being  all  added,  because  the  logarithms  increase  in  proceeding  from  30°  12'  to  30°  13'.     Instead 
of  taking  out  the  logarithms  for  30^  12',  and  adding  the  correction  for  25",  we  may  take  out  the  logarithms  for 
and  subtract  the  correction  for  60"  —  25",  or  35",  found  in  tlie  margin  S' r   thus, 


30°  13 


Logs  for  30°  13'    - Sine  9.  70180 

Corr.  for  35"  in  col.  S',  or 

25"  in  col.  G' —  13 


Logs,  for  30°  12' 25" 9,70167 


Tangent  9.76522 

—  17 


9.  76505 


Secant 10.06342 

—  4 


10.  06338 


The  corrections  are  in  this  case  subtracted,  because  the  logarithms  decrease  in  proceeding  backward  35"  from 
30°  13',  to  attain  30^  12'  25".  The  tangents  and  secants,  in  this  example,  are  the  same  by  both  methods;  the 
sines  liffer  by  one  unit  in  the  last  decimal  place,  and  this  will  frequently  happen,  because  the  difference  of  the 
logarithms  for  i'  sometimes  differ  one  or  two  units  from  the  mean  values  whicli  are  used  in  the  three  columns  of 
differences.  The  error  arising  from  this  cause  is  generally  diminished  by  using  the  smallest  angle, '  S',  when  the 
seconds  of  the  proposed  angle  are  smaller  than  30",  or  the  greatest  angle,  G',  when  the  number  of  seconds  are 

*  If  we  neglect  the  seconds  in  any  proposed  angle  whose  sine,  &c.,  is  required,  we  get  the  angle  denoted  above  by  S',  and 
this  angle,  increased  by  i',  is  represented  by  G' ;  so  tliat  tlie  proposed  angle  falls  between  S'  and  G',  S'  being  a  snialler  and  G' 
^.  greater  angle  than  that  whose  log.  snie,  &c.,  is  requued  ;  the  letters  S'  and  G',  accented  for  minutes,  being  used  because  they 
are  easily  remembered  as  the  initials  of  smaller  2i\v\  t^reater. 


LOGARITHMS.  631 

create?-  thah  30''.  Thus,  in  the  above  example,  where  the  angle  S'  =  30°  12',  and  the  angle  G'  =  3o°  13',  it  is 
best  to  use  the  angle  S'  when  the  given  angle  is  less  than  30^'  12'  30",  but  the  angle  G'  when  it  exceeds  30"  12'  30". 
Thus,  if  it  be  required  to  tind  the  sine  of  30  12'  51",  it  is  best  to  use  the  angle  G'  =30"  13',  and  find  the  correc- 
tion by  entering  the  margin  marked  S'  with  the  difference  60"  —  51'  =  9",  opposite  to  which,  in  the  column  of 
differences,  is  3,  to  be  subtracted  from  log.  sine  30^  13'  =9.70180,  to  gel  the  log.  sine  of  30"^'  12'  51"  =9.70177. 
To  save  the  trouble  of  subtracting  the  seconds  from  60",  we  may  use  the  right-hand  margin,  marked  G',  and  the 
correction  may  then  be  found  by  the  following  rules : 

Rui.K  I.  When  the  snia/Irst  angle  S'  is  used,  ////(/  t/w  sfconJs  in  the  coliiiini  S'  and  take  out  the  corresponding 
correction,  which  is  to  be  applied  to  the  logarithm  corresponding  to  S' ;  by  adding,  if  the  log.  of  G'  be  greater  than 
ihe  log.  of  S' ;  otherwise,  by  subtracting. 

Rule  2.  When  the  greater  angle  G'  is  used,  find  the  seeoitds  in  the  column  G'  and  take  out  the  corresponding 
correction,  which  is  to  be  applied  to  the  logarithm  corresponding  to  G' ;  by  adding,  if  the  log.  of  S'  be  greater 
than  the  log  of  G' ;  otherwise,  by  subtracting;  so  that,  in  all  cases,  the  required  logarithm  may  fall  between  the 
two  logarithms  corresponding  to  the  angles  S'  and  G'. 

The  correctness  of  these  rules  will  evidently  appear  by  comparing  them  with  the  preceding  examples ;  and  by 
the  inverse  process  we  may  find  the  angle  corresponding  to  a  given  logaritlim,  as  in  the  next  article. 

We  have  given  at  the  l:)Ottom  of  the  page,  in  this  table,  a  small  table  for  finding  the  proportional  parts  for  the 
odd  seconds  of  time,  corresponding  to  the  column  of  Hours  A.  M.  or  P.  M.,  to  facilitate  the  process  of  finding  the 
log.  sine,  cosine,  &c.,  corresponding  to  the  nearest  second  of  time  in  the  column  of  hours,  or,  on  the  contrary,  to 
find  the  nearest  second  of  time  corresponding  to  any  given  log.  sine,  cosine,  &c.  Thus,  in  the  preceding  exam- 
ples, where  the  angle  S'  ^30"^  12'  and  the  angle  G'  =  30"^  13',  the  times  corresponding  in  the  column  of  Hours 
P.  M.  are  S'  =4'^  1"'  36^,  G'  ^4''  i'"  44^;  and  if  we  wish  to  find  the  log.  sine,  cosine,  &c.,  corresponding  t  >  any 
intermediate  time,  as,  for  example,  4^^  l"'  39^*,  which  differs  3^^  from  the  angle  S',  we  must  find  the  tabular  logarithm 
corresponding  to  S'  and  apply  the  correction  for  3%  given  by  the  table  at  the  bottom  of  the  page,  as  in  the  follow- 
ing examples : 


Logs,  for  S' =4''  I'll  36^      Sine 9.70159 

Correction  for -|-  3^  +  ^ 


B.  C. 

Tangent 9.  76493   Secant 10.  06335 

+     II  1        +      3 


Logs,  for 4'!  I™  39S      Sine 9.70167     Tangent 9.76504     Secant 10.06338 

Nearly  the  same  results  are  obtained  by  using  the  angle  G'  in  the  manner  we  have  before  explained : 


Logs,  for  G' =4*^  i"'  44s  |  Sine 9.  70180     Tangent 9.  76522 

Correction  for —  5^ 


Logs,  for 4'|  I '"  39S 


13 


18 


Tangent  9. 76504 


Secant 10.06342 


Secant 10.06337 


Sine , ..   9.  70167 

These  corrections  must  be  applied  by  addition  or  subtraction,  according  to  the  directions  given  above,  so  as 
to  make  the  required  logarithm  fall  between  those  which  correspond  to  the  times  S'  and  G  . 

The  inverse  process  will  give  the  time  corresponding  to  any  logarithm.  Thus,  if  the  log.  sine  9. 70167  be 
given,  the  difference  between  this  and  9.70159,  corresponding  to  S'=4"  i'"  36",  is  8;  seeking  this  in  the  column 
A,  in  the  second  line  of  the  table  at  the  bottom  of  the  page,  it  is  found  to  correspond  to  3^;  adding  this  to  the  time 
S'  =4*^  I'"  36^,  we  get  4"  i"i  39"  foi  the  required  time.  We  may  proceed  in  the  same  manner  with  the  logarithms 
in  the  columns  B,  C,  using  the  numbers  corresponding,  marked  B,  C,  respectively,  in  the  table  at  the  bottom  of 
the  page. 

To  find  the  degrees,  minntes,  and  seconds  corresponding  to  any  given  logarithm  sine,  cosine,  drc. ,  by  Table  44. 

Find  the  two  nearest  numbers  to  the  given  log.  sine,  cosine>  &c.,  in  the  column  marked  Sine,  Cosine,  &.C., 
respectively,  one  being  greater  and  the  other  less,  and  take  their  difference,  D;  take  also  the  difference,  d,  between 
the  given  logarithm  and  t.  e  logarithm  corresponding  to  the  smallest  number  of  degrees  and  minutes;  then  say, 
As  the  first  found  difference  is  to  the  second  found  difference  so  is  60"  to  a  number  of  seconds  to  be  annexed  to 
the  smallest  number  of  degrees  and  minutes  before  found.  The  three  columns  of  differences  may  also  be  used  by 
an  inverse  operation  to  that  which  we  have  explained  in  the  preceding  article. 

E.XAMPLE   V. 

Find  the  degrees,  minutes,  and  seconds  (less  than  90°)  corresponding  to  the  log.  sine  9.61400. 

Next  less  log.  S'  =  24^  16' 9.61382      Log.  of  smallest  angle  S' =  24^  16'  is 9.61382 

Greater G'  =  24    17 9.  61411  ;  Given  log 9-  61400 

D  =  29  !  (/=  18 

Then  say,  As  29:  18:  :  6o''  :  38'',  nearly;  which,  annexed  to  24^^  16',  give  24°  16'  38",  answering  to  the  log.  sine 
9.61400.  Subtracting  24  '  16'  38"  from  180",  there  remain  155^^  43'  22  ',  the  log.  sine  of  which  is  also  9.61400.  The 
quantity  38"  may  also  be  found  by  inspection  in  the  side  column  S'  of  the  page  opposite  d=  18,  in  the  column  of 
differences  between  the  two  columns,  A,  A.  If  we  use  the  angle  G',  we  shall  have  d'  equal  to  11,  the  difference 
of  the  logarithms  9.61411  and  9.61400,  and  the  corresponding  number  of  seconds  in  column  C  is  37",  makmg 
24^  16'  37". 

To  find  the  arithmetical  complement  of  any  logarithm. 

The  arithmetical  complement  of  any  logaritlnn  is  what  it  wants  of  10.00000,  and  is  used  to  avoid  subtraction. 
For,  when  working  any  proportion  by  logarithms,  the  arithmetical  complement  of  the  logarithm  of  the  first  term 
may  be  added,  instead  of  subtracting  the  logarithm  itself,  observing  to  neglect  10  in  the  index  of  the  sum  of  the 
logarithms.  The  arithmetical  complement  of  any  logarithm  is  thus  found :  Begin  at  the  index  and  'iOrtte  dmon 
what  each  figure  7i<ants  of  9,  except  the  last  sii;/ii/icant  figure,  lohich  take  from  lo.»  Thus,  the  arithmetical  comple- 
ment of  9.62595  is  037405,  that  of  1.86567  is  8. 13433,  and  ihat  of  10.33133  is  89.66867,  or  9.66867. 

*  When  the  index  of  the  given  logarithm  is  greater  than  10,  as  in  some  of  the  numbers  of  Table  44,  the  left-hand  figure  of 
it  must  be  neglected  ;  and  when  there  are  any  ciphers  to  the  right  hand  of  the  last  significant  figure,  place  the  same  nmnber  of 
ciphers  to  the'right  hand  of  the  other  tigures  of  tlie  arithmetical  complement. 


632 


GEOMETRY. 


GEOMETRY. 

Geometry  is  the  science  which  treats  of  the  description,  properties,  and  relations  of  magnitudes  in  general, 
of  which  there  are  three  kinds  or  species,  viz:  a  line,  which  has  only  length  without  either  breadth  or  thickness; 
a  superficies,  comprehended  by  length  and  breadth;  and  a  solid,  which  lias  length,  lireadlh,  and  thickness. 

K  point,  considered  mathematically,  has  neither  length,  breadth,  nor  thickness. 

A  line  has  length  without  breadth  or  thickness. 

A  surface  has  length  and  breadth. 

A  solid  has  length,  breadth,  and  thickness. 

A  straight  or  right  line  is  the  shortest  distance  between  two  points  on  a  plane  surface. 

K  plane  surface  is  that  in  which  any  two  points  being  taken,  the  straight  line  between  them  lies  wholly  in  that 

surface. 

Parallel  lines  are  such  as  are  in  the  same  plane,  and  if  extended  infinitely  never  meet. 

A  sphere  is  a  solid  bounded  by  a  surface  every  point  of  which  is  equally  distant  from  a  fixed  point  which  is 
called  the  centre  of  the  sphere.  The  straight  line  which  joins  any  point  of  the  surface  witli  the 
centre  is  called  a  radius.  A  straight  line  drawn  through  the  centre  and  terminated  both  ways  by 
the  surface  is  called  a  diameter. 

The  section  rf  the  surface  of  a  sphere  made  by  any  plane  is  called  a  circle.  The  boundary  of 
the  circle  is  called  the  circumference. 

The  radius  of  a  circle,  or  semi-diameter,  is  a  right  line  drawn  from  the  centre  to  the  circum- 
ference, as  AC;  or  it  is  that  line  which  is  taken  between  the  points  of  the  compasses  to  describe 
the  circle. 

A  diameter  of  a  circle  is  a  right  line  drawn  through  the  centre  and  terminated  at  both  ends  by  the  circumfer- 
ence, as  ACB,  and  is  the  double  of  the  tadius,  AC.  A  diameter  divides  the  circle  and  its  circumference  into  two 
equal  parts. 

An  arc  of  a  circle  is  any  part  or  portion  of  the  circumference,  as  DFE.  _    » 

The  chord  of  an  arc  is  a  straight  line  joining  the  ends  of  the  arc ;  it  divides  the  circle  into  two  unequal  parts, 
called  segments,  and  is  a  chord  to  them  both,  as  DE  is  the  chord  of  the  arcs  DFE  and  DGE. 

A  semicircle,  or  half  circle,  is  a  figure  contained  between  a  diameter  and  the  arc  terminated  by  that  diameter, 
as  AGB  or  AFB.     Any  part  of  a  circle  contained  between  two  radii  and  an  arc  is  called  a  sector. 
A  quadrant  i?<  half  a  semicircle,  or  one- fourth  part  of  a  whole  circle,  as  the  figure  CAG. 

Ahde.  All  circles,  whether  great  or  small,  are  supposed  to  have  their  circumference  divided  into  360  equal 
parts,  called  degrees ;  and  each  degree  into  60  equal  parts,  called  minutes ;  and  each  minute  into  60  equal  parts, 
called  seconds ;  and  so  on  into  thirds,  fourths,  &c.;  and  an  arc  is  said  to  be  of  as  many  degrees  as  it  contains  parts 
of  the  360  into  which  the  circumference  is  divided. 

The  sine  of  an  arc  is  a  line  drawn  from  one  end  of  the  arc  perpendicular  to  a  diameter  drawn  througli  the 
other  end  of  the  same  arc;  thus,  RS  is  the  sine  of  the  arc  AS,  RS  being  a  line  drawn  from  one  end,  S,  of  that 
arc,  perpendicular  to  DA,  which  is  the  diameter  passing  through  the  other  end.  A,  of  the  arc. 

The  cosine  of  an  arc  is  the  sine  of  the  complement  of  that  arc,  or  of  what  that  arc 
wants  of  a  quadrant;  thus,  AH  being  a  quadrant,  the  arc  SH  is  the  complement  of  the 
arc  AS;    SZ  is  the  sine  of  the  arc  SIl,  or  the  cosine  of  the  arc  AS. 

The  7'ersed  sine  of  an  arc  is  that  part  of  the  diameter  contained  between  the  sine  and 

the  arc  ;  thus,  RA  is  the  versed  sine  of  the  arc  AS,  and  DCR  is  the  versed  sine' of  the 

arc  DHS. 

_  The  tangent  of  an  arc  is  a  right  Hue  drawn  perpendicular  to  the  diameter,  passing 

§    through  one  end  of  the  arc,  and  terminated  by  a  line  drawn  from  the  centre  through  the 

^   oiher  end  of  the  arc;   thus,  AT  is  the  tangent  of  the  arc  AS. 

The  cotangent  of  an  arc  is  the  tangent  of  the  complement  of  that  arc  to  a  quadrant; 
thus,  IIG  is  the  tangent  of  the  arc  IIS,  or  the  cotangent  of  the  arc  AS. 

The  secant  of  an  arc  is  a  right  line  drawn  from  the  centre  through  one  end  of  the 
arc  to  meet  the  tangent  drawn  from  the  other  end ;  thus,  CT  is  the  secant  of  the  arc  AS. 
The  cosecant  oi  an  arc  is  the  secant  of  the  complement  of  that  arc  to  a  quadrant; 
thus,  CG  is  the  secant  of  the  arc  SFI,  or  cosecant  of  the  arc  AS. 

What  an  arc  wants  of  a  semicircle  is  called  the  supplement  of  the  arc ;  thus,  the  arc 
DHS  is  the  supplement  of  the  arc  AS.     The  sine,  tangent,  or  secant  of  an  arc  is  the 
same  as  the  sine,  tangent,  or  secant  of  its  supplement;  thus,  the  sine  of  80'^  =  sine  of 
100°,  and  the  sine  of  70°  ==  sine  of  1 10",  &c. 
An  angle  is  the  inclination  of  two  lines  which  meet,  and  is  measured  by  the  arc  of  the  circle  comprehended 
between  the  two  legs  that  form  the  angle,  the  centre  of  the  circle  being  the  angular  point. 
A  right  angle  is  one  that  is  equal  to  a  quadrant,  or  90°. 
An  acute  angle  is  less  than  a  right  angle. 
An  obtuse  angle  is  greater  than  a  right  angle. 
A  plane  triangle  is  a  figure  contained  by  three  straight  lines. 

When  the  tliree  sides  are  equal,  the  triangle  is  called  equilateral;  when  two  of  them  are 
equal,  it  is  called  isosceles. 

When  one  of  the  angles  is  90°,  the  triangle  is  said  to  be  right-angled ;_  when  each  angle  is 
less  than  90°,  it  is  said  to  be  acute-angled ;  when  one  is  greater  than  90*^,  it  is  said  to  be  obtuse- 
angled. 

Triangles  that  are  not  right-angled  are  generally  called  oblique-angled. 

In  a  right-angled  triangle,  as  ABC,  the  side  BC  opposite  the  right  angle  is  called  the  hypote- 
nuse;  one  of  the  other  sides,  as  AC,  is  called  iht  perpendicular ;  the  third  side,  AB,  is  called  the  base. 

A  quadrilateral  ^gma  is  one  bounded  by  four  sides,  as  ACDB.  If  the  opposite  sides  are  parallel,  they  are 
caWeA  parallelograms.  Thus,  if  AC  be  parallel  to  BD,  and  AB  parallel  to  CD,  the  figure  ACDB 
is  a  parallelogram.  A  parallelogram  having  all  its  sides  equal,  and  its  angles  right,  is  called  a 
square,  as  B.  When  the  angles  are  right,  and  the  opposite  sides  only  equal,  it  is  called  a  rec- 
tangle, as  A. 

Every  section  of  a  sphere  by  a  p'ane  is  a  circle. 

K great  circle  of  a  sphere  is  a  section  of  the  surface  by  a  plane  whicli  passes  through  its 
centre. 


A 


GEOMETRY. 


633 


A  sntaN  circle  of  a  sphere  is  a  section  of  the  surface  by  a  plane  which  does  not  pass  through  its  centre. 

All  great  circles  of  a  sphere  have  the  same  radius.     All  great  circles  bisect  each  other. 

The  extremities  of  that  diameter  of  the  sphere  which  is  perpendicular  to  the  plane  of  a  circle  are  called  the 
poh's  of  that  circle.  In  the  case  of  a  small  circle  the  jioles  are  named  the  adjacent  pole  and  the  remote  pole.  All 
circles  of  a  j])here  that  aie  parallel  have  the  same  poles.  All  points  in  the  circumference  of  a  circle  are  e<pii-dis- 
taiit  from  the  ))olcs.     In  the  case  of  a  great  circle,  the  poles  are  90"  distant  from  every  point  of  the  circle. 

.'\ssummg  any  great  circle  as  a. />rlmtrry,^\\  great  circles  which  pass  through  its  poles  are  called  its  secondaries. 
All  seconilarie-  cut  the  primary  at  right  angles. 

A  great  circle  may  be  drawn  through  any  two  points  on  the  surface  of  a  sphere. 

The  shortest  distance  between  any  two  points  measured  on  the  surface  of  a  sphere  is  the  arc  of  the  great  circle 
joining  them. 

THEOREMS  OF  GEOMETRY. 


If  pve  Hue,  KE,  fall  any  7vay  upon  another,  CD,  the  sum  of  the  tivo  angles,  ABD,  ABC,  is  always  equal  to  two 


right  angles. 

For,  on  the  point  B  as  a  centre,  describe  the  circular  arc  CAD,  cutting  the  line  CD  in  C  and  D 
is  equal  to  a  semicircle,  but  it  is  also  equal  to  the   sum  of  the  arcs  CA  and  AD,  the  measures 
of  the  two  angles  A1!C,  ABD;   therefore  the  sum  of  the  two  angles  is  ecpuil  to  a  semicircle,  or 
two  right  angles.     Hence,  it  is  evident  that  all  the  angles  which  can  lie  made  from  a  point  in  any 
line,  towards  one  side  of  the  line,  are  equal  to  two  right  angles,  and  that  all  the  angles  which  can     ^ 
be  made  about  a  point  are  equal  to  four  right  angles. 


then  this  arc 


B 


II. 


Jf  a  line,  AC,  cross  another, 
BEA  =  CED,  and  BEC  =  AED. 


BD,   /;/  the  point  E,   the  opposite  angles  will  be  equal,   viz : 


Upon  the  point  E  as  a  centre,  describe  the  circle  ABCD;  then  it  is  evident  that  ABC  is 
a  semicircle,  as  also  BCD;  therefore  the  arc  ABC  ^  arc  BCD;  taking  from  both  the  common 
arc  BC,  there  remains  arc  AB  =  arc  CD;  that  is,  the  angle  BEA  is  equal  to  the  angle  CED. 
After  the  same  manner  we  may  prove  that  the  angle  BEC  is  equal  to  the  angle  AED. 


III. 

If  a  line,  OH,  cross  two  parallel  lines,  AB,  CD,  //  makes  the  external  opposite  angles  equal  to  each  other,  viz : 
GEB  =  CFH,  and  KEG  =  HFD. 

For,  since  AB  and  CD  are  parallel  to  each  other,  they  may  be  considered  as  one  broad  line, 
and  GH  crossing  it;  then  the  vertical  or  opposite  angles,  GEB,  CFH,  are  equal,  as  also 
AEG  =  HFD. 

IV. 

If  a  line,  GH,  cross  two  parallel  lines,  AB,  CD  (see  the  figure),  the  alternate  angles,  AEF  ^ 
and  EFD,  or  CFE  and  FEB,  are  equal.  /jt 

For  GEB  =  AEF,  as  also  CFH  =  EFD,  but  GEB  =  CFH  by  the  last ;  therefore  AEF  is  equal  to  EFD; 
in  the  same  way  may  we  prove  FEB  =:  CFE. 

V. 

If  a  line,  GH,  cross  hvo  parallel  lines,  AB,  CD  (see  the  preceding  figure),  the  external  angle,  GEB,  is  equal  to 
the  internal  opposite  one,  EFD,  or  AEG  equal  to  CFE. 

For  the  angle  AEF  is  equal  to  the  angle  EFD  by  the  last,  and  AEF  =  GEB ;  therefore  GEB  =  EFD ;  in 
the  same  way  we  may  prove  AEG  ^  CFE. 

VI. 

If  a  line,  GH,  cross  tivo  parallel  lines,  AB,  CD  (see  the  preceding  figure),  the  sum  of  the  two  internal  angles, 
BEF  and  DFE,  or  AEF"  and  CFE,  is  equal  to  two  right  angles. 

For  since  the  angle  GEB  is  equal  to  the  angle  EFD,  to  both  add  the  angle  BEF,  and  we  have  GEB  +  BEP" 
=  BEF  4-  EFD ;  but  GEB  +  BEF  =  two  right  angles.  Hence,  BEF  -f-  EF'D  =  two  right  angles  ;  and  in  the 
same  manner  we  may  prove  AEF  -j-  CFE  =  two  right  angles. 

VII. 

In  any  triangle,  ABC,  one  of  its  legs,  as  BC,  being  produced  taivards  D,  the  external  angle,  ACD,  is  equal  to  the 
sum  of  the  internal  and  opposite  angles,  ABC,  BAC. 

To  prove  this,  through  C  draw  CP^  parallel  to  AB  ;  then,  since  CE  is  parallel  to  AB, 
and  the  lines  AC,  BD  cross  them,  the  angle  ECD  =  ABC  and  ACE  =  BAC ;  adding  these 
together  we  have  ECD  +  ACE  =  ABC  -f  BAC;  but  ECD  +  ACE  =  ACD;  therefore 
ACD  =  ABC  +  BAC.  S 


634 


GEOMETRY. 


VIII. 

Hence  it  may  be  proved  that  if  any  tivo  lines,  AB  a>id  CD,  he  crossed  by  a  third  line,  EF,  and  the  alternate  angles, 
AEF  ami  EFD,  he  equal,  the  lines  AB  and  CD  will  be  parallel. 

For,  if  they  are  not  parallel,  they  must  meet  each  other  on  one  side  of  the  line  EF  (suppose 
at  G),  and  so  form  the  triangle  EGF,  one  of  whose  sides,  GE,  being  produced  to  A,  the  exterior 
angle,  AEF.  must  (by  the  preceding  article)  be  equal  to  the  sum  of  the  two  angles  EFG  and 
EGF ;  but  by  supposition  it  is  equal  to  the  angle  EFG  alone  ;  therefore  the  angle  AEF  must  be 
equal  to  the  sum  of  the  two  angles  EFG  and  EGF,  and  at  the  same  time  equal  to  EFG  alone, 
which  is  absurd ;  therefore  the  lines  AB,  CD,  cannot  meet,  and  must  be  parallel. 

IX. 


c   Is  u 


In  any  right-lined  triangle,  ABC,  the  sinn  of  the  three  angles  is  equal  to  two  right  angles. 

To  prove  this,  produce  BC  (in  the  fig.  Theorem  VII)  toward  D;  then  (by  VII)  the  external  angle  ACD  = 
ABC  +  BAC ;  to  both  add  the  angle  ACB,  and  we  have  ACD  +  ACB  =  ABC  +  BAC  +  ACH ;  but  ACD  +  ACB 
:=  two  right  angles  (by  I),  Hence,  ABC  -\-  BAC  +  ACB  =  two  right  angles;  therefore  the  sum  of  the  three 
angles  of  any  plain  triangle,  ACB,  is  equal  to  two  right  angles. 

X. 

Hence,  in  atty  plain  triangle,  if  one  of  its  angles  be  known,  the  sum  of  the  other  two  will  be  also  known. 

> 

For  by  the  last  article  the  sum  of  all  three  angles  is  equal  to  two  right  angles,  or  i8o°;  hence,  by  subtracting 
the  given  angle  from  iSo^,  the  remainder  will  be  the  sum  of  the  other  two. 

In  any  right-angled  triangle,  the  tioo  acute  angles  taken  together  are  just  equal  to  a  right  angle ;  for,  all  three 
angles  being  equal  to  two  right  angles,  and  one  angle  being  right  by  supposition,  the  sum  of  the  other  two  must 
be  equal  to  a  right  angle ;  consequently,  any  one  of  the  acute  angles  being  given,  the  other  one  may  be  found  by 
subtracting  the  given  one  from  90"^. 

XI. 

If  in  any  two  triangles,  ABC,  DEF,  tivo  legs  of  the  one,  AB,  AC,  be  equal  to  two  legs  of  the  other,  DE,  DF, 
each  to  each  respectively,  that  is,  AB  =  DE,  and  AC  =  DF,  and  the  angles  BAC,  EDF,  included  between  the  equal 
legs  he  equal ;  then  the  wmaining  leg  of  the  one  ivill  be  equal  to  the  remaining  leg  of  the  other,  and  the  angles  opposite 
to  the  eqiuil  legs  will  be  equal ;  that  is,  BC  =  EF,  ABC  =  DEF,  and  ACB  =  DFE. 

For  if  the  triangle  ABC  be  supposed  to  be  lifted  up  and  put  upon  the  triangle  DEF,  with  the  point  A  on  the 
point  D  and  the  line  AB  upon  DE,  it  is  plain,  since  AB  ^  DE,  that  the  point  B  will  fall 
upon  E  ;  and  since  the  angles  BAC,  EDF,  are  equal,  the  line  AC  will  fall  upon  DF;  and 
these  lines  being  of  equal  length,  the  point  C  will  fall  upon  F;  consequently,  the  line 
BC  M  ill  fall  exactly  upon  the  line  EF,  and  the  triangle  ABC  will  in  all  respects  be  exactly 
equal  to  the  triangle  DEF,  and  the  angle  ABC  will  be  equal  to  the  angle  DEF,  also  the 


angle  ACB  will  be  equal  to  the  angle  DFE 


XII. 


After  the  same  manner  it  may  be  proved  that  if  in  any  two  triangles,  ABC,  DEF  (see  the  preceding  figure),  tzvo 
angles,  ABC  a>ul  ACB,  of  the  one  be  equal  to  tivo  angles,  DEF,  DFE,  of  the  other,  and  the  included  side,  BC,  be 
equal  to  EF,  the  remaining  sides  ajid  included  angles  will  also  be  equal  to  each  other  respectively ;  that  is,  AB  =  DE, 
AC  =  DF,  and  the  angle  BAC  =  the  angle  EDF. 

For  if  the  triangle  ABC  be  supposed  to  be  lifted  up  and  laid  upon  the  triangle  DEF,  the  point  B  being  upon 
the  point  E  and  the  line  BC  upon  the  line  EF,  then,  since  BC  =  EF,  the  point  C  will  fall  upon  the  point  F;  and, 
as  the  angle  ACB  =:  the  angle  DFE,  the  line  CA  will  fall  upon  the  line  FD ;  by  the  same  way  of  reasoning,  the 
line  BA  will  fall  upon  the  hne  ED;  therefore  the  point  of  intersection.  A,  of  the  two  lines,  BA,  CA,  will  fall  upon 
D,  the  point  of  intersection  of  the  lines  ED,  FD;  consequently,  AB  =  DE,  AC  =:  DF,  and  the  angle  BAC  =  the 
angle  EDF. 

XIII. 

If  tivo  sides  of  a  triangle  are  equal,  the  angles  opposite  these  sides  will  also  be  equal ;  that  is,  if  AB  =:  AC,  the 
angles  ABC,  ACB,  will  also  he  eqiuil. 

For  draw  the  line  AD,  bisecting  the  angle  BAC  and  meeting  the  line  BC  in  D,  dividing  the 
triangle  BAC  into  two  triangles,  ABD,  ACD,  in  which  the  side  AB  ^  AC,  the  si  e  AD  is  com- 
mon to  both  triangles,  and  the  angle  BAD  ^  the  angle  DAC;  consequently  (by  XI),  the  angle 
ABD  must  be  equal  to  the  angle  ACD. 

The  converse  of  this  proposition  is  also  true  ;  that  is,  if  ttuo  angles  of  a  triangle  are  equal,  the 
opposite-  sides  are  also  equal.     This  is  demonstrated  nearly  in  the  same  manner  by  means  of  XII. 

XIV. 

Any  angle  at  the  circumference  of  a  circle  is  equal  to  half  the  angle  at  the  centre,  standing  upon  the  same  arc. 

Thus,  the  angle  BAD  is  half  the  angle  BCD,  standing  upon  the  same  arc,  BD,  of  the  circle 
BEDA  whose  centre  is  C.  To  demonstrate  this,  draw  through  A  and  the  centre  C  the  right  line 
ACE;  then  (by  VII)  the  angle  CAD  +  angle  CDA  =  angle  ECD ;  but  AC  =  CD  (being  two  radii 
of  the  same  circle);  therefore  (by  XIIl),  the  angle  CAD  =  the  angle  CDA,  and  the  sum  of  these 
two  angles  is  the  double  of  either  of  them;  that  is,  CAD  -}-  CDA  =  twice  CAD  ;  therefore,  ECD 
^=  twice  CAD.  In  the  same  manner  it  may  be  proved  that  BCE  =  twice  BAC,  and  by  adding  these 
together  we  have  ECD  -f  BCE  =  twice  CAD  -f  twice  BAC;  that  is,  BCD  =  twice  BAD,  or  BAD 
equal  to  half  of  BCD.     'I'lie  demonstration  is  similar  when  B,  D,  fall  on  the  same  side  of  E. 


GEOMETRY. 


635 


H 


XV. 

An  angle  at  the  circumference  is  measured  by  half  the  are  it  subtends. 

For  an  angle  at  the  centre,  standing  on  the  same  arc,  is  measured  by  the  whole  arc;  but 
since  an  angle  at  the  centre  is  doulile  that  at  the  circumference  (XIX),  it  is  eviclent  that  an  angle  at 
the  circumference  must  be  measured  liy  half  tlie  arc  it  stands  upon.  Hence,  all  angles,  ACB, 
ADB,  AEB,  &c.,  at  the  circumference  of  a  circle  standing  on  the  same  chord,  AB,  are  equal  to  each 
other;  for  they  are  all  measured  by  the  same  arc,  viz :   half  the  arc  AB. 

XVI. 

An  angle  in  a  segment  greater  than  a  semicircle  is  less  than  a  right  angle. 

Thus,  if  ABC  be  a  segment  greater  than  a  semicircle,  the  arc,  AC,  on  which  it  stands 
must  be  less  than  a  semicircle,  and  the  half  of  it  less  than  a  quadrant  or  a  right  angle;  but  the 
angle  ABC  in  the  segment  is  measured  by  the  half  of  the  arc  AC ;  therefore  it  is  less  than  a 
right  angle. 

An  angle  in  a  semicircle  is  a  right  angle. 

For  since  DEF  is  a  semicircle,  the  arc  DKF  must  also  be  a  semicircle ;  but  the  angle  DEF  j^l 
is  measured  by  half  the  arc  DKF,  that  is,  by  half  a  semicircle  or  by  a  quadrant ;  therefore  the 
angle  DEF  is  a  right  one. 

An  angle  in  a  segment  less  than  a  semicircle  is  greater  than  a  right  angle. 

Thus,  if  GHI  be  a  segment  less  than  a  semicircle,  the  arc  GKI  on  which  it  stands  must  be 
greater  than  a  semicircle,  and  its  half  greater  than  a  quadrant  or  right  angle;  therefore  the  angle 
GHI,  which  is  measured  by  half  the  arc  GKI,  is  greater  than  a  right  angle. 

XVII. 

If  from  the  centre,  C,  of  the  circle  ABE  there  be  let  fall  the  perpendicular  CD  on  the  chord 
AB,  it  will  bisect  the  chord  in  the  point  D. 

Draw  the  radii  CA,  CB;  then  (by  XIII)  the  angle  CBA  ^  the  angle  CAB,  and  as  the 
angles  at  D  are  right,  the  angle  ACD  must  be  equal  to  the  angle  BCD  (by  X).  Hence,  in  the 
triangles  ACD,  BCD,  we  have  the  angle  ACD  equal  to  the  angle  BCD,  CA  =  CB,  and  CD 
common  to  both  triangles,  consequently  (by  XI)  AD  =  DB;  that  is,  AB  is  bisected  at  D. 

XVIII. 

If  from  the  centre,  C,  of  the  circle  ABE  there  be  draitn  a  perpendicular,  CD,  to  the  chord  AB,  and  it  be  continuect 
to  meet  the  circle  in  F,  it  zvill  bisect  the  arc  AFB  in  F.     (See  the  preceding  figure.) 

For  in  the  last  article  it  was  proved  that  the  angle  ACD  =  the  angle  BCD;  hence  the  arc  AF  =  the  arc  FB. 

XIX. 

Any  line  bisecting  a  chord  at  right  angles  is  a  diameter. 

For  since  (by  XVII)  a  line  drawn  from  the  centre  perpendicular  to  a  chord  bisects  that  chord  at  right  angles, 
therefore  conversely  a  line  bisecting  a  chord  at  right  angles  must  pass  through  the  centre,  and  consequently  be  a 
diameter. 

XX. 

The  sine  of  any  arc  is  equal  to  half  the  chord  of  twice  that  arc. 

For  (in  the  last  scheme)  AD  is  the  sine  of  the  arc  AF,  and  AF  is  equal  to  half  the  arc  AFB,  and  AD  half  the 
chord  AB ;  hence  the  proposition  is  manifest. 


•XXI. 

If  hvo  equal  and  parallel  lines,  AB,  CD,  be  joined  by  hvo  others,  AC,  BD,  these  ivill  be  also  equal  and  parallel. 

To  demonstrate  this,  join  the  two  opposite  angles  A  and  D  with  the  line  AD;  then  it  is  evident  that  the  line 
AD  divides  the  quadrilateral  ACDB  into  two  triangles,  ABD,  ACD,  in  which  AH  is  equal  to  CD,  by  supposition, 
and  AD  is  common  to  both  triangles  ;  and  since  AB  is  parallel  to  CD,  the  angle  BAD  is  equal  - 

to  the  angle  ADC  (by  IV);  therefore,  in  the  two  triangles,  the  sides  AB,  AD,  and  the  angle 
BAD,  are  equal  resjiectively  to  the  sides  CD,  AD,  and  the  angle  ADC;  hence  (by  XI)  BD  is 
e(iual  to  AC,  and  the  angle  DAC  eciual  to  the  angle  ADB ;  therefore  (by  VIII)  the  hues  BD,  AC, 
must  be  parallel.  O  J) 

Cor.  Hence  it  follows  that  the  quadrilateral  ABDC  is  a  parallelogram,  since  the  opposite  sides  are  parallel. 
It  is  also  evident  that,  in  any  parallelogram,  the  line  joining  the  opposite  angles  (called  the  diagonal),  as  AD, 
divides  the  figure  into  two  equal  parts,  since  it  has  been  proved  that  the  triangles  ABD,  ACD,  are  equal  to  each 
other. 

XXII. 

It  follows  also  from  the  preceding  article,  that  a  triangle,  ACD  (see  the  preceding  figure),  on  the  same  base, 
■ind  beticeen  the  same  parallels  7oith  a  paralleloi^ram,  ABDC,  is  the  half  of  that  parallelogram. 


636 


GEOMETKY. 


XXIII. 

From  the  same  article  it  also  follows,  thai  the  opposite  sides  of  a  parallelogram  are  equal ;  for  it  has  been  proved 
that,  ABDC  being  a  parallelogram,  i\B  is  equal  to  CD,  and  AC  equal  to  BD. 

XXIV. 

All  parallelograms  on  the  sa9>ie  or  equal  bases  and  between  the  same  parallels  are  equal  to  each  other ;  that  is,  if 
BD  atid  GH  be  'equal,  and  the  lines  BH,  AF,  be  parallel,  the  parallelograms  ABDC,  BDFE,  and  EFHG  will  be 
equal  to  each  other. 

For  AC  is  equal  to  EF,  each  being  equal  to  BD  (by  XXIII);  to  both  add  CE,  and  we  have  AE,  equal  to 
AX:  E     F  ^^ '  therefore,  in  the  two  triangles  ABE,  CDF,  AB  is  equal  to  CD,  AE  is  equal  to  CF, 

and  the  angle  BAE  is  equal  to  DCF  (by  V);  therefore  the  two  triangles  ABE,  CDF,  are 
equal  (by  XI);  and  taking  the  triangle  CKE  from  both,  the  figure  ABKC  is  equal  to  the 
figure  KDFE,  to  both  which  add  the  triangle  KBD,  and  we  have  the  parallelogram  ABDC, 
equal  to  the  parallelogram  BDFE.  In  the  same  way  it  may  be  proved  that  the  parallelo- 
gram liFHG  is  equal  to  the  parallelogram  BDFE;  therefore  the  three  parallelograms 
A15I)C,  BDFE,  and  EFHG  are  equal  to  each  other. 

Cor.  Hence  it  follows  that  triangles  on  the  same  base  and  between  the  same  parallels  are  equal,  since  they  are 
the  half  of  the  parallelograms  on  the  same  base  and  between  the  same  parallels^by  XXII). 

XXV. 

In  any  right-angled  triangle  the  square  of  the  hypotenuse  is  equal  to  the  sum  of  the  squares  of  the  tivo  sides.  Thus, 
z/"BAC  bi  a  right-angled  triangle,  the  square  of  the  hypotenuse  BC,  viz:  BCMH,  is  equal  to  the  sum  of  the  squares 
made  on  the  two  sides,  AB  attd  AC,  vis:  /(?  ABDE  ajid  ACGF. 

To  demonstrate  this,  through  the  point  A  draw  AKL  perpendicular  to  the  hypotenuse  BC;  join  AH,  AM, 
DC,  and  BG  ;  then  it  is  evident  that  DB  is  equal  to  BA  and  BH  equal  to  BC;  therefore, 
in  the  triangles  DBC,  ABH,  the  two  legs,  DB,  BC,  of  the  one  are  equal  to  the  two  legs. 
AB,  BH,  of  the  other; 'and  the  included  angles,  DBC  and  ABH,  are  also  equal  (for 
DBA  is  equal  to  CBH,  being  Ijoth  right ;  to  each  add  ABC,  and  we  have  DBC,  equal  to 
ABH);  therefore  the  triangles  DBC,  ABH,  are  equal  (by  XI);  but  the  triangle  DBC  is 
half  of  the  square  ABDE  (by  XXII),  and  the  triangle  ABH  is  half  the  parallelogram 
BKLH  (by  the  same  article);  consequently  the  square  ABDE  is  equal  to  the  parallelo- 
gram BKLH.  In  the  same  way  it  may  be  proved  that  the  square  ACGF  is  equal  to  the 
parallelogram  KCML;  therefore  the  sum  of  the  squares  ABDE  and  ACGF  is  equal  to 
the  sum  of  the  parallelograms  BKLH  and  KCML;  but  the  sum  of  these  parallelograms 
is  equal  to  the  square  BCMH;  therefore  the  sum  of  the  squares  on  AB  and  AC  is  equal 
to  the  square  on  BC. 

Cor.  Hence,  in  any  right  angled  triangle,  if  we  have  the  hypotenuse  and  one  of  the 
legs,  we  may  easily  find  the  other  leg  by  taking  the  square  of  the  given  leg  from  the  square  of  the  hypotenuse; 
the  square  root  of  the  remainder  will  be  the  sought  leg.  Thus,  if  the  hypotenuse  was  13  and  one  leg  was  5,  the 
other  leg  would  be  12;  for  the  square  of  5  is  25,  and  the  square  of  13  is  169;  subtracting  25  from  169  leaves  144, 
the  square  root  of  which  is  12.  If  both  legs  are  given,  the  hypotenuse  may  also  be  found  by  extracting  the  square 
root  of  the  sum  of  the  squares  of  the  legs ;  thus,  if  one  leg  was  6  and  the  other  8,  the  square  of  the  first  is  36,  the 
square  of  the  second  is  64;  adding  36  and  64  together  gives  100,  whose  square  root  is  10,  which  is  the  sought 
hypotenuse. 

XXVI. 

Four  quantities  are  said  to  be  proportioiial  when  the  magnitude  of  the  frst  compared  with  the  second  is  the  same  as 
the  magnitude  of  the  third  compared  with  the  fourth. 

Thus,  4,  8,  12,  and  24  are  proportional,  because  4  is  half  of  8,  and  12  is  half  of  24;  and  if  we  take  equi-multi- 
ples,  A.  X  a,  A  X  b,  of  the  quantities  a  and  /',  and  oher  equi-multiples,  B  X  tf,  B  X  b,  of  the  same  quantities  a 
and  b,  the  four  quantities,  A  X  «,  A  X  ''',  B  X  a,  B  X  b,  will  be  proportional ;  for  A  X  a  compared  with  A  X  b  is 
of  the  same  magnitude  as  a  compared  with  b,  and  B  X  «  compared  with  B  X  /'  is  also  of  the  same  magnitude  as  a 
compared  with  b. 

XXVII. 

In  any  triangle,  A.Gg,  if  a  line,  E^,  be  drawn  parallel  to  either  of  the  sides,  as  Gg,  the  side  AG  tvill  be  to  AK  as 
Ag  to  Ae,  or  as  Gg  to  Ee. 

To  demonstrate  this,  upon  the  line  AG  take  the  line  AB  so  that  a  certain  multiple  of  it  may  be  equal  to  AE, 

and  another  multiple  of  it  may  be  equal  to  AG ;  this  may  be  always  done 
accurately  when  AE  and  AG  are  commensurable;  if  they  are  not  accurately 
commensurable,  the  quantity  AB  may  be  taken  so  small  that  certain  multi- 
ples of  it  may  differ  from  AE  and  AG  respectively  by  quantities  less  than 
any  assignable.  On  the  line  AG,  take  BC,  CD,  DE,  EF,  EG,  &c.,  each 
equal  to  AB ;  and  through  these  points  draw  the  lines  Bb,  Cc,  &c.,  parallel 
to  G^"-,  cutting  the  line  Ag  in  the  points  /',  c,  d,  e,  &c. ;  draw  also  the  lines 
BM,  CL,  DK,  &c.,  parallel  to  A^,  cutting  the  former  parallels  in  the  points 
N,  O,  P,  &c.,  and  the. line  G^  in  the  points  M,  L,  K,  &c.  Then  the  tri- 
„  angles  ABb,  BCN,  CDO,  &c.,  are  similar  and  equal  to  each  other ;   for  the 

'^  •9'    lines  Bb,  CN,  are  parallel;   therefore  the  angle  ABb  =  BCN  (by  V),  and  by 

the  same  article  the  angle  BAb  is  equal  to  CBN  (because  BN  is  parallel  to  Ab),  and  by  construction  AB  =  BC; 
therefore  (by  XII)  the  triangles  AB^  and  BCN  are  equal  to  each  other;  and  in  the  same  manner  we  may  prove 
that  the  others,  CDO,  DEP,  EFQ,  &c.,  are  equal  to  ABb.  Therefore,  A^  =  BN  =  CO  =  DP,  &c.,  and  B/'  = 
CN  =  DO  =  EP,  &c. ;  but  (by  XXIIl)  BN  =  be,  CO  =  cd,  DP  =  de;  therefore,  Ab  =  be  =  cd—dc,  &c. ;  and 


GEOMETRY. 


637 


since  (by  construction)  AB  =r  BC  =  CD,  &c.,  any  line  AE  is  the  same  multiple  of  AB  as  the  corresponding  line 
A(' is  of  A/';  and  AG  is  the  same  multiple  of  AB  as  A^"- is  of  A/';  therefore  the  lines  AG,  AE,  A^,  Ke,  are  propor- 
tional (by  XXVI);  that  is,  AG  is  to  AE  as  A^is  to  A^-;  and  in  a  similar  manner  we  may  prove  that  AG  is  to  AE 


as  G;-"  is  to  Ec' 


XXVIII. 


If  any  two  triangles,  ABC,  abc,  are  similar,  or  liave  all  the  angles  of  the  one  equal  to  all  the  angles  of  the  other, 
each  to  each  respecti^vly,  that  is,  CAB  =  cab,  ACB  =  acb,  ABC  =  abc ;  the  legs  opposite  to  the  equal  angles  will 
be  proportional,  viz:   AB  :  ab  :  :  AC  :  ac ;  AB  :  ab  :  :  BC  :  be ;  and  AC  :  ae  :  :  BC  -.be. 

To  prove  this,  set  off,  upon  a  side,  AB,  of  the  largest  triangle,  AE  =:  ab,  and  through  E  draw  ED  parallel  to 
BC,  to  meet  AC  in  D;  then,  since  DE,  BC,  are  parallel,  the  angle  AED  is  equal  to  ABC  (by  V),  and  this  (by 
supposition)  is  equal  to  the  angle  abc;  also  the  angle  DAK  is  (by  supposition)  equal  to 
cab;  therefore  in  the  triangles  ADE,  abc,  the  two  angles,  DAE,  AED,  of  the  one,  are 
equal  to  the  two  angles,  cab,  abc,  of  the  other,  each  to  each  respectively,  and  the  included 
side,  AE,  is  (by  construction)  equal  to  the  included  side  ab;  therefore  (by  XII)  AD  is 
equal  to  ac,  and  DE  equal  to  be;  but  since,  in  the  triangle  ABC,  there  is  drawn  DE  parallel 
to  BC,  one  of  its  sides,  to  meet  the  other  two  sides  in  the  points  DE,  therefore  (by  the 
preceding  article)  AB  :  AE  :  :  AC  :  AD,  and  AB  :  AE  :  :  BC  :  DE,  and  AC  :  AD  :  :  BC: 
DE;  if,  in  these  three  proportions,  for  DE  we  put  its  equal  be,  for  AE  put  ab,  and  for  AD 
put  ac,  they  will  become  AB  :  ab  :  :  AC  :  ac,  and  AB  :  ab  :  :  BC  :  be,  and  AC  :  ae  :  i  BC  : 

XXIX. 

T/ie  chord,  sine,  tangent,  Q^e.,  of  any  arc  in  one  circle,  is  to  the  chord,  sine,  tangent,  ^e.,  of  the  same  arc  in 
another,  as  the  radius  of  the  one  is  to  the  radiics  of  the  other. 

Let  ABD,  abd,  be  two  circles ;  BD,  bd,  two  arcs  of  these  circles,  equal  to  one  another,  or  consisting  of 
the  same  number  of  degrees;  also  FD,  fl,  the  tangents  ;  BD,  bd,  the  chords;  BE,  be,  the  sines,  &c.,  of  these 
two  arcs  BD,  bd;  and  CD,  cd,  the  radii  of  the  circles;  then  CD  :  cd :  :  FD  :  fd, 
and  CD  :  cd :  :  BD  :  bd,  and  CD  :  cd ::  BE  :  be,  &c.  For  since  the  arcs  BD,  t>d, 
are  equal,  the  angles  BCD,  bed,  are  also  equal,  and  FD,  fl,  being  tangents  to  the 
points  D  and  d,  the  angles  CDF,  cdf  are  each  equal  to  a  right  angle;  therefore, 
since  in  the  two  triangles  CDF,  cdf  the  two  angles  FCD,  CDF,  of  the  one,  are 
equal  to  the  two  angles,  y^-i/,  cdf  of  tlie  other,  each  to  each,  the  remaining  angle, 
CFD,  is  also  equal  to  the  remaining  angle,  cfd{hy  X);  consequently  the  triangles 
CFI3,  cfd,  are  similar.  The  triangles  BCD,  bed,  are  also  similar,  for  the  angle 
CBD  is  equal  to  the  angle  CDB,  being  each  subtended  by  the  radius;  therefore 
(by  X),  each  of  these  angles  is  equal  to  half  the  supplement  of  the  angle  BCD ; 
and  in  the  same  manner  the  angle  cbd  or  cdb  is  equal  to  half  the  supplement  of  the 
angle  bed;  and  since  the  angle  BCD  is  equal  to  bed,  the  angles  of  these  two  tri- 
angles must  be  equal ;  consequently  they  are  similar.  The  triangles  BCE,  bee,  are 
also  similar,  because  BE  is  parallel  to  FD,  and  be  parallel  to  fd.  Hence  we  obtain 
(by  XXVIII)  the  following  analogies :  CD  :  cd :  :  FD  :// ;  CD  :  cd :  :  BD  :  bd; 
CB:cb::BE:  be,  &c. 

XXX. 

Let  ABD  be  a  quadrant  of  a  circle,  described  by  the  radius  CD,  BD  any  arc  of  it,  BA  its  comple- 
ment, BG  or  CF  the  sine,  CG  or  BF  the  cosine,  DE  the  tangent,  AH  the  cotangent,  CE  the  secant, 
and  CH  the  cosecant  of  that  arc  BD.  Then,  since  the  triangles  CDE,  CGB,  are  similar,  we  shall  have 
(by  XXVIII)  DE  :  CE  :  :  BG  :  CB;  that  is,  the  tangent  of  an  arc  is  to  secant  of  the  same  as  the  sine 
of  it  is  to  radius.  Also,  CE  :  CD  :  :  CB  :  CG;  that  is,  the  secant  is  to  radius  as  the  radius  to  the  cosine 
of  the  arc.  Also,  CF  :  CA  :  :  CB  :  CH;  that  is,  the  sine  is  to  radius  as  radius  to  the  cosecant  of  the 
arc ;  and  since  the  triangle  CAH  is  similar  to  the  triangle  CDE,  we  have  AH  :  CA  :  :  CD  :  DE;  that 
is,  the  cotangent  is  to  the  radius  as  the  radius  to  the  tangent  of  the  arc. 

XXXI 

In  all  circles,  the  sine  ofgo°,  the  tangent  ^45°,  and  the  chord  ofbo^,  are  each  equal  to  the  radius. 

For,  in  the  circle  DFAEB,  let  the  arc  BE  be  45°,  the  arc  BA  60°,  and  BF  90^.  Draw 
through  the  centre,  C,  the  diameter  DCB,  and  perpendicular  thereto  the  tangent  BG,  meeting 
CE  produced  in  G  ;  draw  the  chord  BA,  and  join  CF,  CA.  Then,  since  the  arc  BF  is  90°,  DF 
must  be  90°;  whence  the  radius  CF  is  equal  to  the  sine  of  the  arc  BF,  or  sine  of  90°.  Again, 
in  the  triangle  CBG,  since  the  angle  CBG  is  90"^,  and  BCG  is  45^,  by  supposition,  the  angle 
CGB  is  also  45°  (by  X);  therefore  (by  XIII)  BG  is  equal  to  CB;  that  is,  the  tangent  of  45^  is 
equal  to  the  radius.  Again,  the  angle  ACB  is  60°  (being  measured  by  the  arc  BA),  and  the 
angle  CBA  is  also  60°  (being  measured  by  half  the  arc  AD  =  120^,  by  XIV);  therefore  (by  XIII)  CA  =  AB; 
that  is,  the  chord  of  60*^  is  eiiual  to  the  radius. 

GEOMETRICAL    PROBLEMS. 

Problem  I. 

To  draw  a  right  line,  CD,  parallel  to  a  given  right  line,  AB,  at  any  given  distance,  as  at  the  point  D. 

With  a  pair  of  compasses  take  the  nearest  distance  between  the  point  D  and  the  given  right 
line,  AB ;  witli  that  distance  set  one  foot  of  the  compasses  anywhere  on  the  line  Al>,  as  at  A, 
and  draw  the  arc  C  on  the  same  side  of  the  line  A 15  as  the  point  D  ;  from  the  point  D  draw  a 
line  so  as  just  to  touch  the  arc  C,  and  it  is  done;  for  the  line  CD  will  be  parallel  to  the  line  AB, 
and  at  the  distance  of  the  point  given,  D,  as  was  required. 


Gt    O 


D 


-0 


638 


GEOMETRY. 


A 


-f", 


E\ 


>^ 


^- 


■'& 


ig 


Problem  II. 

To  bisect  or  divide  a  given  line,  AB,  into  two  equal  parts. 

Take  any  distance  in  the  compasses  greater  than  half  the  line  AB ;  then,  with  one  foot  in 
B,  describe  the  arc  CFD ;  with  the  same  distance,  and  one  foot  in  A,  describe  the  arc  CGD,  cut- 
ting the  former  arc  in  C  and  D ;  draw  the  hne  CD,  and  it  will  bisect  AB  in  the  point  E. 

Problem  III. 

To  erect  a  perpendicular,  BA,  on  the  end  of  a  given  right  line,  DB. 

Take  any  extent  in  the  compasses,  and  with  one  foot  in  B  fix  the  other  in  any  point,  C,  with- 
out the  given  line ;  then,  with  one  point  of  the  compasses  in  C,  describe,  with  the  other,  the 
circle  ABD ;  through  D  and  C  draw  the  diameter  UCA,  meeting  the  circle  in  A ;  join  B  and  A, 
and  it  is  done;   for  BA  will  be  the  required  line  (by  XVI). 

Or  thus  : 

Take  any  convenient  distance,  as  BH,  in  the  compasses,  and,  with  one  foot  in  B,  describe 
the  arc  HFG,  upon  v  hich  set  off  the  same  distance  as  a  chord  from  H  to  F,  and  from  F  to  G; 
upon  F  and  G  describe  two  arcs  intersecting  each  other  in  A ;  draw  a  line  from  B  to  A,  and  it 
is  done ;  for  BA  will  be  the  perpendicular  required. 

Problem  IV. 

From  a  given  point,  as  C,  to  let  fall  a  perpendicular,  CO,  on  a  given  right  line,  AB. 

Take  any  extent  in  the  compasses  greater  than  the  least  distance  between  C  and  the  given 
line  AB ;  with  one  foot  in  C,  describe  an  arc  to  cut  the  given  line,  AB,  in  F  and  G;  with  one 
foot  in  G,  describe  an  arc,  and  with  the  same  distance,  and  one  foot  in  F,  describe  another  arc 
cutting  the  former  in  D;  from  C  to  D  draw  the  line  COD,  cutting  AB  in  O;  then  CO  will  be 
the  perpendicular  required. 


B 


H 


Problem  V. 

From  a  given  point,  C,  to  let  fall  a  perpendicular,  CB,  on  a  given  line,  AB, 
dicular  is  to  fall  so  near  the  end  of  the  given  line  that  it  cannot  be  done  as  above. 


zvhen  the  perpen- 


\90' 


Upon  any  point,  A,  of  the  line  AB  as  a  centre,  and  with  the  distance  AC,  describe  an  arc, 
E ;  choose  any  other  point  in  the  line  AB,  as  D,  and  with  the  distance  DC  describe  another  arc 
intersecting  the  former  in  E;  join  CE,  cutting  AB  in  B,  and  it  is  done;  for  CD  will  be  the  per- 
pendicular required. 

Problem  VI.  "^ 

To  make  an  angle  that  shall  contain  any  proposed  number  of  degrees,  fro/n  a  givejt  point  in  a  given  line. 

Case  I.  When  the  given  angle  is  right,  or  contains  90°,  let  CA  be  the  given  line  and  C  the 
given  point. 

On  C  erect  a  perpendicular,  CD,  and  it  is  done;  for  the  angle  DCA  is  an  angle  of  90°.  Or 
thus  :  on  the  point  C,  as  a  centre,  with  the  chord  of  60*^,  describe  an  arc,  GH,  and  set  off  thereon, 
from  G  to  H,  the  distance  of  the  chord  of  90^,  and  from  C  through  H  draw  CHD,  which  will 
form  the  angle  DCA  of  90°  required. 

Case  2.  When  the  angle  is  acute,  as  for  example,  36^  30',  let  CB  be  the  given  line,  and  C 
the  point  at  which  the  angle  is  to  be  made. 

W  ith  the  chord  60^^  in  the  compasses,  and  one  foot  on  C,  as  a  centre,  draw  the  arc  FB,  on 
which  set  off,  from  B  to  F,  the  given  angle,  36^'^,  taken  from  the  line  of  chords ;  through  F  and 
the  centre  C  draw  the  right  line  AC,  and  it  is  done;  for  the  angle  ACB  will  be  an  angle  of  36° 
30',  as  was  required. 

Case  3.    When  the  given  angle  is  obtuse,  as,  for  example,  127°,  let  CB  be  the  given  line  and  C  the  angular 
point. 

.  jT jj-  Take  the  chord  of  60"^  in  the  compasses,  and  with  one  foot  on  C  as  a  centre,  describe  an  arc, 

BGHE,  upon  which  set  off  the  chord  of  6o'-'  (which  you  already  have  in  the  compasses)  from  B 
to  G  and  from  G  to  li  ;   then  set  off  from  G  to  E  the  excess  of  the  given  angle  above  60*^,  which 
is  67°,  taken  from  the  line  of  chords ;   or  you  may  set  off,  from  H  to  E,  the  excess  of  the  given 
angle  above  120,  which  is  7°;  draw  the  line  CE,  and  it  is  done;   for  the  angle  ECB  will  be  an  angle  of  127'^. 

Were  it  required  to  measure  a  given  angle,  the  process  would  have  been  nearly  the  same  by  sweeping  an  arc, 
as  BE,  and  measuring  it  on  the  line  of  chords,  as  is  evident. 

Problem  VII. 


To  bisect  a  given  arc  of  a  circle,  AB,  whose  eent?-e  is  C 


■yiD  \' 


Take  in  the  compasses  any  extent  greater  than  the  half  of  AB,  and,  with  one  foot  in  A,  describe 
an  arc;  with  the  same  extent,  and  one  foot  in  B,  describe  another  arc,  cutting  the  former  in  D ; 
join  C"D,  and  it  is  done;  for  this  line  will  bisect  the  arc  Al!  in  the  point  E. 
that  the  line  CD  bisects  the  angle  BCA,  or  divides  it  into  two  equal  parts. 


It  is  also  evident 


PLANE    TRIGONOMETRY. 


639 


Problem  VIII. 


To  find  the  centre  of  a  given  circle. 


With  any  radius,  and  one  foot  in  the  circumference,  as  at  A,  describe  an  arc  of  a  cirde,  as 
CBD,  cutting  the  given  circle  in  15 ;  with  the  same  extent,  and  one  foot  in  B,  describe  ar  other 
arc,  CAD,  cutting  the  former  in  C  and  D;  through  C  and  1^  draw  the  line  CD,  which  will  pass 
through  the  centre  of  the  circle;  in  like  manner  may  another  right  line  be  drawn,  as  EIKj, 
which  shall  cross  the  first  right  line  at  the  centre  required.  This  construction  depends  upon 
Theorem  XVII  of  Geometry. 

Problem  IX. 


To  draw  a  circle  through  any  three  given  points  not  situated  in  a  right  line. 

Let  A,  B,  and  D,  be  the  given  points.  Take  in  the  compasses  any  distance  greater  than  half 
AB,  and,  with  one  foot  in  A,  describe  an  arc,  EF;  with  the  same  extent,  and  one  foot  in  B, 
describe  another  arc,  cutting  the  former  in  the  points  E,  F,  through  which  draw  the  indefinite 
right  line  EFC ;  then  take  in  the  compasses  any  extent  greater  than  half  BD,  and  with  one  foot 
in  B,  describe  an  arc,  (iH  ;  with  the  same  extent,  and  one  foot  in  D,  describe  another  arc  cut- 
ting the  former  in  the  points  G,  H,  through  which  draw  the  right  line  GHC,  cutting  the  former 
right  line  EFC  in  the  point  C ;  upon  the  point  C  as  a  centre,  with  an  extent  equal  to  CA,  CB, 
or  CD,  as  radius,  describe  the  sought  circle. 


Problem  X. 


To  divide  a  circle  into  2,  4,  8.  16,  or  32  equal  parts. 

Draw  a  diameter  through  the  centre,  dividing  the  circle  into  two  equal  parts ;  bisect  this 
diameter  by  another,  drawn  perpendicular  thereto,  and  the  circle  will  be  divided  into  four  equal 
parts  or  quadrants ;  bisect  each  of  these  quadrants  again  by  right  lines  drawn  through  the 
centre,  and  the  circle  will  be  divided  into  eight  equal  parts ;  and  so  continue  the  bisections  any 
number  of  times.     This  problem  is  useful  in  constructing  the  mariner's  compass. 

Problem  XI. 

To  divide  a  given  line  into  any  jiU7?iber  of  equal  parts. 

Let  it  be  required  to  divide  the  line  AB  into  five  equal  parts.  From  the  point  A  draw  any 
line,  AD,  making  an  angle  with  the  line  AB  ;  then  through  the  point  B  draw  a  line,  BC,  parallel 
to  AD;  and  from  A,  with  any  small  opening  in  the  compasses,  set  off  a  number  of  equal  parts 
on  the  line  AD,  less  by  one  than  the  proposed  number  (which  number  of  equal  parts  in  this 
example  is  4) ;  then,  from  B,  set  off  the  same  number  of  the  same  parts  on  the  line  BC ;  then 
join  4  and  I,  3  and  2,  2  and  3,  l  and  4,  and  these  lines  will  cut  the  given  line  as  required. 


PLANE  TRIGONOMETRY. 

Plane  Trigonometry  is  that  branch  of  science  which  comprises  all  the  investigations  wiih  respect  to  jilane 
angles,  and  particularly  the  relations  existing  between  the  sides  and  angles  of  plane  triangles,  whether  light-anglcd 
or  oblique-angled. 

In  every  triangle  there  are  six  parts, 
viz :  the  three  sides  and  the  three  angles. 

The  solution  of  triangles  is  the  pro- 
cess by  which,  when  the  value  of  a  suf- 
ficient number  of  these  parts  are  given, 
the  values  of  the  remaining  parts  may  be 
found.  This  may  be  done  except  in  the 
case  when  the  three  angles  are  given, 
when  the  lengths  of  the  sides  cannot  be 
found,  but  only  the  ratio  they  bear  to 
each  other. 

There  are  various  methods  for  solv- 
ing triangles,  viz :  by  Gunter's  Scale,  by 
the  sliding  scale,  by  the  sector,  by  con- 
struction, and  by  computation.  The  lat- 
ter, being  by  far  the  most  accurate,  will 
only  be  described  hce.  Solution  by  the 
other  methods  may  be  readily  understood 
through  the  descriptions  given  of  the  in- 
struments named  in  Chap.  II,  Part  I. 

The  RATIOS  existing  between  the 
parts  of  any  plane  right  angle  are  as  fol- 
lows : 

Let  ABC  be  a  plane  right  triangle  in 
which  C  is  the  right  angle  ;  A  and  B,  the 
other  angles ;  c,  the  hypotenuse ;  a  and  /<, 


sides  opposite  the  angles  A  and  1!. 


640 


PLANE    TRIGONOMETRY. 


Then 

a 

c 

b 


or  perpendicular^  j^  ^^jj^^  ^^^  ^.^^  ^^^^^^  ^ 
hypotenuse 


or 


base 


,  is  called  the  cosine  of  angle  A. 


or 


hypotenuse 

perpendicular^  j^  ^^jj^^  ^j^^  ^a«_^^«/  of  the  angle  A. 
base 


or 


base 


perpendicular 


is  called  the  cotangent  of  the  angle  A. 


i-,  or  hypotenuse^  j^  ^^jj^^  ^^^  ^^^^^^^  ^^  ^^^  ^     .^  ^ 
b  base 


or 


hypotenuse  ^  j^  ^^jj^^  ^j^^  cosecant  of  the  angle  A. 


a         perpendicular 

I  —  cosine  A,  is  called  the  versed  sine  of  A. 

1  —  sine  A,  is  called  the  co-versed  sine  of  A. 

The  above  ratios  may  be  expressed  thus,  using  the  abbreviations  employed  for  the  trigonometrical  functions, 
sine,  cosine,  &c. : 


Sin  A 

c 

Cos  A 

_  b 
c 

Tan  A 

a 

~1) 

Cot  A 

_  b 
a 

Sec  A 

c 
~1> 

Cosec  A 

__  c 
a 

Vers        A  =  I  —  cos  A 

Co-vers    A  =  i  —  sin  A 

The  complement  oi  an  angle  is  vi'hat  it  wants  of  ()Qp,  and  in  the  triangle  ABC  the  angle  B  is  the  complement 
of  the  angle  A. 

Sin      B  ^  —  =  cos  A 

c 


Tan     B  = 


h 


cot  A 


Sec      B  =       =  cosec  A 
Or,  in  words,  " 

The  sine  of  an  angle  is  the  cosine  of  the  complement  of  that  angle  ; 
The  tangent  of  an  angle  is  the  cotangent  of  the  complement  of  tliat  angle; 
The  secant  of  an  angle  is  the  cosecant  of  the  complement  of  that  angle. 


SOLUTION  OF  TRIANGLES. 


7^  D  C       B 

and  C  arc  acute  angles,  we  have  from  the  left-hand  figure 

AD  —  AB  sin  B,  and  AD  =  AC  sin  C; 
therefore,  AB  sin  B  =  AC  sin  C, 

c sin  C 

^""sirTB" 


With  the  above  ratios  and  the 
following  relations  between  the  sides 
of  .1  triangle  and  the  trigonometrical 
functions  of  the  angh  s  may  be  solved 
the  varicnis  cases  of  plane  triangles. 

Case.  I.  /;/  any  plane  triangle 
the  sides  arc  proportional  to  the  sines 
oj'  the  opposite  angles. 

Let   ABC   1)6  any  triangle,  and 

from   A   draw   AD  perpendicular  to 

the  opposite  side,  meeting  that  side, 

^^  or  that  side  produced,  at  D,     If  B 


and 


PLANE    TRIGONOMETRY. 

I 

■        If  the  "angle  C  be  obtuse,  we  have,  from  the  right-hand  figure, 

AD  =  AB  sin  B  and  AD  =  AC  sin  ACD  =  AC  sin  (180°  —  C)  =  AC  sin  C 
therefore,  AB  sin  B  =  AC  sin  C, 

c       sin  C 
h       sin  B* 


641 


and 


or, 
therefore 


Case  II.  In  any  triangle  the  sum  of  atty  tnvo  sides  is  to  their  differenee  as  the  tangent  of  the  half -sum  of  the  hvo 
opposite  angles  is  to  the  tangent  of  half  their  difference. 

Suppose  /'  and  c  to  be  the  sides,  and  B  and  C  the 
angles  opposite ;  we  then  have 

L  /; :  r  =  sin  B  :  sin  C, 

sin  B       l>  _ 
sin  C        ir' 

sin  B  —  sin  C b  —  c  ^ 

sin  B  -j-  sin  C       b  -\-  c' 

but  by  Trig.,  sin  B  —  sin  C tan  i  (B  —  C) . 

sin  B  +  sin~C  "^  t"anT(B  +  C) ' 
,  tan  i  (B  —  C)       b  —  c 

'"'"""'  tan  i(B+C) -/;  +  .' 

or,      /'  +  r  :  ^  —  r  =  tan  i  (B  -f  C)  :  tan  i  (B  —  C). 

Case  III.   To  express  the  sine,  cosine,  and  the  tangent  of  half  an  angle  of  a  triangle  in  terms  of  the  sides. 

In  the  figure  of  Case  I,  we  have,  by  EucM 

AB2  =  BC2  +  AC2  —  2  BC.CD, 
CD  =  AC  cos  C ; 
c^  —  aP'^b'^  —  lab  cos  C ; 
cos  C  =  ^2  ^  ^2  _  ^s 


and 
therefore, 

hence, 


Similarly, 

We  have 

therefore, 

Let 
Then, 

Hence, 

Also, 

therefore, 

and 


2ab 
cos  A  =  //2  _|.  ^.'2  —  ,ii 

ibc 
cos  B  =:  <r2  4-  ^2  —  /;2 


I  —  cos  A  =  I  — 


2,ca 

1,1  4.  f2  _  ^2 


-  (^  _  C)\ 


2  be 


ibc 


sm' 


A       {^a^  b~  c){a  ^c  —  b) 


i,bc 

2s  ^  a  -\-  b  -\-  c. 
a  -\-  b  —  e  ^=  a  -\-  b  -\-  e  —  2c  ^  2  (s  —  e) 
a  -\-  c  —  b  ^=  a  -\-  b  -\-  c  —  2b  =  2  (s  —  b). 

A       {s  —  b)  {s  —  c) 


sm^      =^ 


.    A 
sm 
2 


=V( 


be 

(j  —  b)  {s  —  f)« 
be 


,  -f  cos  A  =  I  -f  5^^+^:^^^' =  ^'-^^f^^^ 
2bc  2bc 

(^b  ^  c  -\-  a)  (^b  -\- c  —  a)       s  {s  —  a) 


cos''  —  = 


^bc 


be 


A 
cos  — 

2 


'V  be 


.    A 


From  the  values  of  sin      and  cos  —  we  find, 
2  2 


tan^-,^/T^-^)0 
2  ~  A./ 77V—- 


^  I  ■  ^'  ~  '^' 

2        W  s(s  —  a) 

Similarly  for  the  other  angles  of  the  triangle. 


SOLUTION  ( )F  RIGHT-ANGLED  TRIANGLES. 

To  solve  a  right-angled  triangle,  having  given  the  hypotenuse  and  an  acute  angle. 

Given  c  =  250,  A  =  35"  30',  to  find  B,  a  and  /'. 

B  c=  90^  —  A  =  54°  30'. 
a  =  c  sin  A. 
b  ^^  c  sin  B. 
41    B 


642 


PLANE    TRIGONOMETRY. 


c  =  250 
A  =  35°  30' 
B  =  54    30 
a  —  145.2 
/'  =  203.5 


log  2.39794 

log  sin    9. 76395 

log  2. 16189 


2.39794 
lug  sill  9.91069 
losj 


2.30863 


To  solve  a  right-auglcd  triangle,  having  given  (lie  hypotenuse  and  a  side. 
Given  a  -^=  91  and  e  =;  170,  to  find  /',  A,  and  B. 

a 


sin  A  = 


B  =  9oc 


A. 


b  ^  c  cos  A,  or  b'  ^  (T^  —  «^ ;   b  =  \/{{e 


a 

e 


91 

170 


log 
log 


1.95904 
2.23045 


A  =  32°  22' 
B  =  57   38 

b  :=   143.6 


log  sin    9.72859 


2.23045 
log  cos  9.92667 


a)  (e  +  a)). 

e  -\-  a  =  261 

'■  —  "  =  79 


log  2.15712 

To  solve  a  right-angled  triangle,  Iiaving  given  a  side  and  an  acute  attgle. 
Given  A  =  t,t;^  15',  b  =  163,  to  find  B,  c  and  a. 


B  =  90°  - 

A  =  33°  15' 
B  =  56    45 
b  =163 

-A 

b 
cos  A 

log  cos     9.92235 
log           2.21219 

a  ^  b  tan  A. 

log  tan     9.81666 
2.21219 

log          2.28984 

<r    —  194.9 
a  =  106.9 

log           2.02885 

To  solve  a  right-angled  triangle,  having  given  the  tiuo  sides. 
Given  rf  ^  178,  b  ^  141,  to  find  r,  A  and  B. 

a 


Tan  A  = 

rt   =  178 
b   —  141 

A  =51°  37' 
B-38  23 
e    =227.1 


log 
log 


B  =  90^^  —  A 

2.25042 
2.14922 


a 
sin  A* 


log  tan     o.  10120 


2.25042 
log  sin     9.89425 


log 


2-35617 


SOLUTION  OF  OBLIQUE-ANGLED  TRIANGLES. 


To  soh'c  a  triangle,  having  given  huo  angles  and  a  side. 
Given  A  =  100°,  C  =  54°,  and  c  =  220. 


B=l8oO  — (A  +  C) 


c  sin  A 
sin  C 


^  = 


c  sin  B 
sin.  C 


A  =  100 

C  =  54° 
B=26o 
c   =  220 

a  =  267.8 
/'  =  1 19.2 


log  sin        9-99335 
log  cosec    0.09204 


log 
log 


2.34242 
2.42781 


log  cosec  0.09204 
log  sin  9.64184 
log  2.34242 


log 


2.07630 


To  solve  a  triangle,  having  given  tivo  sides  and  the  included  angle. 

Given  r  =  1 10,  /;  =  80,  and  A  :=  96°. 

A 
2 


MC  +  B)  =  9oC 


tan  i  (C  -  B)  =  "^-^  tan  i  (C  +  B) 
c  -\- 1> 


log  2.41664 
log  1.89762 

2)4  31426 


log  2.15713 


c  sin  A 

sin  C 


c—b 

= 

30 

c-^b 

=: 

190 

i(C+B) 

= 

42^ 

0' 

i(C- 

-B) 

= 

8 

5 

C 

=1 

50 

5 

B 

=: 

33  55 

A 

= 

96 

0 

c 

= 

no 

log  1. 47712 

ar-co  log  7.72125 

log  tan  9.95444 

log  tan  9. 1 5  28 1 


log  cosec    o.  1 1522 


log  sin 
log 


9.99761 
2.04139 


=  142,6 


log 


2,15422 


USEFUL    PROBLEMS. 


643 


To  sohk'  a  tnans^lc,  having  given  two  sides  and  an  angle  opposite  one  of  them. 

Note. — It  may  be  proper  to  observe  that  if  the  given  angle  be  obtuse,  the  angle  sought  will  be  acute;  but 
when  the  given  angle  is  acute,  and  opposite  to  a  shorter  given  side,  then  it  is  doubtful  whether  the  retpiired  angle 
be  acute  or  obtuse ;  it  ought,  therefore,  to  be  given  by  the  conditions  of  the  problem. 

Given  a  =  137,  /'  =  213,  and  A  =  23°  30'. 


Sin.  B  = 


h  sin  A 


a  sin  C 
sin.  A 


a 
b 


137 
213 
A=   23^ 

B=    38 
C  =  ii8 


ar-co  log    7.86328 


30' 

19 
II 


log 
log  sin 


2.32838 
9.60070 


C=i8oO  — (A+B). 
log  2.13672 

log  cosec  0.39930 


log  sin        9. 79236 


c  =302.8 
To  soh'e  a  triangle,  having  given  the  three  sides. 


log  sin 
log 


9-94519 
2.48121 


•Of  the  formulae  of  Case  III  for  the  sine,  cosine,  and  tangent  of  the  half-angle,  that  for  the  tangent  should  be 
preferretl  for  the  logarithmic  solution,  because  fewer  logarithms  are  necessary  to  find  all  the  angles. 

Given  a  =  57,  ^  =  108,  <r  =  85. 

s=l{a  -\-  l>  +  c)  =  125. 


tan^A=^/((-^-/)(-^-^)). 

'V    *        s{s  —  a        ' 


s          =  125 

s  —  a  =    68 
s  —  b=    17 
s  —  c  ^    40 

C  =  180"  —  (A  +  B) 
ar-co  log    7  90309 
a'-'CO  log    8.16749 
log              1.23045 
log              1.60206 

|A       =  15C48' 
iB        =  48    32 
A         =  31    36 
B         =  97      4 
C         =  51    20 

2)18.90309 
log  tan       945155 

ar-co  log  7.90309 

log  1.8325 1 

ar-co  log  8.76955 

log  1.60206 


2)20.10721 


log  tan       0.05360 


Note. — This  case  may  be  solved  also  by  dividing  the  triangle  into  two  right-angled  triangles,  as  will  be  self 
evident  upon  inspection  of  the  figure,  Case  I. 

USEFUL  PROBLEMS. 

To  find  the  height  of  an  object  wliose  horizontal  distaiire  is  knmon. 

Being  576  feet  from  the  base  of  a  tower  its  altitude  was  found  to  be  15° 
AB,  the  distance  =  576  feet ;  CAB,  the  measured  angle  =  15°  10'. 
Required  BC. 

BC  =  AB  tan  A 


AB  =  576 
A     =  15^  10' 


log        2. 76042 
log  tan  9.43308 


BC=  156  log        2.19350 

When  an  object,  whose  elevation  above  the  horizon  is  to  be  determined,  is  at  a  very  great  distance,  it  will  be 
necessary  to  notice  the  correction  arising  from  the  curvature  of  the  earth  and  the  refraction,  and  apjily  that  correc- 
tion to  the  height  estimated  by  the  above  method.  Thus,  if  the  angular  elevation  of  a  mountain,  whose  base  was 
more  distant  than  the  limit  of  the  visible  horizon,  was  observed  by  an  instrument  of  reflection,  the  approximate 
height  must  first  be  obtained,  as  in  the  preceding  example,  and  then  the  correction  of  that  approximate  height  for 
the  curvature  of  the  earth,  refraction,  and  dip,  must  be  calculated  by  the  following  rule,  and  added  to  that  height 
the  sum  will  be  the  true  height  alcove  the  level  of  the  sea. 

Rule.  Find  in  Table  6  the  number  of  miles  correspmding  to  the  height  of  the  observer  above  the  level  of 
the  sea,  and  take  the  difference  between  that  number  and  the  distance  of  the  mountain  from  the  observer  in  staiute 
miles;  with  that  difference,  enter  the  same  table,  and  find  the  height  in  feet  corresponding,  which  will  be  the  cor- 
rection to  be  added  to  the  approximate  height  to  obtain  the  true  height  of  the  mountain  above  the  level  of  the  sea. 

Example.  Suppose  the  distance  was  32  statute  miles  (or  168960  feet),  and  the  observed  altitude  i"  2',  the 
observer  being  18  feet  above  the  level  of  the  sea;  required  the  height  of  the  mountain  above  the  same  level. 

AB  =  168960  log  5.22779  AB  =  32  miles. 

'  Corn,  Table  6,  1 8  ft.,  =    5.59 


CAB                  =  1°  2' 

log  tan  8.25616 

Approx.  height,  =  3048 
Corr.,                  =  402 

log          3-48395 

Height,              =  3450  feet. 

Difference,  ^=  26.41 

Corres.  corr,,  Table  6,  =  402  feet. 


644 


USEFUL    PROBLEMS. 


To  find  the  distance  and  height  of  an  inaccessible  object  on  a  horizontal  plane. 

Let  A  be  the  top  of  an  object,  and  let  it  be  required  to  find  its  height,  AB, 
and  the  distance  of  the  object  from  a  point,  I),  in  the  horizontal  plane  through  B. 

At  D  observe  the  angle  ADB  =  44°,  then  measure  any  length,  DC  =  294 
feet,  directly  toward  the  object,  and  at  C  observe  the  angle  ACB  :=  59"-. 

Then,   in   the   triangle  Ar)C,  there  are   given    DC  ^  294,   ADC  :=  44*^; 
ACD  =  1800  —  ACB  =121°. 

To  find  AD, 

DC  sin  ACD 


DC  B 

111  the  triangle  ADB, 

AD 
ADB 


AD  = 

DC     =  294 
ACD  =  121° 

DAC  =    1 50 

AD     =  961 


sin  DAC 

log  2.46835 

log  sin       9.92842 
log  cosec  0.58700 


l0£ 


2.98277 


AB  =  AD  sin  ADB  and  DB  =  AD  cos  ADB. 


=  961 

=  44° 


Height,     AB  =  667.6 
Distance,  DB  =  691.4 


log         2.98277 
log  sin  9.84177 

log         2.82454 


log        2.98277 
log  cos  9.85693 


log        2.83970 


If  it  is  not  convenient  to  measure  the  length  DC  directly  toward  the 
object,  we  may  proceed  thus  :  measure  the  length  PC  in  any  direction  from  D; 
at  D  observe  the  angles  ADB  and  ADC,  and  at  C  observe  the  angle  ACD. 
Then  in  the  triangle  DAC  the  side  DC  and  the  angles  ADC  and  ACD  are 
known ;  hence  AC  can  be  found.  Then  in  the  triangle  ACB  there  may  be 
found  AB  and  BC,  as  before. 


Suppose 


Then 


ACB  =21° 

DC  1=517  feet 
ADC  =  60°  10' 
ACD  =  85      6 

DC  sin  ADC 


AC: 


sin  CAD 


AB  =  AC  sin  ACB,  BC  =  AC  cos  ACB. 


ADC  =  6oo  10' 
CAD  =  34   44 
DC  =  517 

AC 
ACB  =  21° 

log  sin 
log  cosec 
log 

log 

log  sin 

log 

9.93826 
0  24431 
2.71349 

2.89606 
9-55433 

log 
log  COS 

log 

2.89606 
9.97015 

AB  =  282.1 
CB  =  734.9 

2-45039 

2.86621 

To  find  the  distance  betiveen  t'lOo  distant  but  inaccessible  objects. 

Let  P  and  Q  be  the 
objects,  A  and  B  two  ac- 
cessible points  from  which 
both  objects  are  visible. 
At  A  observe  the  angles 
PAQ  and  QAB,  and  if 
A,  B,  Q,  and  P  are  not 
in  the  same  plane,  ob- 
serve also  the  angle  PAB. 
\t  B  observe  the  angles 
PBA  and  QBA.  Meas- 
ure AB.  Then  in  the  tri- 
angle APB  the  side  AB, 
the  angles  PAB  and  PBA 
are  known ;  PA  can  be 
found. 

Again,  in  the  triangle 
ABQ  the  side  AB,  the 
angles  QAB  and  QBA 
are  known ;  AQ  can  be 
found. 

Lasdy,  in  the  triangle  PAQ  the  sides  AP,  A(^,  and  the  angle  PA(^)  are  known  ;   hence,  PQ  can  be  f<nind. 


TTSEFUT.    PROBLEMS. 


645 


Cruising  alongshore,  two  headlands  P  and  (J  were  in  sight.      From  A  the  bearing  of  P  was  N.  E. ;  the  bearing 
of  Q  was  E.  N.  E. 

Running  to  B,  which  was  E.  by  S.,  lo  miles,  the  bearing  of  P  then  was  N.  by  E.,  and  of  Q  N.  E.  by  N 


I 


Required  the  bearing  and  distance  between  P  and  Q. 

In  the  triangle  APB  there  are  known  AB=  lo  miles,  PAB  =  56o  15',  PBA  =  90°;  to  find  PA. 

AB  ^.  AB 


Cos  PAB : 


PA 


PA: 


■  cos  PAB" 


AB=io 
PAB  =  56*^  15' 


log  I. 00000 

log  cos   9-74474 


PA  =18  log  1.25526 

Now,  in  the  triangle  ABQ  there  are  known  AB  =;  10,  QAB  =  33°  45',  and  QBA  =  112°  30';  to  find  AQ. 


^  sin  AQB 


AB=io 
QBA 
AQB 


112°  30' 

33    45 

AQ  =  i6.6 


log  1. 00000 

log  sin      9.96562 
log  cosec  0.25526 


log 


1 . 22088 


And  in  the  triangle  PAQ  there  are  known  AP  =  18,  AQ  =  16.6,  and  PAQ  =  22°  30';  to  find  PQ. 
Tan  i  (AQP  -  APQ)  =  ;^p  ~  ^S  •  t^"  i  ( AQP  +  APQ). 

i(AQP  +  APQ)  =  9oO  — iPAQ  =  780  45'. 

AP  —  AQ  ^1.4  log  0.14613 

AP  +  AQ  =:  36.4  ar-co  log   8.46092 

i  (AQP  +  APQ)  =  78^  45  log  tan       o.  70134 


i(AQP  — APQ)  =  II    30 
AQP  =90    15 


log  tan       9-30839 


646 


USEFUL    MISCELLANEOUS    MEMORANDA. 


Hence, 


PQ  =  AP  sin  PA.Q. 


AP=  i8 

PAQ  =  22°  30' 


log  1.25527 

log  sin    9.58284 


PQ  =  6  9  log         0.8381 1 

Therefore,  the  distance  between  the  two  headlands  was  6.9  miles  and  the  bearing  N.  N.  W.  and  S.  S.  E. 

Sailing  tmoards  the  land,  a  light-house  7vas  discm'ered,  Just  appearing  in  the  horizon,  the  eye  being  elevated  20 
feet  abai'd  the  sea  ;  it  is  required  to  find  the  distance  of  the  light-house,  supposing  it  to  be  elevated  200  feet  abai'e  the 
surface  of  the  sea. 

The  solution  of  this  problem  depends  on  the  uniform  curvature  of  the  sea,  by  means  of  which  all  terrestrial 
objects  di-appear  at  certain  distances  from  the  observer.  These  distances  may  be  computed  by  means  o'  Table 
6,  in  which  the  elevation  in  feet  is  given  in  one  column,  and  the  distance  at  which  it  is  visible  is  expressed  in 
statute  milts  in  the  other  column.  If  the  place  from  which  the  object  is  viewed  be  elevated  above  the  horizon, 
add  together  the  distances  corresponding  to  the  height  of  the  observer  and  the  height  of  the  object ;  the  sum  will  be  the 
greatest  distance  at  which  that  object  is  visible  from  the  observer. 

In  the  present  example,  the  height  of  the  observer  was  20  feet,  and  the  height  of  the  object  200  feet. 

In  Table  6,  opposite  20  feet  is 5.59  miles. 

200  feet  is 18.63 


Distance 24.22  statute  miles. 

To  measttre  the  approximate  height  of  a  mountain  by  means  of  the  heights  of  two  barometers,  taken  at  the  top  and 
bottom,  of  the  mountain. 

Procure  two  barometers,  with  a  thermometer  attached  to  each  of  them,  in  order  to  ascertain  the  temperature 
of  the  meicury  in  the  barometers,  and  two  other  thermometers,  of  the  same  kind,  to  ascertain  the  temperature  of 
the  air.  Then  one  observer  at  the  top  of  the  mountain,  and  another  at  the  bottom,  must  observe,  at  the  same 
time,  the  heights  of  the  barometers,  and  the  thermometers  attached  thereto,  and  the  heights  of  the  detached 
thermometers,  placed  in  the  open  air,  but  sheltered  from  the  sun.  Having  taken  these  observations,  the  height 
of  the  upper  observer,  above  the  lower,  may  be  determined  by  the  following  rule,  which  is  adapted  to  a  scale  of 
English  inches  and  to  Fahrenheit's  thermometer : 

Rule.  Take  the  difference  of  the  logarithms  of  the  observed  heights  of  the  barometers  at  the  two  stations, 
considering  the  first  four  figures,  exclusive  of  the  index,  as  whole  nimbers,  the  remainder  as  decimals;  to  this 
difference  must  be  applied  the  product  of  the  decimal  0.454,  by  the  difference  of  the  altitudes  of  the  two  attached 
thermometers,  by  subtracting,  if  the  thermometer  be  highest  at  the  lowest  station,  otherwise  adding :  the  sum  or 
difference  will  be  the  approximate  height  in  English  fathoms.  Multiply  this  by  the  decimal  o  00244,  ^"^  by  the 
difference  between  the  mean  of  the  two  altitudes  of  the  detached  thermometers  and  32° ;  the  product  will  be  a 
correction,  to  be  added  to  the  approximate  height  when  the  mean  altitude  of  tlie  two  detached  thermometers 
exceeds  32°,  otherwise  subtracted :  the  sum  or  difference  will  be  the  true  height  of  the  upper  above  the  lower 
observer  in  English  fathoms,  which,  being  multiplied  by  6,  will  be  the  height  in  feet. 

Example. 

Suppose  the  following  observations  were  taken  at  the  top  and  at  the  bottom  of  a  mountain ;  required  its  height 
in  fathoms. 


Attached  thermometer. 

Obs.  at  lower  station 57° 

Obs.  at  upper  station 43 

Difference 14 


Detached  thermometer. 


56^ 
42 


Mean 49 


Difference 17 


Barometer. 


29.68  inches log  14724.6 

25.28  log  14027.8 


Difference ...       696.  8 

0.454  X  14  - 6.4 


Approximate  height    690.  4 

690.4  X  17  X  0.00244 28.6 


Height  in  fathoms 

USEFUL  MISCELLANEOUS  MEMORANDA. 

Area  of  a  parallelogram  =r  Base  X  altitude. 

Area  of  a  triangle^  Bast  X  one-half  altitude. 

Area  of  any  right-lined  figure  =r  Sum  of  the  areas  of  the  two  triangles  formed  by  a  diagonal. 

Circumference  of  a  circle  to  diameter,  i.     tt  =  3.14159265         log  o  4971499. 

~  =  0.7853982  log  9.8950899. 

4 


71Q.  o 


1=0.5235988 

Area  of  any  circle  =  d''- 


log  9.7189986. 


■K 


Volume  of  a  sphere  =  a'^ 
Surface  of  a  sphere  ^  d''-  tt. 
Area  of  an  ellipse  =tt  I)  x  '/  X  --. 


USEFUL    MISCELLANEOUS    MEMORANDA, 


647 


Volume  of  a  cube  =  Side  ^ 

Volume  of  a  rectangular  parallelepiped  =  Product  of  three  dimensions. 

Volume  of  a  cylinder  =  d*      I. 

4 
Volume  of  a  pyramid  or  cone  =  Area  of  base  X  ^  ^. 
Earth's  Polar  radius  =  20854477  feet. 
Earth's  Equatorial  radius  =  20926202  feet. 

Earth's  Compression  =  — ;=• 

'^  299.1528 

Earth's  Eccentricity  =  0.0816968 

Number  ol  feet  in  one  statute  mile  :=  5280 

Number  of  feet  in  one  nautical  mile  =  6080.27 

Length  of  arc  equal  to  radius^  20626/^  ■  8 

Sine  of  i"  =  0.00000485 

Sine  of  I '  =  0.000290S9 

The  Napierian  base  f  =  2.7182818 

The  modulus  of  common  logarithms  ==0.4342945 

French  m^tre  in  English  feet,  3.2808992 

French  foot  in  English  feet,  1.065777 

Light  travels  186,389.8  statute  miles  per  second. 

Sound  travels  1,142  feet  per  second 

Velocity  of  electric  fluid,  about  16,000  miles  per  second. 

I  pound  Avoirdupois  ^  7,000  grains  Troy. 

Bar.  30'",  P'ahr.  Ther.  62^.     Cubic  inch  of  distilled  water,  in  grains  =  252.458. 

Bar.  30'",  Fahr.  Ther.  62°.     Cubic  foot  of  water,  in  ounces  Troy  :=  908.8488. 

Bar.  30'",  Fahr.  Ther.  62'-'.     Culiic  foot  of  water,  in  pounds  Troy  =  75.7374. 

Bar.  30'",  Fahr.  Ther.  62'-'.     Cubic  foot  of  water,  in  ounces  Avoirdupois  =  997. 1366691. 

Bar.  30'",  Fahr.  Ther.  62^.     Cubic  foot  of  water,  in  pounds  Avoirdupois  =  62.3210606. 

Length  in  inches,  English,  of  the  pendulum  which  vibrates  seconds  in  the  latitude  of  Greenwich  ^39. 1 393 

French  are  =  0.02471 143  English  acre. 

French  gramme  ^  0.00220606  Imperial  pound  Troy. 

French  kilogramme  =^  0.0196969  English  cwts. 


log  8.9122052. 
1053.7226339. 

log  3-7839232. 
log  1. 7581226. 

log  5-3144251. 
log4-S855749. 
log  6  4637261. 

log  0-4342945- 
log  9.6377843. 
log  0.5159929. 
log  0.0276663. 


?n'i^.  ?3 


